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Approaches for Two-Dimensional Monitoring and Numerical Modeling of Drip Systems

Permanent Link: http://ufdc.ufl.edu/UFE0021417/00001

Material Information

Title: Approaches for Two-Dimensional Monitoring and Numerical Modeling of Drip Systems
Physical Description: 1 online resource (148 p.)
Language: english
Creator: Icerman, Jason
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: drip, fertigation, hydrological, infiltration, insitu, irrigation, model, nitrate, nitrogen, tomato, vadose
Agricultural and Biological Engineering -- Dissertations, Academic -- UF
Genre: Agricultural and Biological Engineering thesis, M.E.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In Florida, intensive bed management systems are commonly used for vegetable production. These systems consist of raised beds for planting covered with plastic mulch, with water and nutrients commonly applied via drip irrigation and fertigation. Currently available dielectric soil moisture sensors provide inexpensive alternatives when compared to Time Domain Reflectometry (TDR) and the labor costs of soil sampling. The CS616 water content reflectometer (WCR) and the Hydra Probe II (Vitel), operating on time-domain and capacitance methods respectively, were installed beneath drip irrigated tomatoes in an intensively managed vegetable production system to examine the monitoring capabilities of each probe through one-to-one and time-series comparisons. The probes were installed in a two-dimensional grid to capture the soil moisture content (SMC) distribution beneath drip irrigation. It was observed during one-to-one comparisons that SMC measured using the factory calibration provided with each probe failed to match volumetric water content (VWC) determined from gravimetric soil samples. However, the longer measurement distance of the WCR probe (150% emitter spacing) allowed for relatively good calibration to VWC data (R2 = 0.74), while the short measurement distance of the Vitel probe (28.5% emitter spacing) resulted in a poor calibration (R2 = 0.26). Time-series observations were more positive as both probes matched the season-long SMC trends well. And the Vitel probe was observed to match soil water salinity trends during time-series following two different fertigation events. The HYDRUS-2D program (H2D) has previously been used for drip irrigation management forecasts. A review of the simulations reported in the literature revealed an assortment of techniques for defining the model simulation space. To examine the effectiveness of these techniques, H2D was calibrated to SMC data collected from a non-planted bed section with soil moisture release curve (SMRC) parameters determined from undisturbed soil cores and saturated hydraulic conductivity determined by inverse optimization. The goodness-of-fit indicator (Ceff) was also modified to account for measurement uncertainty (Ceff*). Semi-spherical (SC) soil wetting geometries proved superior to their surface-radius counterparts in convergence and simulation time, but nearly identical in SMC prediction. Both the axi-symmetrical and two-dimensional SC approaches predicted the SMC data well (Ceff > 0.75) and especially well after uncertainty in the SMC and SMRC measurements was considered (Ceff* = 1.0). It was also observed that most previous studies of fertigation using H2D used mean values for soil parameter estimation. The determination of appropriate soil hydraulic and transport parameters is essential to accurately simulate distributions beneath fertigation. To account for soil parameter uncertainty, inverse optimization methods were applied for soil hydraulic and transport parameter calibration. Calibration of the soil hydraulic parameters revealed high bubbling pressure (~0.17 cm-1) was required to obtain even modest predictions in the bed center (Ceff = 0.27). Calibration of soil transport parameters yielded a longitudinal dispersivity of 2.38 cm and a transverse dispersivity of 0.01 cm (Ceff = 0.56). As before, accounting for measurement uncertainty improved the results of both calibrations, Ceff* = 0.99 and 0.80, respectively.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jason Icerman.
Thesis: Thesis (M.E.)--University of Florida, 2007.
Local: Adviser: Dukes, Michael D.
Local: Co-adviser: Munoz-Carpena, Rafael.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021417:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021417/00001

Material Information

Title: Approaches for Two-Dimensional Monitoring and Numerical Modeling of Drip Systems
Physical Description: 1 online resource (148 p.)
Language: english
Creator: Icerman, Jason
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: drip, fertigation, hydrological, infiltration, insitu, irrigation, model, nitrate, nitrogen, tomato, vadose
Agricultural and Biological Engineering -- Dissertations, Academic -- UF
Genre: Agricultural and Biological Engineering thesis, M.E.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In Florida, intensive bed management systems are commonly used for vegetable production. These systems consist of raised beds for planting covered with plastic mulch, with water and nutrients commonly applied via drip irrigation and fertigation. Currently available dielectric soil moisture sensors provide inexpensive alternatives when compared to Time Domain Reflectometry (TDR) and the labor costs of soil sampling. The CS616 water content reflectometer (WCR) and the Hydra Probe II (Vitel), operating on time-domain and capacitance methods respectively, were installed beneath drip irrigated tomatoes in an intensively managed vegetable production system to examine the monitoring capabilities of each probe through one-to-one and time-series comparisons. The probes were installed in a two-dimensional grid to capture the soil moisture content (SMC) distribution beneath drip irrigation. It was observed during one-to-one comparisons that SMC measured using the factory calibration provided with each probe failed to match volumetric water content (VWC) determined from gravimetric soil samples. However, the longer measurement distance of the WCR probe (150% emitter spacing) allowed for relatively good calibration to VWC data (R2 = 0.74), while the short measurement distance of the Vitel probe (28.5% emitter spacing) resulted in a poor calibration (R2 = 0.26). Time-series observations were more positive as both probes matched the season-long SMC trends well. And the Vitel probe was observed to match soil water salinity trends during time-series following two different fertigation events. The HYDRUS-2D program (H2D) has previously been used for drip irrigation management forecasts. A review of the simulations reported in the literature revealed an assortment of techniques for defining the model simulation space. To examine the effectiveness of these techniques, H2D was calibrated to SMC data collected from a non-planted bed section with soil moisture release curve (SMRC) parameters determined from undisturbed soil cores and saturated hydraulic conductivity determined by inverse optimization. The goodness-of-fit indicator (Ceff) was also modified to account for measurement uncertainty (Ceff*). Semi-spherical (SC) soil wetting geometries proved superior to their surface-radius counterparts in convergence and simulation time, but nearly identical in SMC prediction. Both the axi-symmetrical and two-dimensional SC approaches predicted the SMC data well (Ceff > 0.75) and especially well after uncertainty in the SMC and SMRC measurements was considered (Ceff* = 1.0). It was also observed that most previous studies of fertigation using H2D used mean values for soil parameter estimation. The determination of appropriate soil hydraulic and transport parameters is essential to accurately simulate distributions beneath fertigation. To account for soil parameter uncertainty, inverse optimization methods were applied for soil hydraulic and transport parameter calibration. Calibration of the soil hydraulic parameters revealed high bubbling pressure (~0.17 cm-1) was required to obtain even modest predictions in the bed center (Ceff = 0.27). Calibration of soil transport parameters yielded a longitudinal dispersivity of 2.38 cm and a transverse dispersivity of 0.01 cm (Ceff = 0.56). As before, accounting for measurement uncertainty improved the results of both calibrations, Ceff* = 0.99 and 0.80, respectively.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jason Icerman.
Thesis: Thesis (M.E.)--University of Florida, 2007.
Local: Adviser: Dukes, Michael D.
Local: Co-adviser: Munoz-Carpena, Rafael.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021417:00001


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ee8352412177734bca2e7253a6b157e6
951ed8c263ddf3359fb4b63b6dd3b3978045c8e1







APPROACHES FOR TWO-DIMENSIONAL MONITORING AND NUMERICAL
MODELING OF DRIP SYSTEMS























By

JASON T. ICERMAN


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING

UNIVERSITY OF FLORIDA

2007







































02007 Jason T. Icerman




































To my parents, Drs. Joe and Rhoda Icerman.









ACKNOWLEDGMENTS

The only appropriate way to begin a list of those who have helped me to this point is by

thanking those who helped me enter this discipline. For giving a lost undergraduate a chance to

Eind his direction and never being short on time to listen, I thank Dr. James Leary. Thanks are

also extended to Dr. Wendy Graham for allowing an inquisitive young engineer a chance to get

his hands dirty in the Hield.

For their assistance with my research over the past few years, both in the Hield and out, I

thank Danny Burch, Stacia Davis, Kristen Femminella, Paul Lane, Larry Miller, Jonathan

Schroder, Mary Shedd, Hannah Snyder, and especially Lincoln Zotarelli. Lincoln while your

advice occasionally requires translation, it has proved invaluable time and again.

Special thanks go to Dr. Michael Dukes for reasons too numerous for listing here. You

have allowed me to study as both an undergraduate and graduate student in my own manner,

which anyone reading this document surely knows to be unique. Also Dr. Rafael Mufioz-

Carpena deserves thanks for answering my late-night emails and helping me decipher the endless

world of vadose zone modeling.

Finally as this document is dedicated to them, hearty thanks go to my parents. I thank them

for the encouragement. I thank them for the unyielding support. And I thank them for the greatest

gift I have ever received: their love of learning.












TABLE OF CONTENTS


page

ACKNOWLEDGMENTS .............. ...............4.....


LIST OF TABLES ............ ...... ._ ...............8....


LIST OF FIGURES .............. ...............9.....


AB S TRAC T ............._. .......... ..............._ 1 1..


CHAPTER


1 RE SEARCH BACKGROUND .............. ...............13....


Rationale ................... .... ..._.. .... ....... .............1

Vegetable Production in Florida ........_................. ............_ ........ 1
Drip Irrigation............... ...............1
Drip Irrigation Modeling ................. ...............15...............
Obj ectives ................. ...............17.......... .....

2 COMPARISON OF IN-SITU DIELECTRIC PROBE PERFORMANCE IN A RAISED
VE GET ABLE BED ................. ................. 18..............


Introducti on ................. ................. 18..............
Materials and Methods .............. ...............21....
Measurement Methods .............. ...............21....

Experiment 1: 2005 In-Season .............. ...............24....
Experiment 2: Non-Planted ................. ...............26................
Experiment 3: 2006 In-Season .............. ...............26....
Equations Used in Analysis............... ...............27
Results and Discussion .............. ...............28....

Experiment 1: 2005 In-Season .............. ...............28....
Water content reflectometer precision .............. ...............28....
Soil sample comparisons ................. ...............30........_. ....
Experiment 2: Non-Planted ................. ...............32......... ....
Vi tel precision .............. ...............32....
Probe to probe comparison............... ...............3
Experiment 3: 2006 In-Season .............. ...............33....
Probe to probe comparison............... ...............3
Soil sample comparisons ........_................. ......._._. ......... 3
Summary and Conclusions .............. ...............35....

3 WATER ENTRY BOUNDARY CONDITION IMPACTS ON THE CALIBRATION
OF HYDRUS-2D TO A SURFACE DRIP IRRIGATION SYSTEM ........._..... ................57


Introducti on ............ ..... .._ ...............57...












Materials and Methods .............. ...............60....
Field Experiment .............. ...............60....
M odel Description ................... ...............61.......... ......
Water Entry Boundary Condition............... ...............6
Additional Boundary and Initial Conditions .............. ...............64....
Calibration and Optimization Procedure ................. ...............65................
Prediction Evaluation .............. ...............66....
Results and Discussion .............. ...............67....
Field Results .............. ...............67....
Initial Calibration............... ..............6
Full Calibration............... ..............7
Summary and Conclusions .............. ...............72....


4 UNCERTAINTY IMPACTS ON NUMERICAL MODELING OF FERTIGATION ..........83


Introducti on ................. ...............83.................
Materials and Methods .............. ...............85....
Measurement Methods .............. ...............85....

Experimental Site .............. ...............87....
Experiment 4: 2006 Post-Season ................. ...............88........... ...
Model Description ................. ...............88.................
Initial and Boundary Conditions .............. ...............89....
Calibration and Optimization Procedure ................. ...............92................
Prediction Evaluation .............. ...............93....
Results and Discussion .............. ...............95....
Field Results .............. ..... ... .... ...........9
Soil Hydraulic Parameter Calibration .............. ...............96....
Soil Transport Parameter Calibration ................. ...............98................
Validation Simulations ................. ...............100......... ......
Summary and Conclusions ................. ...............101...............


5 RESEARCH SUMMARY AND FUTURE WORK ................. ............... ......... ...111


Research Summary ................. ...............111......... ......
Future W ork ................. ...............113................


APPENDIX


A SELECT HYDRUS-2D INPUT FILES ...._. ......_._._ .......__. ............1


Initial Calibration of 2D SC 1.0 ........._..... ...._... ...............117.
Initial Calibration of 3D SC 1.0 ........._..... ...._... ...............121.
Full Calibration of 2D SC 1.0 ........._..... ...._... ...............126.
Full Calibration of 3DSC1.0 ........._...... ........_.._....... ...............12
Calibration Bounded by Carsel and Parrish Distributions ....._._._ ........... ...............128
Calibration Bounded by RO SETTA Distributions ................ ...............131..............
Calibration Bounded by Measured Distributions ................. ...............132........... ...













Calibration Bounded by Vanderborght and Vereecken Distributions .........._.... ...............133


B POSSIBLE IN-SEASON IMPACTS ON CALIBRATION ................. .......................138


Introducti on ................. ...............138................
Re sults ................ ...............139................

Summary ................. ...............142......... ......


LIST OF REFERENCES ................. ...............143................


BIOGRAPHICAL SKETCH ................. ...............148......... ......










LIST OF TABLES


Table page

2-1 Summary of experiments performed, data collected, means and methods............._.._.. .....38

2-2 Quantitative comparison of all locations in the timer-based treatment and the sensor-
based treatment using the factory sand calibration ................. ...._.._ ................ ..39

2-3 Quantitative comparison of probe type by location for both the factory and site
calibrations of each probe type .............. ...............40....

3-1 Results of surface area and influx calculations for the different scenarios simulated in
HY DRU S-2D ................. ...............74.__._.......

3-2 Estimated soil hydraulic parameters for van Genuchten model fit to 11 soil core
samples by RETC model .............. ...............74....

3-3 Results from initial calibration ................. ...............75........... ..

3-4 Results from full calibration .............. ...............76....

4-1 Results from soil hydraulic parameter calibrations .............. ...............103....

4-2 Reported dispersivity values used in previous HYDRUS-2D fertigation studies ...........104










LIST OF FIGURES


Figure page

2-1 The 2 X 3 matrix formation used in Experiment 1 with labels used in discussion............40

2-2 The 2 X 4 matrix formation used in Experiment 2 and Experiment 3 for both probe
types with labeling used in discussion ................. ...............41........... ..

2-3 Comparison of edge probes within each TIMER treatment matrix ................. ................42

2-4 Comparison of probes between the TIMER treatment matrices................... ................ .43

2-5 Time-series data from all edge probe locations in the TIMER treatment. ................... ......43

2-6 Comparison of edge probes within each SMS treatment matrix .............. ....................44

2-7 Comparison of probes between the SMS treatment matrices ................ .....................44

2-8 Time-series data from all edge probe locations in the SMS treatment ................... ...........45

2-9 Comparison of WCR SMC and VWC data for the center locations of SMS and
TIM ER treatments .............. ...............45....

2-10 Comparison of WCR SMC and VWC data for the edge locations of SMS and
TIM ER treatments .............. ...............46....

2-11 Comparison and calibration of WCR and gravimetric SMC data ................ ................. 46

2-12 Comparison of calibrations for a selected time-series from the TIMER treatment.......... .47

2-13 Location comparisons within Vitel probe matrix of the TIMER treatment for
Experim ent 2............... ...............48...

2-14 Time-series data from all probe locations in the TIMER treatment ................. ...............49

2-15 Comparison of Vitel to WCR SMC for each location within the bed .............. .... ........._..50

2-16 Relationship of SMC measured in the center of the bed ................. ........................5 1

2-17 Comparison of the WCR and Vitel probes for each location within the bed during
Experim ent 3 .............. ...............52....

2-18 Residuals for each location presented as Vitel WCR within the TIMER treatment
bed during Experiment 3 ................. ...............53................

2-19 Comparison of Vitel KNO3 burden data and soil sample NO3-N data..................... ........._54

2-20 Time-series KNO3 burden for each probe location............... ...............55











2-21 Comparison of VWC to the WCR SMC using the 2005 calibration ................ ...............56

2-22 Comparison of gravimetric SMC to WCR using the factory calibration for sand.............56

3-1 Experiment 2 WCR matrix configuration centered in bed .............. ....................7

3-2 Water entry boundary conditions examined for soil moisture content prediction. ............78

3-3 Averaged soil moisture content from data measured on site. ............. ......................7

3-4 Measured soil moisture content from each probe ................. ......___ ........._ ....8

3-5 Results of RETC model calibration to soil core data. ......___. .... ........ ...............8 1

3-6 Results of initial calibration soil moisture content predictions.. ............._ ..........._ ...82

3-7 Comparison of initial and full calibration soil moisture content predictions...................82

4-1 Experiment 3 and 4 WCR matrix configuration centered in bed. ............. ................1 04

4-2 Experiment 4 WCR soil moisture content measurements .............. ......................0

4-3 Experiment 3 Vitel determined nitrate concentrations .............. .....................0

4-4 Root distribution collected during full canopy .............. ...............106....

4-5 Parameter S ets 1, 2, and 3 soil hydrauli c parameter calibrati on ................. ................. 107

4-6 Nitrate concentration predictions for May 30 fertigation .............. .....................0

4-7 Nitrate concentration predictions for June 6 fertigation .............. ....... .............10

4-8 Nitrate concentration predictions for June 14 fertigation ................. .......................110

A-1 Boundary conditions for 2DSC1.0 simulation ........................_. ........_.........2

A-2 Numerical node structure for 2DSC1.0 simulation............... ..............12

A-3 Boundary conditions for 3DSC1.0 simulation............... ..............12

A-4 Numerical node structure for 3DSC1.0 simulation............... ..............12

B-1 Averaged data used in calibrations .............. ...............140........_._....

B-2 Location by location comparison for measured soil moisture content ................... .........141

B-3 Results of Experiment 2 calibration and Experiment 4 measured data ................... ........141









Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering

APPROACHES FOR TWO-DIMENSIONAL MONITORING AND NUMERICAL
MODELING OF DRIP SYSTEMS

By

Jason T. Icerman

August 2007

Chair: Michael Dukes
Cochair: Rafael Mufioz-Carpena
Major: Agricultural and Biological Engineering

In Florida, intensive bed management systems are commonly used for vegetable

production. These systems consist of raised beds for planting covered with plastic mulch, with

water and nutrients commonly applied via drip irrigation and fertigation. Currently available

dielectric soil moisture sensors provide inexpensive alternatives when compared to Time

Domain Reflectometry (TDR) and the labor costs of soil sampling. The CS616 water content

reflectometer (WCR) and the Hydra Probe II (Vitel), operating on time-domain and capacitance

methods respectively, were installed beneath drip irrigated tomatoes in an intensively managed

vegetable production system to examine the monitoring capabilities of each probe through one-

to-one and time-series comparisons. The probes were installed in a two-dimensional grid to

capture the soil moisture content (SMC) distribution beneath drip irrigation. It was observed

during one-to-one comparisons that SMC measured using the factory calibration provided with

each probe failed to match volumetric water content (VWC) determined from gravimetric soil

samples. However, the longer measurement distance of the WCR probe (150% emitter spacing)

allowed for relatively good calibration to VWC data (R2 = 0.74), while the short measurement

distance of the Vitel probe (28.5% emitter spacing) resulted in a poor calibration (R2 = 0.26).









Time-series observations were more positive as both probes matched the season-long SMC

trends well. And the Vitel probe was observed to match soil water salinity trends during time-

series following two different fertigation events.

The HYDRUS-2D program (H2D) has previously been used for drip irrigation

management forecasts. A review of the simulations reported in the literature revealed an

assortment of techniques for defining the model simulation space. To examine the effectiveness

of these techniques, H2D was calibrated to SMC data collected from a non-planted bed section

with soil moisture release curve (SMRC) parameters determined from undisturbed soil cores and

saturated hydraulic conductivity determined by inverse optimization. The goodness-of-fit

indicator (Cesf) was also modified to account for measurement uncertainty (Cer*"). Semi-spherical

(SC) soil wetting geometries proved superior to their surface-radius counterparts in convergence

and simulation time, but nearly identical in SMC prediction. Both the axi-symmetrical and two-

dimensional SC approaches predicted the SMC data well (Cegf > 0.75) and especially well after

uncertainty in the SMC and SMRC measurements was considered (Cer*" = 1.0).

It was also observed that most previous studies of fertigation using H2D used mean values

for soil parameter estimation. The determination of appropriate soil hydraulic and transport

parameters is essential to accurately simulate distributions beneath fertigation. To account for

soil parameter uncertainty, inverse optimization methods were applied for soil hydraulic and

transport parameter calibration. Calibration of the soil hydraulic parameters revealed high

bubbling pressure (~0.17 cm l) was required to obtain even modest predictions in the bed center

(Cegf= 0.27). Calibration of soil transport parameters yielded a longitudinal dispersivity of 2.38

cm and a transverse dispersivity of 0.01 cm (Cegf= 0.56). As before, accounting for measurement

uncertainty improved the results of both calibrations, Ceg*" = 0.99 and 0.80, respectively.









CHAPTER 1
RESEARCH BACKGROUND

Rationale

The economic importance of vegetable production in Florida was the driving force behind

the research presented in this document. Funding for this research was provided by the Florida

Department of Agriculture and Consumer Services (FDACS) as part of the Integration and

Verification of Water Quality and Crop Yield Models for BMP Planning research program. For

the purpose of direction, the presentation of research is preceded by a brief introduction of

significant water management issues for vegetable production in Florida. Since drip irrigation

systems are currently common for vegetable growers in Florida and the focus of this research,

general information on drip systems is provided. Concurrently, drip systems exhibit many unique

aspects that must be considered for monitoring and modeling efforts. These aspects are also

discussed and provide a solid base for fully understanding the research to be presented.

Ultimately, specific obj ectives of the research will be outlined as related to the subsequent

chapters within this document.

Vegetable Production in Florida

Water is a vital resource and is the first limiting nutrient of crop production. Agricultural

self-supply accounts for 39% of fresh ground water withdrawals and 62% of fresh surface water

withdrawals the highest percentage in either category making agriculture the largest user of

freshwater in Florida (Marella, 1999). As the largest consumer of freshwater resources, improved

agricultural management practices on a field scale possess the potential for large scale

conservation.

Vegetables are a maj or component of Florida agriculture encompassing about 72,000 ha

for production and valued at $1.5 billion annually (USDA, 2006). Most of the soils where these










vegetables are grown are sandy and as such, frequent irrigation and fertigation is required to

minimize crop stress and attain maximum production. Currently, over 30% vegetable production

in the state occurs in raised beds often covered with plastic mulch otherwise known as intensive

bed management systems. Commonly in intensive bed management systems, water is introduced

only by irrigation and fertigation via drip emitters. Conversely, resource extraction is limited

almost solely to transpiration, as plastic mulch covering the raised bed minimizes the influence

of rainfall and soil evaporation (Simonne et al., 2004). Though an established technology still

growing in popularity, intensive bed management systems remain understudied and more

effective management and measurement techniques continue to be developed all over the globe

(Amayreh and Al-Abed, 2005; Vazquez et al., 2006; Zotarelli et al., 2007a).

Drip Irrigation

Drip irrigation has the potential to enhance the sustainability of high intensity vegetable

production by eliminating excess irrigation and reducing chemical leaching. Correct surface

placement of drip emitters enables the infiltration process to occur over a small area and

promotes three dimensional flows in shapes that have been described as a wet bulb. And most

importantly, drip irrigation targets water and nutrient delivery to the root zone, increasing water

and nutrient uptake efficiency (Goldberg at al., 1971).

Drip irrigation also helps reduce foliar disease incidence compared to overhead sprinkler

systems. By maintaining drier plants drip irrigation reduces outbreaks of bacteria and fungal

diseases, hence reducing the need for bactericides and fungicides (Hochmuth and Smaj strla,

1998). Also, fertilizers can be prescription-applied during the season based on crop needs. These

small, controlled applications of fertilizer not only save fertilizer, but also have the potential to

eliminate groundwater pollution caused by leaching from over-irrigation (Schroder, 2006).










Though resource conservation is the strength of intensive bed management systems, the

added cost of drip irrigation places a greater strain on resource management for these systems.

Assuming common Florida conditions, annual drip irrigation costs have been estimated at $363

per acre for drip irrigation systems, which is over $100 per acre more than other common

irrigation methods such as semi-closed and open-ditch irrigation systems (Pitts et al., 1990). In

order to ensure further transition of the vegetable industry to intensive bed management systems,

the systems must be proven an economical option. And while drip irrigation and fertigation can

be very efficient, mismanagement can lead to over-irrigation and excessive nutrient losses due to

leaching. Enhanced monitoring and modeling techniques are necessary to achieve the most

effective management cost conserving techniques for intensive bed management systems;

moreover, two-dimensional monitoring remains a research need for the assessment of forecasting

models (Cote et al., 2003).

Drip Irrigation Modeling

To accurately predict environmental impacts associated with human practices, a

quantitative description of both water and solute movement through the vadose zone is required;

furthermore, for drip irrigation it is essential to account for the two-dimensional nature of the

system (Mufioz-Carpena et al., 2005b).

Lubana and Narda (2001) reviewed modeling approaches specific to drip irrigation and

found both over-simplifieation and over-complexity to have adverse affects in modeling drip

irrigation flow dynamics. Feyen et al. (1998) reviewed several models in existence at the time,

focusing on the inclusion of both micro- and macro-heterogeneity; it was noted that micro-

heterogeneity on a Hield scale, such as macropores, could increase the risk of leaching pollutants

making such Hield characteristics vital for accurate modeling to occur. Such a need for dual-

permeability models able to handle micro-heterogeneity and simulate chemical transport under









Hield conditions has become an outstanding research need for determining the fate of nutrients

and other non-point source pollutants (Simunek et al., 2003). Recently the two-dimensional,

Einite element model HYDRUS-2D, which numerically solves Richards' equation for saturated-

unsaturated water flow and the convection-dispersion equation for solute flow, has been applied

to multiple drip irrigation systems and proven to be a reliable predictor of soil moisture dynamics

(Gardenas et al., 2005).

Emitter placement and other characteristics of drip systems allow for different assumptions

when modeling the system in HYDRUS-2D, which correspond to boundary conditions

representing point source and line source assumptions. A point source boundary, representative

of an isolated emitter, creates a quasi-spherical wetted soil region, more or less elongated

depending on soil textural characteristics. A line source boundary is applicable when several

point sources overlap along an axis placed in the soil surface (i.e. along a crop bed), as may be

the case under drip tape.

A review of the literature conducted for this study noted there have been three distinct drip

system validations of HYDRUS-2D soil moisture predictions using Hield data (Fernandez-Galvez

et al., 2006; Mmolawa and Or, 2003; Skaggs et al., 2004). Two validations were performed on

subsurface drip irrigation (SDI) systems, with only Fernandez-Galvez et al. (2006) presenting

Hield data collected beneath surface drip irrigation. Field validation of fertilizer distributions

beneath drip systems is even more limited, as only Aj dary et al. (2007) has presented HYDRUS-

2D simulations validated by Hield measurements (nitrogen fertilizer in the form of urea). In a

laboratory setting, Li et al. (2005) measured soil moisture and nitrate-nitrogen in soil cores

following fertigation and showed HYDRUS-2D to be an accurate predictor of the system. As can

be inferred through this summary of the existing literature, the conclusions of Cote et al. (2003)










remain valid. Two-dimensional field monitoring of drip irrigation and fertigation systems

remains a research need to both strengthen the literature data set and further validate two-

dimensional model predictions, especially fertigation systems.

Obj ectives

* Examine the ability of current low cost technologies to measure two-dimensional
distributions beneath drip irrigation in a raised vegetable bed

* Calibrate in-situ soil moisture sensors to volumetric moisture obtained from gravimetric
sampling on a one-to-one basis

* Examine the ability of in-situ measurements to track time-series of property changes
following irrigation and fertigation events in a raised vegetable bed

* Reproduce measured two-dimensional soil moisture distributions using HYDRUS-2D

* Examine the effect of different water entry boundary conditions

* Reproduce measured two-dimensional nitrate distributions following fertigation events
using HYDRUS-2D

* Examine the effect of uncertainty in soil hydraulic and transport parameter estimation on
fertigation predictions

* Direct future research efforts in the field









CHAPTER 2
COMPARISON OF IN-SITU DIELECTRIC PROBE PERFORMANCE INT A RAISED
VEGETABLE BED

Introduction

Vegetables are a maj or component of Florida agriculture encompassing about 72,000 ha

for production and valued at $1.5 billion annually (USDA, 2006). Most of the soils where these

vegetables are grown are sands, with frequent irrigation and fertigation required to minimize

crop stress and attain maximum production. Water and nutrient delivery to these systems is

commonly provided by drip irrigation. Although drip irrigation and fertigation can be very

efficient, delivering water and nutrients to the crop root zone (Goldberg et al., 1971),

mismanagement can lead to over-irrigation and excessive nutrient losses due to leaching. Also

much of the vegetable production in the state occurs on raised beds covered with plastic mulch.

Plastic mulch minimizes the influence of evaporation and rainfall in the system (Simonne et al.,

2004) isolating irrigation effects and making these systems ideal for experimental monitoring of

distributions beneath drip irrigation.

To date, two-dimensional monitoring of soil moisture content (SMC) and nutrient

distributions for the assessment of drip system effectiveness as well as forecasting model

predictions remains a research need (Cote et al., 2003). Traditionally SMC is determined by

gravimetric soil sampling, often reported as volumetric moisture content (VWC) after

multiplying by bulk density. While VWC is easily calculated from gravimetric data, soil

sampling is labor intensive and physically destructive. Any system disturbance is compounded

when lateral distributions are desired, especially in confined areas such as raised bed systems.

Also errors inherent with soil sampling both for collected gravimetric and bulk density samples

creates a sizable source for potential error in reported VWC. The combination of labor cost,










system disturbance, and potential errors makes non-destructive in-situ measurement techniques a

preferable alternative.

Time domain reflectrometry (TDR) is perhaps the most well known in-situ technique and

is widely accepted as one of the most accurate methods. TDR can be used on a variety of soils

using only a single calibration equation (Topp et al., 1980). Yet due to the high cost of TDR,

multiple alternative in-situ sensors have been developed. Two common alternatives to TDR are

the CS616 (Campbell Scientific, Inc., Logan, Utah) water content reflectometer (WCR) and the

Hydra Probe (Stevens Water Monitoring Systems, Inc., Portland, Oregon).

The WCR probe is a dielectric probe that uses time-domain methods for measuring SMC,

meaning the probe response for equal VWC in varying soils will be similar (Campbell Scientific,

Inc., 2002). The Hydra Probe is also a dielectric probe, but uses bulk capacitance measurements

to calculate soil properties, like SMC. The utilization of capacitance methods means the probe

response for equal VWC in varying soils will not be similar, ie. capacitance probes require at

minimum soil class specific calibration (Stevens Water Monitoring Systems, Inc., 2007). Hydra

Probe success resulted in the recent development of a similar product, the Hydra Probe II

(Stevens Water Monitoring Systems, Inc., Portland, Oregon), with both commonly referred to as

Vitel probes. The main advantages of the new Vitel probe (Hydra Probe II) relative to the old

Vitel probe (Hydra Probe) are a decrease in power usage and an increase in cable length. All

future references to the Vitel probe in this document are references to the new Vitel probe.

Another feature of the Vitel probe is the ability to measure bulk salinity and soil water

salinity, which can be reported as a NaCl burden or KNO3 burden (g L ). While soil water

salinity is not a common plant stressor for vegetable production in Florida, it can be considered a

tracer for agricultural systems in sandy soils representative of applied nutrient dynamics due to









near zero soil water salinity initial conditions, oxidation conditions, and the negatively charged

soil matrix.

Also when collecting "point" measurements to outline distributions it is important to bear

in mind the collection volume for a specific method. The WCR has an estimated sensing volume

of ~900 cm3 and sensing length of 30 cm (Campbell Scientific, Inc., 2002). Due to the probe

length of a WCR, horizontal probe installation is required to capture both vertical and transverse

distributions. Plauborg et al. (2005) noted that horizontally installed WCRs exhibited large

variation between probe replicates in the field. The authors considered the probe variation to be a

product of both poor factory calibration provided by the manufacturer and the natural

heterogeneity found in top soil. The study also found better probe correlation at lower SMC,

while reporting WCR probes to measure SMC consistently lower than TDR measurements.

The Vitel probe differs from the WCR in sensing volume, 40.3 cm3, and sensing length,

5.7 cm (Stevens Water Monitoring Systems, Inc., 2007). Yet similar to the WCR, the old Vitel

probe has been observed to underestimate SMC in sandy soils when compared to VWC obtained

from gravimetric samples (Kennedy et al., 2003); however, the opposite has been reported when

the old Vitel probe is compared to TDR. Seyfried and Murdock (2004) concluded that while soil

specific calibrations of the old Vitel probe increased accuracy relative to TDR across most soil

types, for sandy soils the manufacturer provided factory calibration matched TDR values for

SMC very well.

As has been previously described through examples here and is often the case in

monitoring studies, probe results are commonly compared on a one-to-one basis to established

methods. Yet one of the known advantages for continuous in-situ monitoring is the ability to

track soil properties over extended time-series (Kennedy et al., 2003); therefore, in this study









another approach will also be employed for probe examination, comparing the probe

measurements over event-long and season-long time-series. Time-series comparison inclusions

allows for a more descriptive examination of probe performance, as probe SMC measurements

may be consistently off +/- 0.03 cm3 Cm-3 relative to established methods, but able to match the

wetting and drying trends following an irrigation event very well. Simply capturing these trends

can be very useful for irrigation management and like studies. Similarly, soil water salinity

burdens can be examined over an entire fertigation event or the season-long build-up and

reduction of fertigation constituents in the soil. These comparisons will be referred to as time-

series comparisons. Considering this, the obj ective of this study was to analyze the potential for

using a time-domain probe (WCR) and a capacitance probe (Vitel) for two-dimensional

monitoring beneath drip irrigation by comparing probe SMC measurements to VWC

measurements obtained from gravimetric samples and also comparing Vitel probe measured soil

water salinity to soil water nitrate-nitrogen (NO3-N) obtained from soil samples, in each case

using one-to-one and time-series comparisons.

Materials and Methods

Three distinct experiments were performed at the University of Florida, Plant Science

Research and Education Unit located near Citra, Florida. Buster (1979) classified the soil at the

research site as a Tavares sand and Candler sand. These soils contains >97% sand-sized particles

and have a field capacity of 0.05-0.07 (cm3 Cm-3) in the upper 100 cm of the profile (Carlisle et

al., 1978). The experiments are summarized in Table 2-1, with further discussion to follow.

Measurement Methods

SMC was measured in-situ by dielectric probes, the WCR and Vitel. The WCR probe uses

time-domain methods for SMC measurement and consists of two 30 cm long stainless steel rods

connected to a printed circuit board. The probe rods can be inserted from the surface or as in the









case of this study, the probe can be buried at any orientation to the surface. The differentially-

driven probe rods form a transmission line with a wave propagation velocity that is dependent on

the dielectric permittivity of the medium surrounding the rods. Since water has a dielectric

permittivity significantly larger than other soil constituents, the resulting oscillation frequency is

dependent upon the average SMC of the medium surrounding the rods (Campbell Scientific, Inc.,

2002).

The Vitel probe uses bulk capacitance measurements to calculate SMC, by making a high

frequency (50 MHz) complex dielectric constant measurement. The probe head contains the

necessary electronics to generate the 50 MHz stimulus and generate voltages that reflect the soil's

electrical properties. The three outer and one center tine form the sensing volume of soil. The

capacitive part of the response is most indicative of SMC, while the conductive part reflects bulk

salinity. Through the use of appropriate calibration curves that are related to soil type, the

dielectric constant measurement can be directly related to SMC (Stevens Water Monitoring

Systems, Inc., 2007).

For SMC comparison, VWC was determined using collected gravimetric samples. Soil

samples were collected by a 5 cm diameter soil auger. Each reported soil sample location yielded

two depths of composite samples: 0-15 and 15-30 cm. All collected samples were immediately

placed on ice and refrigerated until analyzed. A 20 g subsample was used to determine the

gravimetric water content for each composite sample, which in turn was used to calculate

(multiplying by the bulk density) the VWC.

In order to determine VWC from collected gravimetric data, bulk density measurements

were also collected. The field bulk density was estimated by the average bulk density of 11 soil

samples collected by an undisturbed core sampler. Soil cores measured 5.4 cm in diameter and









6.0 cm in height and samples were collected between a depth of 0-6 and 6-12 cm below the bed

surface at various places in the field. The samples were saturated to measure wet weight and

oven dried to measure dry weight. The average measured bulk density in the field beds was 1.26

g cm-3 with a 6.92% standard deviation. Through this method, it is assumed that bulk density is

constant with depth.

To track applied fertigation, the soil water salinity burden (KNO3 g L^1) was measured by

the Vitel probes. However, the fertigation applied during the study was not KNO3, but consisted

of Ca(NO3)2, KC1, and Mg(SO4) COmpounds. Previous studies have used electrical conductivity

(EC) measured by capacitance probes to track individual ions such as Br, Cl, and NO3 (Mufioz-

Carpena et al., 2005a), but the KNO3 burden measured by the Vitel probe is reported here since it

is included with the manufacturer provided program and requires no extra work on part of the

end user. This is inline with the study obj ective of testing the probe' s effective as a monitoring

tool, not necessarily electrical quantities measured by the probe; therefore, all reported KNO3

burdens in this study are actually representative of all applied fertigation compounds. It should

also be noted that the measured KNO3 burden is subj ect to calculation errors as well as

measurement errors, since the conversion from bulk burden to soil water burden used was simply

a division by SMC (Stevens Water Monitoring Systems, Inc., 2007) and previous studies have

shown the relationship between bulk burden and soil water burden to be much more complex

(Mufioz-Carpena et al., 2005a).

For soil water salinity comparison, soil water NO3-N was determined from collected soil

samples. These samples were collected in the center of the bed with one sample uniformly mixed

from the 0-30 cm depth. The samples were collected -1, 1, 3, and 7 days following a given

fertigation event. For NO3-N analysis a 10 g sub sample was extracted and 50 mL of 2 M KCl









was added to the subsample. The resulting mixture was filtered by gravity using Fisherbrand

filter paper within one day of soil sampling (Mulvaney, 1996). Soil solution extracts were stored

at -18 deg C. They were analyzed for NO3-N using an air-segmentedautomated

spectrophotometer (Flow Solution IV, OI Analytical, College Station, Texas) coupled with a Cd

reduction approach similar to the work of Zotarelli et al. (2007a).

Experiment 1: 2005 In-Season

Between April 12 and June 27, 2005 SMC distributions were monitored under surface drip

irrigated tomatoes (Lycopersicon esculentum, 'FL 47'). The tomatoes were planted in raised

beds covered with black plastic mulch. The two treatments of interest were a timer-based

irrigation scheme (TIMER) and a soil moisture sensor-based irrigation scheme (SMS). Both

treatments received the University of Florida, Institute of Food and Agricultural Sciences (IFAS)

recommended seasonal fertilizer amount of 208 kg ha-l nitrogen (N) applied as calcium nitrate in

weekly fertigation events (Maynard et al., 2003) and were replicated four times within the field.

Each treatment contained two surface drip lines (Turbulent Twin Wall, 20 cm emitter spacing,

0.25 mm thickness, 3.72 L min' at 69 kPa, Chapin Watermatics, Inc., Watertown, New York),

one for irrigation and one for fertigation. The surface drip lines were laid side by side in the

center of the bed. Transplants were approximately 45 days old at transplanting on April 7, 2005

and transplanted in a single row approximately 10 cm from the bed center with 45 cm spacing

for a plant population of 11,960 plants ha- .

The SMS treatment was set near effective field capacity (~0.10 cm3 Cm-3) and was

controlled by a Quantified Irrigation Controller (QIC) developed at the University of Florida

(Mufioz-Carpena et al., 2006). The QIC device uses a 20 cm long ECH20 probe (Decagon

Devices, Inc., Pullman, Washington) that was inserted vertically into one representative bed

replicate and controlled all replicates to monitor SMC. The QIC was queried every minute at five









selected time windows during the day, if during any query the ECH20 probe returned a SMC

below field capacity the QIC allowed irrigation. Conversely, the QIC bypassed irrigation events

if the SMC was above field capacity (Dukes and Mufioz-Carpena, 2006). At the beginning of the

season, the application windows for the QIC were 12 minutes long beginning at 0812, 1012,

1212, 1412, and 1612 hours and the period of application for the TIMER treatment was 0600 to

0700 hours. Starting May 26, the time windows for the QIC were 24 minutes long beginning at

0824, 1024, 1224, 1424, and 1624 hours and the period of application for the TIMER treatment

was 0600 to 0800 hours. During the establishment phase SMC in the beds was maintained at or

above field capacity with daily irrigation events to ensure even establishment of all plots.

Irrigation treatments were implemented 18 days after transplanting.

SMC was measured on an hourly basis by WCRs with the manufacturer provided factory

calibration for sand used in data collection. Four matrices each containing six WCRs were

installed, two in the SMS treatment and two the TIMER treatment. A 40 cm long section of the

entire bed width was removed from both installation locations, centered under an emitter. The

section provided enough space for WCR installation parallel to the surface. After installation the

section was repacked with the original soil. For each treatment, one WCR matrix was located on

the north face of the removed section and one on the south face. The matrices were configured in

a 2 X 3 formation (Vertical X Transverse), with a top row buried at 8 cm and a bottom row at 23

cm below the surface. The three columns were spaced 23 cm apart with the center column

located in the bed center (Figure 2-1). The purpose of the matrix configuration was to capture the

wet-bulb shape of SMC redistribution under the emitter.

Soil samples, analyzed for VWC, were collected five times to validate the WCR SMC

measurements: April 27; May 11; May 25; June 8; and June 22. Samples were collected from










each treatment and from all four replicates, compared to the single installation location of the

probes. Similar to the probe matrix, soil samples were collected from three points laterally across

the bed. A center location and two other locations near the edge, approximately 23 cm from the

bed center in each direction.

Experiment 2: Non-Planted

From October 10 to October 23, 2006 SMC was measured from the same field as

Experiment 1 with similar irrigation treatments. For the entire period, the application windows

for the QIC were 24 minutes long beginning at 0824, 1024, 1224, 1424, and 1624 hours and the

application window for the TIMER treatment was 0600 to 0800 hours, daily.

As before, a 40 cm section was removed from one replicate of each treatment; however,

for this experiment two changes to the probe matrices occurred. First, each treatment had one

WCR probe matrix and one Vitel probe matrix for monitoring. The second change was the

matrix size. The 2 X 3 matrix was replaced by a 2 X 4 matrix for each probe type (Figure 2-2).

The probes were located 8 cm and 23 cm away from the bed center laterally in each direction and

the depths were again 8 cm and 23 cm. The bed sections monitored in this experiment were not

planted nor fertigated.

Experiment 3: 2006 In-Season

From April 14 to July 5, 2006 SMC was measured from the same Hield as Experiment 1

and Experiment 2, with irrigation treatments identical to Experiment 2. The 2 X 4 matrix

configuration and installation method used in Experiment 2 was also used for this experiment

(Figure 2-2). The Hield setup, fertigation, and crop were identical to Experiment 1, with

transplanting occurring on April 10, 2006.

Also similar to Experiment 1, soil samples analyzed for VWC, were collected Hyve times

during the season to validate WCR and Vitel SMC measurements: April 27; May 9; May 23;









June 6; and June 26. The same approach as Experiment 1 was used as samples were collected

from each treatment of interest and from all four replicates. To account for the change in probe

matrix locations, soil samples were collected from four points laterally across the bed. Two

locations 8 cm from the bed center in each direction and the other two locations near the edge,

approximately 23 cm from the bed center in each direction. A second group of samples was also

collected to capture fertigation distributions. Again, these samples were collected in the center of

the bed with one sample uniformly mixed from the 0-30 cm depth. The samples were collected -

1, 1, 3, and 7 days following two unique fertigation events that occurred on May 23 and June 13.

Equations Used in Analysis

In a sandy soil Plauborg et al. (2005) calibrated horizontally installed WCR probes to TDR

measured SMC. Their reported linear relationship was rearranged to yield Equation 2-1.

WCR 0.0 13
TDR = (mc-)(2-1)
0.59

All data unless otherwise noted was collected using the manufacturer provided factory

calibration for sand for each probe and is presented using this method. Since TDR was not

available at the field site to perform a site specific calibration, the Plauborg calibration is

presented as an alternative for horizontally installed WCR probes in sandy soils to the

manufacturer provided factory calibration and eventual VWC calibration obtained during the

study .

To compare time-series of probe SMC measurements and established methods the Nash-

Sutcliffe (1970) efficiency coefficient (Cesf) was used. The range of Cegf lies between 1.0 (perfect

fit) and -oo. When Cegf is lower than zero the mean value of the measured time-series would have

been a better predictor than the probe (Nash and Sutcliffe, 1970). Cegf is the reported goodness-









of-fit indicator in this study because it has been previously reported as a better indicator for time-

series compared to other indicators based on squared residuals (Legates and McCabe, 1999).

Results and Discussion

Experiment 1: 2005 In-Season

Water content reflectometer precision

To examine the probe precision, WCR measurements are compared by location. The edge

locations are compared both within the matrix (NW8 to NE8, NW23 to NE23, SW8 to SE8, and

SW23 to SE23) and between matrices (NW8 to SW8, NW23 to SW23, NE8 to SE8, and NE23 to

SE23), while the center locations are compared only between matrices for each treatment

(TIMER and SMS) individually (NC8 to SC8 and NC23 to SC23). It is important to establish the

probe precision in relation to the monitoring locations before embarking on comparisons

between measurement methods. Any significant lack in probe precision would speak to

heterogeneity present within the system, making a comparison of methods difficult and likely

fruitless. The TIMER treatment results are presented first with SMC reported using the factory

sand calibration.

Examination of Figure 2-3 reveals reasonable correlation for field data across between the

edge locations in each face of the TIMER treatment. And Figure 2-4 shows no consistent bias

toward either face, except for in the center of the bed where the center locations appear

consistently wetter in the north face.

While the measured SMC at the edge locations fall close, but away from the 1:1 line in

Figure 2-3, 2-4, and 2-5 displays the time-series of the edge locations and reveals the probe

replicates to be very similar. This is especially true once the 0.025 cm3 Cm-3 SMC probe accuracy

is considered (Campbell Scientific, Inc., 2002) as each probes deviation from the average SMC

is under 0.01 cm3 CA-3 for the 8 cm depth and under 0.02 cm3 Cm-3 for the 23 cm depth. It was










also observed that the spread of the data increases for the center locations as SMC increases. The

relation of spread to SMC is in agreement with results reported by Plauborg et al. (2005) as their

study revealed more precision for measurement replications at lower SMC.

In fact all observations made from Figures 2-3, 2-4, and 2-5 are strengthened when the

Hield setup is considered in addition to the probe accuracy. The double drip line setup prevents

the irrigation emitter, or fertigation emitter, or both from being located directly in the center of

the bed. While either emitter would be located no further than 2-3 cm from the bed center, the

distance is enough to observe a consistent variation in probe moisture. In all, like locations were

observed to be within reasonable agreement so that the east and west locations within each face

as well as the north and south face of each matrix can be considered replicates for future

comparisons.

A quick examination of the SMS treatment figures reveals similar precision results when

compared to the TIMER treatment results, except at the 23 cm edge locations. No physical

explanation exists for the variation observed between probe replicates at 23 cm edge location.

When both Figure 2-6 and 2-7 are considered, it is observed that the variation is mostly due to

one probe (SW23), which is confirmed when by the time-series presented in Figure 2-8. Ignoring

the SW23 location, the north and south matrices can again be considered replicates. And, the

previously reported negative relationship between SMC and precision is also visible for the

center locations (Figure 2-7).

Table 2-2 shows the problem with one-to-one comparisons for Hield monitoring. Results in

Table 2-2 are poor, with Cefr values often below 0. Only when the entire time-series is considered

(Figure 2-5 and 2-8) do the probes measurements appear to be location replicates. Concurrently

considering the entire time-series along with the probe accuracy reported by the manufacturer









allows for the replicate assumption by location, where as solely one-to-one comparisons preclude

such assumptions.

Soil sample comparisons

In general the VWC obtained from gravimetric samples was more variable than WCR

SMC and SMS treatment results were more variable than TIMER treatment results with standard

deviations of the data as follows: TIMER WCR, 0.009 cm3 Cm-3; TIMER VWC, 0.018 cm3 Cm-3;

SMS WCR, 0.015 cm3 Cm-3; SMS VWC, 0.026 cm3 Cm-3. The difference in variation between

the WCR SMC and VWC is largely a result of their measurement volumes and monitoring

location. WCR SMC represents an average over the 900 cm3 VOlume, which corresponds to a 30

cm length within the bed. The VWC data represents an average over the 294.5 cm3 auger

volume, which encompasses only 5 cm of bed length. The shorter length included in the average

places more importance on the measurement location relative to a drip emitter, which were

spaced 20 cm apart. Recall the reported VWC is an average across the four sampling locations in

the field, which are at a similar normal distance from an emitter, but could be from multiple

radial distances. This is because soil samples were collected relative to the drip tape and plant

location, but without regard for emitter location. Averaging samples alleviates some error

relative to WCR SMC since the WCR measurement length is 1.5 X emitter spacing, effectively

an average of the entire spacing.

Figure 2-9 and 2-10 present WCR SMC and VWC determined from gravimetric data for

both treatments. A general trend of WCRs returning lower SMC values than soil samples is seen

in the figures, similar to the observations made by Plauborg et al. (2005) when comparing WCR

to TDR SMC. That being said, some potential errors in the gravimetric data exist. Beyond the

previously reported bulk density uncertainty, the subsample size used for gravimetric soil









moisture was relatively small (20 g) and could have induced further errors. Though in general,

soil sampling occurred too infrequently to make observations on a time-series scale.

In traditional one-to-one style, the WCR SMC measurements were calibrated to VWC

obtained from gravimetric soil sample results. Both the TIMER and SMS treatment data was

included in the calibration. Since the soil samples could not be collected instantaneously and are

instead spread on a timeline of collection for each collection date, the WCR readings were

accordingly averaged from 1000 hours to 1400 hours for both the north and south locations, for

each treatment. Gravimetric data was averaged across the four replicates for each treatment for

VWC determination. The resultant calibration equation displayed in Figure 2-11 was

transformed to match Equation 2-1 (Equation 2-2). If we consider the equations to be of the

general form Y = (X A) / B, it can be seen that though the sample variability results in a

relatively low R2 Value Of 0.74, Equation 2-1 and Equation 2-2 return similar A parameters, but

different B parameters.

WCR 0.03
VPVC = (cm3 Cm-3) (2-2)
0.69

The R2 value can be explained by the uncertainty in collecting WCR SMC and VWC data.

Interestingly, the factory and Plauborg calibrations proved similar in their ability to match

collected VWC for this study site. The factory calibration appears to underestimate SMC, while

the Plauborg calibration overestimates SMC (Figure 2-12).

Regardless of calibration, the WCR SMC collection frequency was an inherent problem for

both treatments, but is more obvious in the presented SMS treatment results. With the maximum

application period for the SMS treatment set at 24 min and occurring up to five times daily,

several states of redistribution are captured randomly each hour in the data set. This is less of a

problem for the TIMER treatment, since water application occurs in hour blocks at the same time









each day. The consistent timing and hourly application allows for a reasonable reproduction of

the entire redistribution process. To obtain further accuracy, the measurement frequency was

increased to 15 min intervals for the remaining experiments.

Experiment 2: Non-Planted

Vitel precision

First the Vitel probe precision was examined similar to the examination of the WCR probe.

For Figure 2-13 the west bias seen in the Vitel probe matrix was likely a by-product of the

irrigation drip emitter being off-center intensified by the smaller measurement volume of the

Vitel probe. Still the agreement is reasonable for Hield data and the Vitel probe can also be

considered location replicates.

Probe to probe comparison

In order to examine the accuracy of SMC measured by Vitel probes in Hield conditions, a

comparison to measured WCR SMC was performed for each probe location. Only the TIMER

treatment is presented, with WCR SMC reported using the site calibration (Equation 2-2).

Since a time-series comparison was previously observed to be a more descriptive

comparison, a time-series comparison of TIMER treatment SMC measured by the WCR and

Vitel probe is presented prior to a one-to-one comparison (Figure 2-14). It is seen that the Vitel

probes located in the center of the bed to consistently measure higher SMC than the WCR

probes. No consistent relationship between the edge probe locations can be discerned, especially

compared to the center of the bed. These observations are confirmed by the one-to-one

comparisons (Figure 2-15). While no general trend can be determined accurately location by

location (Vitel E8 to WCR E8, etc.), a very good relationship between the Vitel and WCR probes

can be developed if the locations are averaged symmetrically about the drip tape and only the









center probes are considered (Figure 2-16). Averaging the probes about the bed center can serve

to reduce errors associated with the differences produce by drip emitters being off center.

It was hoped the averaged locations would return a more representative picture of SMC

distribution in the center region of the bed, though replication is admittedly minimal. The results

presented in Table 2-3 indicate improvement in location comparison after the WCR site

calibration is applied, but little or no improvement is seen after the Vitel site calibration obtained

from averaged data is applied. The Vitel site calibration does improve the averaged center

locations, but no improvement is seen location by location with some locations actually

decreasing in correlation. Regardless, the calibration equation resulting from the Vitel to WCR

comparison for averaged center locations is presented here (Equation 2-3).

Vitel 0.04
WCR = (c3C-)(2-3)
0.91

The low Cegf values (Table 2-3) are again mainly an artifact of the probes' measurement

volume. To restate, the WCR represents an average over the 900 cm3 VOlume, which

encompasses 30 cm of bed length. And, the Vitel represents an average over a 40.3 cm3 VOlume,

which encompasses only 5.7 cm of bed length. High correlation (large Cegf) will never be

obtained comparing horizontally installed WCR and Vitel data, since WCR monitors 150% of

emitter spacing compared to 28.5% for the Vitel probes.

Experiment 3: 2006 In-Season

Again only the timer-based treatment data is presented. WCR SMC reported was calibrated

using the site calibration (Equation 2-2). Vitel SMC was again determined using the factory sand

calibration.









Probe to probe comparison

The probe comparison is displayed location by location in Figure 2-17. As before, the Vitel

probes return slightly higher SMCs a trend more evident for the center locations. The individual

probes were averaged symmetrically about the drip tape and the averaged data visually shows

slightly better correlation between probes overall.

A large difference between some of the probe readings for the center locations can be

observed in Figure 2-17. A time-series of these differences is displayed in Figure 2-18. Again the

time-series proves to be a more descriptive comparison, as the large spikes in the residuals are

now observed to be associated with weekly fertigation events. The WCR probes return overly

high SMC values during the irrigation event following each fertigation, suggesting the WCR

probes are influenced by high ion concentrations. In fact, WCR SMC measurements are reported

to be accurate only below 0.5 dS ml (Campbell Scientific, Inc., 2002), a value exceeded around

the emitter following fertigation events.

Soil sample comparisons

Again due to the measurement volumes and lengths (relative to emitter spacing) a poor

correlation between Vitel SMC and VWC was anticipated and observed (R2 = 0.26) though the

calibration equation is not presented here. Accordingly, a one-to-one comparison of Vitel soil

water salinity burden to soil sample NO3-N data was observed to be extremely poor (R2 < 0.10)

and is not presented here. However, a time-series comparison again proves valuable as Vitel soil

water salinity burden tracks NO3-N results from soil samples fairly well (Figure 2-19).

The Vitel probe soil water salinity burden time-series also follows what is anticipated at

the site following fertigation over the entire season, especially for the TIMER treatment. It is

seen in Figure 2-20 that large spikes in soil water salinity occur following fertigation events and

are quickly leached or extracted from the profile following only a few irrigation events in the









TIMER treatment bed. Conversely, no discernable pattern is revealed for the SMS treatment,

likely due to the very dry soil moisture regime present in the bed which can lead to measurement

errors (Stevens Water Monitoring Systems, Inc., 2007). The results of this calibration effort

confirm that while trends may be assessed between Vitel data and soil sample data, due to the

measurement methods in this study high correlation is unlikely.

Since WCR SMC and VWC was again collected during Experiment 3, the previous WCR

calibration was examined for VWC prediction ability. The result of comparing the transformed

WCR SMC (Equation 2-2) to VWC obtained from gravimetric samples during Experiment 3 is

displayed in Figure 2-21. Two of the three criteria for a good calibration are met, as the A

parameter is at zero (0.00) and the B parameter is near one (0.93), but the regression coefficient

of determination is poor (R2 = 0.55). Another method of comparison is to once again calibrate

the factory sand calibration to VWC and compare the resulting equation to the previous

calibration (Figure 2-22). The resulting calibration equation for this comparison is seen in

Equation 2-4. When compared to Equation 2-2, Equation 2-4 is seen to be of similar construct

with reasonably similar A and B parameters, but again suffers from the variability of soil sample

results (R2 = 0.54).

WCR 0.03
VPVC =(m 3 (2-4)
0.63

Summary and Conclusions

Overall, both probes captured the SMC trends in the field, with results improving once a

15 min interval was instituted. The probe data was generally more consistent than soil sample

data, but this is likely due to the single radial distance from the emitter established by probe

installation compared to varying and unknown distances of soil samples collected without regard

to emitter location.









The message from this study is the importance of considering measurement volumes when

comparing or selecting different monitoring methods. The horizontally installed WCR probes

had the largest measurement volume and covered the most bed length (30 cm). Hence, the WCR

probes can be considered the best, most appropriate match to the bed's representative elemental

volume when plant and emitter spacing are considered. Both the Vitel probe SMC and VWC

obtain from gravimetric samples with relatively small measurement volumes and more

importantly, measurement lengths (5.7 cm and 5 cm respectively), captured differences resulting

the monitoring point' s radial distance from an emitter in addition to the normal distance. The

WCR probes thus provided an average along the bed horizontal while Vitel probes provided

closer to true point measurements on the horizontal. Since gravimetric data was collected without

regard for the radial emitter distance effectively creating an average over the entire emitter

spacing through averaging, it stands that the WCR was reasonably calibrated to VWC obtained

from gravimetric samples (R2 = 0.74), while the Vitel probe was not (R2 = 0.26). Similarly, the

Vitel and WCR SMC measurements did not respond similarly on a one-to-one basis; however,

time-series comparisons of Vitel and WCR SMC showed the probes to have similar responses to

SMC changes and to capture the wetting and drying trends following irrigation events.

As expected due to the inability to match VWC, Vitel soil water salinity burdens revealed

no consistent relationship with soil sample NO3-N results on a one-to-one basis. But again time-

series comparisons yielded different observations, as the ability of the Vitel probes to measure

in-situ soil water salinity burdens was observed to be a very useful tool for quantifying leaching

and soil retention of nutrients over the entire season.

Finally, there was one observed problem with the two probes examined. The horizontally

installed WCR probes were influenced by higher ion (fertigation) concentrations. During periods









immediately following fertigation, the WCR measured SMC reaching and exceeding soil

porosity for both treatments. Vitel probes returned more predictable results during these periods.

The erratic response of WCR probes following fertigation events is especially hazardous for in-

season measurements beneath drip irrigation with fertigation.










Table 2-1. Summary of experiments performed, data collected, means and methods
Data collected Features Data application Dates


WCR SMC'
gravimetric samples,
undisturbed soil
cores

WCR SMC, Vitel
SMC

WCR SMC, Vitel
SMC, gravimetric
samples, fertigation
samples


WCR SMC, Vitel
SMC


In-season SMC distributions
hour interval, hydraulic
parameter estimation

Non-planted SMC
distributions, no
transpiration or root impacts

In-season SMC distributions
and fertigation distributions
15min interval


Plants clipped post-season,
eliminates transpiration and
accounts for root growth
impacts, SMC distributions


WCR probe precision, WCR
calibration to VWC

WCR probe precision, Vitel
calibration to WCR, WCR SMC
used for H2D calibration (Ch. 3)

WCR calibration check, Vitel
calibration to VWC, Vitel
calibration to NO3-N, Vitel EC
used for H2D calibration (Ch. 4)


4/12/2005 -
7/5/2005


10/10/2006 -
10/23/2006


4/14/2006 -
7/5/2006


Experiment 1



Experiment 2




Experiment 3


WCR SMC used for H2D
calibration (Ch. 4)


7/5/2006 -
7/1 8/2006


Experiment 4


SMC is soil moisture content. VWC is volumetric water content obtain from gravimetric samples. NO3-N iS measured
nitrate-nitrogen from soil samples. EC is electrical conductivity.





Table 2-2. Quantitative comparison of all locations in the timer-based treatment and the sensor-based treatment using the factory sand
calibration


Sensor-Based Treatment

Locaion ace Depth Average Maximum Minimum Ceff(face ( to
(cm) SMC SMC SMC to face)
west)


Timer-Based Treatment

Locaion ace Depth Average Maximum Minimum Ceff(face (e t
(cm) SMC SMC SMC to face)
west)


Center North 8 0.155 0.538 0.078

JWest North 8 0.089 0.137 0.066

East North 8 0.065 0.087 0.050

Center South 8 0.161 0.677 0.086 0.79

West South 8 0.068 0.133 0.064 -0.64

East South 8 0.080 0.130 0.061 -5.15

Center North 23 0.142 0.266 0.089

West North 23 0.048 0.063 0.038

East North 23 0.077 0.104 0.058

Center South 23 0.161 0.311 0.104 0.20

West South 23 0.115 0.215 0.086 -200.69

East South 23 0.074 0.090 0.060 0.75

SSMC is soil moisture content. Ceff is Nash and Sutcliffe (1970) coefficient of efficiency


Center North 8 0.135 0.341 0.090

VWest North 8 0.074 0.089 0.062
-4.63
East North 8 0.094 0.120 0.076

Center South 8 0.125 0.538 0.066 -3.65

West South 8 0.083 0.109 0.070 -0.45
-1.14
East South 8 0.086 0.106 0.077 -1.52

Center North 23 0.147 0.314 0.110

West North 23 0.086 0.098 0.073
-37.39
East North 23 0.110 0.130 0.095

Center South 23 0.127 0.227 0.093 -6.87

West South 23 0.098 0.129 0.086 -0.14
-7.19
East South 23 0.117 0.146 0.107 -0.62


-17.89




0.02




-24.87




-8.41











Table 2-3. Quantitative comparison of probe type by location for both the factory and site
calibrations of each probe type. Only TIMER treatment data is displayed. Values
averaged by symmetrical location are also included
Cenf (Vitel to WCR)
Location Factory WCR site Both probes
calibrations calibrated site calibrated


W8
WC8
EC8
E8
W23
WC23
EC23
E23


-125.33
-3.04
-8.49
0.08
-3.38
-19.32
-6.65
-108.53


-62.48
-0.23
-1.28
-1.69
0.52
-7.02
0.60
-77.79


-17.78
0.80
0.59
-10.65
-12.33
-1.39
-3.51
-273.45

-0.59
0.97
-97.01
0.91


AVG EDGE 8 -9.34 -1.76
AVG CENTER 8 -2.49 -0.40
AVG EDGE 23 -7.05 -13.52
AVG CENTER 23 -5.94 -2.67
Cegf is Nash and Sutcliffe (1970) coefficient of efficiency.


Figure 2-1. The 2 X 3 matrix formation used in Experiment 1 with labels used in discussion.





Figure 2-2. The 2 X 4 matrix formation used in Experiment 2 and Experiment 3 for both probe
types with labeling used in discussion.














0.25 0.25
NORTH FACE SOUTH FACE


E E
o a
S0.20 0.20
E E
o a
o o


rr0.15 rr 0.15



ow0.10 o 8 cm a 0.10 + 8 cm




23 cm 23 cm

0.05 Y 0.05
0.05 0. 10 0.15 0.20 0.25 0.05 0.10 0.15 0.20 0.25

WEST SIDE WCR SMC (cm3 -m3) WEST SIDE WCR SMC (cm3 -m3


Figure 2-3. Comparison of edge probes within each TIMER treatment matrix. Both 8 cm and 23 cm data is shown.


^ ^r


^ ^r












025 025 *025
8 CM EDGE 23 CM EDGE 8 & 23 CM CENTER s


0 2 0 20 0 20 I 02


O A O O ^^


2 0 10 + West 8cm 0 10 + West 23 cm 0 10 Center 8 cm

East 8 cm East,, 23 cm Center 23 cm
005 005, 005
O 05 0 10 0 15 0 20 0 25 0 05 0 10 0 15 0 20 0 25 0 05 0 10 0 15 0 20 0 25
WCR SMC (cm3 c3) NORTH FACE WCR SMC (cm3 -m3) NORTH FACE WCR SMC (cm3 c3) NORTH FACE

Figure 2-4. Comparison of probes between the TIMER treatment matrices for all like locations and depths.


0.20 0.20
8 CM 23 CM


i 0.15 i00.15
E E


0.10 -0.10 -

a a





0.00 0.00
4/12 5/2 5/22 6/11 4/12 5/2 5/22 6/11

DATE (2005) DATE (2005)

NW NE SW -SE NW NE SW SE

Figure 2-5. Time-series data from all edge probe locations in the TIMER treatment grouped by depth.












































8 CM EDGE









+ West 8 cm
--11
East 8 cm


0.20




S0.15
E



S0.10




'/ 0.05


0.20




S0.15
E



S0.10

O


m/ 0.05


-o ~


0.00 -Y


0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15

WEST SIDE WCR SMC (cm3 -3") WEST SIDE WCR SMC (cm3 -3"


SFigure 2-6. Comparison of edge probes within each SMS treatment matrix. Both 8 cm and 23 cm data is shown.


0.20


020



S015


E 010


1005


coo I 0 ooo 00 c
0 00 0 05 0 10 0 15 0 20 0 00 0 05 0 10 0 15 0 20 0 05 0 10
WCR SMC (cm3 c3) NORTH FACE WCR SMC (cm3 -m3) NORTH FACE W~

Figure 2-7. Comparison of probes between the SMS treatment matrices for all like locations and depths.


0 15 0 20 0 25 0 30 0 35
ICR SMC (cm3 -m3) NORTH FACE
















































O 300
0 25 -
0 20 -
015 -
0100
0 055




DAT(205

NC8 --SC8 SS-8 NC23 -SC23 + SS-23


0.20



0.15



0.10



a ,,


0.20


8 CM


0.10

a



0.100
-





4/12


0.00
4/12


5/2 5/22 6/11

DATE (2005)

NW NE SW -SE


5/2 5/22 6/11

DATE (2005)

NW NE SW SE


Figure 2-8. Time-series data from all edge probe locations in the SMS treatment grouped by depth.


4/25 5/5 5/15 5/25 6/4 6/14 6/24
DATE (2005)
NC8 -SC8 SS-8 NC23 -SC23 + SS-23


Figure 2-9. Comparison of WCR SMC and VWC data for the center locations of SMS and TIMER treatments. VWC soil sample data
is labeled SS "location depth (cm)". Error bars represent one standard deviation each.














TIMER


0 20 ~
015
010 T .
005
000 ,
4/25 5/5 5/15 5/25 6/4 6/14 6/24
DATE (2005)
NW8 NE8 -SW8 -SE8 SS-W8 4 SS-E8
-NW23 -NE23 -SW23 -SE23 SS-W23 o SS-E23


SMS 02




015
010 fG~Y CP~1 z
005 i
0000




DAE 205


NW8 NE8 SW -E8 SS-W8 +SS-E8
-NW23 -NE23 -SW23 SE23 SS-W23 O SS-E23]


Figure 2-10. Comparison of WCR SMC and VWC data for the edge locations of SMS and TIMER treatments. VWC soil sample data
is labeled SS "location depth (cm)". Error bars represent one standard deviation each.


0.20




mp0.15

E
a

0.10




0.05


mp0.15


o

0.0


0.05


y =0.69x +0.03
R2 =0.74


0.00
0.00


0.05 0.10

VWC (cm3 cm-3)


VWC (cm3 cm-3)


Figure 2-1 1. Comparison and calibration of WCR and VWC data, displays TIMER and SMS treatment data. All error bars represent
one standard deviation.


















PLAUBORG


SITE


0: 50


040


E 030
O
O
1020


010%1'


060


0 50


060


0 50


FACTORY


040
E
o
E 030
O
O
1020


010


t
o
E 0 30
O
O
1020


hi


010


5/3 5/13 5/23 6/2 6/12 5/3 5/13 5/23 6/2 6/12 5/3 5/13 5/23 6/2 6/12

DATE (2005) DATE (2005) DATE (2005)

-FACTCAL C8 FACTCAL C23 FACTCAL E8 FACTCAL E23 PLAUCAL C8 -PLAUCAL C23 PLAUCAL E8 PLAUCAL E23 -SITECAL C8 -SITECAL C23 SITECAL E8 SITECAL E23


Figure 2-12. Comparison of calibrations for a selected time-series from the TIMER treatment. The factory calibration for sand, the

Plauborg et al. (2005) calibration and the site calibration are displayed. East and west locations were averaged for

presentation, labeled E8 and E23 for the edge and labeled C8 and C23 for the center locations.














0.25


8 & 23 CM CENTER


,0.10-





0.05 5


m
E
o
; 0.20
o
o
cn
~ 0.15
w


w
o
(n 0.10


w

0.05


+ Cer


Central 23 cm


ntral 8 cm


35 0.10


0.10 0.15 0.20

WEST SIDE VITEL SMC (cm3 -3")


0.15


0.20


0.25


WEST SIDE VITEL SMC (cm3 -3"


Figure 2-13. Location comparisons within Vitel probe matrix of the TIMER treatment for Experiment 2. E8, W8, E23, and W23 are
edge locations while EC8, WC8, EC23, and WC23 are center locations.


o O$Qob~?t/





















.

-1-1-1


- -- --


0.08 CM CENTER


0.023 CM CENTER


0 0.25

E 02
o


(1 0.15



0.10



0.05


m 0.25


mE 0.20 -- -



(1 0.15



0.10 -- -



0.05


10/12 10/14 10/16 10/18 10/20 10/22 10/24

DATE (2006)

VITEL WC VITEL EC -WCR WC -WCR EC


10/12 10/14 10/16 10/18 10/20 10/22 10/24

DATE (2006)

VITEL WC VITEL EC -WCR WC -WCR EC


8 CM EDGE


0.30



,0.25



E 0.20



( 0.15 -



0.10



0 05


0.3U



,0.25


E 0.20


-
( 0.15



S0.10


n-:


23 CM EDGE


10/12 10/14 10/16 10/18 10/20 10/22 10/24 10/12 10/14 10/16 10/18 10/20 10/22 10/24

DATE (2006) DATE (2006)

VITEL W VITEL E --WCR W --WCR E VITEL W VITEL E --WCR W WCR E


Figure 2-14. Time-series data from all probe locations in the TIMER treatment, for both WCR and Vitel probes. Grouped by similar
locations.


-

----



- -- -- --







































25
+ 8 cm

20 -


15


10


05


AVERAGE EDGE
00


0 25


,0 20-



015-



0 10 -



005 *
0 05


a 015 -



S0 10


I CM CENTER 23
005 '
0 20 0 25 0 05 0 10 0 15

VITEL SMC (cm3 c3)


S015



S0 10


;CM CENTER AVERAGE CENTER
005 .
0 20 0 25 0 05 0 10 0 15 0 20 0 25

VITEL SMC (cm3 c3)


0 10 0 15

VITEL SMC (cm3 c3)


0 25 -


0 20 -


E0 15 -

O~ O
S010-


005 -


000 -
O00


E0 15


S010


005


1 CM EDGE
~000 '
0 20 0 25 0 00 0 05 0 10 0 15

VITEL SMC (cm3 c3)


0 20 0 25 0 00


_


0 05 0 10 0 15

VITEL SMC (cm3 -m3)


0 05 0 10 0 15

VITEL SMC (cm3 c3)


0 25


Figure 2-15. Comparison of Vitel to WCR SMC for each location within the bed. Also, location averages are presented for

comparison. Averages were calculated using the drip tape as a symmetrical axis, EC8 and WC8 become C8, etc. WCR

SMC displayed post-site calibration.













0.30


0.30


0.25

E
0 0.20


0 0.15





0.05


0.25

E
o 0.20


a 0.15





0.05


y =0.91x +0.04
R2 =0.97


y =0.33x +0.12
R2 =0.29


0.00


0.00
0.00


0.05


0.10 0.15

WCR SMC (cm3 -m3)


0.10 0.15

WCR SMC (cm3 -3"


0.20


0.25


Figure 2-16. Relationship of SMC measured in the center of the bed at both 8 cm and 23 cm depths by the Vitel and WCR probes. A.
data match location by location B. data averaged by location and match depth by depth. WCR SMC displayed post-site
calibration.















































7"~~


UUD


025


025


<~ ..





8 CM CENTER

0 10 0 15 0 20
VITEL SMC (cm3 c3)

+ West Central 8 cm --1 1 East Central 8 cr


0 20


015


S010-


005 .
O 05


0 20 -


015-


4 010-


005 >
0 25 0 05


015-


4 010-

AVERAGE CENTER
-- 005
0 25 0 05 0 10 0 15 0 20
VITEL SMC (cm3 c3)

+ Central 8 cm --1 1 Central 23 cm


m


+ W


0 10 0 15 0 20
VITEL SMC (cm3 -m3)

'est Central 23 cm --1 1 East Central 23 cm


0 25


025


0 20
E

E 015

03 0 0 10

005


025


0 20
E

E 015

O

005


O


00 8 CM EDGE 0 023 CM EDGE 0 0,a AVERAGE EDGE
0 00 0 05 0 10 0 15 0 20 0 25 0 00 0 05 0 10 0 15 0 20 0 25 0 00 0 05 0 10 0 15 0 20 0 25
VITEL SMC (cm3 -m3) VITEL SMC (cm3 -m3) VITEL SMC (cm3 c3)

+ West 8 cm --1 1 East 8 cm + West 23 cm --1 1 East 23 cm + Edge 8 cm --1 1 Edge 23 cm

Figure 2-17. Comparison of the WCR and Vitel probes for each location within the bed during Experiment 3. Also, location averages

are presented for comparison. Averages were calculated using the drip tape as a symmetrical axis, EC8 and WC8 become
C8, etc. WCR SMC displayed post-site calibration.












A. B. C.
O 10 010 0 20 0



0 000 0 000


I 8 m1
a a a -0 40

S-0 20 -0 20 -0 50 01 11 1


4/23 5/3 5/13 5/23 6/2 6/12 4/23 5/3 5/13 5/23 6/2 6/12 4/23 5/3 5/13 5/23 6/2 6/12
DATE (2006) DATE (2006) DATE (2006)
-WC 8cm -EC 8cm -WC 23 cm EC 23 cm W 8cm -E 8cm -W 23cm E 23 cm WC8 -EC8 -WC23 EC23 -BURDEN

Figure 2-18. Residuals for each location presented as Vitel WCR within the TIMER treatment bed during Experiment 3. A. displays
center locations B. displays the edge locations C. displays relationship between residuals averaged for each location and
soil salinity in the shallow center region.













May 23, 2006


0.25 2.5


0.25


- 2.0
m

rn 1.5


Ir1.0


0.5


- 2.0


rn1.5


Ir1.0


0.5


0.20 -


0.15 z


0.10 2


0.05 ~


0.20 -
0

0.15 z


0.10 a


0.05


0.00


5/22


0.0


5/30


0.00


0.0 0
6/12


5/26
DATE (2006)


5/28


6/14 6/16 6/18 6/20

DATE (2006)


- C8 C23 o NO3-N


|- C8 C23 o NO3-N


Figure 2-19. Comparison of Vitel KNO3 burden data (lines) and soil sample NO3-N data (points) for center probe locations within the
TIMER treatment bed during Experiment 3. All error bars represent one standard error.











SMS
4/13


TIMER
7/2 4/13


5/3 5/23


6/12


5/3 5/23


-

-

-


13


3.5

3.0

0 2.5

S2.0

1.5





0.0
4/1


3.5

3.0
-
0 2.5

S2.0

1.5





0.0
4/13


5/3 5/23
DATE (2006)


6/12


5/3 5/23 6/12 7/2
DATE (2006)


-- E8 -- C8


E23 C23


-- E8 -- C8


E23 C23


Figure 2-20. Time-series KNO3 burden for each probe location within the TIMER and SMS treatment beds during Experiment 3.
Location averages are presented for comparison. Averages were calculated using the drip tape as a symmetrical axis, EC8
and WC8 become C8, etc.


I11111 I


Illlllllli


tf






~~iv~~i~













0 30


0 25 -1T 1025-

S0 20 0 20 -1 + *

j015 FPL ,015-

S0 10 0 10-
y = 0 93x 0 00
R = 055
0 05 0 05-

0 00 n 0 00 *
000 005 010 015 020 025 030 000 005 010 015 020 025 030
VWC (cm3 cm ) VWC (cm3 cm )

Figure 2-21. Comparison of VWC to the WCR SMC using the 2005 calibration, for each
location within the TIMER and SMS treatments during Experiment 3. Error bars

equal to one standard deviation.


030

025

~020

0 15
0 0
005


030

025

~020

015
0 1
00


0 00& L
000


0 00 '
025 030 000


005 010 015 020
VWC (cm3 cm )


005 010 015 020 025 030
VWC (cm cm )


Figure 2-22. Comparison of VWC to WCR using the factory calibration for sand, for each
location within the TIMER and SMS treatments during Experiment 3. Error bars

equal to one standard deviation.









CHAPTER 3
WATER ENTRY BOUNDARY CONDITION IMPACTS ON THE CALIBRATION OF
HYDRUS-2D TO A SURFACE DRIP IRRIGATION SYSTEM

Introduction

Vegetables are a maj or component of Florida agriculture encompassing about 72,000 ha

for production and valued at $1.5 billion annually (USDA, 2006). Most of the soils where these

vegetables are grown are sands, with frequent irrigation and fertigation required to minimize

crop stress and attain maximum production. Water and nutrient delivery to these systems is

commonly provided by drip irrigation. Also much of the vegetable production in the state occurs

on raised beds covered with plastic mulch, which serves to control weed growth and root zone

temperatures. The plastic mulch covering also minimizes the influence of evaporation and

rainfall in the system (Simonne et al., 2004) isolating irrigation effects and making these systems

ideal for experimental monitoring of water and nutrient distributions beneath drip irrigation.

In order to accurately predict environmental impacts associated with intensively managed

vegetable production systems, a quantitative description of water movement through the vadose

zone is required. In the case of drip irrigation, a minimum of two dimensions is required to

accurately model soil moisture content (SMC) distributions. Recently the two-dimensional

HYDRUS-2D model (H2D), which numerically solves Richards' equation for saturated-

unsaturated water flow (Simunek et al., 1999), has been applied to multiple drip irrigation

systems and proven to be a reliable predictor of SMC distributions. To numerically simulate

water flow beneath drip irrigation in H2D and thus predict SMC distributions, the user first needs

to quantify how water moves within the simulation domain by estimating soil hydraulic

parameter. While soil hydraulic properties can be readily measured at the field site, they are

commonly estimated based on minimal data. Skaggs et al. (2004) addressed the uncertainty of









soil hydraulic parameters, comparing the ability of different pedotransfer functions to predict

SMCs measured beneath drip irrigation.

Yet uncertainty associated with quantifying how water enters the simulation domain,

described here as the water entry boundary condition, is often overlooked. The water entry

boundary condition in H2D can be decomposed into two parts: simulation domain dimensions

and the soil wetting geometry. The simulation domain can either be quasi three-dimensional (3D)

or two-dimensional (2D). When using the 3D simulation domain, the left boundary of the two-

dimensional model area established by the user is assumed to be a radial axis of symmetry

compared to 2D simulations that assume a one unit linear depth [L] in addition to the user

defined model area (Simunek et al., 1999). As exhibited by Gardenas et al. (2005) both a 3D

simulation domain, commonly referred to as axi-symmetrical, and 2D simulation domain can be

used for surface drip irrigation simulation. A 3D domain assumes the drip system is composed of

isolated emitters, commonly described as point source assumptions. A 2D simulation domain

assumes the drip system is a line source with water entering the system the full length between

emitters. While no 2D drip simulations have yet to be validated by field data, the 3D simulation

domain has been successfully used to predict SMC distributions beneath surface drip irrigation in

the field (Fernandez-Galvez and Simmonds, 2006) and in a laboratory setting (Li et al., 2005).

In either a 2D or 3D simulation domain, the boundary over which water enters the domain

must be defined. As described here, the soil wetting geometry is analogous to the assigned water

inflow boundary within the model for drip irrigation simulations. The soil wetting geometry can

vary both in shape and length. Two shapes have been used previously to initiate water inflow, a

quarter-circle or a surface-line, referred to in previous studies as a semi-sphere (SC) and a

surface-radius (SR) respectively (Li et al., 2005). Skaggs et al. (2004) assumed a SC soil wetting









geometry with a 0.50 cm radius. The study reported good SMC predictions, but noted for high

flow rates or low permeability soils the constant pressure assignment induced excessive,

unrealistic pressure build-ups near the emitter. Li et al. (2005) used a SC shape for a sandy soil

and a SR shape for a loam soil. For both soils, their work provided an optimal water entry

boundary radius for a given flow rate by comparing predicted and measured SMC; however, the

conclusions of both studies were highly dependent on their assignment of the soil wetting

boundary as a constant pressure boundary, effectively assuming full saturation at the boundary.

By comparison, the assignment of the soil wetting boundary as a flux boundary should allow for

more flexibility when defining the soil wetting boundary length while still obtaining accurate

predictions, since the boundary is not necessarily kept at saturation.

Flexibility when defining the soil wetting boundary length can be very valuable since H2D

requires all boundary conditions to be static during simulation. In fact, most reported H2D drip

simulations use a constant soil wetting boundary length throughout the simulation (Li et al.,

2005; Cook et al., 2006; Cote et al., 2003) even though the wetted radius under a drip emitter is

in fact dynamic, expanding as the irrigation event progresses (Goldberg et al., 1971). Gardenas et

al. (2005) addressed the constant soil wetting boundary length by modifying the H2D code. The

soil wetting boundary for their simulations was not constrained to a constant length, but instead

allowed for a time-variable ponded boundary length. However, short of code modification no

study has addressed the soil wetting boundary length question when the boundary is assigned as

a flux boundary.

It is also important to consider the impacts of different water entry boundary conditions on

SMC prediction before undertaking a management study. While there are some cases that clearly

define which condition, notably 2D or 3D, should be employed, there are many instances where









examples of both line and point source assumptions can be found in the field. A common

example is a drip system with short emitter spacing on a sandy soil, as commonly found for

vegetable production in Florida. If field data is not collected, a strong understanding of water

entry boundary condition impacts on SMC prediction is required.

The obj ective of the study presented in this document was to compare four water entry

boundary conditions for their ability to predict SMC distributions measured in-situ beneath

surface drip irrigation in a plastic mulched raised vegetable production system.

Materials and Methods

Field Experiment

The experimental site was located at the University of Florida, Plant Science Research and

Education Unit, near Citra, Florida. Buster (1979) classified the soil at the research site as a

Tavares sand and Candler sand. These soils contain >97% sand-sized particles and have a field

capacity of 0.05-0.07 cm3 CA-3 in the upper 100 cm of the profile (Carlisle et al., 1978).

SMC distributions were measured beneath a non-planted section of a drip irrigated, raised

bed, vegetable production system. The experimental setup is fully detailed as Experiment 2 in

Chapter 2 (Table 2-1), but a short summary of relevant details follows. Irrigation occurred daily

from 0600 to 0800 hrs with a nominal emitter flow rate of 0.76 L hr- at 69 kPa, with drip

emitters spaced 20 cm apart and located at the center of the bed surface. SMC was measured at

15 minute intervals by CS616 (Campbell Scientific Inc., Logan, UT) water content reflectometer

(WCR) calibrated to volumetric water content calculated from gravimetric soil sampling at the

field site (Figure 2-11; Chapter 2). The WCR is a dielectric probe that utilizes time-domain

methods to determine the SMC of the medium. A matrix containing eight WCRs was installed in

a representative section of the bed (Figure 3-1). An approximately 40 cm long section of the

entire bed width was removed from the installation location. The section provided enough space









for horizontal WCR installation parallel to the surface. After installation, the section was

repacked with the original soil and covered with black plastic mulch. The matrix was configured

in a 2 X 4 (Vertical X Transverse) formation, with the top row buried at 8 cm and a bottom row

at 23 cm below the surface of the bed. The four columns were spaced on center 16 cm apart

centered in the raised bed. The in-situ matrix monitoring approach is similar to the work of

Mmolawa and Or (2003).

The soil moisture release curve (SMRC) for the Hield site was determined from 11

undisturbed soil cores collected at the site, similar to the work of Al-Yahyai et al. (2006). Soil

cores measured 5.4 cm in diameter and 6.0 cm in height and samples were collected between a

depth of 0-6 and 6-12 cm at various places in the Hield. Tempe cells with 10 pressure steps, up to

750 cm H20, were used to develop the SMRC. The final soil hydraulic parameters were

developed by fitting the van Genuchten-Mualem model (van Genuchten, 1980) to the data using

the RETC program (van Genuchten et al., 1991). The average SMRC was calculated by

averaging measured SMC at each pressure step across the 11 samples. A SMRC was developed

for each of the 11 sample sites.

Model Description

The H2D program numerically solves the mixed formulation of the Richards' equation, as

proposed by Celia et al. (1990), for saturated-unsaturated water flow using Galerkin-type linear

Einite element schemes. The mixed formulation of Richard' s equation used in H2D is seen in

Equation 3-1, where 6 is the volumetric water content [L3L-3], h is the pressure head [L], S is a

sink term [T ], xi are the spatial coordinates [L], t is time [T], K~ are components of a

dimensionless anisotropy tensor KA, and K is the unsaturated hydraulic conductivity function

[LT- ].










KA + K -S(31
dt Dx, i 8x dr

An accurate soil-water retention curve is required to model the described system.

Accordingly, the van Genuchten-Mualem model (Equation 3-2 to 3-4) for unsaturated hydraulic

conductivity was calibrated to the system.

8, + h <
0(h) 1+ hi. i (3 -2)
8, h>0


K(h)= K,S I1- -S lm( (3-3)

where

m= 1- 1/n, n> 1 (3 -4)

The van Genuchten-Mualem equations are defined where 6, is residual water content

[L3L-3] Bs is saturated water content [L3L-3]; h is pressure head [L]; a is soil water retention

coefficient [L^]~; n and m are scaling factors [-]; Se is degree of saturation [-]; and Ks is saturated

hydraulic conductivity [LT- ]. The van Genuchten-Mualem model within H2D contains Hyve soil

dependent input parameters ( 8,, 8,, a, n, and Ks), and a pore-connectivity parameter 1 [-]

commonly estimated to be 0.5 for all soils (Simunek et al., 1999).

Water Entry Boundary Condition

The water entry boundary condition refers to the combination of simulation domain and

wetted emitter geometry. The simulation domain can be two-dimensional (2D) or quasi three-

dimensional (3D) in H2D, while the soil wetting geometry was specified as either semi-spherical

(SC) with water flow initiated over a quarter-circle or a surface-radius (SR) with water flow

initiated over a surface-line. The 2D simulation domain assumes the drip tape acts as a line









source with equal flow between emitters, while 3D simulation domain assumes each emitter acts

as an independent point source. The line source assumption is reasonable for our data set

considering the relatively close (20 cm) emitter spacing at the site. Also, the 30 cm measurement

length of the WCR probe relative to the emitter spacing (150% of emitter spacing) means the

measured SMC can be considered an average of the bed at a given depth and distance. The SC

soil wetting geometry represents a wetted quarter-cylinder that forms below the drip tape when

coupled with a 2D simulation domain (2DSC) or a wetted hemi-sphere that forms below an

emitter when coupled with a 3D simulation domain (3DSC). The SR soil wetting geometry

represents a wetted rectangle band that forms below the drip tape when coupled with a 2D

simulation domain (2DSR) or a wetted circle that forms below an emitter when coupled with a

3D simulation domain (3DSR). The four distinct water entry boundary conditions that were

examined are displayed in Figure 3-2.

Five boundary radius lengths were examined for their ability to fit the measured SMC data

using each water entry boundary condition and totaling 20 simulations. The five boundary radii

examined were: 0.25, 0.50, 0.57, 0.75, and 1.0 cm. Radius lengths were limited to 1.0 cm to best

approximate a point source and to eliminate errors due to the water entry boundary approaching

the monitoring locations. The 0.57 cm radius was recommended for the 3DSC simulations on

sandy soils at this study's flow rate when using a constant pressure boundary (Li et al., 2005) and

it is included here for comparison with results in the literature. For SR simulations, the radius

length is equivalent to the boundary length along the surface.

The water entry boundary (Figure 3-2) was assigned as a variable flux boundary. And

while each method requires a flux value (cm min ) for simulation, the flux values change









depending on the soil wetting geometry and boundary length of each simulation. The general

approach of flow rate divided by surface area was employed for each method (Table 3-1).

Additional Boundary and Initial Conditions

For all model runs, only half of the bed area was considered with calibration performed

under the assumption that water flow is symmetrical across the vertical plane directly beneath the

emitter (Wooding, 1968; Warrick, 1974). The nominal emitter flow rate of 0.76 L hrl was used

in all simulations. The defined simulation area had the general shape of a rectangle, representing

a soil half-section below the surface, bounded by the bed center and bed edge, and located to the

right of an emitter. Accordingly, the soil wetting geometry was located at the intersection of the

left vertical boundary and the upper boundary. The left vertical boundary and upper boundary

were assigned as no flux, representing the symmetry across the vertical plane and plastic mulch

covering the surface, respectively. The lower boundary of the profile was assigned as a free

drainage boundary located 60 cm subsurface. The right vertical boundary, which represents the

boundary between the soil half-section and the inter-row area, was also assigned as a free

drainage boundary for 3D simulations and a free drainage boundary below 25 cm subsurface for

2D simulations. Between 0 and 25 cm subsurface, the right vertical boundary was assigned as a

no flux boundary for 2D simulations, again due to the plastic mulch covering. Assignment of the

upper 25 cm of the right vertical boundary as free drainage or no flux for the 3D domain

simulations was assumed to be equivalent, as water flow should not reach this region due to the

point source assumption.

All simulation data sets started on October 13, day of simulation (DOS) 0, and ended

October 23, DOS 10. The entire model domain was initialized (DOS -4) at 0.10 cm3 Cm-3 SMC.

From DOS -4 to 0 SMC distributions were allowed to reach a quasi-static state by applying the

same irrigation events as between DOS 0 and 10. The water content tolerance was set at 0.001










(cm3 Cm-3) representing the absolute magnitude of change allowed for unsaturated nodes between

two iterations within a time step (Simunek et al., 1999). The finite element dimensions were

generated automatically by H2D MESHGEN. Smaller elements were created around the water

entry boundary to account for rapid variable changes, increasing model stability. Generally

element size increased as the lower and right vertical boundary intersection was approach, with

MESHGEN densities 200% greater at the lower and right vertical boundary intersection as

compared to around the water entry boundary.

Calibration and Optimization Procedure

The initial calibration included the 20 simulations accounting for the four water entry

boundary conditions and five boundary radii (Table 3-1). The initial calibration simulations used

the average SMRC measured at the field site while inversely optimizing for Ks. To account for

the uncertainty associated with soil hydraulic parameter estimation, each simulation setup used

during the initial calibration was rerun while allowing for the optimization of five soil hydraulic

parameters (full calibration). During the full calibration 6,., 6,, a, and n were bounded during

optimization by the range of values determined from the collected undisturbed soil cores. Ks was

again included in the optimization process, which simultaneously occurred for all five

parameters.

Each inverse optimization was based on the numerical solutions of Richards' Equation

(Equation 3-1). All optimizations were performed using the built-in Levenberg-Marquardt

nonlinear minimization method in H2D. During the inverse optimization process, the unknown

parameters are determined by the minimization of an established obj ective function (Simunek et

al., 1999). All weighing coefficients were set to 1. Measured SMC was used during optimization

to determine Ks for the initial calibrations and to simultaneously determine 6,., 8,, a, n, and Ks









for the full calibrations. Multiple optimizations were performed for each calibration simulation

using different initial values for the parameters to be determined in order to increase the

probability of finding the global minimum.

Prediction Evaluation

Two goodness-of-fit indicators are reported by H2D following a given simulation, sum of

squares (SSQ) and the coefficient of determination (R2) (Simunek et al., 1999). Both indicators

simply use the squared residual to represent the deviation between paired measured and

predicted data.

The Nash-Sutcliffe (1970) coefficient of efficiency (Cesf) uses a similar approach, where

O, is measured data; 14 is predicted data; and O is the mean of the measured data (Equation 3-

5). The range of Cegf lies between 1.0 (perfect fit) and -oo. When Cegf is lower than zero the mean

value of the measured time series would have been a better predictor than the model (Nash and

Sutcliffe, 1970). Cegf is the reported goodness-of-fit indicator in this study because it is better

suited to evaluate model goodness-of-fit compared to SSQ or R2 (Legates and McCabe, 1999).



C4, = 1.0 (3-5)



In the presence of measurement uncertainty, it is also valuable to evaluate paired measured

and predicted data against the uncertainty boundaries of the measured data instead of against

individual data values. When the uncertainty boundary, but not the distribution of uncertainty

around each measured data point is known, Harmel and Smith (2007) proposed that the chosen

goodness-of-fit indicator can be improved by a modification that accounts for this uncertainty,

summarily described here.










P E R [ E 2 + E + E f + ... E )( 3 .6 )


The probable error range (PER), where n is the number of potential error sources and En is

the uncertainty associated with each potential error source (%), was used to establish an upper

and lower bound for the measured SMC at a given time (Equation 3-6). If P4 fell within the

established boundary, the residual used in Cegf calculation is changed to zero. If 4q fell outside

the established boundary, the residual used in Cegf calculation is changed to the difference

between 14 and the nearest boundary value (Harmel and Smith, 2007). To account for the

measured SMC uncertainty, the modified Cegf is also presented, reported in this study as Cer*.

For SMC measurements in this study, three sources of error were considered. The first was

the reported WCR accuracy, 0.025 cm3 Cm-3 (Campbell Scientific, Inc. 2002). Recall the WCR

measurements were further calibrated to the field site (Chapter 2) using measured gravimetric

data that was converted to volumetric soil moisture by using bulk density measurements. The

WCR error (El) was calculated as the reported accuracy divided by the average SMC for each

probe used in model calibration over the time-series of interest, 18.8%. The errors for the soil

samples were calculated by dividing the standard error of the measurements by the mean of the

measurements, resulting in a gravimetric error (E2) Of 10.3% and a bulk density error (E3) Of

2.0%. The three error sources result in a PER of 21.5% for SMC measurements.

Results and Discussion

Field Results

Since symmetry in SMC distribution was assumed across each half of the raised vegetable

bed, probe measurements at similar locations on each half-bed were averaged. After averaging,

the probes as labeled in Figure 3-1 were renamed with respect to their location, center of the bed









(C) or edge of the bed (E), and their depth, 8 cm (8) or 23 cm (23) subsurface. Therefore, E8 is

the average of probe 1 and 4; C8 is the average of probe 2 and 3; E23 is the average of probe 5

and 8; and C23 is the average of probe 6 and 7. Averaging also minimizes errors associated with

the drip tape lying away from the exact bed center. Since the experiment site required separate

irrigation and fertigation drip lines (Chapter 2), locations are never truly symmetrical, but

averaging yields a representative SMC for the location of interest (Figure 3-3).

SMC from the outer edges of the raised bed differed substantially. Differences between

probes 1 and 4 at the E8 location ranged between 0.06 cm3 Cm-3 and 0.10 cm3 Cm-3. The

difference could be due to a number of factors; however, SMC at the E8 location was only

minimally impacted by irrigation with SMC ranging from 0. 11 cm3 Cm-3 and 0. 14 cm3 Cm-3 On

average (Figure 3-3). Due to the observed difference in measurements a three location data set

(C8, C23, and E23) was used for model calibration. The C23 location yielded the most variable

data of the remaining three locations, with consistent deviations in SMC between probe 6 and 7

near 0.04 cm3 Cm-3 and as high as 0.05 cm3 Cm-3 (Figure 3-4). Measurement variability was also

observed in the soil core data (Table 3-2), with only 8, having a standard error less than 10% of

the parameter average (3.2%). The average SMRC is presented in Figure 3-5.

Initial Calibration

During initial calibration, only Ks was optimized to measured SMC data. It was observed

that the SC and SR soil wetting geometries returned nearly identical Ks values and SMC time

series for each simulation domain (2D and 3D) with a similar boundary radius (eg. 2DSCO.50 =

2DSRO.50). However, the SC simulations required less than half the run time as SR simulations,

meaning the SR simulations can be considered less efficient replicates of the SC simulations. For

this reason, only the results of SC simulations are reported here, with the soil hydraulic










parameters, Ceef, and Cer*" for the 2DSC and 3DSC simulations for all five boundary radii

presented in Table 3-3.

From Table 3-3 and Figure 3-6, it can be said that using a flux boundary condition allows

for maximal flexibility in boundary length assignment. In fact, allowing for the optimization of a

single hydraulic parameter (Ks), which regardless is difficult to measure, yields similar fits

independent of water entry boundary radius for all 2D and 3D simulations, respectively. Thus, a

flux boundary in H2D with a known SMRC results in maximal correlation (data prediction) for

SC boundary radii less than 1.0 cm.

With the soil wetting geometry settled and the observed flexibility in boundary radius, for

situations where the SMRC is known the only water entry boundary condition unknown is the

simulation domain. Based on correlation to the averaged data, the 2D simulations (Cegf ranging

from 0.872 to 0.914) perform better than their 3D counterparts (Cegf ranging from 0.771 to 0.774)

for our data set (Table 3-3). The superior correlation is probably a result of the measurement

technique used at the site, as the 150% emitter spacing collection volume of the WCR probe

coupled with the relatively short emitter spacing in general (20 cm) matches the line source

assumptions of the 2D simulations; however, when the measured uncertainty is accounted for

(Cer*" values; Table 3-3), the 3D simulation domains are also observed to provide very good

predictions (Ceg*" = 1.0). This means that the measured SMC uncertainty in our study was greater

than the impact on model predictions of either line source or point source assumptions or more

generally, water entry boundary conditions.

The larger impact of measurement uncertainty compared to simulation domain uncertainty

may not be the case for all drip irrigation simulations, but likely is the case when examples of

both line source and point source assumptions are evident in the field. As previously noted, the









Hield site in this study is such an example as the short emitter spacing (20 cm) coupled with the

sandy soil at the research site created a system that shares both line source (at deeper depths) and

point source (at shallow depths) characteristics. If a system were more physically representative

of line source or point source assumptions, a larger impact on model predictions would be

expected based on using the 2D or 3D simulation domains. Also a more accurate determination

of SMC, such as the use of TDR, would reduce the SMC uncertainty increasing the relative

impact of water entry boundary conditions.

There is also a noticeable difference between conductivity values optimized for 2D

simulations compared to 3D simulations, which all optimized at the same Ks value. The observed

similarity of the 3D simulation Ks values is likely unique to the measured data used in this study.

Full Calibration

During the full calibration, all soil hydraulic parameters were optimized within the range of

values measured on site. While uncertainty in the measured SMC data can be accounted for by

improved goodness-of-fit methods (Cer*"), neither these methods nor any of the initial

calibrations presented directly account for soil hydraulic parameter uncertainty. Since simply

accounting for SMC measurement uncertainty during the initial calibration already resulted in

excellent model prediction goodness-of-fit, similarly high correlations were expected and

observed during the full calibration (Table 3-4).

The 3D simulations did not predict the SMC distributions as well as the 2D simulations

prior to accounting for SMC uncertainty (Table 3.-3); therefore, the increase in 3D simulation

Cegf values (0.771 to 0.906) is a better indicator of model prediction improvement when

accounting for soil hydraulic parameter uncertainty (Table 3-4). But, a modest improvement in

2D predictions was also observed following the full calibration (increasing Cegf values from

0.872 to 0.961). The improvement of the 3D simulation model fit is best seen visually at the C23









location (Figure 3-7) where the 3D full calibration is nearly indistinguishable from the 2D full

calibration.

Considering the difficulties in estimating soil hydraulic parameters from site

measurements, inverse optimization of soil parameters can be a reliable alternative that can

alleviate errors associated with using a predetermined (or inaccurately estimated) SMRC. While

in our study each parameter range was established by measured data, the parameter ranges could

be established by previously tabulated parameter distribution data (Carsel and Parrish, 1988)

eliminating the need for field measurements. Table 3-4 shows that optimal parameters varied

with boundary radius length, but Cegf and Cer*" remained above 0.9 for nearly all simulations.

Again, these results indicate flexibility in assigning a water entry boundary radius length. If the

SMRC is known, optimization of Ks mitigates any influence of different radius lengths. If only

minimal knowledge of the soil is obtainable, optimization of all hydraulic parameters will

account for any influence of different radius lengths, as again Ks is included. And if we are

assuming minimal knowledge of the site, no set of hydraulic parameters can be considered better

than another set, so the water entry boundary radius length can be considered flexible.

It is also noteworthy that all 3D simulations optimized 8, above 0.09, a value exceed at

only one sample location (Table 3-2). This is the only observation made in the study that

champions one simulation domain over another while accounting for uncertainty. It was

observed in simulations not reported here that as 8, was reduced so were Cegf values for 3D

simulations even following soil hydraulic parameter optimization. Decreasing Cegf values would

favor the 2D simulation domain, but again once SMC measurement uncertainty is considered

(Cer*") both simulation domains can be considered excellent predictors.









Summary and Conclusions

For drip simulations on a sandy soil, run time efficiency was doubled when a SC soil

wetting geometry was used instead of a SR soil wetting geometry. Given the similarity of SMC

distributions predicted by the different soil wetting geometries, the SC geometry is thus superior.

For both simulation domains, little difference in model prediction was observed between

different boundary radius lengths. This is due to the water entry boundary condition being

designated as a flux, instead of constant pressure (saturation) and allowing for optimization of

Ks. In terms of model use, the selection of a flux boundary condition allows for flexibility when

assigning a boundary radius and eliminates one more potential unknown. Radius lengths under

1.0 cm represent the physical system well and are shown in this study to be adequate for

simulating surface drip irrigation. The superiority of the SC soil wetting geometry and the

flexibility observed for defining the water entry boundary radius length leaves only the

simulation domain as a potential unknown during water entry method selection.

For the raised bed vegetable production system on a sandy soil, both the 2D simulation

domain and the 3D simulation domain provided reasonable predictions of the measured SMC

data once SMC measurement uncertainty was considered. Due to the monitoring equipment

measuring the average soil moisture content over a bed length equivalent to 150% emitter

spacing and the relatively short emitter spacing (20 cm), the line source assumptions seemed

more representative of the measured data. And initially, the 2D simulation domain appeared

superior in our study. But as observed following the consideration of estimated soil hydraulic

parameter uncertainty during the full calibration, both the 2D and 3D simulation domains lead to

very good model predictions (Cegf > 0.9). The sandy soil at the study site added point source

characteristics to the system and is likely the reason the high goodness-of-fit indicators observed

for 3D simulations, improved further after the consideration of measured SMC uncertainty (Cer*"










= 1.0). This means that for the study site, which was representative of sites sharing line source

and point source characteristics, measurement uncertainty has more impact on model

performance than the selection of a simulation domain.





Table 3-2. Estimated soil hydraulic parameters for van Genuchten model (van Genuchten, 1980)
fit to 11 soil core samples by RETC model (van Genuchten et al., 1991).
Parameter Average -t One standard deviation (-,+) Range


Table 3-1. Results of surface area and influx calculations for the different scenarios simulated in
HYDRUS-2D


Simulation Soil wetting Radius Surface Calculated influx
domain geometry (cm) area (cm ) (cm min l)


Simulation


2DSCO.25
2DSRO.25
2DSCO.50
2DSRO.50
2DSCO.57
2DSRO.57
2DSCO.75
2DSRO.75
2DSC1.0
2DSR1.0
3DSCO.25
3DSRO.25
3DSCO.50
3DSRO.50
3DSCO.57
3DSRO.57
3DSCO.75
3DSRO.75
3DSC1.0
3DSR1.0


0.393
0.250
0.785
0.500
0.895
0.570
1.178
0.750
1.571
1.000
0.393
0.196
1.571
0.785
2.041
1.021
3.534
1.767
6.283
3.142


0.803
1.262
0.402
0.631
0.352
0.553
0.268
0.421
0.201
0.315
32.132
64.263
8.033
16.066
6.181
12.362
3.570
7.140
2.008
4.016


SC is semi-sphere and SR is surface-radius. Half of the nominal flow rate (0.757 L hr ')
was considered for the two-dimensional (2D) simulations to match the half-bed setup.
Influx values for 2D simulations are for 1 cm of the 20 cm emitter spacing. Three-
dimensional (3D) simulations used the nominal flow rate to calculate influx and did not
consider emitter spacing in calculation.


8r (cm3 -3")
8, (cm3 -3")
a (cm )


0.061
0.393
0.025


(0.014,0.108)
(0.351,0.435)
(0.016,0.034)


(0.001,0.150)
(0.329,0.462)
(0.016,0.044)


n (-) 2.286 (1.318,3.254) (1.586,4.572)
8r is residual water content. 8, is saturated water content. a and n are fitting
parameters for the van Genuchten model.










Table 3-3. Results from initial calibration
Simulation K, (cm min l) Ceef Cen*

2DSCO.25 0.807 (0.779,0.835) 0.882 1.000

2DSCO.50 0.670 (0.651,0.689) 0.914 1.000

2DSCO.57 0.670 (0.646,0.694) 0.914 1.000

2DSCO.75 0.808 (0.793,0.825) 0.882 1.000

2DSC1.0 0.849 (0.832,0.866) 0.872 1.000

3DSCO.25 0.264 (0.191,0.334) 0.771 1.000

3DSCO.50 0.264 (0.191,0.334) 0.772 1.000

3DSCO.57 0.264 (0.193,0.335) 0.773 1.000

3DSCO.75 0.264 (0.194,0.335) 0.774 1.000

3DSC1.0 0.264 (0.194,0.335) 0.774 1.000
Average values used: residual water content (6,) = 0.061; saturated
water content (Os) = 0.393; a = 0.025; and n = 2.286. 95%
confidence intervals calculated by HYDRUS-2D (-,+) displayed
following saturated hydraulic conductivity (Ks) mean values. Ceef is
Nash and Sutcliffe (1970) coefficient of efficiency. Cenf* is Nash and
Sutcliffe (1970) coefficient of efficiency with measurement
uncertainty (Harmel and Smith, 2007).












K, (cm minl)
0.585
(-0.420,1.590)
0.599
(-0.285,1.483)
0.617
(-0.288,1.521)
0.597
(-0.221,1.415)
0.475
(-0.078,1.027)
0.376
(0.335,0.417)
0.299
(0.119,0.469)
0.293
(0.292,0.788)
0.390
(0.225,0.554)
0.281
(0.108,0.455)


Simulation

2DSCO.25

2DSCO.50

2DSCO.57

2DSCO.75

2DSC1.0

3DSCO.25

3DSCO.50

3DSCO.57

3DSCO.75

3DSC1.0


n (-)
2.228
(1.640,2.816)
2.380
(1.859,2.902)
2.376
(1.743,3.010)
2.389
(1.821,2.597)
2.452
(1.920,2.985)
4.570
(4.167,4.973)
4.567
(3.706,5.427)
4.570
(3.740,5.401)
3.535
(2.462,4.609)
3.208
(2.787,3.629)


Cee

0.947

0.956

0.957

0.957

0.961

0.906

0.912

0.908

0.908


Cen*

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000


0.895 1.000


8r is residual water content; 8, is saturated water content; and K, is saturated hydraulic conductivity. 95%
confidence intervals calculated by HYDRUS-2D (-,+) displayed following reported mean values. Ceef is
Nash and Sutcliffe (1970) coefficient of efficiency. Ceyf* is Nash and Sutcliffe (1970) coefficient of
efficiency with measurement uncertainty (Harmel and Smith, 2007).


Table 3-4. Results from full calibration


6, (cm3 -3")
0.057
(0.040,0.075)
0.062
(0.050,0.074)
0.060
(0.044,0.076)
0.062
(0.049,0.076)
0.063
(0.051,0.075)
0.099
(0.098,0.101)
0.098
(0.095, 0.100)
0.093
(0.097,0.102)
0.094
(0.088, 0.100)
0.092
(0.088,0.095)


8s (c 3 -3 )
0.357
(0.257,0.458)
0.372
(0.285,0.459)
0.379
(0.284,0.474)
0.372
(0.284,0.461)
0.362
(0.291,0.433)
0.386
(0.374,0.397)
0.368
(0.322,0.415)
0.334
(0.384,0.460)
0.365
(0.318,0.412)
0.336
(0.289,0.384)


-1 (ml
0.044
(0.016,0.072)
0.044
(0.020,0.068)
0.044
(0.018,0.070)
0.044
(0.021,0.067)
0.044
(0.024,0.064)
0.037
(0.032,0.042)
0.036
(0.027,0.045)
0.044
(0.028,0.046)
0.044
(0.025,0.063)
0.044
(0.035,0.051)





Figure 3-1. Experiment 2 WCR matrix configuration centered in bed. Numbering of probes used
in results discussion also shown.










surface-radius (SR) semi-sphere (SC)




so


o n





2DSR 2DSC





.- I-----





3DSR 3DSC


Figure 3-2. Water entry boundary conditions examined for soil moisture content prediction.



















-~


0.25


0.20



S0.15



0. 10


0.05 t
10/13


10/15


10/17


10/19


10/21


10/23


DATE


- E8 C8


E23 C23


Figure 3-3. Averaged soil moisture content (SMC) from data measured on site.


















J~~d~` ~~


0 25

0 20

E015

0 10

0 05


0 25


0 25


0 20

, ,,


0 20


f0 15

0 10


0 10


0 00 1 00 2 00 3 00 4 00 5 00
DAY OF SIMULATION


0 00 1 00 2 00 3 00 4 00 5 00
DAY OF SIMULATION


0 00 1 00 2 00 3 00 4 00 5 00
DAY OF SIMULATION


Figure 3-4. Measured soil moisture content (SMC) from each probe representing locations C8, C23, and E23. Thin light lines
represent the measured data from an individual probe and thick dark lines represent the resulting average.


IZ R


1\1\11


~~,W\W\IU'; ~W











0.50



-0.40



0.30



-0.20



-0. 10



0.00
0 0.5 1 1.5 2 2.5 3

log [h (cm)]



Figure 3-5. Results of RETC model (van Genuchten et al., 1991) calibration to soil core data.
Displays average soil moisture content (SMC) for each pressure step and the resulting
SMRC (van Genuchten, 1980) from the RETC calibration. Error bars represent one
standard deviation of measured data.















C' I




'' : I


C23: Full Calibration


i\ I,


0 25


0 25


0 25


0 20


S0 15


0 10


0 05


0 20


S0 15


0 10


0 05


0 20


f0 15


0 10


0 05


~cl ^c-_ 1-4


CI~
I


00 10 20 30
DAY OF SIMULATION

---PER BOUNDS -2DSCO 50


40 50 00 10 20 30
DAY OF SIMULATION

3DSC 50---PER BOUNDS -2DSCO 50


40 50 00 10 20 30
DAY OF SIMULATION

3DSCO 50---PER BOUNDS -2DSCO 50


40 50


Figure 3-6. Results of initial calibration soil moisture content (SMC) predictions for a representative period of simulation, DOS 2 to 3.
PER BOUNDS represents the upper and lower boundary of measured data collected when measured uncertainty is
included.


0.20 11








S0.05





0.0 1 .0 2.0 3.0
DAY OF SIMULATION


I\
I\
I, \ I \ I

0.15 ~
'I\ \ '. I\
~I

nin


0.05


~1 -~


0.0 1 .0 2.0 3.0
DAY OF SIMULATION

-PER BOUNDS -2DSCO.50


4.0 5.0


4.0 5.0


3DSCO.50


- -PER BOUNDS -2DSCO.50


3DSCO.50


Figure 3-7. Comparison of initial and full calibration soil moisture content (SMC) predictions of the C23 location for a representative

period of simulation, DOS 0 to 5. PER BOUNDS represents the upper and lower boundary of measured data collected
when measured uncertainty is included.










CHAPTER 4
UNCERTAINTTY IMPACTS ON NUMERICAL MODELINTG OF FERTIGATION

Introduction

Vegetables are a maj or component of Florida agriculture encompassing about 72,000 ha

for production and valued at $1.5 billion annually (USDA, 2006). Much of the vegetable

production in the state occurs on raised beds covered with plastic mulch. Water and nutrient

delivery to these systems is commonly provided by drip irrigation. The term fertigation describes

the process of applying fertilizers through a drip irrigation system. With most of the soils where

these vegetables are grown classified as sands, frequent irrigation and fertigation is required to

minimize crop stress and attain maximum production. Also the plastic mulch covering the raised

bed minimizes the influence of evaporation and rainfall in the system (Simonne et al., 2004)

isolating irrigation effects and making these systems ideal for experimental monitoring of

distributions beneath drip irrigation.

Recently the numerical, two-dimensional model HYDRUS-2D (H2D) has been applied to

drip irrigation systems and proven to be a reliable predictor of water and nutrient dynamics

(Gardenas et al., 2005). The H2D program numerically solves Richards' equation for saturated-

unsaturated water flow and the convection-dispersion equation for solute transport. The flow

equation also incorporates a sink term to account for water uptake by plant roots (Simunek et al.,

1999). Still prediction inaccuracies can be found in the literature that stem from soil hydraulic

and transport parameter estimations; moreover, measurements of these parameters are often

costly, time consuming, and cumbersome.

Studies using H2D for drip irrigation simulations have employed several different methods

to estimate soil hydraulic parameters. Many use previously tabulated values, such as Cote et al.

(2003) where a subsurface drip irrigation system was simulated on three different soils,









employing the soil hydraulic parameters previously tabulated by Carsel and Parrish (1988),

provided in the H2D soil catalog. Skaggs et al. (2004) examined predictions of soil moisture

content (SMC) using soil hydraulic parameters derived from different pedotransfer functions.

Their results emphasized the importance of saturated water content and saturated hydraulic

conductivity over other soil hydraulic parameters as well as crowning the ROSETTA model

(Schaap et al., 1998) predictions based on soil class superior to Carsel and Parrish (1988)

predictions due to excess vertical drainage predicted by the latter. The study focused on drip

irrigation of a sandy loam, but stopped short of considering solute transport.

In fact, only a few studies using H2D have dealt with fertigation. Gardenas et al. (2005)

modeled nitrate (NO3) fertigation beneath both surface and subsurface drip systems, using

tabulated soil hydraulic parameters (Carsel and Parrish, 1988; Schaap et al., 1998) for each soil

type and assuming fixed soil transport parameters. Hanson et al. (2006) extended this work for

urea-ammonium-nitrate fertilizer, but neither study presented field measurements beneath a

fertigation system. In the laboratory, Li et al. (2005) assumed a longitudinal dispersivity of 0. 1

cm to predict NO3 transport through a soil core and reported good correlation to laboratory

measurements. Yet, Aj dary et al. (2007) was the only study found that applied H2D to a

fertigation system with nutrient data collected in-season. They used tabulated values for soil

hydraulic parameters and fixed soil transport parameters to validate predictions against soil

sample data that was collected periodically following fertigation events.

Inverse optimization can help alleviate uncertainty from using mean parameter values

within distributions of soil parameters. During inverse optimization soil parameters are bounded

by a known range that can be determined through field measurements or previously established

parameter distributions. The inverse optimization process attempts several parameter









combinations until the error between model prediction and measurement is minimized.

Simulating furrow irrigation with H2D, Abbasi et al. (2003) employed an inverse optimization

soil parameter estimation reporting a two-step approach, first soil hydraulic parameters then

transport parameters, to better predict SMC compared to a single-step optimization approach, but

little difference in concentration estimates was observed between approaches. Uncertainty in

measured values can also be accounted for through improved goodness-of-fit indicators (Harmel

and Smith, 2007).

For a technology that carries high resource conservation potential, it speaks to the

difficulty of obtaining measurements that only one study to date has coupled detailed in-season

monitoring of fertigation with the two-dimensional modeling of nutrient transport available with

H2D. The objective of this study was to strengthen the existing data set in the literature by

collecting in-situ measurements of SMC and nutrient distributions following in-season

fertigation of a raised bed vegetable production system covered with plastic mulch and compare

H2D predictions to the measurements while considering soil parameter estimation uncertainty

through inverse optimization of soil parameters and measurement uncertainty using improved

goodness-of-fit indicators.

Materials and Methods

Measurement Methods

SMC was measured at 15 minute intervals by the CS616 (Campbell Scientific Inc., Logan,

Utah) water content reflectometer (WCR) calibrated to volumetric water content calculated from

gravimetric soil sampling at the field site (Chapter 2). Soil water conductivity (K) was also

measured at 15 minute intervals by the Hydra Probe II (Stevens Water Monitoring Systems, Inc.,

Portland, Oregon), commonly referred to as a Vitel Probe. A matrix containing eight WCRs was

installed in a representative section of the bed (Figure 4-1). An approximately 40 cm long section









of the entire bed width was removed from the installation location. The section provided enough

space for horizontal WCR installation parallel to the surface. A matrix containing eight Vitel

probes was installed on the opposite trench face. Analysis of a similar field setup revealed the

opposite trench face locations can be considered replicates (Chapter 2). After installation of each

matrix, the section was repacked and covered with plastic mulch. Each matrix was configured in

a 2 X 4 (Vertical X Transverse) formation, with the top row buried at 8 cm and a bottom row at

23 cm below the surface of the bed. The four columns were spaced on center 16 cm apart

centered directly under the drip tape. Tomato plants were located near the interface of the probe

rods and the portion containing the electronics.

Due to difficulties experienced at the field site the actual Vitel matrix location placed the

center of the probe measurement volumes approximately 3 cm away from the nearest emitter,

measured along the drip line. Also the probe measured K (S m ) represents the combined effect

of all the fertigation constituents; however, it has previously been observed that non-adsorbing,

non-transforming ions such as NO3 and chloride (Cl) exhibit similar relationships between

concentration and K (Mufioz-Carpena et al., 2005a). Considering this and assuming that NO3

was the most influential ion, since it represented 79% of the fertigation anion weight, probe

measured K was transformed to NO3 COncentrations using the equation presented by Neve et al.

(2000). Still the probe location and combined concentration assumption introduce measurement

uncertainty that was not quantified here.

A weather station located within 500 m of the experimental site provided hourly

temperature, relative humidity, solar radiation and wind speed data that was used to calculate

reference evapotranspiration (ETo) according to FAO-56 (Allen et al., 1998). Crop

evapotranspiration (ET,) was calculated based on the product of ETo and the crop coefficient









(Ke) for a given crop growth stage (Simonne et al., 2004) and values were reduced by 30% to

account for the effect of plastic mulched vegetable beds on overall ET, values (Amayreh and Al-

Abed, 2005). ET, averaged 0.26 cm dayl with a standard deviation of 0.01 cm dayl for the

period surrounding the fertigation events of interest.

To determine the root distribution, root samples were collected with a 5 cm diameter soil

auger at 0-15, 15-30, 30-60, and 60 to 90 cm depth layers and in three positions: 0, 12.5, and 25

cm distance on a transverse line perpendicular to the plant row. Root samples were collected 66

days after transplanting to ensure full root growth and can be considered a reasonable estimate of

the root distribution for Experiment 3 and Experiment 4. Immediately after collection, samples

were put in plastic bags and refrigerated at 4oC until cleaning. The samples were washed on a 2

mm sieve and organic debris was cleaned manually. Roots were then placed in Petri dishes and

frozen until further analysis. The root samples were scanned and the root length and diameter

was measured by WINRHIZO software (Regent Instrument, Inc., Canada).

Experimental Site

The experimental site was located at the University of Florida, Plant Science Research and

Education Unit, near Citra, Florida. Buster (1979) classified the soil at the research site as a

Tavares sand and Candler sand. These soils contain >97% sand-sized particles and have a field

capacity of 0.05-0.07 cm3 CA-3 in the upper 100 cm of the profile (Carlisle et al., 1978).

Two distinct data sets were used in this study, one collected in-season and one collected

post-season, previously summarized in Table 2-1 as Experiment 3 and Experiment 4

respectively. The Experiment 3 setup was previously described (Chapter 2) with additional

relevant information provided here. Experiment 3 SMC and K measurements transformed to

NO3 COncentrations were used for solute predictions, focusing on fertigation events that occurred

on May 30, June 6, and June 14, 2006. The three fertigation events were chosen due to their









similar applications, associated evapotranspiration (0.26 cm day )~, and associated root

distribution. Fertigation events were applied manually inline and occurred in the early afternoon.

Fertilizer for the three fertigation events focused on in this study was composed of 71.7%

Ca(NO3)2*H20, 21.5% KC1, and 6.8% Mg(SO4)*7H20.

Experiment 4: 2006 Post-Season

Experiment 4 involved the collection of post-season WCR SMC measurements to account

for any in-season modifications to the soil hydraulic parameters, but eliminate the influence of

transpiration. To accomplish this, following harvest on July 5 the tomato plants surrounding the

Experiment 3 monitoring sites were clipped near the soil surface. Data was collected until July

14. The data collected from July 8 to July 14 thus represents a bed modified by root growth (or

other in-season processes), but under no transpiration influence. Experiment 4 SMC was used for

calibration of soil hydraulic parameters. Similar to Experiment 3, irrigation occurred daily from

0600 to 0800 hrs with a nominal emitter flow rate of 0.76 L hr- at 69 kPa.

Model Description

The H2D program numerically solves the mixed formulation of Richards' equation, as

proposed by Celia et al. (1990), for saturated-unsaturated water flow using Galerkin-type linear

finite element schemes (Equation 3-1) and the convection-dispersion equation for solute

transport as well as incorporating a sink term to account for water uptake by plant roots. An

accurate soil moisture release curve is also required to model the system. Accordingly, the van

Genuchten-Mualem model (van Genuchten, 1980) was calibrated to the system (Equations 4-1 to

4-3 ).



0(h)=d~ 1+' (4-1)
8, h>0










K(h)= K,S 1- (1-S '"') (4-2)

where

m= 1- 1/n, n> 1 (4-3)

The van Genuchten-Mualem equations are defined where 6,. is residual water content

[L3L-3] Bs is saturated water content [L3L-3], h is pressure head [L], a is soil water retention

coefficient [L^]~, n and m are scaling factors [-], So is degree of saturation [-], and Ks is saturated

hydraulic conductivity [LT- ]. The van Genuchten-Mualem model within H2D requires a pore-

connectivity parameter 1 [-] that was estimated to be 0.5 for all scenarios and also contains five

soil dependent input parameters (8,., 8,, a, n, and Ks). The water content tolerance was set at

0.001 [L3L-3] representing the absolute magnitude of change allowed for unsaturated nodes

between two iterations within a time step. For solute transport, the Crank-Nicholson implicit

scheme was used along with a Galerkin spatial weighting scheme (Simunek et al., 1999).

Initial and Boundary Conditions

For all model runs, only half of the bed area was considered with calibration performed

under the assumption that water flow is symmetrical across the vertical plane directly beneath the

emitter (Wooding, 1968; Warrick, 1974). The nominal emitter flow rate of 0.76 L hr- was used

in all simulations. The defined simulation area had the general shape of a rectangle, representing

a soil half-section below the surface, bounded by the bed center and bed edge, and located to the

right of an emitter. A two-dimensional simulation domain, semi-spherical soil wetting geometry,

and 0.50 cm boundary radius (water entry boundary) was chosen to represent the system due to

the superior performance prior to uncertainty consideration previously observed for similar

systems (Chapter 3). The water entry boundary was located at the intersection of the left vertical

boundary and the upper boundary. During irrigation, the water entry boundary was assigned as a









variable flux boundary. During fertigation, the water entry boundary was set as a third-type

boundary, representing a concentration influx (Simunek et al., 1999). The left vertical boundary

and upper boundary were assigned as no flux, representing the symmetry across the vertical

plane and plastic mulch covering the surface, respectively. The lower boundary of the profile

was assigned as a free drainage boundary located 60 cm subsurface. The right vertical boundary,

which represents the boundary between the soil half-section and the inter-row area, was also

assigned as a free drainage boundary below 25 cm subsurface. Between 0 and 25 cm subsurface,

the right vertical boundary was assigned as a no flux boundary, again due to the plastic mulch

covering.

For soil transport parameter calibration, the area assigned as rooted was estimated from the

root distribution data, with relative distributions equivalent to root concentrations. The van

Genuchten S-shaped model (van Genuchten, 1987) was used for root water uptake, with the p

exponent [-] set to the recommended value of 3 and the 50% pressure head uptake coefficient,

h50 [L], set to -800 cm. It was assumed that the potential evapotranspiration was equal to the

potential crop transpiration calculated for the site. All soil transport parameter calibrations began

the morning of (prior to irrigation) the fertigation event and lasted for four days (four irrigation

events) following fertigation.

Since probe K measurements were transformed to NO3, the fertigation concentration was

simulated as the combined NO3 and Cl concentration and is also represented by a single

constituent, NO3. The combined concentration assumption is reasonable for our study since the

combined NO3 and Cl concentration was over 95% of the total anion concentration and these

anions exhibit similar impacts on K (Mufioz-Carpena et al., 2005a). Following this assumption

and using fertilizer weight, composition, and flow data, the inline fertigation concentration used









during simulation was determined to be 13.78 g NO3 L^. The applied concentration was assumed

to be non-adsorbing and non-transforming. The diffusion coefficient was set at 0.001 cm2 min-1,

again representing NO3 in free water (Robinson and Stokes, 1968). The diffusion coefficient was

not varied during this study as such a small value will have little impact relative to dispersivity

effects on predicted concentrations in a high velocity regime. In fact, diffusion effects have been

ignored in previous studies focusing on NO3 (Aj dary et al., 2007; Gardenas et al., 2005);

moreover, smaller values have been reported for saturated soils compared to free water due to

soil matrix impedance (Gardner et al., 2001).

The time-series of model prediction comparisons to measured data are presented as day of

simulation (DOS). The entire model domain was initialized four days prior to the beginning of

this comparison (DOS -4). From DOS -4 to 0 model variables were allowed to reach a quasi-

static state by applying the same irrigation events as between DOS 0 and 8 for soil hydraulic

parameter calibration and DOS 0 and 5 for soil transport parameter calibration. Fertigation was

applied between DOS 0 and DOS 1 depending on the actual application time at the site. For soil

hydraulic parameter calibration the simulation domain was initialized at 0.10 cm3 Cm-3 SMC. For

soil transport parameter calibration the simulation domain was initialized at 0. 10 cm3 Cm-3 SMC

and 0.50 g NO3 L^ soil water. The initial NO3 COncentration was established to match

background measurements observed at the bed edge, but it was observed during the calibration

process that only a few irrigation events were required to leach all the concentration from the bed

center. So at DOS 0 for the soil transport parameter calibrations, monitoring location C8 and C23

always predicted 0.0 g NO3 L^. The finite element dimensions were generated automatically by

H2D MESHGEN. Smaller elements were created around the water entry boundary to account for

rapid variable changes, increasing model stability. Generally element size increased as the lower









and right vertical boundary intersection was approach, with MESHGEN densities 200% greater

at the lower and right vertical boundary intersection as compared to around the water entry

boundary.

Calibration and Optimization Procedure

As suggested by Abbasi et al. (2003), soil parameters were determined by a two-step

calibration, soil hydraulic parameters followed by soil transport parameters. In addition, during

both steps in the calibration process uncertainty of estimated parameters was accounted for

through an inverse optimization process. Inverse optimization was utilized in this study as it had

been previously reported to improve H2D predictions (Chapter 3).

Three different hydraulic parameter distribution sets were examined for their ability to

match measured SMC: Carsel and Parrish (1988) parameters for sand (1), the ROSETTA model

(Schaap et al., 1998) parameters for sand (2), and the measured soil moisture release curve

(Chapter 3; Figure 3-5) determined from undisturbed soil cores collected nearby (3). Inverse

optimization during soil hydraulic parameter calibration was performed within two standard

deviations range of the soil hydraulic parameters: 8,, 8,, a, n, and Ks. For parameter set 3, no

bounds were placed on Ks during calibration as it was not estimated from the undisturbed soil

cores (Chapter 3). Also although soil hydraulic parameters are known to follow log-normal

distributions, for parameter set 3 all measured parameters were fit to normal distributions for

simplicity and due to the small sample size.

The set of hydraulic parameters yielding the best SMC prediction following the soil

hydraulic parameter calibration was used for soil transport parameter calibration. The range for

soil transport parameters was derived from previously reported values for field studies in sandy

soils (Vanderborght and Vereecken, 2007). Longitudinal dispersivity (DL) and transverse









dispersivity (DT) WeTO Optimized to NO3 COncentrations obtained from Vitel probe K

measurements following the May 30 fertigation.

Each inverse optimization was based on the numerical solutions of Richards' equation for

soil hydraulic parameters and the convection-di spersion equation for soil transport parameters.

All optimizations were performed using the built-in Levenberg-Marquardt nonlinear

minimization method in H2D. During the inverse optimization process, the unknown parameters

are determined by the minimization of an established obj ective function (Simunek et al., 1999).

All weighing coefficients were set to 1. Multiple optimizations were performed for each

calibration simulation using different initial values for the parameters to be determined in order

to increase the probability of finding the global minimum.

To validate model predictions, the combined parameter set resulting from soil hydraulic

and transport parameter calibrations was used to simulate two more fertigation events: June 6

and June 14.

Prediction Evaluation

Two goodness-of-fit indicators are reported by H2D following a given simulation, sum of

squares (SSQ) and the coefficient of determination (R2) (Simunek et al., 1999). Both indicators

simply use the squared residual to represent the deviation between paired measured and

predicted data.



C4, = 1.0 (4-4)



The Nash-Sutcliffe (1970) coefficient of efficiency (Cere) uses a similar approach, where

O, is measured data; 14 is predicted data; and O is the mean of the measured data (Equation 4-









4). The range of Cegf lies between 1.0 (perfect fit) and -oo. When Cegf is lower than zero the mean

value of the measured time series would have been a better predictor than the model (Nash and

Sutcliffe, 1970). Cegf is the reported goodness-of-fit indicator in this study because it is better

suited to evaluate model goodness-of-fit compared to SSQ or R2 (Legates and McCabe, 1999).

In the presence of measurement uncertainty, it is also valuable to evaluate paired measured

and predicted data against the uncertainty boundaries of the measured data instead of against

individual data values. When the uncertainty boundary, but not the distribution of uncertainty

around each measured data point is known, Harmel and Smith (2007) proposed that the chosen

goodness-of-fit indicator can be improved by a modification that accounts for this uncertainty,

summarily described here.


PER = [ E,2 +E(, +E C+...+E ) (4-5)


The probable error range (PER), where n is the number of potential error sources and En is

the uncertainty associated with each potential error source (%), was used to establish an upper

and lower bound for the measured SMC and NO3 COncentrations at a given time (Equation 4-5).

If 14 fell within the established boundary, the residual used in Cegf calculation is changed to zero.

If 4q fell outside the established boundary, the residual used in Cegf calculation is changed to the

difference between Iq and the nearest boundary value (Harmel and Smith, 2007). To account for

the measured uncertainty, the modified Ceg is also reported, designated in this document as Cer*.

For SMC measurements in this study, three sources of error were considered. The first was

the reported WCR accuracy, 0.025 cm3 Cm-3 (Campbell Scientific, Inc. 2002). Recall the WCR

measurements were further calibrated to the field site (Chapter 2) using measured gravimetric

data that was converted to volumetric soil moisture by using bulk density measurements. The









WCR error (El) was calculated as the reported accuracy divided by the average SMC for all

probes used in model calibration over the time-series of interest, 19.7%. The errors for the soil

samples were calculated by dividing the standard error of the measurements by the mean of the

measurements, resulting in a gravimetric error (E2) Of 10.3% and a bulk density error (E3) Of

2.0%. The three error sources result in a PER of 22.3% for SMC measurements.

For NO3 COncentrations obtained from K measurements in this study, the only source of

error considered was the Vitel K measurement. K errors have been reported to be 20% (Stevens

Water Monitoring Systems, Inc., 2007), yielding a PER of 20.0% for NO3 meaSurements. This

PER can be considered low as possible errors resulting from the Vitel probe location and

combined concentration assumption were unable to be quantified.

Results and Discussion

Field Results

Since symmetry across the half-bed was assumed, probe locations (WCR and Vitel) at

similar locations on each half-bed were averaged. After averaging, the probes as labeled in

Figure 3-1 were renamed with respect to their location, center of the bed (C) or edge of the bed

(E), and their depth, 8 cm (8) or 23 cm (23) subsurface. Therefore, E8 is the average of probe 1

and 4; C8 is the average of probe 2 and 3; E23 is the average of probe 5 and 8; and C23 is the

average of probe 6 and 7. Averaging also minimizes errors associated with the drip tape lying

away from the exact bed center. Since the experiment site required separate irrigation and

fertigation drip lines (Chapter 2), locations are never truly symmetrical, but averaging yields a

representative measurement for the location of interest (Figure 4-2 and 4-3).

WCR SMC measured at the bed edge differed substantially at the E8 location, probe 1 and

4. Differences between the probe 1 and 4 were observed to be as high as 0.09 cm3 Cm-3. The

observed difference could be due to a number of factors; however, SMC at these locations was









only minimally impacted by irrigation events, with the average SMC for the location (E8)

ranging from 0.05 cm3 Cm-3 to 0.08 cm3 Cm-3. Due to these differences a three location data set

(C8, C23, and E23) was used for soil hydraulic parameter calibration. Large differences were

also observed for the C23 location, with consistent deviations in SMC between probe 6 and 7

near 0.04 cm3 Cm-3 and as high as 0.13 cm3 Cm-3, but the range of average SMC from 0. 10 cm3

cm-3 to 0.23 cm3 Cm-3 made the location important to retain in the data set (Figure 4-2).

Measurement variability was also observed in the soil core data (Chapter 3; Table 3-2), with only

8, having a standard error less than 10% of the parameter average (3.2%).

Figure 4-3 displays the in-season Vitel K measurements transformed to NO3

concentrations, with fertigation leaving the system after only a few subsequent irrigation events.

No physical explanation exists for the trend observed at the E8 location and for consistency E8

was not included in soil transport parameter calibration.

In general, the root distribution measured at the peak of plant development agrees with

previously reported distributions (Scholberg, 1996) with the highest density near the emitter.

But, as seen in Figure 4-4, roots have penetrated much deeper than the bed depth. For more detail

on root distribution at the site, the reader is referred to Zotarelli et al. (2007b). For soil transport

parameter calibration, the area assigned as rooted was estimated from the root distribution data

(Figure 4-4), with relative distributions equivalent to input root concentrations.

Soil Hydraulic Parameter Calibration

The three different soil hydraulic parameter sets were used during inverse optimization to

predict SMC from Experiment 4. The C23 location, where large differences were observed

between probes, was the driving force behind calibration. To predict the C23 location a large a

parameter was required (Table 4-1); however, large a parameters result in large drainage










predictions from the center of the bed and thus little impact is predicted at the E23 location

following irrigation events (Figure 4-5). While the measured data does reveal a relatively dry bed

edge, SMC increases were observed following irrigation events (Figure 4-2). In fact, prior to

considering SMC measurement uncertainty no representative fit was observed with only Set 1

(Cegf = 0.266) yielding a Cegf value greater than 0.0. Recall Cegf values below 0.0 imply the

location average measured SMC over the entire time-series acts as a better predictor than H2D

results. Following uncertainty consideration, all three parameter sets provide a good fit (Cer*" >

0.9). Again focusing on the E23 location, one could even make the argument that parameter Set

2 and 3 provide a better visual match of all three locations (Figure 4-5), regardless of their poor

predictions prior to uncertainty consideration (Table 4-1).

The inability to achieve a very accurate fit (Cesf) of all three monitoring locations prior to

measurement uncertainty considerations could be an artifact of the site setup. Since separate drip

lines for irrigation and fertigation were required at the site, the drip emitter was not located in the

exact center of the bed, but monitoring locations were installed relative to the bed center. The

probes on each side of the bed center were subsequently averaged to alleviate this concern;

however, with only two monitoring locations per average, the linear interpolation is admittedly

simple. Also micro-heterogeneity at the monitoring location could be responsible. Since SMC

data collected at a near-by location (Chapter 3) by similar methods was predicted well (Cewf >

0.9), site specific characteristics are likely the cause not measurement methods. Even so, such

errors are not egregious for field monitoring and once accounted for representative fits were

achieved (Cer*" > 0.9; Table 4-1).

To proceed with the soil transport parameter calibration, a representative set of hydraulic

parameters had to be selected. While Set 1 preformed best prior to measurement uncertainty









considerations, the prediction was poor and after measurement uncertainty considerations, all

three parameter sets predicted SMC well (Cer*" > 0.9). And while parameter Set I was yielded

the highest goodness-of-fit indicators, the prediction failed to visually match the E23 SMC time-

series. Regardless, since it was previously observed (Figure 4-3) that most fertigation is

transported through the center of the bed, Set I was chosen for soil transport parameter

optimization since Set 1 also has the largest a parameter, again an indicator of vertical drainage.

Set 1 should provide the most representative water transport in the bed center, allowing for

accurate soil transport parameter calibration.

Soil Transport Parameter Calibration

As previously discussed, the fertigation concentration was determined to be 13.78 g NO3

L and in-situ K measurements were transformed to NO3 COncentrations. Using the optimized

soil hydraulic parameter Set 1 and the transformed NO3 COncentrations, the soil transport

parameters DL and DT were calibrated using inverse optimization. Since it had been previously

observed that soil hydraulic parameter Set 1 does not predict much water transport to the outer

regions of the bed and in preliminary simulations initial concentrations had an unfair impact on

goodness-of-fit indicators due to the small range of concentrations measured at the E23 location,

the build-up ofNO3 COncentrations in the bed edge observed in the field (Figure 4-3) was

ignored. As such, the reported Ceef and Cer*" values are related to the C8 and C23 monitoring

sites only.

The soil transport parameter calibration yielded a DL Of 2.38 cm and a DT Of 0.01 cm, best

representing the system (Figure 4-6) with Cegf= 0.562 and Cer*" = 0.799. While prior to

considering measurement uncertainty, the calibration may seem poor (Cegf = 0.562) when

compared to the soil hydraulic parameter calibration prior to uncertainty considerations (Cerf =

0.266) the soil transport parameter calibration results are impressive. When measurement









uncertainty is considered, a decrease in Cer*" is observed from the prior calibration. Still the soil

transport parameter calibration predicts measured NO3 COncentrations well after measurement

uncertainty is considered (Cer*" = 0.799).

The soil transport parameters determined in this study are also within the range of

compiled data reported by Vanderborght and Vereecken (2007) and near their mean value of

~3.0 cm (DL). But while the values are within the range established by previous studies using

H2D (Table 4-2), the values are higher than those reported for the laboratory sand study (Li et

al., 2005). The increase in DL frOm a laboraltory experiment to the field is a trend that has

previously been observed (Vanderborght and Vereecken, 2007) and lends further credence to the

importance of obtaining strong field measurement data sets.

Upon further examination of Figure 4-6, distinct differences were observed between the

predicted and observed NO3 COncentration time-series at both the C8 and C23 location.

Concentrations at the C8 location are under predicted immediately following the first irrigation

event (after DOS 1), while the C23 site is predicted fairly accurately. Similar results were also

reported by Aj dary et al. (2007) with under predictions between 10 and 15 cm subsurface and

more accurate predictions reported for deeper depths. Further examination of the C8 location in

Figure 4-6 reveals the simulated concentrations arriving at the C8 location powered only by

fertigation. Where as, it takes the following irrigation event before the measured NO3

concentration arrive at the location.

Both observations could be a product of the two-dimensional simulation domain

assumption, which states that all irrigation and fertigation enters the bed evenly across the

distance between two emitters as a line source. While the line source assumptions have

previously been shown to predict well SMC under drip irrigation (Chapter 3), the assumption










may not hold for Vitel probe measurements. The WCR probe has a 30 cm (150% emitter

spacing) collection length within the bed, much larger than the 5.7 cm (28.5% emitter spacing)

length collected associated with the Vitel probe (Chapter 2). Though both probes were located at

similar normal distances for each monitoring location (C8, C23, and E23) the smaller collection

length of the Vitel probe causes measured concentration values to be more susceptible to

variations created by the radial distance from the emitter. The difference immediately following

fertigation could also be a product of H2D nutrient uptake prediction. During simulation, NO3

concentration uptake occurs only with root water uptake (Simunek et al., 1999). The process

could be more complicated in our system, especially when the relatively low SMCs following

fertigation are considered.

As previously stated, the center of the 5.7 cm measurement length was located ~3 cm from

the nearest emitter. At this location, if water applied during fertigation is enough to allow

transport to the C8 location some impact, though perhaps mitigated, should still be observed by

the Vitel probe. Considering this, the difference observed immediately following fertigation also

draws into question the optimized DT value (2.38 cm). A lower value as assumed in previous

studies (Table 4-2) will alleviate the deviation between predicted and observed concentrations

immediately following fertigation, but will not match the remainder of the time-series as well.

Such curve-fitting as compared to finding values representing the physical system is one of the

possible drawbacks that have been previously reported for inverse optimization techniques

(Ritter et al., 2003).

Validation Simulations

During the validation simulations similar fertigation concentration was applied, but

different fertigation timing and different amounts of water applied as irrigation. For example, the

site scheduled irrigation DOS -1 and 0 for the June 14 fertigation event did not occur due to









electrical problems. Even so, the model continued to predict the events reasonably well. Prior to

uncertainty consideration, values were again low yet relatively high compared to the soil

hydraulic parameter calibration with Cegf values of 0.635 and 0.432 for the June 6 and 14 events

respectively. After considering measurement uncertainty, validation simulations were observed

to predicted measured values well with Cer*" values of 0.854 and 0.684 for the June 6 and 14

events respectively. As before prediction improvement was observed after measurement

uncertainty was accounted for and the C8 location was again under predicted while the C23

location was more accurately simulated.

Summary and Conclusions

A representative data set of SMC and NO3 COncentrations was collected in-situ beneath a

plastic mulch covered, raised bed vegetable production system. The data collected was complete

enough to apply inverse optimization methods for simulating the site. Soil hydraulic parameters

were obtained through inverse optimization of SMC measured on site. The optimization process

was limited by the van Genuchten model a parameter. A large a parameter was required to

match SMC reported by monitoring locations in the center of the bed (C8 and C23). Since the

large a parameter prevented water from reaching the bed edge (E23) during simulation, a

representative parameter set could not be determined until uncertainty in SMC measurements

was considered. The soil hydraulic parameter distribution reported by Carsel and Parrish (1988)

for sand provided the best fit as the distribution provided the largest range for the a parameter.

Soil transport parameters were also calibrated to the system by inverse optimization to NO3

concentration data using the best results of the soil hydraulic parameter calibration. The inverse

optimization process revealed DL Of 2.3 8 cm and DT Of 0.01 cm to best represent the system (CeKf

= 0.562). Prediction results were again improved after measurement uncertainty was considered

(Cer*" = 0.799). Similar improvements were observed for both validation simulations with










goodness-of-fit indicators increasing from 0.635 to 0.854 and 0.432 to 0.684 for the June 6 and

June 14 fertigation simulations respectively, once measurement uncertainty was considered.

The soil transport parameters reported here are higher than those reported for a laboratory

sand study that used H2D (Li et al., 2005), but within the range of previously reported field sites

(Vanderborght and Vereecken, 2007). This supports the optimization results and further confirms

the value of field measurements compared to laboratory or theoretical estimations. Also as

reported by Ajdary et al. (2007), in our study H2D under predicted concentrations at shallow

monitoring location (C8), while more accurate predictions were observed at the deeper

monitoring location (C23). The difference between measured and predicted concentrations at the

location nearest the fertigation emitter (C8) was observed between the simulated fertigation

event and following day irrigation event. In short, predicted concentrations arrived at the

monitoring location several hours before any rise in concentration was measured. It is unclear

from the results in this study whether this observed difference is a byproduct of the line source

assumptions used for simulation or errors associated with root nutrient uptake simulated by the

model .










Table 4-1. Results from soil hydraulic parameter calibrations to Experiment 4 soil moisture content at C8, C23, and E23
Pa rameter sou rce Set 6, (cm3 -3") 8s (c 3 -3" -1(m~) n (-) K, (cm min l) Ceef Cen*
Carsel and Parrish 1 0.035 0.370 0.174 2.390 0.235 0.266 0.991
ROSETTA 2 0.072 0.370 0.063 3.882 0.169 -0.145 0.989
Measured 3 0.052 0.383 0.035 2.838 0.276 -0.089 0.958
8r is residual water content; 8, is saturated water content; a and n are fitting parameters for the van Genuchten (1980) model. K, is
saturated hydraulic conductivity. Ceef is Nash and Sutcliffe (1970) coefficient of efficiency. Cenf* is Nash and Sutcliffe (1970)
coefficient of efficiency with measurement uncertainty (Harmel and Smith, 2007).





Table 4-2. Reported dispersivity values used in previous HYDRUS-2D fertigation studies
Dispersivity
Parameter source Soil type
DL (cm) DT (cm)
Li et al. (2005) Sand 0.10 0.001
Li et al. (2005) Loam 0.32 0.003


Gardenas et al. (2005)
& Hanson et al. (2006)


Ajdary et al. (2007)


Sandy loam, loam, silty
clay, anisotropic clay

Sandy clay loam, sandy
loam, loam, silty clay
loam, silt


5.00 0.500



0.30 0.030


DL iS longitudinal dispersivity and DT is transverse dispersivity.


Figure 4-1. Experiment 3 and 4 WCR matrix configuration centered in bed. Numbering of probes
used in results discussion also shown.
















r~R~S-~


0.25


0.20

S0.15

0. 10


0.05
7/8 7/9 7/10 7/11 7/12 7/13
DATE (2006)
E8 -C8 E23 -C23
Figure 4-2. Experiment 4 WCR soil moisture content (SMC) measurements.

1.5






0 .0



4/13 5/3 5/23 6/12 7/2
DATE (2006)
E8 -C8 E23 -C23
Figure 4-3. Experiment 3 Vitel determined nitrate (NO3) COncentrations.










LATERAL DISTANCE FROM DRIP (cm)
0 5 10 15 20 25


,FP~
~
2PO
0.75

q







o
F3~


80


90


Figure 4-4. Root distribution collected during full canopy, 66 DAT.















0 30 0 30 0 30
C8 C23 E23

0 250 25 I0 25


0 20 E 020E 2



0 500 0 05
00 10 20 30 4 500 10 20 30 40 50 00 1 0 30 5
DA OFSMLTO A FSMLTO A FSMLTO
-- PR OUD 2 \ 3 PR O NS 1 2 3- E BUD -
Figure~ 4-5 Paamte Set 1, 2,ad3si ydalcprmte airto, olmitr onet(M )DO 0to5














C8 C23




an 1.0 rIm 1.0
SFertigation I Fertigation '"I






0.0 0.0
0 1 .





0.01 cm..


















Z
co 1.0

O



z 0.5





0.0


Z
co 1.0

O



z 0.5
Z




0.0


0.0 1.0 2.0 3.0 4.0 5.0 0.0
DAY OF SIMULATION

-- -- -- PER BOUNDS -Simulated


SFigure 4-7. Nitrate (NO3) COncentration predictions for June 6 fertigation. Soil
cm.


1.0 2.0 3.0 4.0 5.0
DAY OF SIMULATION

-- -- -- PER BOUNDS -Simulated


hydraulic parameter set 1, DL = 2.38 cm, and DT = 0.01













C8 C23







o a

0n .0 0n .0






0.01~h cm.










CHAPTER 5
RESEARCH SUMMARY AND FUTURE WORK

Research Summary

In Florida, intensive bed management systems are commonly used for vegetable

production. These systems consist of raised beds for planting covered with plastic mulch, with

water and nutrients commonly applied via drip irrigation and fertigation. Currently available

dielectric soil moisture sensors provide inexpensive alternatives when compared to Time

Domain Reflectometry (TDR) and the labor costs of soil sampling. The CS616 water content

reflectometer (WCR) and the Hydra Probe II (Vitel), operating on time-domain and capacitance

methods respectively, were installed beneath drip irrigated tomatoes in an intensively managed

vegetable production system. The monitoring capability of each probe was examined through

one-to-one and time-series comparisons. The probes were installed in a two-dimensional grid to

capture the soil moisture content (SMC) distribution beneath drip irrigation. It was observed

during one-to-one comparisons that SMC measured using the factory calibration provided with

each probe failed to match volumetric water content (VWC) determined from gravimetric soil

samples. However, the longer measurement distance of the WCR probe (150% emitter spacing)

allowed for relatively good calibration to VWC data (R2 = 0.74) since soil samples were

collected at like normal distances from the bed center as probe locations, but without regard to

emitter location. Accordingly, the short measurement distance of the Vitel probe (28.5% emitter

spacing) resulted in a poor calibration for to SMC measurements (R2 = 0.26) and soil water

salinity measurements (R2 < 0.10). More importantly, time-series observations were observed to

provide accurate description of the system, as both probes matched the season-long SMC trends

well. And the Vitel probe was observed to match soil water salinity trends during time-series









following two different fertigation events. The ability to capture descriptive time-series allowed

for the probe measurements to be used during model calibration (Chapter 2).

The HYDRUS-2D program (H2D) has previously been used for drip irrigation

management forecasts. A review of the simulations reported in the literature revealed an

assortment of techniques for defining the model simulation space. To examine the effectiveness

of these techniques, H2D was calibrated to SMC data collected from a non-planted bed section

with soil moisture release curve (SMRC) parameters determined from undisturbed soil cores and

saturated hydraulic conductivity determined by inverse optimization. The goodness-of-fit

indicator (Cesf) was also modified to account for measurement uncertainty (Cer*"). Semi-spherical

(SC) soil wetting geometries proved superior to their surface-radius counterparts in convergence

and simulation time, but nearly identical in SMC prediction. Both the axis-symmetrical and two-

dimensional SC approaches predicted the SMC data well, Cegf ~ 0.77 and ~0.91 respectively.

Goodness-of-fit indicators obtained near perfect values after uncertainty in the SMC and SMRC

measurements was considered (Cer*" = 1.0). This means SMC measurement uncertainty at the

site was greater than any water entry boundary condition impact on SMC (Chapter 3).

It was also observed that most previous studies of fertigation using H2D used mean values

for soil parameter estimation. The determination of appropriate soil hydraulic and transport

parameters is essential to accurately simulate distributions beneath fertigation. To account for

soil parameter uncertainty, inverse optimization methods were applied for soil hydraulic and

transport parameter calibration. Calibration of the soil hydraulic parameters revealed high

bubbling pressure (~0.17 cm l) was required to obtain even modest predictions in the bed center

(Cegf = 0.27). Calibration of soil transport parameters yielded a longitudinal dispersivity of 2.38

cm and a transverse dispersivity of 0.01 cm (Cegf= 0.56). As before, accounting for measurement










uncertainty improved the results of both calibrations, Ceff* = 0.99 and 0.80, respectively.

Observations made following the soil transport parameter calibration question the applicability

of line source assumptions for comparison to Vitel measurements (Chapter 4).

Future Work

As is often the case with scientific research, as many questions were raised as were

answered. The adage is especially true in this case as the experimental site was managed for a

larger proj ect. Each experimental design had to account for the often different goals of the larger

proj ect. The results presented in this document are not weakened by this fact, but the door

remains open for experiments with more goal specific designs. Some suggestions for these

proj ects are presented in the following paragraphs and are intended to both direct and inspire.

More work is needed to specifically address any parameter impacts or other modeling

needs for sensor-based drip irrigation. From results obtained at the experiment site but not

addressed in this document, sensor-based irrigation should greatly enhance agricultural water

conservation. As such, monitoring and modeling these systems will become a need and may be

more complex than applying models developed for low frequency, timed irrigation. In our case,

modeling a sensor-based system was complicated by measurement errors resulting from

consistently low SMC. If in-situ probes are to be used for data collections beneath these systems,

additional calibration to low SMC may be necessary.

As was most evident beneath the sensor-based treatment if the WCR is to be used for

monitoring drip irrigation systems, experiments need to be conducted to determine the extent of

the fertigation impact on SMC measurements. Similar experiments could be replicated on

different soils or using different fertigation constituents. For these experiments, a lab setup

would likely prove superior.










As evident by replication in the final summary, the most important take home message that

impacted all the works documented here is the impact of measurement volumes on monitoring

drip systems. To properly calibrate the Vitel, or any monitoring device with a measurement

length less than the emitter spacing used on site, the benchmark measurements, be it gravimetric

samples or TDR, must be collected at the same normal distance and radial distance from the

emitter. The benchmark measurements should also have a similar measurement volume to the

probe being calibrated. Calibrations in a lab setting can easily eliminate this need, but would

likely struggle to account for other impacts inherent to intensive bed management systems, such

as soil structure and temperature. Concurrently, model selection should also consider whether the

measured data set consists of true point measurements or measurements averaged over several

emitters.

One question that loomed over this work from beginning to end was the influence of root

growth on hydraulic parameters. Hindered by the need to monitor distributions at different sites

within the field to find areas un-impacted and impacted by root growth, the results obtained in

our study could neither confirm nor deny root growth impacts. The need in this work to have two

monitoring sites was a result of the setup method required for such a large field, both

construction and planting. Though some discussion is provided in the appendix, a more specific

experiment should allow for one monitoring location and further isolate root growth effects. An

experimental design to address root effects on hydraulic parameters in intensive bed management

systems is detailed below.

Probes need to be installed and monitor distributions of interest for several days -

irrigation events prior to planting. An appropriate model such as H2D should then be calibrated

to the data set collected prior to planting. After fruiting, plants should be clipped near the surface









to eliminate as much transpiration as possible. Monitoring should continue for several days after

the plants are clipped, and the previously calibrated model could then be applied to the data set

collected after clipping. A simple forecast should be enough to test the root growth impact

hypothesis. Further analysis could involve a comparison of soil moisture retention curves

optimized or measured prior to planting and after clipping.

If a time dependent relationship between root growth and soil hydraulic parameter

modification is to be developed, several monitoring sites should be initiated at the same time.

Each site would again require data collected prior to planting for calibration and should be

assigned a different length of the growing season to allow plant growth. For example if three

sites are monitored, plants could be clipped at one site at 1/3, 1/2, and 2/3 the season. Each site

should continue to monitor distributions after clipping, with similar analysis used to determine

the relative impact seen throughout the season. A time dependent relationship between root

growth and hydraulic parameter modification would enhance the ability to model a season long

data set. Similar experiments could be replicated on different soils or beneath different crops.

The analysis could be repeated for soil transport parameters.

Another question raised that could no be addressed through the data collected in this study

is the impact of bed construction techniques on soil parameters. Different bed compaction levels

may be used for different crops, soils, or even from year to year at the same site. No work to date

has quantified impacts from different bed construction techniques. A simple experiment could be

designed to compare measured distributions beneath drip irrigation in beds of varying

compaction.

Though H2D was observed to be a powerful tool and quite applicable to drip systems in

this study, due to the amount of data needed to properly calibrate H2D, a simpler, analytical









model specifically designed for drip irrigation and intensive bed management systems would be

ideal. The model should account for all the unique aspects associated with intensive bed

management systems, while requiring minimal inputs such as soil type and emitter flow rate.

Such a model is currently under development at the University of Florida. The 3DMGAR model,

which will be fully described in a dissertation yet to be published by Leslie Gowdish, should

provide easy computations of SMC beneath drip irrigation; however, if solute transport is desired

3DMGAR needs to be coupled with another model or else, H2D is again required. To validate

3DMGAR, experiments similar to those documented here should be performed and replicated

across different soil types and different flow rates.

Finally for all future works addressed here or not, if the goal of collected data is the

eventual use in model calibration due to the symmetry often assumed in drip irrigation modeling,

a single drip line should be used for both irrigation and fertigation at the experiment site.









APPENDIX A
SELECT HYDRUS-2D INPUT FILES

Initial Calibration of 2DSC1.0

The following input files were from the 2DSC1.0 simulation used during the initial

calibration process in Chapter 3, where only Ks was included in the inverse optimization process.

The files are generally representative of all two-dimensional, semi-spherical simulations.

*** BLOCK I: ATMOSPHERIC INFORMATION **********************************
MaxAL (MaxAL = number of atmospheric data-records)
31
hCritS (max. allowed pressure head at the soil surface)

tAtm Prec rSoil rRoot hCritA rt ht
360 0 0 0 10000 0 0
480 0 0 0 10000 -0.200822 0
1800 0 0 0 10000 0 0
1920 0 0 0 10000 -0.200822 0
3240 0 0 0 10000 0 0
3360 0 0 0 10000 -0.200822 0
4680 0 0 0 10000 0 0
4800 0 0 0 10000 -0.200822 0
6120 0 0 0 10000 0 0
6240 0 0 0 10000 -0.200822 0
7560 0 0 0 10000 0 0
7680 0 0 0 10000 -0.200822 0
9000 0 0 0 10000 0 0
9120 0 0 0 10000 -0.200822 0
10440 0 0 0 10000 0 0
10560 0 0 0 10000 -0.200822 0
11880 0 0 0 10000 0 0
12000 0 0 0 10000 -0.200822 0
13320 0 0 0 10000 0 0
13440 0 0 0 10000 -0.200822 0
14760 0 0 0 10000 0 0
14880 0 0 0 10000 -0.200822 0
16200 0 0 0 10000 0 0
16320 0 0 0 10000 -0.200822 0
17640 0 0 0 10000 0 0
17760 0 0 0 10000 -0.200822 0
19080 0 0 0 10000 0 0
19200 0 0 0 10000 -0.200822 0
20520 0 0 0 10000 0 0
20640 0 0 0 10000 -(1200822 0










21000 0 0 0 10000 0 0
*** END OF INPUT FILE 'ATMOSPH.IN' *************************************

*** BLOCK ?: BOUNDARY INFORMATION

NumBP NObs SeepF FreeD DrainF qQWLF
29 3 f t f f
Node Number Array
12345678910
11 12 13 14 15 16 17 18 66 67
68 69 70 71 72 73 74 75 76
Width Array
0.0461842 0.0923672 0.092366 0.092366 0.0923677 0.0923675 0.0923662 0.0923666 0.092367
0.0923665
0.0923664 0.0923677 0.0923673 0.0923668 0.0923668 0.0923668 0.0923672 0.0461837 2.1875
4.66667
5.25 5.83333 6.41667 7 7.39583 7.33333 7 6.66667 3.25
Length of soil surface associated with transpiration

Ob servation nodes. Node(1,....NOb s)
121 122 123
*** End of input file 'BOUNDARY.IN' ******************************************

*** BLOCK A: BASIC INFORMATION *****************************************
Heading
Welcome to HYDRUS-2D
LUnit TUnit MUnit (indicated units are obligatory for all input data)
cm
mmn
mmol
Kat (0:horizontal plane, 1:axisymmetric vertical flow, 2:vertical plane)

Maxlt TolTh TolH InitH/W (max. number of iterations and tolerances)
200 0.0001 0.1 t
lWat IChem ISink Short Flux IScrn Atmln ITemp lWTDep IEquil IExtGen IIny
tf ff tt t ff t t t
*** BLOCK B: MATERIAL INFORMATION **************************************
NMat NLay hTab1 hTabN
11 00
Model Hysteresis
00O
thr ths Alfa n Ks 1
0.061 0.393 0.0249 2.286 0.8 0.5
*** BLOCK C: TIME INFORMATION *****************************************
dt dtMin dtMax DMul DMul2 ItMin ItMax MPL
0.5 0.0001 15 1.3 0.7 3 7 10









tInit tMax
0 21000
TPrint(1), TPrint(2),..., TPrint(MPL)
2100 4200 6300 8400 10500 12600
14700 16800 18900 21000
*** END OF INPUT FILE 'SELECTOR.INT' ************************************

Welcome to HYDRUS-FIT
Parameter Estimation of Soil Hydraulic Properties
NOBB MIT iWeight
2904 20 0
lWatF IChemF NMat ITempF
t f 1f
Model Hyster Aniz
0 0f
thr ths Alfa n Ks1
0.061 0.393 0.0249 2.286 0.8 0.5
0 0 001 0
0 0 0 0O 0.4 0O
0 0 00 2 0
HO(N) FOS ITYPE(N) POS WTS
5760 0.119884 2 3 1
5775 0. 12061 2 3 1
5790 0. 12061 2 3 1
5805 0.119158 2 3 1
5820 0.118433 2 3 1
5835 0.119884 2 3 1
5850 0.118433 2 3 1
5865 0.116981 2 3 1
5880 0.117707 2 3 1
5895 0.116981 2 3 1
5910 0.117707 2 3 1
5925 0.116981 2 3 1
5940 0.116255 2 3 1
5955 0.116255 2 3 1
5970 0.11553 2 3 1
5985 0.116255 2 3 1
6000 0.114804 2 3 1

[Remainder of file not included to save space]

end*** END OF UMPUT FTLE 'FYTIN'**********************************"




































Figure A-1. Boundary conditions for 2DSC1.0 simulation. Pink is variable flux and represents
the water entry boundary. Red is free drainage. White is no flux.




































Figure A-2. Numerical node structure for 2DSC 1.0 simulation. Red dots represent monitoring
locations. Location 1 corresponds to C8, location 2 to C23, and location 3 to E23
from the field.

Initial Calibration of 3DSC1.0

The following input files were from the 3DSC1.0 simulation used during the initial

calibration process in Chapter 3, where only Ks was included in the inverse optimization process.

The files are generally representative of all three-dimensional, semi-spherical simulations.

*** BLOCK I: ATMOSPHERIC INFORMATION **********************************
MaxAL (MaxAL = number of atmospheric data-records)
31
hCritS (max. allowed pressure head at the soil surface)

tAtm Prec rSoil rRoot hCritA rt ht
360 0 0 0 10000 0 0
480 0 0 0 10000 -2.00822 0
1800 0 0 0 10000 0 0
1920 0 0 0 10000 -2.00822 0
3240 0 0 0 10000 0 0
3360 0 0 0 10000 -2.00822 0









4680 0 0 0 10000 0 0
4800 0 0 0 10000 -2.00822 0
6120 0 0 0 10000 0 0
6240 0 0 0 10000 -2.00822 0
7560 0 0 0 10000 0 0
7680 0 0 0 10000 -2.00822 0
9000 0 0 0 10000 0 0
9120 0 0 0 10000 -2.00822 0
10440 0 0 0 10000 0 0
10560 0 0 0 10000 -11.00822 0
11880 0 0 0 10000 0 0
12000 0 0 0 10000 -2.00822 0
13320 0 0 0 10000 0 0
13440 0 0 0 10000 -2.00822 0
14760 0 0 0 10000 0 0
14880 0 0 0 10000 -2.00822 0
16200 0 0 0 10000 0 0
16320 0 0 0 10000 -11.00822 0
17640 0 0 0 10000 0 0
17760 0 0 0 10000 -2.00822 0
19080 0 0 0 10000 0 0
19200 0 0 0 10000 -2.00822 0
20520 0 0 0 10000 0 0
20640 0 0 0 10000 -2.00822 0
21000 0 0 0 10000 0 0
*** END OF INPUT FILE 'ATMOSPH.IN' *************************************

*** BLOCK ?: BOUNDARY INFORMATION

NumBP NObs SeepF FreeD DrainF qQWLF
35 3 f t f f
Node Number Array
1 23 45 67 8 9 0
11 12 13 14 15 16 17 18 66 67
68 69 70 71 72 73 74 75 76 77
78 79 80 81 82
Width Array
0.289557 0.576635 0.569237 0.556991 0.540003 0.518396 0.49236 0.462133 0.427963
0.390138
0.348986 0.304861 0.25813 0.209196 0.158479 0.10641 0.0534333 0.0133869 20.0434 133 979
314.281 552.308 854.474 1227.19 1570.7 1612.64 1539.33 1466.03 1392.73 1319.43
1246.13 1172.83 1099.53 1026.22 494.786
Length of soil surface associated with transpiration

Ob servation nodes. Node(1,....NOb s)
121 122 123










*** End of input file 'BOUNDARY.IN' ******************************************

*** BLOCK A: BASIC INFORMATION *****************************************
Heading
Welcome to HYDRUS-2D
LUnit TUnit MUnit (indicated units are obligatory for all input data)
cm
mmn
mmol
Kat (0:horizontal plane, 1:axisymmetric vertical flow, 2:vertical plane)

Maxlt TolTh TolH InitH/W (max. number of iterations and tolerances)
200 0.001 0.1 t
lWat IChem ISink Short Flux IScrn Atmln ITemp lWTDep IEquil IExtGen IIny
tf ff tt t ff t t t
*** BLOCK B: MATERIAL INFORMATION **************************************
NMat NLay hTab1 hTabN
11 00
Model Hysteresis
00O
thr ths Alfa n Ks1
0.061 0.393 0.0249 2.286 0.88 0.5
*** BLOCK C: TIME INFORMATION *****************************************
dt dtMin dtMax DMul DMul2 ItMin ItMax MPL
1 0.0001 15 1.3 0.7 3 7 100
tInit tMax
0 21000
TPrint(1), TPrint(2),..., TPrint(MPL)
210 420 630 840 1050 1260
1470 1680 1890 2100 2310 2520
2730 2940 3150 3360 3570 3780
3990 4200 4410 4620 4830 5040
5250 5460 5670 5880 6090 6300
6510 6720 6930 7140 7350 7560
7770 7980 8190 8400 8610 8820
9030 9240 9450 9660 9870 10080
10290 10500 10710 10920 11130 11340
11550 11760 11970 12180 12390 12600
12810 13020 13230 13440 13650 13860
14070 14280 14490 14700 14910 15120
15330 15540 15750 15960 16170 16380
16590 16800 17010 17220 17430 17640
17850 18060 18270 18480 18690 18900
19110 19320 19530 19740 19950 20160
20370 20580 20790 21000
*** END OF INPUT FILE 'SELECTOR.IN' ************************************











Welcome to HYDRUS-FIT
Parameter Estimation of Soil Hydraulic Properties
NOBB MIT iWeight
2904 20 0
lWatF IChemF NMat ITempF
t f 1f
Model Hyster Aniz
0 0f
thr ths Alfa n Ks 1
0.061 0.393 0.0249 2.286 0.26 0.5
0 0 001 0
0 0 0 0 0.1 0
0 0 0 0O 0.6 0O
HO(N) FOS ITYPE(N) POS WTS
5760 0.119884 2 3 1
5775 0. 12061 2 3 1
5790 0. 12061 2 3 1
5805 0.119158 2 3 1
5820 0.118433 2 3 1
5835 0.119884 2 3 1
5850 0.118433 2 3 1
5865 0.116981 2 3 1
5880 0.117707 2 3 1
5895 0.116981 2 3 1
5910 0.117707 2 3 1
5925 0.116981 2 3 1
5940 0.116255 2 3 1
5955 0.116255 2 3 1
5970 0.11553 2 3 1
5985 0.116255 2 3 1
6000 0.114804 2 3 1

[Remainder of file not included to save space]

end***F20D OF UMPUT FILE 'FYTIN'**********************************"











~


Figure A-3. Boundary conditions for 3DSC1.0 simulation. Pink is variable flux and represents
the water entry boundary. Red is free drainage. White is no flux





































Figure A-4. Numerical node structure for 3DSC1.0 simulation. Red dots represent monitoring
locations. Location 1 corresponds to C8, location 2 to C23, and location 3 to E23
from the field.

Full Calibration of 2DSC1.0

The following input files were from the 2DSC1.0 simulation used during the full

calibration process in Chapter 3, where all soil hydraulic parameters were included in the inverse

optimization process. Boundary conditions and the node distribution were similar to Figure A-1

and A-2. Atmospheric, boundary, basic, material, and time information are identical to initial

calibration of 2D SC 1.0.

Welcome to HYDRUS-FIT
Parameter Estimation of Soil Hydraulic Properties
NOBB MIT iWeight
2904 20 0
lWatF IChemF NMat ITempF
tflf
Model Hyster Aniz









0 f
ths Alfa n Ks 1
0.393 0.04 2.286 0.7 0.5


0
thr
0.061


1 1
0.01 0.32
0.15 0.46
HO(N)
5760
5775
5790
5805
5820
5835
5850
5865
5880
5895
5910
5925
5940
5955
5970
5985
6000


1 11 0
9 0.0158 1.586 0.1
S0.044 4.57 0.8
FOS ITYPE(N) POS
0.119884 2 3 1
0.12061 2 3 1
0.12061 2 3 1
0.119158 2 3 1
0.118433 2 3 1
0.119884 2 3 1
0.118433 2 3 1
0.116981 2 3 1
0.117707 2 3 1
0.116981 2 3 1
0.117707 2 3 1
0.116981 2 3 1
0.116255 2 3 1
0.116255 2 3 1
0.11553 2 3 1
0.116255 2 3 1
0.114804 2 3 1


0
0
WTS


[Remainder of file not included to save space]

end***F20D OF UMPUT FILE 'FYTIN'**********************************"

Full Calibration of 3DSC1.0

The following input files were from the 3DSC1.0 simulation used during the full

calibration process in Chapter 3, where all soil hydraulic parameters were included in the inverse

optimization process. Boundary conditions and the node distribution were similar to Figure A-3

and A-4. Atmospheric, boundary, basic, material, and time information are identical to initial

calibration of 3D SC 1.0.

Welcome to HYDRUS-FIT
Parameter Estimation of Soil Hydraulic Properties
NOBB MIT iWeight
2904 20 0
lWatF IChemF NMat ITempF
t f 1f










Model Hyster Aniz
0 0f
thr ths Alfa n Ks 1
0.061 0.393 0.0249 2.286 0.26 0.5
1 11 11 0
0.01 0.329 0.0158 1.586 0.1 0
0.15 0.46 0.044 4.57 0.8 0
HO(N) FOS ITYPE(N) POS WTS
5760 0.119884 2 3 1
5775 0. 12061 2 3 1
5790 0. 12061 2 3 1
5805 0.119158 2 3 1
5820 0.118433 2 3 1
5835 0.119884 2 3 1
5850 0.118433 2 3 1
5865 0.116981 2 3 1
5880 0.117707 2 3 1
5895 0.116981 2 3 1
5910 0.117707 2 3 1
5925 0.116981 2 3 1
5940 0.116255 2 3 1
5955 0.116255 2 3 1
5970 0.11553 2 3 1
5985 0.116255 2 3 1
6000 0.114804 2 3 1

[Remainder of file not included to save space]

end***F20D OF UMPUT FILE 'FYTIN'**********************************"

Calibration Bounded by Carsel and Parrish Distributions

The following input files were from the Carsel and Parrish soil hydraulic parameter

calibration in Chapter 4. Boundary conditions and the node distribution were similar to Figure A-

1 and A-2.

*** BIACK I: ENIOSPIDERIC ]NFRMFAlhlTIOR **********************************
MaxAL (MaxAL = number of atmospheric data-records)
31
hCritS (max. allowed pressure head at the soil surface)

tAtm Prec rSoil rRoot hCritA rt ht
360 0 0 0 10000 0 0
480 0 0 0 10000 -0.401644 0
1800 0 0 0 10000 0 0









1920 0 0 0 10000 -01401644 0
3240 0 0 0 10000 0 0
3360 0 0 0 10000 -01401644 0
4680 0 0 0 10000 0 0
4800 0 0 0 10000 -01401644 0
6120 0 0 0 10000 0 0
6240 0 0 0 10000 -01401644 0
7560 0 0 0 10000 0 0
7680 0 0 0 10000 -01401644 0
9000 0 0 0 10000 0 0
9120 0 0 0 10000 -01401644 0
10440 0 0 0 10000 0 0
10560 0 0 0 10000 -01401644 0
11880 0 0 0 10000 0 0
12000 0 0 0 10000 -01401644 0
13320 0 0 0 10000 0 0
13440 0 0 0 10000 -01401644 0
14760 0 0 0 10000 0 0
14880 0 0 0 10000 -01401644 0
16200 0 0 0 10000 0 0
16320 0 0 0 10000 -01401644 0
17640 0 0 0 10000 0 0
17760 0 0 0 10000 -01401644 0
19080 0 0 0 10000 0 0
19200 0 0 0 10000 -01401644 0
20520 0 0 0 10000 0 0
20640 0 0 0 10000 -01401644 0
21000 0 0 0 10000 0 0
***FEND OF U9PUT FILE 'KENOSPH.R4'*************************************

*** BLOCK ?: BOUNDARY INFORMATION

NumBP NObs SeepF FreeD DrainF qQWLF
20 3 f t f f
Node Number Array
1 23 45 67 8 9 3
64 65 66 67 68 69 70 71 72 73
Width Array
0.0490088 0.098017 0.0980174 0.0980175 0.0980161 0.0980171 0.0980174 0.0980169
0.0490087 1.66667
3.83333 4.83333 5.83333 6.83333 7.83333 8.45238 8.28572 7.71428 7.14285 3.42857
Length of soil surface associated with transpiration

Ob servation nodes. Node(1,....NOb s)
121 122 123
*** End of input file 'BOUUTDAUY.IN'******************************************











*** BLOCK A: BASIC INFORMATION *****************************************
Heading
Welcome to HYDRUS-2D
LUnit TUnit MUnit (indicated units are obligatory for all input data)
cm
mmn
mmol
Kat (0:horizontal plane, 1:axisymmetric vertical flow, 2:vertical plane)

Maxlt TolTh TolH InitH/W (max. number of iterations and tolerances)
200 0.001 0.1 t
lWat IChem ISink Short Flux IScrn Atmln ITemp lWTDep IEquil IExtGen IIny
tf ff tt t ff t t t
*** BLOCK B: MATERIAL INFORMATION **************************************
NMat NLay hTab1 hTabN
11 00
Model Hysteresis
00O
thr ths Alfa n Ks1
0.04 0.4 0.03 2.3804 0.4 0.5
*** BLOCK C: TIME INFORMATION *****************************************
dt dtMin dtMax DMul DMul2 ItMin ItMax MPL
0.5 0.0001 15 1.3 0.7 3 7 10
tInit tMax
0 21000
TPrint(1), TPrint(2),..., TPrint(MPL)
2100 4200 6300 8400 10500 12600
14700 16800 18900 21000
*** END OF INPUT FILE 'SELECTOR.IN' ************************************

Welcome to HYDRUS-FIT
Parameter Estimation of Soil Hydraulic Properties
NOBB MIT iWeight
1731 50 0
lWatF IChemF NMat ITempF
tflf
Model Hyster Aniz
00f
thr ths Alfa n Ks1
0.04 0.4 0.03 2.3804 0.4 0.5
1 11 11 0
0.025 0.31 0.087 2.1 0 0
0.065 0.55 0.203 3.26 1.015 0
HO(N) FOS ITYPE(N) POS WTS
5760 0.119884 2 3 1









5775 0.119884 2 3 1
5790 0.119158 2 3 1
5805 0.119158 2 3 1
5820 0.119158 2 3 1
5835 0.118433 2 3 1
5850 0.118433 2 3 1
5865 0.118433 2 3 1
5880 0.117707 2 3 1
5895 0.117707 2 3 1
5910 0.117707 2 3 1
5925 0.117707 2 3 1
5940 0.116981 2 3 1
5955 0.116981 2 3 1
5970 0.116255 2 3 1
5985 0.116255 2 3 1
6000 0.116255 2 3 1

[Remainder of file not included to save space]

end***F20D OF UMPUT FILE 'FYTIN'**********************************"

Calibration Bounded by ROSETTA Distributions

The following input files were from the ROSETTA soil hydraulic parameter calibration in

Chapter 4. Boundary conditions and the node distribution were similar to Figure A-1 and A-2.

Atmospheric, boundary, basic, material, and time information are identical to the calibration

bounded by Carsel and Pan-ish (1988) distributions.

Welcome to HYDRUS-FIT
Parameter Estimation of Soil Hydraulic Properties
NOBB MIT iWeight
1731 50 0
lWatF IChemF NMat ITempF
t f 1f
Model Hyster Aniz
0 0f
thr ths Alfa n Ks 1
0.04 0.4 0.03 2.3804 0.4 0.5
1 11 11 0
0 0.265 0.011 1.387 0.029 0
0.111 0.485 0.111 7.277 6.755 0
HO(N) FOS ITYPE(N) POS WTS
5760 0.119884 2 3 1
5775 0.119884 2 3 1









5790 0.119158 2 3 1
5805 0.119158 2 3 1
5820 0.119158 2 3 1
5835 0.118433 2 3 1
5850 0.118433 2 3 1
5865 0.118433 2 3 1
5880 0.117707 2 3 1
5895 0.117707 2 3 1
5910 0.117707 2 3 1
5925 0.117707 2 3 1
5940 0.116981 2 3 1
5955 0.116981 2 3 1
5970 0.116255 2 3 1
5985 0.116255 2 3 1
6000 0.116255 2 3 1

[Remainder of file not included to save space]

end***F20D OF UMPUT FILE 'FYTIN'**********************************"

Calibration Bounded by Measured Distributions

The following input files were from the measured soil hydraulic parameter calibration in

Chapter 4. Boundary conditions and the node distribution were similar to Figure A-1 and A-2.

Atmospheric, boundary, basic, material, and time information are identical to the calibration

bounded by Carsel and Parrish (1988) distributions.

Welcome to HYDRUS-FIT
Parameter Estimation of Soil Hydraulic Properties
NOBB MIT iWeight
1731 50 0
lWatF IChemF NMat ITempF
t f 1f
Model Hyster Aniz
0 0f
thr ths Alfa n Ks 1
0.04 0.4 0.03 2.3804 0.4 0.5
1 11 11 0
0 0.311 0.009 0.733 0.1 0
0.147 0.478 0.043 4.605 2 0
HO(N) FOS ITYPE(N) POS WTS
5760 0.119884 2 3 1
5775 0.119884 2 3 1
5790 0.119158 2 3 1









5805
5820
5835
5850
5865
5880
5895
5910
5925
5940
5955
5970
5985
6000


0.119158
0.119158
0.118433
0.118433
0.118433
0.117707
0.117707
0.117707
0.117707
0.116981
0.116981
0.116255
0.116255
0.116255


[Remainder of file not included to save space]

end***F20D OF UMPUT FILE 'FYTIN'**********************************"

Calibration bounded by Vanderborght and Vereecken distributions

The following input files were from the soil transport parameter calibration in Chapter 4.

Boundary conditions and the node distribution were similar to Figure A-1 and A-2.

*** BIACK I: ENIOSPIDERIC ]NFRMFAlhlTIOR **********************************
MaxAL (MaxAL = number of atmospheric data-records)


hCritS
0


(max. allowed pressure head at the soil surface)


tAtm Prec rSoil rRoot hCritA
c~ralue3


rt ht c~raluel1 c~ralue2


360
480
1080
1800
1920
2520
3240
3360
3960
4680
4800
5400
6120
6240
6630


0 0
0 0.00036
0 Os.00036
0 0
0 0.00036
0 Os.00036
0 0
0 0.00036
0 Os.00036
0 0
0 0.00036
0 Os.00036
0 0
0 0.00036
0 Os.00036


10000 0 0
10000 -0.401644
10000 0
10000 0 0
10000 -0.401644
10000 0
10000 0 0
10000 -0.401644
10000 0
10000 0 0
10000 -0.401644
10000 0
10000 0 0
10000 -0.401644
10000 0


0 0 0 0
0 0 0
0 0 0
0 0 0 0
0 0 0
0 0 0
0 0 0 0
0 0 0
0 0 0
0 0 0 0
0 0 0
0 0 0
0 0 0 0










6640 0 0 0.00036 10000 -0.401644 0 0 13.78 0
6840 0 0 O.00036 10000 0 0 0 0 0
7560 0 0 0 10000 0 0 0 0 0
7680 0 0 0.00036 10000 -0.401644 0 0 0 0
8280 0 0 O.00036 10000 0 0 0 0 0
9000 0 0 0 10000 0 0 0 0 0
9120 0 0 0.00036 10000 -0.401644 0 0 0 0
9720 0 0 O.00036 10000 0 0 0 0 0
10440 0 0 0 10000 0 0 0 0 0
10560 0 0 0.00036 10000 -01401644 0 0 0 0
11160 0 0 0.00036 10000 0 0 0 0 0
11880 0 0 0 10000 0 0 0 0 0
12000 0 0 0.00036 10000 -01401644 0 0 0 0
12600 0 0 0.00036 10000 0 0 0 0 0
13000 0 0 0 10000 0 0 0 0 0
*** END OF INPUT FILE 'ATMOSPH.IN' *************************************

*** BLOCK ?: BOUNDARY INFORMATION

NumBP NObs SeepF FreeD DrainF qQWLF
24 3 f t f f
Node Number Array
1 23 45 6 7 89 3
64 65 66 67 68 69 70 71 72 73
86 87 88 89
Width Array
0.0490088 0.098017 0.0980174 0.0980175 0.0980161 0.0980171 0.0980174 0.0980169
0.0490087 1.66667
3.83333 4.83333 5.83333 6.83333 7.83333 8.45238 8.28572 7.71428 7.14285 3.42857
0.955681 1.8125 1.61477 0.757954
Length of soil surface associatexiwith transpiration
5.14091
Ob servation nodes. Node(1,....NOb s)
121 122 123
*** BLOCK ?: Solute transport boundary conditions *****************************
KodCB(1),KodCB(2), .....,KodCB(NumBP)
-2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1
*** End of input file 'BOUUTDAUY.IN'******************************************

*** BIDCK A:BASIC bPOFORMATICR4*****************************************
Heading
Welcome to HYDRUS-2D
LUnit TUnit MUnit (indicated units are obligatory for all input data)
cm
mmn










mg
Kat (0:horizontal plane, 1:axisymmetric vertical flow, 2:vertical plane)

Maxlt TolTh TolH InitH/W (max. number of iterations and tolerances)
200 0.001 0.1 t
lWat IChem ISink Short Flux IScrn Atmln ITemp lWTDep IEquil IExtGen IIny
tt tf tt t ff t t t
*** BLOCK B: MATERIAL INFORMATION **************************************
NMat NLay hTab1 hTabN
11 00
Model Hysteresis
00O
thr ths Alfa n Ks1
0.065 0.31 0.203 3.0809 0.077401 0.5
*** BLOCK C: TIME INFORMATION *****************************************
dt dtMin dtMax DMul DMul2 ItMin ItMax MPL


0.5 0.0001 15 1.3 0.7
tInit tMax
0 13000
TPrint(1), TPrint(2),..., TPrint(MPL)
130 260 390 520
910 1040 1170 1300
1690 1820 1950 2080
2470 2600 2730 2860
3250 3380 3510 3640
4030 4160 4290 4420
4810 4940 5070 5200
5590 5720 5850 5980
6370 6500 6630 6760
7150 7280 7410 7540
7930 8060 8190 8320
8710 8840 8970 9100
9490 9620 9750 9880
10270 10400 10530 10660
11050 11180 11310 11440
11830 11960 12090 12220
12610 12740 12870 13000


3 7 100


650 7
1430
2210
2990
3770
4550
5330
6110
6890
7670
8450
9230
10010
10790
11570
12350


80
1560
2340
3120
3900
4680
5460
6240
7020
7800
8580
9360
10140
10920
11700
12480


*** BLOCK G: SOLUTE TRANSPORT INFORMATION

Epsi 1UpW 1ArtD ITDep cTolA cTolR MaxltC PeCr Nu.of Solutes Tortuosity
0.5 f ff 0 0 1 2 1 t
Bulk.d. DisperL. DisperT Frac ThImob (1..NMat)
1.5 0.5 0.1 1 0
DifW DifG n-th solute
00O









Ks Nu Beta Henry SnkL 1 SnkS 1 SnkG1 SnkL 1' SnkS 1'
SnkGl' SnkLO SnkSO SnkGO Alfa
0 0 1 0 0 0 0 0 0 0 0 0

cTop cBot
0 0 0 0 O 30 0 0 0 0O
tPul se
13000
*** BLOCK G: ROOT WATER UPTAKE INFORMATION

Model ( Feddes, S shape)

h50 P3
-800 3
Solute Reduction

*** END OF INPUT FILE 'SELECTOR.INT' ************************************

Welcome to HYDRUS-FIT
Parameter Estimation of Soil Hydraulic Properties
NOBB MIT iWeight
962 20 0
lWatF IChemF NMat ITempF
ftlf
NS

Bulk.d. DisperL. Frac ThImob DifW DifG Ks Nu Beta Henry SnkL 1
SnkS 1 SnkG1 SnkL1' SnkS1' SnkGl' SnkLO SnkSO SnkGO Alfa
1.5 1.2 0.01 1 0 0.001 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 O
0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 O
0 0 0 0 0 0 O
0 0.01 0.01 0 0 0 0 0 0 0 0 0 0 0 0 O O
0 0 0 0 0 0 O
0 5 5 0 0 0 0 0 0 0 0 0 0 0 0 O
0 0 0 0 0 0 O
HO(N) FOS ITYPE(N) POS WTS
5760 0.180045 4 3 1
5775 0.180318 4 3 1
5790 0.174323 4 3 1
5805 0.177593 4 3 1
5820 0.178138 4 3 1
5835 0.177048 4 3 1
5850 0. 17732 4 3 1
5865 0.185223 4 3 1
5880 0. 17405 4 3 1










5895 0.186312 4 3 1
5910 0.182225 4 3 1
5925 0. 18277 4 3 1
5940 0.184678 4 3 1
5955 0.177865 4 3 1
5970 0.185495 4 3 1
5985 0.178683 4 3 1
6000 0. 18931 4 3 1

[Remainder of file not included to save space]

end***F20D OF UMPUT FILE 'FYTIN'**********************************"









APPENDIX B
POSSIBLE IN-SEASON IMPACTS ON CALIBRATION

Introduction

As previously discussed in this document, the H2D program has become a popular tool for

modeling drip irrigation systems due to its two-dimensional capabilities. While the model has

been validated across many sites, commonly only a few irrigation events are chosen or reported

in the calibration and validation process (Chapter 3 and Chapter 4). The question remains

whether soil hydraulic properties beneath these intensive management systems are truly static

throughout the growing season.

Notably no study to date has accounted for the impact soil structure modifications, such as

root development, on numerical simulations of drip irrigation (Gardenas et al. 2005). If drip

systems undergo significant hydraulic modification from in-season impacts, it is essential to

quantify these shifts if season long simulations are to be successful.

The most likely catalyst of in-season hydraulic parameter modification is root growth.

Previous studies have focused on root distributions under drip irrigated crops (Scholberg, 1996),

but to date no work has been reported specifically focusing on the soil hydraulic parameter

impact of root growth within intensive management systems. Comparing the results of these

studies, independent of crop selection, root development in drip systems is concentrated around

the emitter.

Mmolawa and Or (2003) reported H2D to predict SMC distributions well when no plants

were present, but to consistently over predict water extraction from roots when a crop was

present; moreover, while H2D matched the total soil profile water distribution fairly well, most

of the error was located near the drip emitter. Errors observed in this area are likely either the









result of poor root uptake simulation or an inability to account for root zone modification of soil

hydraulic parameters.

Outside of drip irrigation, Whalley et al. (2004) analyzed the change in physical soil

properties and the SMRC differences between rhizosphere soil and bulk soil, with bulk soil

defined as soil located over 10 mm from the roots. The study showed SMRCs to remain

relatively constant before and after root growth. Similarly, Whalley et al. (2005) reported no

significant shift in SMRCs, but did find a noticeable increase in macro-pores in the rhizosphere

soil. The results are comparable with Gish et al. (1998), where dye tracers were used to visually

observe the water movement through cropped root system and it was concluded that roots are a

maj or contributor to preferential flow paths.

With roots concentrated around the emitter under drip irrigated crops, it was hypothesized

that the concentrated root growth creates a highly dynamic zone of soil hydraulic properties

around the emitter that in-turn requires time specific data for calibration. The obj ective of this

study was to examine any impacts of root growth on soil hydraulic parameters by using H2D to

determine representative sets of hydraulic parameters for different seasonal periods by inverse

optimization.

Results

All results observed during this study were influenced by the two site design of the

experiment. Experiment 2 and Experiment 4 were performed at different locations within the

same field and homogeneity of soil properties was assumed; however, after reviewing the results

of this study it is clear at the emitter scale the field was not homogeneous thus voiding all

observation of root growth impact. Interestingly, the heterogeneity was not observed at the C8

location, possibly due to the tillage method thoroughly mixing the top most soil layer.














025
No Crop Data











10/13 10/14 10/15 10/16 10/17 10/18
DATE
E8 C8 E23 C23


kliA


7/8 7/9 7/10 7/11 7/12 7/13
DATE
E8 C8 E23 C23


Figure B-1. Averaged data used in calibrations. Representative five days displayed for each. No

Crop Data was taken from Experiment 2 and End of Season Data was taken from

Experiment 4. SMC is soil moisture content (cm3 Cm-3.


025
End of Season Data














C8


C23


0 20


0 15


0 10


nnR


r\ r- J~-
rr h


C8


0 25


0 20


S0 15


0 10


005


0 00 1 00 2 00 3 00 4 00 5 00 0 00 1 00 2 00 3 00 4 00 5 00 0 00 1 00 2 00 3 00 4 00 5 00


DAY

NP EOS


DAY

NP EOS


- NP EOS


Figure B-2. Location by location comparison for measured soil moisture content (cm3 Cm-3) (SMC) from each experiment. NP is

Experiment 2 and EOS is Experiment 4.


O 25


0 20



S0 15


0 10



005


0 25


0 20



S0 15


0 10



005


~--~s,


S0 15


0 10



005


2 22 24 26
DAY OF SIMULATION


28 3


22 24 26
DAY OF SIMULATION


22 24 26
DAY OF SIMULATION


Figure B-3. Results of Experiment 2 calibration (line) and measured data during Experiment 4 (data points). SMC is soil moisture
content (cm3 Cm-3









Summary

More work is needed to verify the existence or absence of in-season root impacts on soil

hydraulic parameters within bedded systems. The drastic difference between the two monitored

SMC distributions inhibited any efforts of isolating in-season changes to saturated hydraulic

conductivity. Human impacts such as staking, tightness of bed construction, or the use of a

tractor-pulled rolling hole-punch during planting could also be the cause of the heterogeneity

effects observed in this study. If these man-made impacts are the culprit, results from soil

sampling performed prior to these seasonal modifications would be rendered useless. A study

that maintains one monitoring location after bed construction, but prior to seasonal preparations

and through the growing season is ideal.










LIST OF REFERENCES


Abbasi, F., D. Jacques, J. Simunek, J. Feyen, M.Th. Van Genuchten. 2003. Inverse estimation of
soil hydraulic and solute transport parameters from transient Hield experiments:
Heterogeneous soil. Transactions of the ASAE 46, 1097-1111.

Ajdary, K., D.K. Singh, A.K. Singh, M. Khanna. 2007. Modelling of nitrogen leaching from
experimental onion Hield under drip fertigation. Agricultural and Water Management 89,
15-28.

Allen R.G., L.S. Pereira, D. Raes, M. Smith. 1998. Crop evapotranspiration. Guidelines for
computing crop water requirements. FAO Irrigation and Drainage Paper No. 56, Rome.

Al-Yahyai, R., B. Schaffer, F.S. Davies, R. Munoz-Carpena. 2006. Characterization of soil-water
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BIOGRAPHICAL SKETCH

Born in Tallahasse, Florida on July 4th, 1982, Jason Icerman started his academic career at

Timberlane Preschool. From there, he attended Gilchrist Elementary, Desoto Trail Elementary,

and Augusta Raa Middle School before finishing his grade school education at Maclay School.

Staying as involved in athletics as natural ability would allow, Jason also managed to achieve

high marks in the classroom passing seven AP examinations. In August 2000, he enrolled at the

University of Florida as an electrical engineering maj or. After trying his hand at pre-law, pre-

med, and mechanical engineering, Jason settled on land and water resource engineering and

graduated summa cum laude with a Bachelor of Science degree in December 2004. It was at this

time that he accepted an offer to study under Dr. Michael Dukes and pursue a Master of

Engineering degree.





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1 APPROACHES FOR TWO-DIMENSIO NAL MONITORING AND NUMERICAL MODELING OF DRIP SYSTEMS By JASON T. ICERMAN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2007

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2 Jason T. Icerman

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3 To my parents, Drs. Joe and Rhoda Icerman.

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4 ACKNOWLEDGMENTS The only appropriate way to begi n a list of those who have help ed me to this point is by thanking those who helped me ente r this discipline. For giving a lost undergraduate a chance to find his direction and never being short on time to listen, I thank Dr. James Leary. Thanks are also extended to Dr. Wendy Graham for allowing an inquisitive young engineer a chance to get his hands dirty in the field. For their assistance with my research over the past few years, both in the field and out, I thank Danny Burch, Stacia Davis, Kristen Femmi nella, Paul Lane, La rry Miller, Jonathan Schroder, Mary Shedd, Hannah Snyder, and especi ally Lincoln Zotarelli. Lincoln while your advice occasionally requires translation, it has proved invaluable time and again. Special thanks go to Dr. Michael Dukes fo r reasons too numerous for listing here. You have allowed me to study as both an undergradu ate and graduate student in my own manner, which anyone reading this document surely kno ws to be unique. Also Dr. Rafael MuozCarpena deserves thanks for answering my late-n ight emails and helping me decipher the endless world of vadose zone modeling. Finally as this document is dedicated to them, h earty thanks go to my parents. I thank them for the encouragement. I thank them for the unyiel ding support. And I thank them for the greatest gift I have ever received: their love of learning.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........8 LIST OF FIGURES................................................................................................................ .........9 ABSTRACT....................................................................................................................... ............11 CHAPTER 1 RESEARCH BACKGROUND..............................................................................................13 Rationale...................................................................................................................... ...........13 Vegetable Production in Florida......................................................................................13 Drip Irrigation................................................................................................................ ..14 Drip Irrigation Modeling.................................................................................................15 Objectives..................................................................................................................... ..........17 2 COMPARISON OF IN-SITU DIELECTRIC PROBE PERFORMANCE IN A RAISED VEGETABLE BED................................................................................................................18 Introduction................................................................................................................... ..........18 Materials and Methods.......................................................................................................... .21 Measurement Methods....................................................................................................21 Experiment 1: 2005 In-Season........................................................................................24 Experiment 2: Non-Planted.............................................................................................26 Experiment 3: 2006 In-Season........................................................................................26 Equations Used in Analysis.............................................................................................27 Results and Discussion......................................................................................................... ..28 Experiment 1: 2005 In-Season........................................................................................28 Water content reflectometer precision.....................................................................28 Soil sample comparisons..........................................................................................30 Experiment 2: Non-Planted.............................................................................................32 Vitel precision..........................................................................................................32 Probe to probe comparison.......................................................................................32 Experiment 3: 2006 In-Season........................................................................................33 Probe to probe comparison.......................................................................................34 Soil sample comparisons..........................................................................................34 Summary and Conclusions.....................................................................................................35 3 WATER ENTRY BOUNDARY CONDITI ON IMPACTS ON THE CALIBRATION OF HYDRUS-2D TO A SURFAC E DRIP IRRIGATION SYSTEM...................................57 Introduction................................................................................................................... ..........57

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6 Materials and Methods.......................................................................................................... .60 Field Experiment.............................................................................................................60 Model Description...........................................................................................................61 Water Entry Boundary Condition....................................................................................62 Additional Boundary and Initial Conditions...................................................................64 Calibration and Optimization Procedure.........................................................................65 Prediction Evaluation......................................................................................................66 Results and Discussion......................................................................................................... ..67 Field Results.................................................................................................................. ..67 Initial Calibration............................................................................................................ .68 Full Calibration............................................................................................................... .70 Summary and Conclusions.....................................................................................................72 4 UNCERTAINTY IMPACTS ON NUMERICAL MODELING OF FERTIGATION..........83 Introduction................................................................................................................... ..........83 Materials and Methods.......................................................................................................... .85 Measurement Methods....................................................................................................85 Experimental Site............................................................................................................87 Experiment 4: 2006 Post-Season.....................................................................................88 Model Description...........................................................................................................88 Initial and Boundary Conditions.....................................................................................89 Calibration and Optimization Procedure.........................................................................92 Prediction Evaluation......................................................................................................93 Results and Discussion......................................................................................................... ..95 Field Results.................................................................................................................. ..95 Soil Hydraulic Parameter Calibration.............................................................................96 Soil Transport Parameter Calibration..............................................................................98 Validation Simulations..................................................................................................100 Summary and Conclusions...................................................................................................101 5 RESEARCH SUMMARY AND FUTURE WORK............................................................111 Research Summary...............................................................................................................111 Future Work.................................................................................................................... ......113 APPENDIX A SELECT HYDRUS-2D INPUT FILES................................................................................117 Initial Calibration of 2DSC1.0..............................................................................................117 Initial Calibration of 3DSC1.0..............................................................................................121 Full Calibration of 2DSC1.0.................................................................................................126 Full Calibration of 3DSC1.0.................................................................................................127 Calibration Bounded by Carsel and Parrish Distributions....................................................128 Calibration Bounded by ROSETTA Distributions...............................................................131 Calibration Bounded by Measured Distributions.................................................................132

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7 Calibration Bounded by Vanderborght and Vereecken Distributions..................................133 B POSSIBLE IN-SEASON IMPACTS ON CALIBRATION.................................................138 Introduction................................................................................................................... ........138 Results........................................................................................................................ ...........139 Summary........................................................................................................................ .......142 LIST OF REFERENCES.............................................................................................................143 BIOGRAPHICAL SKETCH.......................................................................................................148

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8 LIST OF TABLES Table page 2-1 Summary of experiments performed, data collected, means and methods........................38 2-2 Quantitative comparison of all locations in the timer-based treatment and the sensorbased treatment using the factory sand calibration............................................................39 2-3 Quantitative comparison of probe type by location for both the factory and site calibrations of each probe type..........................................................................................40 3-1 Results of surface area and influx calculations for the different scenarios simulated in HYDRUS-2D.....................................................................................................................74 3-2 Estimated soil hydraulic parameters for van Genuchten model fit to 11 soil core samples by RETC model...................................................................................................74 3-3 Results from initial calibration...........................................................................................75 3-4 Results from full calibration..............................................................................................76 4-1 Results from soil hydraulic parameter calibrations.........................................................103 4-2 Reported dispersivity values used in previous HYDRUS-2D fertigation studies...........104

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9 LIST OF FIGURES Figure page 2-1 The 2 X 3 matrix formation used in Expe riment 1 with labels used in discussion............40 2-2 The 2 X 4 matrix formation used in Expe riment 2 and Experiment 3 for both probe types with labeling used in discussion...............................................................................41 2-3 Comparison of edge probes with in each TIMER treatment matrix...................................42 2-4 Comparison of probes between the TIMER treatment matrices........................................43 2-5 Time-series data from all edge pr obe locations in the TIMER treatment..........................43 2-6 Comparison of edge probes with in each SMS treatment matrix.......................................44 2-7 Comparison of probes between the SMS treatment matrices............................................44 2-8 Time-series data from all edge pr obe locations in the SMS treatment..............................45 2-9 Comparison of WCR SMC and VWC data for the center locations of SMS and TIMER treatments.............................................................................................................45 2-10 Comparison of WCR SMC and VWC data for the edge locations of SMS and TIMER treatments.............................................................................................................46 2-11 Comparison and calibration of WCR and gravimetric SMC data.....................................46 2-12 Comparison of calibrations for a selected time-series from the TIMER treatment...........47 2-13 Location comparisons within Vitel pr obe matrix of the TIMER treatment for Experiment 2................................................................................................................... ...48 2-14 Time-series data from all probe locations in the TIMER treatment..................................49 2-15 Comparison of Vitel to WCR SMC for each location within the bed...............................50 2-16 Relationship of SMC measured in the center of the bed...................................................51 2-17 Comparison of the WCR and Vitel probe s for each location within the bed during Experiment 3................................................................................................................... ...52 2-18 Residuals for each location presented as Vitel WCR within the TIMER treatment bed during Experiment 3....................................................................................................53 2-19 Comparison of Vitel KNO3 burden data and soil sample NO3-N data..............................54 2-20 Time-series KNO3 burden for each probe location............................................................55

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10 2-21 Comparison of VWC to the WC R SMC using the 2005 calibration.................................56 2-22 Comparison of gravimetric SMC to WC R using the factory calibration for sand.............56 3-1 Experiment 2 WCR matrix c onfiguration centered in bed................................................77 3-2 Water entry boundary conditions examined for soil moisture content prediction.............78 3-3 Averaged soil moisture content from data measured on site.............................................79 3-4 Measured soil moisture content from each probe..............................................................80 3-5 Results of RETC model ca libration to soil core data.........................................................81 3-6 Results of initial calibration soil moisture content predictions..........................................82 3-7 Comparison of initial and full calibration soil moisture content predictions.....................82 4-1 Experiment 3 and 4 WCR matrix configuration centered in bed.....................................104 4-2 Experiment 4 WCR soil moisture content measurements...............................................105 4-3 Experiment 3 Vitel determined nitrate concentrations....................................................105 4-4 Root distribution collected during full canopy................................................................106 4-5 Parameter Sets 1, 2, and 3 so il hydraulic parameter calibration......................................107 4-6 Nitrate concentration predic tions for May 30 fertigation................................................108 4-7 Nitrate concentration predic tions for June 6 fertigation..................................................109 4-8 Nitrate concentration predic tions for June 14 fertigation................................................110 A-1 Boundary conditions for 2DSC1.0 simulation.................................................................120 A-2 Numerical node structur e for 2DSC1.0 simulation..........................................................121 A-3 Boundary conditions for 3DSC1.0 simulation.................................................................125 A-4 Numerical node structur e for 3DSC1.0 simulation..........................................................126 B-1 Averaged data used in calibrations..................................................................................140 B-2 Location by location comparison for measured soil moisture content............................141 B-3 Results of Experiment 2 calibrati on and Experiment 4 measured data...........................141

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11 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering APPROACHES FOR TWO-DIMENSIO NAL MONITORING AND NUMERICAL MODELING OF DRIP SYSTEMS By Jason T. Icerman August 2007 Chair: Michael Dukes Cochair: Rafael Muoz-Carpena Major: Agricultural and Biological Engineering In Florida, intensive bed management systems are commonly used for vegetable production. These systems consist of raised beds for planting covered with plastic mulch, with water and nutrients commonly applied via drip i rrigation and fertigation. Currently available dielectric soil moisture sensors provide inexpe nsive alternatives when compared to Time Domain Reflectometry (TDR) and the labor co sts of soil sampling. The CS616 water content reflectometer (WCR) and the Hydra Probe II (V itel), operating on time-domain and capacitance methods respectively, were installe d beneath drip irrigated tomato es in an intensively managed vegetable production system to examine the m onitoring capabilities of each probe through oneto-one and time-series comparisons. The probes we re installed in a two-dimensional grid to capture the soil moisture content (SMC) distribu tion beneath drip irriga tion. It was observed during one-to-one comparisons that SMC measured using the factor y calibration provided with each probe failed to match volumetric water content (VWC) determined from gravimetric soil samples. However, the longer measurement dist ance of the WCR probe (150% emitter spacing) allowed for relatively good calibration to VWC data (R2 = 0.74), while the short measurement distance of the Vitel probe (28.5% emitter spacing) resulted in a poor calibration (R2 = 0.26).

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12 Time-series observations were more positive as both probes matched the season-long SMC trends well. And the Vitel probe was observed to match soil wa ter salinity trends during timeseries following two different fertigation events. The HYDRUS-2D program (H2D) has previo usly been used for drip irrigation management forecasts. A review of the simulatio ns reported in the literature revealed an assortment of techniques for defining the model simulation space. To examine the effectiveness of these techniques, H2D was calibrated to SMC data collected from a non-planted bed section with soil moisture release curve (SMRC) paramete rs determined from un disturbed soil cores and saturated hydraulic conductiv ity determined by inverse optimization. The goodness-of-fit indicator (Ceff) was also modified to account for measurement uncertainty (Ceff*). Semi-spherical (SC) soil wetting geometries proved superior to th eir surface-radius counterparts in convergence and simulation time, but nearly identical in SM C prediction. Both the axi-symmetrical and twodimensional SC approaches predicted the SMC data well (Ceff > 0.75) and especially well after uncertainty in the SMC and SMRC measurements was considered (Ceff* = 1.0). It was also observed that most previous studi es of fertigation using H2D used mean values for soil parameter estimation. The determinatio n of appropriate soil hydraulic and transport parameters is essential to accurately simulate distributions beneath fertigation. To account for soil parameter uncertainty, inverse optimization methods were applied for soil hydraulic and transport parameter calibration. Calibration of the soil hydraulic parameters revealed high bubbling pressure (~0.17 cm-1) was required to obtain even mode st predictions in the bed center (Ceff = 0.27). Calibration of soil transport paramete rs yielded a longitudina l dispersivity of 2.38 cm and a transverse disp ersivity of 0.01 cm (Ceff = 0.56). As before, accounting for measurement uncertainty improved the results of both calibrations, Ceff* = 0.99 and 0.80, respectively.

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13 CHAPTER 1 RESEARCH BACKGROUND Rationale The economic importance of vegetable productio n in Florida was the driving force behind the research presented in this document. Funding for this research was provided by the Florida Department of Agriculture and Consumer Servic es (FDACS) as part of the Integration and Verification of Water Quality a nd Crop Yield Models for BMP Planning research program. For the purpose of direction, the pr esentation of research is preceded by a brief introduction of significant water management issues for vegetabl e production in Florida. Since drip irrigation systems are currently common for vegetable grower s in Florida and the focus of this research, general information on drip systems is provided. Concurrently, drip systems exhibit many unique aspects that must be considered for monitori ng and modeling efforts. These aspects are also discussed and provide a solid base for fully understanding the research to be presented. Ultimately, specific objectives of the research wi ll be outlined as related to the subsequent chapters within this document. Vegetable Production in Florida Water is a vital resource and is the first limiting nutrient of crop production. Agricultural self-supply accounts for 39% of fresh ground water withdrawals and 62% of fresh surface water withdrawals the highest percentage in either category making agriculture the largest user of freshwater in Florida (Marella, 1999). As the largest consumer of freshwater resources, improved agricultural management practices on a fiel d scale possess the potential for large scale conservation. Vegetables are a major component of Flor ida agriculture encompassing about 72,000 ha for production and valued at $1.5 billion annually (USDA, 2006). Most of the soils where these

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14 vegetables are grown are sandy and as such, frequent irrigation a nd fertigation is required to minimize crop stress and attain maximum pr oduction. Currently, over 30% vegetable production in the state occurs in raised beds often covered with plastic mulch otherwise known as intensive bed management systems. Commonly in intensive bed management systems, water is introduced only by irrigation and fertigation via drip emitters. Conversely, resource extraction is limited almost solely to transpiration, as plastic mulc h covering the raised bed minimizes the influence of rainfall and soil ev aporation (Simonne et al., 2004). Though an established technology still growing in popularity, intensiv e bed management systems remain understudied and more effective management and measurem ent techniques continue to be developed all over the globe (Amayreh and Al-Abed, 2005; Vazquez et al., 2006; Zotarelli et al., 2007a). Drip Irrigation Drip irrigation has the potential to enhance th e sustainability of hi gh intensity vegetable production by eliminating excess irrigation a nd reducing chemical leaching. Correct surface placement of drip emitters enables the infiltra tion process to occur over a small area and promotes three dimensional flows in shapes that have been described as a wet bulb. And most importantly, drip irrigation target s water and nutrient delivery to the root zone, increasing water and nutrient uptake efficiency (Goldberg at al., 1971). Drip irrigation also helps redu ce foliar disease incidence compared to overhead sprinkler systems. By maintaining drier pl ants drip irrigation reduces ou tbreaks of bacteria and fungal diseases, hence reducing the need for bacteric ides and fungicides (Hochmuth and Smajstrla, 1998). Also, fertilizers can be pr escription-applied during the s eason based on crop needs. These small, controlled applications of fertilizer not only save fertilizer, but also ha ve the potential to eliminate groundwater pollution caused by leaching from over-irrigation (Schroder, 2006).

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15 Though resource conservation is th e strength of intensive be d management systems, the added cost of drip irrigation pl aces a greater strain on resource management for these systems. Assuming common Florida conditions, annual drip ir rigation costs have been estimated at $363 per acre for drip irrigation systems, whic h is over $100 per acre more than other common irrigation methods such as semi -closed and open-ditch irrigation systems (Pitts et al., 1990). In order to ensure further transition of the vegetabl e industry to intensive bed management systems, the systems must be proven an economical optio n. And while drip irriga tion and fertigation can be very efficient, mismanagement can lead to ov er-irrigation and excessive nutrient losses due to leaching. Enhanced monitoring and modeling tec hniques are necessary to achieve the most effective management cost conserving tech niques for intensive bed management systems; moreover, two-dimensional monitoring remains a research need for the assessment of forecasting models (Cote et al., 2003). Drip Irrigation Modeling To accurately predict environmental imp acts associated with human practices, a quantitative description of both water and solute movement thr ough the vadose zone is required; furthermore, for drip irrigation it is essential to account for th e two-dimensional nature of the system (Muoz-Carpena et al., 2005b). Lubana and Narda (2001) review ed modeling approaches speci fic to drip irrigation and found both over-simplification and over-complexity to have adverse affects in modeling drip irrigation flow dynamics. Feyen et al. (1998) reviewed several mode ls in existence at the time, focusing on the inclusion of both microand macro-heterogeneity; it was noted that microheterogeneity on a field scale, such as macropores could increase the risk of leaching pollutants making such field characteristics vital for accura te modeling to occur. Such a need for dualpermeability models able to handle micro-hetero geneity and simulate chemical transport under

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16 field conditions has become an outstanding research need for determining the fate of nutrients and other non-point source pollutants (Simunek et al., 2003). Recently the two-dimensional, finite element model HYDRUS-2D, which numeric ally solves Richards' equation for saturatedunsaturated water flow and the convection-dispersion equation for solute flow, has been applied to multiple drip irrigation systems and proven to be a reliable predictor of soil moisture dynamics (Gardenas et al., 2005). Emitter placement and other characteristics of drip systems allow for different assumptions when modeling the system in HYDRUS-2D which correspond to boundary conditions representing point source a nd line source assumptions. A point source boundary, representative of an isolated emitter, creates a quasi-sphe rical wetted soil region, more or less elongated depending on soil textural characteristics. A line source boundary is applicable when several point sources overlap along an axis placed in th e soil surface (i.e. along a crop bed), as may be the case under drip tape. A review of the literatu re conducted for this study noted ther e have been thr ee distinct drip system validations of HYDRUS-2D soil moisture predictions using field data (Fernandez-Galvez et al., 2006; Mmolawa and Or, 2003; Skaggs et al., 2004). Two validations were performed on subsurface drip irrigation (SDI) systems, with only Fernandez-Galvez et al. (2006) presenting field data collected beneath surface drip irrigati on. Field validation of fertilizer distributions beneath drip systems is even more limited, as only Ajdary et al. (2007) has presented HYDRUS2D simulations validated by field measurements (nit rogen fertilizer in the form of urea). In a laboratory setting, Li et al. ( 2005) measured soil moisture and nitrate-nitrogen in soil cores following fertigation and showed HYDRUS-2D to be an accurate predictor of the system. As can be inferred through this summary of the existing lit erature, the conclusions of Cote et al. (2003)

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17 remain valid. Two-dimensional field monitoring of drip irrigation and fertigation systems remains a research need to both strengthen the literature data set a nd further validate twodimensional model predictions, espe cially fertigation systems. Objectives Examine the ability of curre nt low cost technologies to measure two-dimensional distributions beneath drip irriga tion in a raised vegetable bed Calibrate in-situ soil moisture sensors to volumetric moisture obtained from gravimetric sampling on a one-to-one basis Examine the ability of in-situ measurements to track time-series of property changes following irrigation and fertigation ev ents in a raised vegetable bed Reproduce measured two-dimensional soil moisture distributions using HYDRUS-2D Examine the effect of differen t water entry bound ary conditions Reproduce measured two-dimensional nitrate distributions following fertigation events using HYDRUS-2D Examine the effect of uncertainty in soil hydraulic and transport parameter estimation on fertigation predictions Direct future research efforts in the field

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18 CHAPTER 2 COMPARISON OF IN-SITU DIELECTRIC PROBE PERFORMANCE IN A RAISED VEGETABLE BED Introduction Vegetables are a major component of Flor ida agriculture encompassing about 72,000 ha for production and valued at $1.5 billion annually (USDA, 2006). Most of the soils where these vegetables are grown are sands, with frequent irrigation and fe rtigation required to minimize crop stress and attain maximum production. Water and nutrient delivery to these systems is commonly provided by drip irriga tion. Although drip irrigation and fertigation can be very efficient, delivering water and nutrients to the crop root zone (Goldberg et al., 1971), mismanagement can lead to over-irrigation and ex cessive nutrient losses due to leaching. Also much of the vegetable production in the state occu rs on raised beds cove red with plastic mulch. Plastic mulch minimizes the influence of evapora tion and rainfall in the sy stem (Simonne et al., 2004) isolating irrigation effects and making thes e systems ideal for experimental monitoring of distributions beneat h drip irrigation. To date, two-dimensional monitoring of soil moisture content (SMC) and nutrient distributions for the assessment of drip system effectiveness as well as forecasting model predictions remains a research need (Cote et al., 2003). Tradit ionally SMC is determined by gravimetric soil sampling, often reported as volumetric moisture content (VWC) after multiplying by bulk density. While VWC is easily calculated from gravimetric data, soil sampling is labor intensive and physically dest ructive. Any system disturbance is compounded when lateral distributions are desired, especially in confined areas such as raised bed systems. Also errors inherent with so il sampling both for collected gravimetric and bulk density samples creates a sizable source for poten tial error in reported VWC. Th e combination of labor cost,

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19 system disturbance, and potential errors make s non-destructive in-situ measurement techniques a preferable alternative. Time domain reflectrometry (TDR) is perhap s the most well known in -situ technique and is widely accepted as one of the most accurate methods. TDR can be used on a variety of soils using only a single calibration e quation (Topp et al., 1980). Yet due to the high cost of TDR, multiple alternative in-situ sensors have been developed. Two common alternatives to TDR are the CS616 (Campbell Scientific, Inc., Logan, Utah ) water content reflect ometer (WCR) and the Hydra Probe (Stevens Water Monitori ng Systems, Inc., Portland, Oregon). The WCR probe is a dielectric probe that us es time-domain methods for measuring SMC, meaning the probe response for equal VWC in varying soils will be similar (Campbell Scientific, Inc., 2002). The Hydra Probe is also a dielectri c probe, but uses bulk capacitance measurements to calculate soil proper ties, like SMC. The utilization of capacitance methods means the probe response for equal VWC in varying soils will not be similar, ie. capac itance probes require at minimum soil class specific calibration (Stevens Water Monitoring System s, Inc., 2007). Hydra Probe success resulted in the re cent development of a similar product, the Hydra Probe II (Stevens Water Monitoring System s, Inc., Portland, Oregon), with both commonly referred to as Vitel probes. The main advantages of the new Vitel probe (Hydra Probe II) relative to the old Vitel probe (Hydra Probe) are a decrease in power usage and an increase in cable length. All future references to the Vitel probe in this document are references to the new Vitel probe. Another feature of the Vitel probe is the ab ility to measure bulk salinity and soil water salinity, which can be reporte d as a NaCl burden or KNO3 burden (g L-1). While soil water salinity is not a common plant stre ssor for vegetable production in Fl orida, it can be considered a tracer for agricultural sy stems in sandy soils representative of applied nutrient dynamics due to

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20 near zero soil water salinity initial conditions oxidation conditions, and the negatively charged soil matrix. Also when collecting point measurements to outline distributions it is important to bear in mind the collection volume for a specific me thod. The WCR has an estimated sensing volume of ~900 cm3 and sensing length of 30 cm (Campbell Scientific, Inc., 2002). Due to the probe length of a WCR, horizontal probe installation is required to capture both vertical and transverse distributions. Plauborg et al. ( 2005) noted that horizontally in stalled WCRs exhibited large variation between probe replicates in the field. The authors consider ed the probe variation to be a product of both poor factory calibration provi ded by the manufacturer and the natural heterogeneity found in top soil. The study also found better probe correl ation at lower SMC, while reporting WCR probes to measure SMC c onsistently lower than TDR measurements. The Vitel probe differs from th e WCR in sensing volume, 40.3 cm3, and sensing length, 5.7 cm (Stevens Water Monitoring Systems, Inc ., 2007). Yet similar to th e WCR, the old Vitel probe has been observed to underestimate SMC in sandy soils when compared to VWC obtained from gravimetric samples (Kennedy et al., 2003); however, the opposite has been reported when the old Vitel probe is compared to TDR. Seyfri ed and Murdock (2004) conc luded that while soil specific calibrations of the ol d Vitel probe increased accuracy relative to TDR across most soil types, for sandy soils the manufacturer provide d factory calibration matched TDR values for SMC very well. As has been previously described through examples here and is often the case in monitoring studies, probe results are commonly co mpared on a one-to-one basis to established methods. Yet one of the known advantages for c ontinuous in-situ monitori ng is the ability to track soil properties over extended time-series (Kennedy et al., 2003); therefore, in this study

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21 another approach will also be employed for probe examination, comparing the probe measurements over event-long and season-long time -series. Time-series comparison inclusions allows for a more descriptive examination of probe performance, as probe SMC measurements may be consistently off +/0.03 cm3 cm-3 relative to established me thods, but able to match the wetting and drying trends following an irrigation event very well. Simply capturing these trends can be very useful for irrigation management and like studies. Similarly, soil water salinity burdens can be examined over an entire fert igation event or the s eason-long build-up and reduction of fertigation constituents in the soil. These comparisons will be referred to as timeseries comparisons. Considering this, the objective of this study was to analyze the potential for using a time-domain probe (WCR) and a capac itance probe (Vitel) for two-dimensional monitoring beneath drip irrigation by co mparing probe SMC measurements to VWC measurements obtained from gravimetric samples and also comparing Vitel probe measured soil water salinity to soil water nitrate-nitrogen (NO3-N) obtained from soil samples, in each case using one-to-one and time-series comparisons. Materials and Methods Three distinct experiments were performed at the University of Florida, Plant Science Research and Education Unit locate d near Citra, Florida. Buster (1979) classified the soil at the research site as a Tavares sand and Candler sand. These soils contains >9 7% sand-sized particles and have a field capacity of 0.05-0.07 (cm3 cm-3) in the upper 100 cm of th e profile (Carlisle et al., 1978). The experiments are summarized in Ta ble 2-1, with further discussion to follow. Measurement Methods SMC was measured in-situ by di electric probes, the WCR and Vitel. The WCR probe uses time-domain methods for SMC measurement and cons ists of two 30 cm long stainless steel rods connected to a printed circ uit board. The probe rods can be insert ed from the surface or as in the

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22 case of this study, the probe can be buried at a ny orientation to the surface. The differentiallydriven probe rods form a transmission line with a wave propagation velocity that is dependent on the dielectric permittivity of the medium su rrounding the rods. Since water has a dielectric permittivity significantly larger than other soil cons tituents, the resulting oscillation frequency is dependent upon the average SMC of the medium surrounding the rods (Cam pbell Scientific, Inc., 2002). The Vitel probe uses bulk capacitance measurem ents to calculate SMC, by making a high frequency (50 MHz) complex dielectric constant measurement. The probe head contains the necessary electronics to generate the 50 MHz stimulus and generate voltages that reflect the soil's electrical properties. The thre e outer and one center tine form the sensing volume of soil. The capacitive part of the response is most indicative of SMC, while th e conductive part reflects bulk salinity. Through the use of appropriate calibrati on curves that are rela ted to soil type, the dielectric constant measurement can be direc tly related to SMC (Stevens Water Monitoring Systems, Inc., 2007). For SMC comparison, VWC was determined us ing collected gravimetric samples. Soil samples were collected by a 5 cm diameter soil auger. Each reported soil sample location yielded two depths of composite samples: 0-15 and 1530 cm. All collected samples were immediately placed on ice and refrigerated until analyzed. A 20 g subsample was used to determine the gravimetric water content for each composite sa mple, which in turn was used to calculate (multiplying by the bulk density) the VWC. In order to determine VWC from collected gravimetric data, bulk density measurements were also collected. The field bulk density was estimated by the average bulk density of 11 soil samples collected by an undisturbed core sampler. Soil cores measured 5.4 cm in diameter and

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23 6.0 cm in height and samples were collected be tween a depth of 0-6 and 6-12 cm below the bed surface at various places in the field. The sample s were saturated to measure wet weight and oven dried to measure dry weight The average measured bulk dens ity in the field beds was 1.26 g cm-3 with a 6.92% standard deviation. Through this method, it is assumed that bulk density is constant with depth. To track applied fertigation, th e soil water salinity burden (KNO3 g L-1) was measured by the Vitel probes. However, the fertig ation applied during the study was not KNO3, but consisted of Ca(NO3)2, KCl, and Mg(SO4) compounds. Previous studies have used electric al conductivity (EC) measured by capacitance probes to track individual ions such as Br, Cl, and NO3 (MuozCarpena et al., 2005a), but the KNO3 burden measured by the Vitel probe is reported here since it is included with the manufacturer provided prog ram and requires no extra work on part of the end user. This is inline with th e study objective of testing the pr obes effectives as a monitoring tool, not necessarily electrical quantities measured by the prob e; therefore, all reported KNO3 burdens in this study are actually representative of all applie d fertigation compounds. It should also be noted that the measured KNO3 burden is subject to calc ulation errors as well as measurement errors, since the conversion from bulk burden to soil water burden used was simply a division by SMC (Stevens Water Monitoring Sy stems, Inc., 2007) and previous studies have shown the relationship between bulk burden and soil water burden to be much more complex (Muoz-Carpena et al., 2005a). For soil water salinity comparison, soil water NO3-N was determined from collected soil samples. These samples were collected in the cen ter of the bed with one sample uniformly mixed from the 0-30 cm depth. The samples were co llected -1, 1, 3, and 7 days following a given fertigation event. For NO3-N analysis a 10 g subsample was extracted and 50 mL of 2 M KCl

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24 was added to the subsample. The resulting mixt ure was filtered by gravity using Fisherbrand filter paper within one day of soil sampling (Mulvaney, 1996). Soil so lution extracts were stored at -18 deg C. They were analyzed for NO3-N using an air-segmentedautomated spectrophotometer (Flow Solution IV, OI Analytical College Station, Texas) coupled with a Cd reduction approach similar to the wo rk of Zotarelli et al. (2007a). Experiment 1: 2005 In-Season Between April 12 and June 27, 2005 SMC distribu tions were monitored under surface drip irrigated tomatoes (Lycopersicon esculentum, FL 47). The tomatoes were planted in raised beds covered with black plastic mulch. The tw o treatments of interest were a timer-based irrigation scheme (TIMER) and a soil moisture sensor-based irrigation scheme (SMS). Both treatments received the University of Florida, Institute of Food and Agri cultural Sciences (IFAS) recommended seasonal fertilizer amount of 208 kg ha-1 nitrogen (N) applied as calcium nitrate in weekly fertigation events (Mayna rd et al., 2003) and were replicat ed four times within the field. Each treatment contained two surface drip lines (Turbulent Tw in Wall, 20 cm emitter spacing, 0.25 mm thickness, 3.72 L min-1 at 69 kPa, Chapin Watermatics, Inc., Watertown, New York), one for irrigation and one for fertigation. The surf ace drip lines were laid side by side in the center of the bed. Transplants were approximate ly 45 days old at transplanting on April 7, 2005 and transplanted in a single row approximately 10 cm from the bed center with 45 cm spacing for a plant population of 11,960 plants ha-1. The SMS treatment was set near effective field capacity (~0.10 cm3 cm-3) and was controlled by a Quantified Irrigation Controller (QIC) developed at the University of Florida (Muoz-Carpena et al., 2006). The QIC device uses a 20 cm long ECH2O probe (Decagon Devices, Inc., Pullman, Washington ) that was inserted vertically into one representative bed replicate and contro lled all replicates to monitor SMC. Th e QIC was queried every minute at five

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25 selected time windows during the day, if during any query the ECH2O probe returned a SMC below field capacity the QIC allowed irrigati on. Conversely, the QIC bypassed irrigation events if the SMC was above field capacity (Dukes and Muoz-Carpena, 2006). At the beginning of the season, the application windows for the QIC were 12 minutes long beginning at 0812, 1012, 1212, 1412, and 1612 hours and the period of applica tion for the TIMER treatment was 0600 to 0700 hours. Starting May 26, the time windows for the QIC were 24 minutes long beginning at 0824, 1024, 1224, 1424, and 1624 hours and the period of application for the TIMER treatment was 0600 to 0800 hours. During the establishment phase SMC in the beds was maintained at or above field capacity with daily ir rigation events to ensure even establishment of all plots. Irrigation treatments were implemented 18 days after transplanting. SMC was measured on an hourly basis by WCRs with the manufacturer provided factory calibration for sand used in data collection. Fo ur matrices each contai ning six WCRs were installed, two in the SM S treatment and two the TIMER treatm ent. A 40 cm long section of the entire bed width was removed from both insta llation locations, centered under an emitter. The section provided enough space for WCR installation parallel to the surface. After installation the section was repacked with the original soil. Fo r each treatment, one WCR matrix was located on the north face of the removed section and one on th e south face. The matrices were configured in a 2 X 3 formation (Vertical X Transverse), with a top row buried at 8 cm and a bottom row at 23 cm below the surface. The three columns were spaced 23 cm apart with the center column located in the bed center (Figure 2-1). The purpose of the matrix configuration was to capture the wet-bulb shape of SMC redistribution under the emitter. Soil samples, analyzed for VWC, were collected five times to validate the WCR SMC measurements: April 27; May 11; May 25; June 8; and June 22. Samples were collected from

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26 each treatment and from all four replicates, comp ared to the single inst allation location of the probes. Similar to the probe matrix, soil samples were collected from three points laterally across the bed. A center location and two other locations near the edge, approximately 23 cm from the bed center in each direction. Experiment 2: Non-Planted From October 10 to October 23, 2006 SMC was measured from the same field as Experiment 1 with similar irrigation treatmen ts. For the entire period, the application windows for the QIC were 24 minutes long beginning at 0824, 1024, 1224, 1424, and 1624 hours and the application window for the TIMER treat ment was 0600 to 0800 hours, daily. As before, a 40 cm section was removed from one replicate of each treatment; however, for this experiment two changes to the probe ma trices occurred. First, each treatment had one WCR probe matrix and one Vitel probe matrix for monitoring. The second change was the matrix size. The 2 X 3 matrix was replaced by a 2 X 4 matrix for each probe type (Figure 2-2). The probes were located 8 cm and 23 cm away fro m the bed center laterally in each direction and the depths were again 8 cm and 23 cm. The bed s ections monitored in this experiment were not planted nor fertigated. Experiment 3: 2006 In-Season From April 14 to July 5, 2006 SMC was measur ed from the same field as Experiment 1 and Experiment 2, with irrigation treatments id entical to Experiment 2. The 2 X 4 matrix configuration and installation method used in Expe riment 2 was also used for this experiment (Figure 2-2). The field setup, fe rtigation, and crop were iden tical to Experiment 1, with transplanting occu rring on April 10, 2006. Also similar to Experiment 1, soil samples an alyzed for VWC, were collected five times during the season to validate WCR and Vitel SMC measurements: April 27; May 9; May 23;

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27 June 6; and June 26. The same approach as Expe riment 1 was used as samples were collected from each treatment of interest and from all four replicates. To account for the change in probe matrix locations, soil samples were collected fr om four points laterally across the bed. Two locations 8 cm from the bed center in each direct ion and the other two locations near the edge, approximately 23 cm from the bed center in each direction. A second group of samples was also collected to capture fertigation distributions. Agai n, these samples were collected in the center of the bed with one sample uniformly mixed from the 0-30 cm depth. The samples were collected 1, 1, 3, and 7 days following two unique fertigati on events that occurred on May 23 and June 13. Equations Used in Analysis In a sandy soil Plauborg et al (2005) calibrated horizontally installed WCR probes to TDR measured SMC. Their reported linear relati onship was rearranged to yield Equation 2-1. 59 0 01 0 WCR TDR (cm3 cm-3) (2-1) All data unless otherwise noted was collected using the manu facturer provided factory calibration for sand for each probe and is pres ented using this met hod. Since TDR was not available at the field site to perform a site specific calibration, the Plauborg calibration is presented as an alternative for horizontally installed WCR probes in sandy soils to the manufacturer provided factory calibration and eventual VWC calibration obtained during the study. To compare time-series of probe SMC measur ements and established methods the NashSutcliffe (1970) efficiency coefficient (Ceff) was used. The range of Ceff lies between 1.0 (perfect fit) and When Ceff is lower than zero the mean value of the measured time-series would have been a better predictor than th e probe (Nash and Sutcliffe, 1970). Ceff is the reported goodness-

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28 of-fit indicator in this study because it has been previously reported as a better indicator for timeseries compared to other indicators based on squared residuals (Legates and McCabe, 1999). Results and Discussion Experiment 1: 2005 In-Season Water content reflectometer precision To examine the probe precision, WCR measurem ents are compared by location. The edge locations are compared both within the matrix (NW8 to NE8, NW23 to NE23, SW8 to SE8, and SW23 to SE23) and between matric es (NW8 to SW8, NW23 to SW 23, NE8 to SE8, and NE23 to SE23), while the center locations are compared only between matrices for each treatment (TIMER and SMS) individually (NC8 to SC8 and NC 23 to SC23). It is important to establish the probe precision in relation to the monitori ng locations before embarking on comparisons between measurement methods. Any significant lack in probe precis ion would speak to heterogeneity present within the system, maki ng a comparison of methods difficult and likely fruitless. The TIMER treatment results are presented first with SMC reported using the factory sand calibration. Examination of Figure 2-3 reveals reasonable co rrelation for field data across between the edge locations in each face of the TIMER treat ment. And Figure 2-4 shows no consistent bias toward either face, except for in the center of the bed where the center locations appear consistently wetter in the north face. While the measured SMC at the edge locations fall close, but away from the 1:1 line in Figure 2-3, 2-4, and 2-5 displays the time-series of the edge locations and reveals the probe replicates to be very similar. This is especially true once the 0.025 cm3 cm-3 SMC probe accuracy is considered (Campbell Scientific, Inc., 2002) as each probes deviation from the average SMC is under 0.01 cm3 cm-3 for the 8 cm depth and under 0.02 cm3 cm-3 for the 23 cm depth. It was

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29 also observed that the spread of the data increa ses for the center locations as SMC increases. The relation of spread to SMC is in agreement with results reported by Plauborg et al. (2005) as their study revealed more precision for measur ement replications at lower SMC. In fact all observations made from Figures 2-3, 2-4, and 2-5 are strengthened when the field setup is considered in addition to the pr obe accuracy. The double dr ip line setup prevents the irrigation emitter, or fertigation emitter, or bo th from being located directly in the center of the bed. While either emitter would be located no further than 2-3 cm fr om the bed center, the distance is enough to observe a cons istent variation in probe moistu re. In all, like locations were observed to be within reasonable agreement so that the east and west locations within each face as well as the north and south face of each matr ix can be considered replicates for future comparisons. A quick examination of the SMS treatment fi gures reveals similar precision results when compared to the TIMER treatm ent results, except at the 23 cm edge locations. No physical explanation exists for the varia tion observed between probe repli cates at 23 cm edge location. When both Figure 2-6 and 2-7 are c onsidered, it is observed that th e variation is mostly due to one probe (SW23), which is confirmed when by th e time-series presented in Figure 2-8. Ignoring the SW23 location, the north and south matrices can again be considered replicates. And, the previously reported negative relationship betw een SMC and precision is also visible for the center locations (Figure 2-7). Table 2-2 shows the problem with one-to-one co mparisons for field monitoring. Results in Table 2-2 are poor, with Ceff values often below 0. Only when the entire time-series is considered (Figure 2-5 and 2-8) do the probes measurements appear to be lo cation replicates. Concurrently considering the entire time-ser ies along with the probe accuracy reported by the manufacturer

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30 allows for the replicate assumption by location, where as solely one-to-one comparisons preclude such assumptions. Soil sample comparisons In general the VWC obtained from gravimetric samples was more variable than WCR SMC and SMS treatment results were more variable than TIMER treatment results with standard deviations of the data as follows: TIMER WCR, 0.009 cm3 cm-3; TIMER VWC, 0.018 cm3 cm-3; SMS WCR, 0.015 cm3 cm-3; SMS VWC, 0.026 cm3 cm-3. The difference in variation between the WCR SMC and VWC is largely a result of their measurement volumes and monitoring location. WCR SMC represents an average over the 900 cm3 volume, which corresponds to a 30 cm length within the bed. The VWC data represents an average over the 294.5 cm3 auger volume, which encompasses only 5 cm of bed lengt h. The shorter length included in the average places more importance on the measurement location relative to a drip emitter, which were spaced 20 cm apart. Recall the reported VWC is an average across the four sampling locations in the field, which are at a similar normal distance from an emitter, but could be from multiple radial distances. This is because soil samples were collected relative to the drip tape and plant location, but without regard for emitter locati on. Averaging samples alleviates some error relative to WCR SMC since the WCR measurement length is 1.5 X emitter spacing, effectively an average of the entire spacing. Figure 2-9 and 2-10 present WCR SMC and VWC determined from gravimetric data for both treatments. A general trend of WCRs returni ng lower SMC values than soil samples is seen in the figures, similar to the observations made by Plauborg et al. (2005) when comparing WCR to TDR SMC. That being said, some potential er rors in the gravimetric data exist. Beyond the previously reported bulk density uncertainty, the subsample size used for gravimetric soil

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31 moisture was relatively small (20 g) and could have induced further er rors. Though in general, soil sampling occurred too infrequently to make observations on a time-series scale. In traditional one-to-one st yle, the WCR SMC measurements were calibrated to VWC obtained from gravimetric soil sample results. Both the TIMER and SMS treatment data was included in the calibration. Since the soil samples could not be collected instantaneously and are instead spread on a timeline of collection for each collection date, the WCR readings were accordingly averaged from 1000 hours to 1400 hours for both the north and south locations, for each treatment. Gravimetric data was averaged acr oss the four replicates for each treatment for VWC determination. The resultant calibrati on equation displayed in Figure 2-11 was transformed to match Equation 2-1 (Equation 2-2). If we consider the equations to be of the general form Y = (X A) / B, it can be seen that though the sample variability results in a relatively low R2 value of 0.74, Equation 2-1 and Equati on 2-2 return similar A parameters, but different B parameters. 69 0 03 0 WCR VWC (cm3 cm-3) (2-2) The R2 value can be explained by the uncertain ty in collecting WCR SMC and VWC data. Interestingly, the factory and Plauborg calibrations proved simila r in their ability to match collected VWC for this study site. The factory ca libration appears to underestimate SMC, while the Plauborg calibration overe stimates SMC (Figure 2-12). Regardless of calibration, the WCR SMC collect ion frequency was an inherent problem for both treatments, but is more obvious in the pres ented SMS treatment results. With the maximum application period for the SMS treatment set at 24 min and occurring up to five times daily, several states of redistribution are captured rando mly each hour in the data set. This is less of a problem for the TIMER treatment, since water applic ation occurs in hour blocks at the same time

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32 each day. The consistent timing and hourly appli cation allows for a reasonable reproduction of the entire redistribution proce ss. To obtain further accuracy, the measurement frequency was increased to 15 min intervals fo r the remaining experiments. Experiment 2: Non-Planted Vitel precision First the Vitel probe precision was examined similar to the examination of the WCR probe. For Figure 2-13 the west bias seen in the V itel probe matrix was lik ely a by-product of the irrigation drip emitter being off-center intensified by the smaller measurement volume of the Vitel probe. Still the agreement is reasonable fo r field data and the Vitel probe can also be considered location replicates. Probe to probe comparison In order to examine the accuracy of SMC m easured by Vitel probes in field conditions, a comparison to measured WCR SMC was performe d for each probe location. Only the TIMER treatment is presented, with WCR SMC reported using the site calibration (Equation 2-2). Since a time-series comparison was previously observed to be a more descriptive comparison, a time-series comparison of TI MER treatment SMC measured by the WCR and Vitel probe is presented prior to a one-to-one comp arison (Figure 2-14). It is seen that the Vitel probes located in the center of the bed to c onsistently measure higher SMC than the WCR probes. No consistent relationship between the edge probe locations can be discerned, especially compared to the center of the bed. These observations are confirmed by the one-to-one comparisons (Figure 2-15). While no general trend can be determined accurately location by location (Vitel E8 to WCR E8, etc.), a very good relationship between the Vitel and WCR probes can be developed if the locations are averaged symmetrically about the drip tape and only the

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33 center probes are considered (Figure 2-16). Aver aging the probes about the bed center can serve to reduce errors associated with the differences produce by drip emitters being off center. It was hoped the averaged locations would retu rn a more representative picture of SMC distribution in the center region of the bed, thoug h replication is admittedl y minimal. The results presented in Table 2-3 indicate improvement in location comparison after the WCR site calibration is applied, but little or no improvement is seen after the Vitel site calibration obtained from averaged data is applied. The Vitel si te calibration does improve the averaged center locations, but no improvement is seen locati on by location with some locations actually decreasing in correlation. Regardless, the calibra tion equation resulting from the Vitel to WCR comparison for averaged center locations is presented here (Equation 2-3). 91 0 04 0 Vitel WCR (cm3 cm-3) (2-3) The low Ceff values (Table 2-3) are again mainly an artifact of the probes measurement volume. To restate, the WCR repr esents an average over the 900 cm3 volume, which encompasses 30 cm of bed length. And, the Vitel represents an average over a 40.3 cm3 volume, which encompasses only 5.7 cm of be d length. High correlation (large Ceff) will never be obtained comparing horizontally installed WCR and Vitel data, since WCR monitors 150% of emitter spacing compared to 28.5% for the Vitel probes. Experiment 3: 2006 In-Season Again only the timer-based treatment data is presented. WCR SMC reported was calibrated using the site calibration (Equation 2-2). Vitel SM C was again determined using the factory sand calibration.

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34 Probe to probe comparison The probe comparison is displa yed location by location in Figur e 2-17. As before, the Vitel probes return slightly higher SMCs a trend more evident for the center locations. The individual probes were averaged symmetrically about the drip tape and the averaged data visually shows slightly better correla tion between probes overall. A large difference between some of the probe readings for the center locations can be observed in Figure 2-17. A time-series of these di fferences is displayed in Figure 2-18. Again the time-series proves to be a more descriptive compar ison, as the large spikes in the residuals are now observed to be associated with weekly fertigation events The WCR probes return overly high SMC values during the irrigation event fo llowing each fertigation, suggesting the WCR probes are influenced by high ion concentrations In fact, WCR SMC measurements are reported to be accurate only below 0.5 dS m-1 (Campbell Scientific, Inc., 2002), a value exceeded around the emitter following fertigation events. Soil sample comparisons Again due to the measurement volumes and lengths (relative to emitter spacing) a poor correlation between Vitel SMC and VW C was anticipated and observed (R2 = 0.26) though the calibration equation is not presen ted here. Accordingly, a one-to -one comparison of Vitel soil water salinity burden to soil sample NO3-N data was observed to be extremely poor (R2 < 0.10) and is not presented here. However, a time-series comparison again proves valuable as Vitel soil water salinity burden tracks NO3-N results from soil samples fairly well (Figure 2-19). The Vitel probe soil water salinity burden time -series also follows wh at is anticipated at the site following fertigation over the entire seas on, especially for the TIMER treatment. It is seen in Figure 2-20 that large spikes in soil wa ter salinity occur following fertigation events and are quickly leached or extracte d from the profile following only a few irrigation events in the

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35 TIMER treatment bed. Conversely, no discernable pattern is revealed for the SMS treatment, likely due to the very dry soil moisture regime present in the bed which can lead to measurement errors (Stevens Water Monitoring Systems, Inc ., 2007). The results of this calibration effort confirm that while trends may be assessed between Vitel data and soil sample data, due to the measurement methods in this study high correlation is unlikely. Since WCR SMC and VWC was again collected during Experiment 3, the previous WCR calibration was examined for VWC prediction abili ty. The result of comparing the transformed WCR SMC (Equation 2-2) to VWC obtained from gravimetric samples during Experiment 3 is displayed in Figure 2-21. Two of the three criteria for a good calibration are met, as the A parameter is at zero (0.00) and the B parameter is near one (0.93), but the regression coefficient of determination is poor (R2 = 0.55). Another method of compar ison is to once again calibrate the factory sand calibration to VWC and compar e the resulting equation to the previous calibration (Figure 2-22). The resulting calibrati on equation for this comparison is seen in Equation 2-4. When compared to Equation 2-2, E quation 2-4 is seen to be of similar construct with reasonably similar A and B parameters, but ag ain suffers from the variability of soil sample results (R2 = 0.54). 63 0 03 0 WCR VWC (cm3 cm-3) (2-4) Summary and Conclusions Overall, both probes captured the SMC trends in the field, with results improving once a 15 min interval was instituted. Th e probe data was generally more consistent than soil sample data, but this is likely due to the single ra dial distance from the emitter established by probe installation compared to varying and unknown distan ces of soil samples collected without regard to emitter location.

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36 The message from this study is the importan ce of considering measurement volumes when comparing or selecting different monitoring methods. The horizontally installed WCR probes had the largest measurement volume and covered the most bed length (30 cm). Hence, the WCR probes can be considered the best, most appropri ate match to the beds representative elemental volume when plant and emitter spacing are cons idered. Both the Vitel probe SMC and VWC obtain from gravimetric samples with rela tively small measurement volumes and more importantly, measurement lengths (5.7 cm and 5 cm respectively), captured differences resulting the monitoring points radial dist ance from an emitter in additi on to the normal distance. The WCR probes thus provided an average along th e bed horizontal while Vitel probes provided closer to true point measurements on the horizont al. Since gravimetric data was collected without regard for the radial emitter distance effectiv ely creating an average over the entire emitter spacing through averaging, it stands that the WCR was reason ably calibrated to VWC obtained from gravimetric samples (R2 = 0.74), while the Vitel probe was not (R2 = 0.26). Similarly, the Vitel and WCR SMC measurements did not resp ond similarly on a one-to-one basis; however, time-series comparisons of Vite l and WCR SMC showed the probes to have similar responses to SMC changes and to capture the wetting and drying trends followi ng irrigation events. As expected due to the inability to match VW C, Vitel soil water salinity burdens revealed no consistent relationship with soil sample NO3-N results on a one-to-one basis. But again timeseries comparisons yielded differe nt observations, as the ability of the Vitel probes to measure in-situ soil water salinity burdens was observed to be a very useful tool for quantifying leaching and soil retention of nutrients over the entire season. Finally, there was one observed problem with the two probes examined. The horizontally installed WCR probes were influenced by higher i on (fertigation) concentr ations. During periods

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37 immediately following fertigation, the W CR measured SMC reaching and exceeding soil porosity for both treatments. Vite l probes returned more predicta ble results duri ng these periods. The erratic response of WCR probes following fertig ation events is especi ally hazardous for inseason measurements beneath drip irrigation with fertigation.

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38Table 2-1. Summary of experiments perfor med, data collected, means and methods Data collected Features Data application Dates Experiment 1 WCR SMC, gravimetric samples, undisturbed soil cores In-season SMC distributions hour interval, hydraulic parameter estimation WCR probe precision, WCR calibration to VWC 4/12/2005 7/5/2005 Experiment 2 WCR SMC, Vitel SMC Non-planted SMC distributions, no transpiration or root impacts WCR probe precision, Vitel calibration to WCR, WCR SMC used for H2D calibration (Ch. 3) 10/10/2006 10/23/2006 Experiment 3 WCR SMC, Vitel SMC, gravimetric samples, fertigation samples In-season SMC distributions and fertigation distributions 15min interval WCR calibration check, Vitel calibration to VWC, Vitel calibration to NO3-N, Vitel EC used for H2D calibration (Ch. 4) 4/14/2006 7/5/2006 Experiment 4 WCR SMC, Vitel SMC Plants clipped post-season, eliminates transpiration and accounts for root growth impacts, SMC distributions WCR SMC used for H2D calibration (Ch. 4) 7/5/2006 7/18/2006 SMC is soil moisture content. VWC is volumetric water content obtain from gravimetric samples. NO3-N is measured nitrate-nitrogen from soil samples. EC is electrical conductivity.

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39Table 2-2. Quantitative comparison of all locations in the time r-based treatment and the sensor-b ased treatment using the facto ry sand calibration Sensor-Based Treatment Timer-Based Treatment Location Face Depth (cm) Average SMC Maximum SMC Minimum SMC Ceff (face to face) Ceff (east to west) Location Face Depth (cm) Average SMC Maximum SMC Minimum SMC Ceff (face to face) Ceff (east to west) Center North 8 0.155 0.538 0.078 Center North 8 0.135 0.341 0.090 West North 8 0.089 0.137 0.066 West North 8 0.074 0.089 0.062 East North 8 0.065 0.087 0.050 -4.63 East North 8 0.094 0.120 0.076 -17.89 Center South 8 0. 161 0.677 0.086 0.79 Center South 8 0. 125 0.538 0.066 -3.65 West South 8 0. 068 0.133 0.064 -0.64 West South 8 0. 083 0.109 0.070 -0.45 East South 8 0. 080 0.130 0.061 -5.15 -1.14 East South 8 0. 086 0.106 0.077 -1.52 0.02 Center North 23 0.142 0.266 0.089 Center North 23 0.147 0.314 0.110 West North 23 0.048 0.063 0.038 West North 23 0.086 0.098 0.073 East North 23 0.077 0.104 0.058 -37.39 East North 23 0.110 0.130 0.095 -24.87 Center South 23 0. 161 0.311 0.104 0.20 Center South 23 0. 127 0.227 0.093 -6.87 West South 23 0. 115 0.215 0.086 -200.69 West South 23 0. 098 0.129 0.086 -0.14 East South 23 0. 074 0.090 0.060 0.75 -7.19 East South 23 0. 117 0.146 0.107 -0.62 -8.41 SMC is soil moisture content. Ceff is Nash and Sutcliffe (1970) coefficient of efficiency.

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40 Table 2-3. Quantitative comparison of probe type by location for both the factory and site calibrations of each probe type. Only TIME R treatment data is displayed. Values averaged by symmetrical location are also included Ceff (Vitel to WCR) Location Factory calibrations WCR site calibrated Both probes site calibrated W8 -125.33 -62.48-17.78 WC8 -3.04 -0.230.80 EC8 -8.49 -1.280.59 E8 0.08 -1.69-10.65 W23 -3.38 0.52-12.33 WC23 -19.32 -7.02-1.39 EC23 -6.65 0.60-3.51 E23 -108.53 -77.79-273.45 AVG EDGE 8 -9.34 -1.76-0.59 AVG CENTER 8 -2.49 -0.400.97 AVG EDGE 23 -7.05 -13.52-97.01 AVG CENTER 23 -5.94 -2.670.91 Ceff is Nash and Sutcliffe (1970) coefficient of efficiency. Figure 2-1. The 2 X 3 matrix formation used in Experiment 1 with labels used in discussion.

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41 Figure 2-2. The 2 X 4 matrix formation used in Experiment 2 and Experiment 3 for both probe types with labeling used in discussion.

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42 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 WEST SIDE WCR SMC (cm3 cm-3)EAST SIDE WCR SMC (cm3 cm-3) 8 cm 1:1 23 cm NORTH FACE 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 WEST SIDE WCR SMC (cm3 cm-3)EAST SIDE WCR SMC (cm3 cm-3) 8 cm 1:1 23 cm SOUTH FACE Figure 2-3. Comparison of edge probes within each TIMER treatment matrix. Both 8 cm and 23 cm data is shown.

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43 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 WCR SMC (cm3 cm-3) NORTH FACE WCR SMC (cm3 cm-3) SOUTH FACE West 8 cm 1:1 East 8 cm 8 CM EDGE 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 WCR SMC (cm3 cm-3) NORTH FACE WCR SMC (cm3 cm-3) SOUTH FACE West 23 cm 1:1 East 23 cm 23 CM EDGE 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 WCR SMC (cm3 cm-3) NORTH FACE WCR SMC (cm3 cm-3) SOUTH FACE Center 8 cm 1:1 Center 23 cm 8 & 23 CM CENTER Figure 2-4. Comparison of probes betw een the TIMER treatment matrices for all like locations and depths. 0.00 0.05 0.10 0.15 0.20 4/125/25/226/11 DATE (2005)WCR SMC (cm3 cm-3) NW NE SW SE 8 CM 0.00 0.05 0.10 0.15 0.20 4/125/25/226/11 DATE (2005)WCR SMC (cm3 cm-3) NW NE SW SE 23 CM Figure 2-5. Time-series data from all edge probe locations in the TIMER treatment grouped by depth.

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44 0.00 0.05 0.10 0.15 0.20 0.000.050.100.150.20 WEST SIDE WCR SMC (cm3 cm-3)EAST SIDE WCR SMC (cm3 cm-3) 8 cm 1:1 23 cm NORTH FACE 0.00 0.05 0.10 0.15 0.20 0.000.050.100.150.20 WEST SIDE WCR SMC (cm3 cm-3)EAST SIDE WCR SMC (cm3 cm-3) 8 cm 1:1 23 cm SOUTH FACE Figure 2-6. Comparison of edge probes within each SMS treatment matrix. Both 8 cm and 23 cm data is shown. 0.00 0.05 0.10 0.15 0.20 0.000.050.100.150.20 WCR SMC (cm3 cm-3) NORTH FACE WCR SMC (cm3 cm-3) SOUTH FACE West 8 cm 1:1 East 8 cm 8 CM EDGE 0.00 0.05 0.10 0.15 0.20 0.000.050.100.150.20 WCR SMC (cm3 cm-3) NORTH FACE WCR SMC (cm3 cm-3) SOUTH FACE West 23 cm 1:1 East 23 cm 23 CM EDGE 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.050.100.150.200.250.300.35 WCR SMC (cm3 cm-3) NORTH FACE WCR SMC (cm3 cm-3) SOUTH FACE Center 8 cm 1:1 Center 23 cm 8 & 23 CM CENTER Figure 2-7. Comparison of probes between the SMS trea tment matrices for all like locations and depths.

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45 0.00 0.05 0.10 0.15 0.20 4/125/25/226/11 DATE (2005)WCR SMC (cm3 cm-3) NW NE SW SE 8 CM 0.00 0.05 0.10 0.15 0.20 4/125/25/226/11 DATE (2005)WCR SMC (cm3 cm-3) NW NE SW SE 23 CM Figure 2-8. Time-series data from all edge probe locations in th e SMS treatment grouped by depth. 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 4/255/55/155/256/46/146/24 DATE (2005)SMC (cm3 cm-3) FOR 8 cm LOCATION-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 NC8 SC8 SS-8 NC23 SC23 SS-23TIMER 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 4/255/55/155/256/46/146/24 DATE (2005)SMC (cm3 cm-3) FOR 8 cm LOCATION-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 NC8 SC8 SS-8 NC23 SC23 SS-23SMS SMC (cm3cm-3) FOR 23 cm LOCATION SMC (cm3cm-3) FOR 23 cm LOCATION Figure 2-9. Comparison of WCR SM C and VWC data for the center locations of SMS and TIMER treatments. VWC soil sample data is labeled SS location depth (cm). Error bars represent one standard deviation each.

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46 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 4/255/55/155/256/46/146/24 DATE (2005) -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 NW8 NE8 SW8 SE8 SS-W8 SS-E8 NW23 NE23 SW23 SE23 SS-W23 SS-E23SMS 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 4/255/55/155/256/46/146/24 DATE (2005) -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 NW8 NE8 SW8 SE8 SS-W8 SS-E8 NW23 NE23 SW23 SE23 SS-W23 SS-E23TIMER SMC (cm3 cm-3) FOR 23 cm LOCATIONSMC (cm3 cm-3) FOR 8 cm LOCATION SMC (cm3 cm-3) FOR 8 cm LOCATIONSMC (cm3 cm-3) FOR 23 cm LOCATION Figure 2-10. Comparison of WCR SM C and VWC data for the edge locations of SM S and TIMER treatments. VWC soil sample data is labeled SS location depth (cm). Error bars represent one standard deviation each. 0.00 0.05 0.10 0.15 0.20 0.000.050.100.150.20 VWC (cm3 cm-3)WCR SMC (cm3 cm-3) y = 0.69x + 0.03 R2 = 0.74 0.00 0.05 0.10 0.15 0.20 0.000.050.100.150.20 VWC (cm3 cm-3)WCR SMC (cm3 cm-3) Figure 2-11. Comparison and calibration of WC R and VWC data, displays TIMER and SMS tr eatment data. All error bars represent one standard deviation.

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47 0.00 0.10 0.20 0.30 0.40 0.50 0.60 5/35/135/236/26/12 DATE (2005)SMC (cm3 cm-3) FACTCAL C8 FACTCAL C23 FACTCAL E8 FACTCAL E23FACTORY 0.00 0.10 0.20 0.30 0.40 0.50 0.60 5/35/135/236/26/12 DATE (2005)SMC (cm3 cm-3) PLAUCAL C8 PLAUCAL C23 PLAUCAL E8 PLAUCAL E23PLAUBORG 0.00 0.10 0.20 0.30 0.40 0.50 0.60 5/35/135/236/26/12 DATE (2005)SMC (cm3 cm-3) SITECAL C8 SITECAL C23 SITECAL E8 SITECAL E23SITE Figure 2-12. Comparison of calibrations for a selected time-series from the TIMER tr eatment. The factory calibration for sand, the Plauborg et al. (2005) calibrati on and the site calibration are displayed. Ea st and west locations were averaged for presentation, labeled E8 and E23 for the edge and labeled C8 and C23 for the center locations.

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48 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 WEST SIDE VITEL SMC (cm3 cm-3) EAST SIDE VITEL SMC (cm3 cm-3) 8 cm 1:1 23 cm 8 & 23 CM EDGE 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 WEST SIDE VITEL SMC (cm3 cm-3) EAST SIDE VITEL SMC (cm3 cm-3) Central 8 cm 1:1 Central 23 cm 8 & 23 CM CENTER Figure 2-13. Location comparisons within Vite l probe matrix of the TIMER treatment for Experiment 2. E8, W8, E23, and W23 are edge locations while EC8, WC8, EC23, and WC23 are center locations.

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49 0.05 0.10 0.15 0.20 0.25 0.30 10/1210/1410/1610/1810/2010/2210/24 DATE (2006)VITEL SMC (cm3 cm-3) VITEL WC VITEL EC WCR WC WCR EC 8 CM CENTER 0.05 0.10 0.15 0.20 0.25 0.30 10/1210/1410/1610/1810/2010/2210/24 DATE (2006)VITEL SMC (cm3 cm-3) VITEL WC VITEL EC WCR WC WCR EC 23 CM CENTER 0.05 0.10 0.15 0.20 0.25 0.30 10/1210/1410/1610/1810/2010/2210/24 DATE (2006)VITEL SMC (cm3 cm-3) VITEL W VITEL E WCR W WCR E 8 CM EDGE 0.05 0.10 0.15 0.20 0.25 0.30 10/1210/1410/1610/1810/2010/2210/24 DATE (2006)VITEL SMC (cm3 cm-3) VITEL W VITEL E WCR W WCR E 23 CM EDGE Figure 2-14. Time-series data from all probe locations in the TIMER treatment, for both WCR and Vitel probes. Grouped by simila r locations.

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50 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 VITEL SMC (cm3 cm-3) WCR SMC (cm3 cm-3) West Central 8 cm 1:1 East Central 8 cm 8 CM CENTER 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 VITEL SMC (cm3 cm-3) WCR SMC (cm3 cm-3) West Central 23 cm 1:1 East Central 23 cm 23 CM CENTER 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 VITEL SMC (cm3 cm-3) WCR SMC (cm3 cm-3) Central 8 cm 1:1 Central 23 cm AVERAGE CENTER 0.00 0.05 0.10 0.15 0.20 0.25 0.000.050.100.150.200.25 VITEL SMC (cm3 cm-3)WCR SMC (cm3 cm-3) West 8 cm 1:1 East 8 cm 8 CM EDGE 0.00 0.05 0.10 0.15 0.20 0.25 0.000.050.100.150.200.25 VITEL SMC (cm3 cm-3) WCR SMC (cm3 cm-3) West 23 cm 1:1 East 23 cm 23 CM EDGE 0.00 0.05 0.10 0.15 0.20 0.25 0.000.050.100.150.200.25 VITEL SMC (cm3 cm-3) WCR SMC (cm3 cm-3) 8 cm 1:1 23 cm AVERAGE EDGE Figure 2-15. Comparison of Vitel to WCR SMC for each location within the bed. Al so, location averages are presented for comparison. Averages were calculated using the drip tape as a symmetrical axis, EC8 and WC8 become C8, etc. WCR SMC displayed post-site calibration.

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51 y = 0.33x + 0.12 R2 = 0.29 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.000.050.100.150.200.25 WCR SMC (cm3 cm-3)VITEL SMC (cm3 cm-3)A. y = 0.91x + 0.04 R2 = 0.97 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.000.050.100.150.200.25 WCR SMC (cm3 cm-3)VITEL SMC (cm3 cm-3)B. Figure 2-16. Relationship of SMC measured in the center of the bed at both 8 cm and 23 cm depths by the Vitel and WCR probes. A data match location by location B. data averaged by locati on and match depth by depth. WCR SMC displayed post-site calibration.

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52 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 VITEL SMC (cm3 cm-3) WCR SMC (cm3 cm-3) West Central 8 cm 1:1 East Central 8 cm 8 CM CENTER 0.00 0.05 0.10 0.15 0.20 0.25 0.000.050.100.150.200.25 VITEL SMC (cm3 cm-3) WCR SMC (cm3 cm-3) West 8 cm 1:1 East 8 cm 8 CM EDGE 0.00 0.05 0.10 0.15 0.20 0.25 0.000.050.100.150.200.25 VITEL SMC (cm3 cm-3) WCR SMC (cm3 cm-3) West 23 cm 1:1 East 23 cm 23 CM EDGE 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 VITEL SMC (cm3 cm-3) WCR SMC (cm3 cm-3) West Central 23 cm 1:1 East Central 23 cm 23 CM CENTER 0.05 0.10 0.15 0.20 0.25 0.050.100.150.200.25 VITEL SMC (cm3 cm-3) WCR SMC (cm3 cm-3) Central 8 cm 1:1 Central 23 cm AVERAGE CENTER 0.00 0.05 0.10 0.15 0.20 0.25 0.000.050.100.150.200.25 VITEL SMC (cm3 cm-3) WCR SMC (cm3 cm-3) Edge 8 cm 1:1 Edge 23 cm AVERAGE EDGE Figure 2-17. Comparison of the WCR and Vite l probes for each location within the bed during Experiment 3. Also, location averag es are presented for comparison. Averages were calculated usin g the drip tape as a symmetrical axis, EC8 and WC8 become C8, etc. WCR SMC displayed post-site calibration.

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53 -0.20 -0.10 0.00 0.10 4/235/35/135/236/26/12 DATE (2006)VITEL SMC WCR SMC (cm3 cm-3) WC 8 cm EC 8 cm WC 23 cm EC 23 cm A. -0.20 -0.10 0.00 0.10 4/235/35/135/236/26/12 DATE (2006)VITEL SMC WCR SMC (cm3 cm-3) W 8 cm E 8 cm W 23 cm E 23 cm B. -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 4/235/35/135/236/26/12 DATE (2006)0 2 4 6 8 10BURDEN (g KNO3 L-1) WC8 EC8 WC23 EC23 BURDEN C.VITEL SMC WCR SMC (cm3 cm-3) Figure 2-18. Residuals for each location presen ted as Vitel WCR within the TIMER treatment bed during Experiment 3. A. displa ys center locations B. displays the edge locations C. displays relationship between residuals averaged for each location and soil salinity in the shallow center region.

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54 0.0 0.5 1.0 1.5 2.0 2.5 5/225/245/265/285/30 DATE (2006)VITEL BURDEN (g KNO3 L-1)0.00 0.05 0.10 0.15 0.20 0.25SOIL SAMPLE (g NO3-N L-1) C8 C23 NO3-N May 23, 2006 0.0 0.5 1.0 1.5 2.0 2.5 6/126/146/166/186/20 DATE (2006)VITEL BURDEN (g KNO3 L-1)0.00 0.05 0.10 0.15 0.20 0.25SOIL SAMPLE (g NO3-N L-1) C8 C23 NO3-N June 15, 2006 Figure 2-19. Comparison of Vitel KNO3 burden data (lines) and soil sample NO3-N data (points) for center probe locations within the TIMER treatment bed during Experiment 3. All error bars represent one standard error.

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55 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4/135/35/236/127/2 DATE (2006)SW SALINITY (g KNO3 L-1)4/135/35/236/127/2 E8 C8 E23 C23 SMS 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4/135/35/236/127/2 DATE (2006)SW SALINITY (g KNO3 L-1)4/135/35/236/127/2 E8 C8 E23 C23 TIMER Figure 2-20. Time-series KNO3 burden for each probe location within the TIMER and SMS treatment beds during Experiment 3. Location averages are presented for comparison. Averages were calculated using the drip tape as a symmetrical axis, EC8 and WC8 become C8, etc.

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56 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.000.050.100.150.200.250.30 VWC (cm3 cm-3)WCR SMC (cm3 cm-3) y = 0.93x 0.00 R2 = 0.55 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.000.050.100.150.200.250.30 VWC (cm3 cm-3)WCR SMC (cm3 cm-3) Figure 2-21. Comparison of VWC to the WC R SMC using the 2005 calibration, for each location within the TIMER and SMS treatments during Experiment 3. Error bars equal to one standard deviation. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.000.050.100.150.200.250.30 VWC (cm3 cm-3)WCR SMC (cm3 cm-3) y = 0.63x + 0.03 R2 = 0.54 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.000.050.100.150.200.250.30 VWC (cm3 cm-3)WCR SMC (cm3 cm-3) Figure 2-22. Comparison of VWC to WCR usi ng the factory calibration for sand, for each location within the TIMER and SMS treatments during Experiment 3. Error bars equal to one standard deviation.

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57 CHAPTER 3 WATER ENTRY BOUNDARY CONDITION IMPACTS ON THE CALIBRATION OF HYDRUS-2D TO A SURFACE DRIP IRRIGATION SYSTEM Introduction Vegetables are a major component of Florid a agriculture encompassing about 72,000 ha for production and valued at $1.5 billion annually (USDA, 2006). Most of the soils where these vegetables are grown are sands, with frequent irrigation and fe rtigation required to minimize crop stress and attain maximum production. Water and nutrient delivery to these systems is commonly provided by drip irrigation Also much of the vegetable production in the state occurs on raised beds covered with plastic mulch, which serves to control weed growth and root zone temperatures. The plastic mulch covering also minimizes the influence of evaporation and rainfall in the system (Simonne et al., 2004) isol ating irrigation effects and making these systems ideal for experimental monitoring of water and nu trient distributions beneath drip irrigation. In order to accurately predict environmental impacts associated with intensively managed vegetable production systems, a quantitative desc ription of water movement through the vadose zone is required. In the case of drip irrigati on, a minimum of two dimensions is required to accurately model soil moisture content (SMC) distributions. Recently the two-dimensional HYDRUS-2D model (H2D), which numerically solves Richards' equation for saturatedunsaturated water flow (Simunek et al., 1999), ha s been applied to multiple drip irrigation systems and proven to be a reliable predictor of SMC distributions. To numerically simulate water flow beneath drip irrigati on in H2D and thus predict SMC di stributions, the us er first needs to quantify how water moves within the simulation domain by estimating soil hydraulic parameter. While soil hydraulic properties can be readily measured at the field site, they are commonly estimated based on minimal data. Skaggs et al. (2004) addressed the uncertainty of

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58 soil hydraulic parameters, comparing the ability of different pedotransfer functions to predict SMCs measured beneath drip irrigation. Yet uncertainty associated with quantifying how water enters the simulation domain, described here as the water entry boundary c ondition, is often overlooked. The water entry boundary condition in H2D can be decomposed into two parts: simulation domain dimensions and the soil wetting geometry. The simulation domain can either be quasi th ree-dimensional (3D) or two-dimensional (2D). When using the 3D simulation domain, the left boundary of the twodimensional model area established by the user is assumed to be a radial axis of symmetry compared to 2D simulations that assume a one unit linear depth [L] in addition to the user defined model area (Simunek et al., 1999). As exhi bited by Gardenas et al. (2005) both a 3D simulation domain, commonly referred to as ax i-symmetrical, and 2D simulation domain can be used for surface drip irrigation simulation. A 3D do main assumes the drip system is composed of isolated emitters, commonly described as point source assumptions. A 2D simulation domain assumes the drip system is a line source with water entering the system the full length between emitters. While no 2D drip simulations have yet to be validated by field data, the 3D simulation domain has been successfully used to predict SM C distributions beneath surface drip irrigation in the field (Fernandez-Galvez and Simmonds, 2006) and in a laborat ory setting (Li et al., 2005). In either a 2D or 3D simulation domain, th e boundary over which water enters the domain must be defined. As described here, the soil we tting geometry is analogous to the assigned water inflow boundary within the model for drip irrigation simulations. The soil wetting geometry can vary both in shape and length. Two shapes have b een used previously to initiate water inflow, a quarter-circle or a surface-line, referred to in previous studies as a semi-sphere (SC) and a surface-radius (SR) respectively (Li et al., 2005). Skaggs et al. (2004) assumed a SC soil wetting

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59 geometry with a 0.50 cm radius. The study repo rted good SMC predictions, but noted for high flow rates or low permeability soils the cons tant pressure assignment induced excessive, unrealistic pressure build-ups near the emitter. Li et al. (2005) used a SC shape for a sandy soil and a SR shape for a loam soil. For both soils, their work provided an optimal water entry boundary radius for a given flow rate by compari ng predicted and measured SMC; however, the conclusions of both studies were highly de pendent on their assignment of the soil wetting boundary as a constant pressure boundary, eff ectively assuming full saturation at the boundary. By comparison, the assignment of the soil we tting boundary as a flux boundary should allow for more flexibility when defining the soil wetting boundary length while still obtaining accurate predictions, since the boundary is no t necessarily kept at saturation. Flexibility when defining the so il wetting boundary length can be very valuable since H2D requires all boundary conditions to be static during simulation. In fact, most reported H2D drip simulations use a constant soil wetting boundary length throughout the simulation (Li et al., 2005; Cook et al., 2006; Cote et al., 2003) even though the wetted radius under a drip emitter is in fact dynamic, expanding as the irrigation even t progresses (Goldberg et al., 1971). Gardenas et al. (2005) addressed the consta nt soil wetting boundary length by modifying the H2D code. The soil wetting boundary for their simulations was not constrained to a constant length, but instead allowed for a time-variable ponded boundary length. However, short of code modification no study has addressed the soil wetting boundary leng th question when the boundary is assigned as a flux boundary. It is also important to cons ider the impacts of different water entry boundary conditions on SMC prediction before undertaki ng a management study. While ther e are some cases that clearly define which condition, notably 2D or 3D, should be employed, there are many instances where

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60 examples of both line and point source assumptions can be found in the field. A common example is a drip system with short emitter spacing on a sandy soil, as commonly found for vegetable production in Florida. If field data is not collected, a strong understanding of water entry boundary condition impacts on SMC prediction is required. The objective of the study presented in this document was to compare four water entry boundary conditions for their ability to predict SMC distributions measured in-situ beneath surface drip irrigation in a plastic mulched raised vegetable production system. Materials and Methods Field Experiment The experimental site was located at the Univer sity of Florida, Plant Science Research and Education Unit, near Citra, Florid a. Buster (1979) classi fied the soil at the research site as a Tavares sand and Candler sand. These soils cont ain >97% sand-sized particles and have a field capacity of 0.05-0.07 cm3 cm-3 in the upper 100 cm of the pr ofile (Carlisle et al., 1978). SMC distributions were measured beneath a non-planted section of a drip irrigated, raised bed, vegetable production system. The experimental setup is fully detailed as Experiment 2 in Chapter 2 (Table 2-1), but a short summary of re levant details follows. Irrigation occurred daily from 0600 to 0800 hrs with a nominal emitter flow rate of 0.76 L hr-1 at 69 kPa, with drip emitters spaced 20 cm apart and located at the ce nter of the bed surface. SMC was measured at 15 minute intervals by CS616 (Campbe ll Scientific Inc., Logan, UT ) water content reflectometer (WCR) calibrated to volumetric water content calc ulated from gravimetric soil sampling at the field site (Figure 2-11; Chapter 2). The WCR is a dielectric probe that utilizes time-domain methods to determine the SMC of the medium. A matrix containing eight WCRs was installed in a representative section of the bed (Figure 31). An approximately 40 cm long section of the entire bed width was removed from the instal lation location. The section provided enough space

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61 for horizontal WCR installation parallel to the surf ace. After installati on, the section was repacked with the original soil and covered with black plastic mulch. The matrix was configured in a 2 X 4 (Vertical X Transverse) formation, w ith the top row buried at 8 cm and a bottom row at 23 cm below the surface of the bed. The four columns were spaced on center 16 cm apart centered in the raised bed. The in-situ matrix monitoring approach is similar to the work of Mmolawa and Or (2003). The soil moisture release curve (SMRC) fo r the field site was determined from 11 undisturbed soil cores collected at the site, simila r to the work of Al-Yahyai et al. (2006). Soil cores measured 5.4 cm in diameter and 6.0 cm in height and samples were collected between a depth of 0-6 and 6-12 cm at various places in the field. Tempe cells with 10 pressure steps, up to 750 cm H20, were used to develop the SMRC. The final soil hydraulic parameters were developed by fitting the van Genuchten-Mualem m odel (van Genuchten, 1980) to the data using the RETC program (van Genuchten et al., 1991). The average SMRC was calculated by averaging measured SMC at each pressure step across the 11 samples. A SMRC was developed for each of the 11 sample sites. Model Description The H2D program numerically solves the mixed formulation of the Richards' equation, as proposed by Celia et al. (1990), for saturated-un saturated water flow using Galerkin-type linear finite element schemes. The mixed formulation of Richards equation used in H2D is seen in Equation 3-1, where is the volumetric water content [L3L-3], h is the pressure head [L], S is a sink term [T-1], xi are the spatial coordinates [L], t is time [T], A ijK are components of a dimensionless anisotropy tensor KA, and K is the unsaturated hydraulic conductivity function [LT-1].

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62 S K x h K K x tA iz j A ij i (3-1) An accurate soil-water retent ion curve is required to model the described system. Accordingly, the van Genuchten-Mualem model (E quation 3-2 to 3-4) fo r unsaturated hydraulic conductivity was calibrate d to the system. 0 0 1 h h h hs m n r s r (3-2) 2 /1 1m m l e l e sS S K h K (3-3) where m = 1 1/n, n > 1 (3-4) The van Genuchten-Mualem equations are defined where r is residual water content [L3L-3]; s is saturated water content [L3L-3]; h is pressure head [L]; is soil water retention coefficient [L-1]; n and m are scaling factors [-]; Se is degree of saturation [-]; and Ks is saturated hydraulic conductivity [LT-1]. The van Genuchten-Mualem model within H2D contains five soil dependent input parameters (r s n, and Ks), and a pore-conn ectivity parameter l [-] commonly estimated to be 0.5 for al l soils (Simunek et al., 1999). Water Entry Boundary Condition The water entry boundary condition refers to the combination of simulation domain and wetted emitter geometry. The simulation domain can be two-dimensional (2D) or quasi threedimensional (3D) in H2D, while the soil wetting geometry was specified as either semi-spherical (SC) with water flow initiated over a quarter-cir cle or a surface-radius (SR) with water flow initiated over a surface-line. The 2D simulati on domain assumes the drip tape acts as a line

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63 source with equal flow between emitters, while 3D simulation domain assumes each emitter acts as an independent point sour ce. The line source assumption is reasonable for our data set considering the relatively close (20 cm) emitter spacing at the site. Also, the 30 cm measurement length of the WCR probe relative to the emitter spacing (150% of emitter spacing) means the measured SMC can be considered an average of the bed at a given dept h and distance. The SC soil wetting geometry represents a wetted quartercylinder that forms below the drip tape when coupled with a 2D simulation domain (2DSC) or a wetted hemi-sphere that forms below an emitter when coupled with a 3D simulation domain (3DSC). The SR soil wetting geometry represents a wetted rectangle ba nd that forms below the drip tape when coupled with a 2D simulation domain (2DSR) or a wetted circle th at forms below an emitter when coupled with a 3D simulation domain (3DSR). The four distin ct water entry boundary conditions that were examined are displayed in Figure 3-2. Five boundary radius lengths were examined for their ability to fit the measured SMC data using each water entry boundary condition and to taling 20 simulations. The five boundary radii examined were: 0.25, 0.50, 0.57, 0.75, and 1.0 cm. Radius lengths were limited to 1.0 cm to best approximate a point source and to eliminate erro rs due to the water en try boundary approaching the monitoring locations. The 0.57 cm radius was recommended for the 3DSC simulations on sandy soils at this studys flow rate when using a constant pressure boundar y (Li et al., 2005) and it is included here for comparison with results in the literature. For SR simulations, the radius length is equivalent to the boundary length along the surface. The water entry boundary (Figure 3-2) was a ssigned as a variable flux boundary. And while each method requires a flux value (cm min-1) for simulation, the flux values change

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64 depending on the soil wetting geometry and bounda ry length of each simulation. The general approach of flow rate divided by surface area was employed for each method (Table 3-1). Additional Boundary and Initial Conditions For all model runs, only half of the bed ar ea was considered with calibration performed under the assumption that water flow is symmetrical across the vertical plan e directly beneath the emitter (Wooding, 1968; Warrick, 1974). The nominal emitter flow rate of 0.76 L hr-1 was used in all simulations. The defined simulation area had the general shape of a rectangle, representing a soil half-section below the surface, bounded by the bed center and bed edge, and located to the right of an emitter. Accordingly, the soil wetting geometry was located at the intersection of the left vertical boundary and the upper boundary. Th e left vertical boundary and upper boundary were assigned as no flux, representing the symmet ry across the vertical plane and plastic mulch covering the surface, respectively. The lower bo undary of the profile was assigned as a free drainage boundary located 60 cm subsurface. The right vertical boundary, which represents the boundary between the soil half-section and the inter-row area, was also assigned as a free drainage boundary for 3D simulations and a free drainage boundary below 25 cm subsurface for 2D simulations. Between 0 and 25 cm subsurface, the right vertical boundary was assigned as a no flux boundary for 2D simulations, again due to th e plastic mulch covering. Assignment of the upper 25 cm of the right vertical boundary as free drainage or no flux for the 3D domain simulations was assumed to be equivalent, as wate r flow should not reach this region due to the point source assumption. All simulation data sets started on October 13, day of simulation (DOS) 0, and ended October 23, DOS 10. The entire model dom ain was initialized (DOS -4) at 0.10 cm3 cm-3 SMC. From DOS -4 to 0 SMC distributions were allo wed to reach a quasi-sta tic state by applying the same irrigation events as between DOS 0 and 10. The water content tolerance was set at 0.001

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65 (cm3 cm-3) representing the absolute ma gnitude of change allowed for unsaturated nodes between two iterations within a time step (Simunek et al., 1999). The finite element dimensions were generated automatically by H2D MESHGEN. Sma ller elements were created around the water entry boundary to account for rapid variable ch anges, increasing model stability. Generally element size increased as the lower and right vertical boundary intersection was approach, with MESHGEN densities 200% greate r at the lower and right vert ical boundary in tersection as compared to around the water entry boundary. Calibration and Optimization Procedure The initial calibration include d the 20 simulations accounting for the four water entry boundary conditions and five boundary radii (Table 3-1). The initial calibration simulations used the average SMRC measured at the field site while inversely optimizing for Ks. To account for the uncertainty associated with soil hydraulic parameter estimation, each simulation setup used during the initial ca libration was rerun while al lowing for the optimization of five soil hydraulic parameters (full calibration). During the full calibration r s and n were bounded during optimization by the range of values determined from the collected undisturbed soil cores. Ks was again included in the optimization process, which simultaneously occurred for all five parameters. Each inverse optimization was based on the numerical solutions of Richards Equation (Equation 3-1). All optimizations were perf ormed using the built-i n Levenberg-Marquardt nonlinear minimization method in H2D. During the inverse optimization process, the unknown parameters are determined by the minimization of an established objectiv e function (Simunek et al., 1999). All weighing coefficients were set to 1. Measured SM C was used during optimization to determine Ks for the initial calibrations and to simultaneously determine r s n, and Ks

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66 for the full calibrations. Multiple optimizations were performed for each calibration simulation using different initial values for the parameters to be determined in order to increase the probability of finding the global minimum. Prediction Evaluation Two goodness-of-fit indicators ar e reported by H2D following a given simulation, sum of squares (SSQ) and the coefficient of determination (R2) (Simunek et al., 1999). Both indicators simply use the squared residual to represent the deviation between paired measured and predicted data. The NashSutcliffe (1970) co efficient of efficiency (Ceff) uses a similar approach, where iO is measured data; iP is predicted data; and O is the mean of the measured data (Equation 35). The range of Ceff lies between 1.0 (p erfect fit) and When Ceff is lower than zero the mean value of the measured time series would have be en a better predictor than the model (Nash and Sutcliffe, 1970). Ceff is the reported goodness-of-fit indicator in this study because it is better suited to evaluate model goodness-of-fit compared to SSQ or R2 (Legates and McCabe, 1999). n i i n i i i effO O P O C1 2 1 20 1 (3-5) In the presence of measurement un certainty, it is also valuable to evaluate paired measured and predicted data against the uncertainty boundar ies of the measured data instead of against individual data values. When the uncertainty boundary, but not the distribution of uncertainty around each measured data point is known, Harmel and Smith (2007) proposed that the chosen goodness-of-fit indicator can be improved by a modi fication that accounts for this uncertainty, summarily described here.

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67 n i nE E E E PER1 2 2 3 2 2 2 1... (3.6) The probable error range (PER), where n is th e number of potentia l error sources and En is the uncertainty associated with each potential er ror source (%), was used to establish an upper and lower bound for the measured SMC at a given time (Equation 3-6). If iP fell within the established boundary, the residual used in Ceff calculation is changed to zero. If iP fell outside the established boundary, the residual used in Ceff calculation is changed to the difference between iP and the nearest boundary value (Harmel and Smith, 2007). To account for the measured SMC uncertainty, the modified Ceff is also presented, re ported in this study as Ceff*. For SMC measurements in this study, three so urces of error were considered. The first was the reported WCR accuracy, 0.025 cm3 cm-3 (Campbell Scientific, Inc. 2002). Recall the WCR measurements were further calibrated to the fiel d site (Chapter 2) usi ng measured gravimetric data that was converted to volumetric soil mois ture by using bulk density measurements. The WCR error (E1) was calculated as the reported accuracy divided by the average SMC for each probe used in model calibration over the time-ser ies of interest, 18.8%. The errors for the soil samples were calculated by dividi ng the standard error of the m easurements by the mean of the measurements, resulting in a gravimetric error (E2) of 10.3% and a bulk density error (E3) of 2.0%. The three error sources result in a PER of 21.5% for SMC measurements. Results and Discussion Field Results Since symmetry in SMC distribut ion was assumed across each half of the raised vegetable bed, probe measurements at similar locations on each half-bed were averaged. After averaging, the probes as labeled in Figure 31 were renamed with respect to their location, center of the bed

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68 (C) or edge of the bed (E), and their depth, 8 cm (8) or 23 cm (23) subsurface. Therefore, E8 is the average of probe 1 and 4; C8 is the average of probe 2 and 3; E23 is the average of probe 5 and 8; and C23 is the average of probe 6 and 7. Averaging also minimizes errors associated with the drip tape lying away from th e exact bed center. Since the expe riment site required separate irrigation and fertigation drip lines (Chapter 2), locations ar e never truly symmetrical, but averaging yields a representative SMC fo r the location of interest (Figure 3-3). SMC from the outer edges of the raised be d differed substantially. Differences between probes 1 and 4 at the E8 lo cation ranged between 0.06 cm3 cm-3 and 0.10 cm3 cm-3. The difference could be due to a number of factor s; however, SMC at the E8 location was only minimally impacted by irrigation with SMC ranging from 0.11 cm3 cm-3 and 0.14 cm3 cm-3 on average (Figure 3-3). Due to the observed differe nce in measurements a three location data set (C8, C23, and E23) was used for model calibrati on. The C23 location yielded the most variable data of the remaining three locations, with cons istent deviations in SMC between probe 6 and 7 near 0.04 cm3 cm-3 and as high as 0.05 cm3 cm-3 (Figure 3-4). Measurement variability was also observed in the soil core da ta (Table 3-2), with only s having a standard er ror less than 10% of the parameter average (3.2%). The average SMRC is presented in Figure 3-5. Initial Calibration During initial calibration, only Ks was optimized to measured SMC data. It was observed that the SC and SR soil wetting geomet ries returned nearly identical Ks values and SMC time series for each simulation domain (2D and 3D) with a similar boundary radius (eg. 2DSC0.50 = 2DSR0.50). However, the SC simulations required less than half the run time as SR simulations, meaning the SR simulations can be considered less efficient replic ates of the SC simulations. For this reason, only the results of SC simulati ons are reported here, with the soil hydraulic

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69 parameters, Ceff, and Ceff* for the 2DSC and 3DSC simulations for all five boundary radii presented in Table 3-3. From Table 3-3 and Figure 3-6, it can be said that using a flux boundary condition allows for maximal flexibility in boundary length assignme nt. In fact, allowing for the optimization of a single hydraulic parameter (Ks), which regardless is difficult to measure, yields similar fits independent of water entry boundary radius for all 2D and 3D si mulations, respectively. Thus, a flux boundary in H2D with a known SMRC results in maximal correlation (data prediction) for SC boundary radii less than 1.0 cm. With the soil wetting geometry settled and the observed flexibility in boundary radius, for situations where the SMRC is known the only water entry boundary condition unknown is the simulation domain. Based on correlation to the averaged data, the 2D simulations (Ceff ranging from 0.872 to 0.914) perform better than their 3D counterparts (Ceff ranging from 0.771 to 0.774) for our data set (Table 3-3). Th e superior correlation is proba bly a result of the measurement technique used at the site, as the 150% em itter spacing collection volume of the WCR probe coupled with the relatively short emitter spac ing in general (20 cm) matches the line source assumptions of the 2D simulations; however, wh en the measured uncertainty is accounted for (Ceff* values; Table 3-3), the 3D simulation domai ns are also observed to provide very good predictions (Ceff* = 1.0). This means that the measured SMC uncertainty in our study was greater than the impact on model predicti ons of either line source or point source assumptions or more generally, water entry boundary conditions. The larger impact of measurement uncertainty compared to simulation domain uncertainty may not be the case for all drip irrigation simula tions, but likely is the case when examples of both line source and point source assumptions are evident in th e field. As previously noted, the

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70 field site in this study is such an example as the short emitter spacing (20 cm) coupled with the sandy soil at the resear ch site created a system that shares both line source (at deeper depths) and point source (at shallow depths) characteristics. If a system were more physically representative of line source or point source assumptions, a larger impact on model predictions would be expected based on using the 2D or 3D simulati on domains. Also a more accurate determination of SMC, such as the use of TDR, would reduc e the SMC uncertainty in creasing the relative impact of water entry boundary conditions. There is also a noticeable difference betw een conductivity values optimized for 2D simulations compared to 3D simulations which all optimized at the same Ks value. The observed similarity of the 3D simulation Ks values is likely unique to the m easured data used in this study. Full Calibration During the full calibration, all soil hydraulic parameters were optimized within the range of values measured on site. While uncertainty in the measured SMC data can be accounted for by improved goodness-of-fit methods (Ceff*), neither these methods nor any of the initial calibrations presented directly account for soil hydraulic parameter uncertainty. Since simply accounting for SMC measurement uncertainty duri ng the initial cal ibration already resulted in excellent model prediction goodness-of-fit, sim ilarly high correlations were expected and observed during the full ca libration (Table 3-4). The 3D simulations did not pr edict the SMC distributions as well as the 2D simulations prior to accounting for SMC uncertainty (Table 3.-3 ); therefore, the incr ease in 3D simulation Ceff values (0.771 to 0.906) is a better indi cator of model predic tion improvement when accounting for soil hydraulic parame ter uncertainty (Table 3-4). But, a modest improvement in 2D predictions was also observed follow ing the full calibration (increasing Ceff values from 0.872 to 0.961). The improvement of the 3D simulati on model fit is best seen visually at the C23

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71 location (Figure 3-7) where the 3D full calibration is nearly indi stinguishable from the 2D full calibration. Considering the difficulties in estimating soil hydraulic parameters from site measurements, inverse optimization of soil parame ters can be a reliable alternative that can alleviate errors associated with using a predet ermined (or inaccurately estimated) SMRC. While in our study each parameter range was established by measured data, the parameter ranges could be established by previously tabulated parame ter distribution data (Carsel and Parrish, 1988) eliminating the need for field measurements. Ta ble 3-4 shows that optimal parameters varied with boundary radius length, but Ceff and Ceff* remained above 0.9 for nearly all simulations. Again, these results indicate flexibility in assi gning a water entry boundary radius length. If the SMRC is known, optimization of Ks mitigates any influence of different radius lengths. If only minimal knowledge of the soil is obtainable, optimization of all hydraulic parameters will account for any influence of differe nt radius lengths, as again Ks is included. And if we are assuming minimal knowledge of the site, no set of hydraulic parameters can be considered better than another set, so the wate r entry boundary radius length ca n be considered flexible. It is also noteworthy that all 3D simulations optimized r above 0.09, a value exceed at only one sample location (Table 3-2). This is the only observation ma de in the study that champions one simulation domain over anothe r while accounting for uncertainty. It was observed in simulations not reported here that as r was reduced so were Ceff values for 3D simulations even following soil hydraulic parameter optimization. Decreasing Ceff values would favor the 2D simulation domain but again once SMC measurement uncertainty is considered (Ceff*) both simulation domains can be considered excellent predictors.

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72 Summary and Conclusions For drip simulations on a sandy soil, run time efficiency was doubled when a SC soil wetting geometry was used instead of a SR soil wetting geometry. Given the similarity of SMC distributions predicted by the different soil wetti ng geometries, the SC geometry is thus superior. For both simulation domains, little difference in model prediction was observed between different boundary radius lengths. This is due to the water entr y boundary condition being designated as a flux, instead of constant pressure (saturation) and allowi ng for optimization of Ks. In terms of model use, the selection of a flux boundary condition allows for flexibility when assigning a boundary radius and eliminates one more potential unknown. Radius lengths under 1.0 cm represent the physical sy stem well and are shown in this study to be adequate for simulating surface drip irrigation. The superior ity of the SC soil wetting geometry and the flexibility observed for defining the water entry boundary radius le ngth leaves only the simulation domain as a potential unknow n during water entry method selection. For the raised bed vegetable production syst em on a sandy soil, both the 2D simulation domain and the 3D simulation domain provided reasonable predictions of the measured SMC data once SMC measurement uncertainty was considered. Due to the monitoring equipment measuring the average soil moisture content ov er a bed length equivalent to 150% emitter spacing and the relatively short emitter spacing (20 cm), the line source assumptions seemed more representative of the measured data. A nd initially, the 2D simulation domain appeared superior in our study. But as observed followi ng the consideration of estimated soil hydraulic parameter uncertainty during the full calibration, both the 2D and 3D simulation domains lead to very good model predictions (Ceff > 0.9). The sandy soil at th e study site added point source characteristics to the system and is likely the reason the high goodness-of -fit indicators observed for 3D simulations, improved further after the consideration of measured SMC uncertainty (Ceff*

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73 = 1.0). This means that for the study site, which was representative of sites sharing line source and point source characteristics, measurem ent uncertainty has more impact on model performance than the selection of a simulation domain.

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74 Table 3-1. Results of surface area and influx calcula tions for the different scenarios simulated in HYDRUS-2D Simulation Simulation domain Soil wetting geometry Radius (cm) Surface area (cm2) Calculated influx (cm min-1) 2DSC0.25 2D SC 0.25 0.393 0.803 2DSR0.25 2D SR 0.25 0.250 1.262 2DSC0.50 2D SC 0.50 0.785 0.402 2DSR0.50 2D SR 0.50 0.500 0.631 2DSC0.57 2D SC 0.57 0.895 0.352 2DSR0.57 2D SR 0.57 0.570 0.553 2DSC0.75 2D SC 0.75 1.178 0.268 2DSR0.75 2D SR 0.75 0.750 0.421 2DSC1.0 2D SC 1.00 1.571 0.201 2DSR1.0 2D SR 1.00 1.000 0.315 3DSC0.25 3D SC 0.25 0.393 32.132 3DSR0.25 3D SR 0.25 0.196 64.263 3DSC0.50 3D SC 0.50 1.571 8.033 3DSR0.50 3D SR 0.50 0.785 16.066 3DSC0.57 3D SC 0.57 2.041 6.181 3DSR0.57 3D SR 0.57 1.021 12.362 3DSC0.75 3D SC 0.75 3.534 3.570 3DSR0.75 3D SR 0.75 1.767 7.140 3DSC1.0 3D SC 1.00 6.283 2.008 3DSR1.0 3D SR 1.00 3.142 4.016 SC is semi-sphere and SR is surface-radius Half of the nominal flow rate (0.757 L hr-1) was considered for the two-dimensional (2D) simulations to match the half-bed setup. Influx values for 2D simulations are for 1 cm of the 20 cm emitter spacing. Threedimensional (3D) simulations used the nominal flow rate to calculate influx and did not consider emitter spacing in calculation. Table 3-2. Estimated soil hydraulic parameters for van Genuchten model (van Genuchten, 1980) fit to 11 soil core samples by RETC model (van Genuchten et al., 1991). Parameter Average One standard deviation (-,+) Range r (cm3 cm-3) 0.061 (0.014,0.108) (0.001,0.150) s (cm3 cm-3) 0.393 (0.351,0.435) (0.329,0.462) (cm-1) 0.025 (0.016,0.034) (0.016,0.044) n (-) 2.286 (1.318,3.254) (1.586,4.572) r is residual water content. s is saturated water content. and n are fitting parameters for the van Genuchten model.

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75 Table 3-3. Results from initial calibration Simulation Ks (cm min-1) Ceff Ceff* 2DSC0.25 0.807 (0.779,0.835) 0.882 1.000 2DSC0.50 0.670 (0.651,0.689) 0.914 1.000 2DSC0.57 0.670 (0.646,0.694) 0.914 1.000 2DSC0.75 0.808 (0.793,0.825) 0.882 1.000 2DSC1.0 0.849 (0.832,0.866) 0.872 1.000 3DSC0.25 0.264 (0.191,0.334) 0.771 1.000 3DSC0.50 0.264 (0.191,0.334) 0.772 1.000 3DSC0.57 0.264 (0.193,0.335) 0.773 1.000 3DSC0.75 0.264 (0.194,0.335) 0.774 1.000 3DSC1.0 0.264 (0.194,0.335) 0.774 1.000 Average values used: residual water content ( r) = 0.061; saturated water content ( s) = 0.393; = 0.025; and n = 2.286. 95% confidence intervals calculated by HYDRUS-2D (-,+) displayed following saturated hydraulic conductivity (Ks) mean values. Ceff is Nash and Sutcliffe (1970) coefficient of efficiency. Ceff* is Nash and Sutcliffe (1970) coefficient of efficiency with measurement uncertainty (Harmel and Smith, 2007).

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76Table 3-4. Results from full calibration Simulation r (cm3 cm-3) s (cm3 cm-3) (cm-1) n (-) Ks (cm min-1) Ceff Ceff* 2DSC0.25 0.057 (0.040,0.075) 0.357 (0.257,0.458) 0.044 (0.016,0.072) 2.228 (1.640,2.816) 0.585 (-0.420,1.590) 0.947 1.000 2DSC0.50 0.062 (0.050,0.074) 0.372 (0.285,0.459) 0.044 (0.020,0.068) 2.380 (1.859,2.902) 0.599 (-0.285,1.483) 0.956 1.000 2DSC0.57 0.060 (0.044,0.076) 0.379 (0.284,0.474) 0.044 (0.018,0.070) 2.376 (1.743,3.010) 0.617 (-0.288,1.521) 0.957 1.000 2DSC0.75 0.062 (0.049,0.076) 0.372 (0.284,0.461) 0.044 (0.021,0.067) 2.389 (1.821,2.597) 0.597 (-0.221,1.415) 0.957 1.000 2DSC1.0 0.063 (0.051,0.075) 0.362 (0.291,0.433) 0.044 (0.024,0.064) 2.452 (1.920,2.985) 0.475 (-0.078,1.027) 0.961 1.000 3DSC0.25 0.099 (0.098,0.101) 0.386 (0.374,0.397) 0.037 (0.032,0.042) 4.570 (4.167,4.973) 0.376 (0.335,0.417) 0.906 1.000 3DSC0.50 0.098 (0.095,0.100) 0.368 (0.322,0.415) 0.036 (0.027,0.045) 4.567 (3.706,5.427) 0.299 (0.119,0.469) 0.912 1.000 3DSC0.57 0.093 (0.097,0.102) 0.334 (0.384,0.460) 0.044 (0.028,0.046) 4.570 (3.740,5.401) 0.293 (0.292,0.788) 0.908 1.000 3DSC0.75 0.094 (0.088,0.100) 0.365 (0.318,0.412) 0.044 (0.025,0.063) 3.535 (2.462,4.609) 0.390 (0.225,0.554) 0.908 1.000 3DSC1.0 0.092 (0.088,0.095) 0.336 (0.289,0.384) 0.044 (0.035,0.051) 3.208 (2.787,3.629) 0.281 (0.108,0.455) 0.895 1.000 r is residual water content; s is saturated water content; and Ks is saturated hydraulic conductivity. 95% confidence intervals calculated by HYDRUS-2D (-,+) displayed following reported mean values. Ceff is Nash and Sutcliffe (1970) coefficient of efficiency. Ceff* is Nash and Sutcliffe (1970) coefficient of efficiency with measurement uncertainty (Harmel and Smith, 2007).

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77 Figure 3-1. Experiment 2 WCR ma trix configuration centered in bed. Numbering of probes used in results discussion also shown.

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78 line source / two-dimensional (2D) point source / axi-symmetrical (3D)surface-radius (SR)semi-sphere (SC) 2DSR 3DSR3DSC 2DSC Figure 3-2. Water entry boundary conditions exam ined for soil moisture content prediction.

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79 0.05 0.10 0.15 0.20 0.25 10/1310/1510/1710/1910/2110/23 DATESMC (cm3 cm-3) E8 C8 E23 C23 Figure 3-3. Averaged soil moisture conten t (SMC) from data measured on site.

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80 0.05 0.10 0.15 0.20 0.25 0.001.002.003.004.005.00 DAY OF SIMULATIONSMC (cm3 cm-3)C8 0.05 0.10 0.15 0.20 0.25 0.001.002.003.004.005.00 DAY OF SIMULATIONSMC (cm3 cm-3)C23 0.05 0.10 0.15 0.20 0.25 0.001.002.003.004.005.00 DAY OF SIMULATIONSMC (cm3 cm-3)E23 Figure 3-4. Measured soil moisture conten t (SMC) from each probe representing locations C8, C23, and E23. Thin light lines represent the measured data from an individual probe and thick dark li nes represent the resulting average.

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81 0.00 0.10 0.20 0.30 0.40 0.50 00.511.522.53 log [h (cm)]SMC (cm3 cm-3) Figure 3-5. Results of RETC mode l (van Genuchten et al., 1991) calibration to soil core data. Displays average soil moisture content (SMC ) for each pressure step and the resulting SMRC (van Genuchten, 1980) from the RETC calibration. Error bars represent one standard deviation of measured data.

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82 0.05 0.10 0.15 0.20 0.25 0.01.02.03.04.05.0 DAY OF SIMULATIONSMC (cm3 cm-3) PER BOUNDS 2DSC0.50 3DSC0.50 C8 0.05 0.10 0.15 0.20 0.25 0.01.02.03.04.05.0 DAY OF SIMULATIONSMC (cm3 cm-3) PER BOUNDS 2DSC0.50 3DSC0.50 C23 0.05 0.10 0.15 0.20 0.25 0.01.02.03.04.05.0 DAY OF SIMULATIONSMC (cm3 cm-3) PER BOUNDS 2DSC0.50 3DSC0.50 E23 Figure 3-6. Results of initial calibration soil moisture content (SMC) predictions for a represen tative period of simulation, D OS 2 to 3. PER BOUNDS represents the upper and lower boundary of measured data coll ected when measured uncertainty is included. 0.05 0.10 0.15 0.20 0.25 0.01.02.03.04.05.0 DAY OF SIMULATIONSMC (cm3 cm-3) PER BOUNDS 2DSC0.50 3DSC0.50 C23: Full Calibration 0.05 0.10 0.15 0.20 0.25 0.01.02.03.04.05.0 DAY OF SIMULATIONSMC (cm3 cm-3) PER BOUNDS 2DSC0.50 3DSC0.50 C23: Initial Calibration Figure 3-7. Comparison of initial and full calibration soil moistu re content (SMC) predictions of the C23 location for a repres entative period of simulation, DOS 0 to 5. PER BOUNDS represents the upper and lower boundary of measured data collected when measured uncertainty is included.

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83 CHAPTER 4 UNCERTAINTY IMPACTS ON NUMERICAL MODELING OF FERTIGATION Introduction Vegetables are a major component of Florid a agriculture encompassing about 72,000 ha for production and valued at $1.5 billion annua lly (USDA, 2006). Much of the vegetable production in the state occurs on raised beds co vered with plastic mulch. Water and nutrient delivery to these systems is comm only provided by drip irrigation. The term fertigation describes the process of applying fertilizer s through a drip irrigation system. With most of the soils where these vegetables are grown classified as sands, fr equent irrigation and fer tigation is required to minimize crop stress and attain maximum production. Also the plastic mulch covering the raised bed minimizes the influence of evaporation a nd rainfall in the system (Simonne et al., 2004) isolating irrigation effects and making these sy stems ideal for experimental monitoring of distributions beneath drip irrigation. Recently the numerical, two-dimensional mode l HYDRUS-2D (H2D) has been applied to drip irrigation systems and proven to be a re liable predictor of water and nutrient dynamics (Gardenas et al., 2005). The H2D program numerically solves Ri chards' equation for saturatedunsaturated water flow and the convection-dispersion equation for solute transport. The flow equation also incorporates a sink term to account for water uptake by plant roots (Simunek et al., 1999). Still prediction inaccuracies can be found in the literature that stem from soil hydraulic and transport parameter estimations; moreover, measurements of these parameters are often costly, time consuming, and cumbersome. Studies using H2D for drip irrigation simula tions have employed seve ral different methods to estimate soil hydraulic parameters. Many use prev iously tabulated values, such as Cote et al. (2003) where a subsurface drip irrigation syst em was simulated on three different soils,

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84 employing the soil hydraulic parameters previo usly tabulated by Carsel and Parrish (1988), provided in the H2D soil catalog. Skaggs et al. (2004) examined predictions of soil moisture content (SMC) using soil hydraulic parameters de rived from different pedotransfer functions. Their results emphasized the importance of satu rated water content a nd saturated hydraulic conductivity over other soil hydrau lic parameters as well as crowning the ROSETTA model (Schaap et al., 1998) predictions based on soil cl ass superior to Cars el and Parrish (1988) predictions due to excess vertical drainage predicted by the latter. The study focused on drip irrigation of a sandy loam, but stopped shor t of considering solute transport. In fact, only a few studies using H2D have deal t with fertigation. Gardenas et al. (2005) modeled nitrate (NO3) fertigation beneath both surface a nd subsurface drip systems, using tabulated soil hydraulic parameters (Carsel and Parrish, 1988; Schaap et al., 1998) for each soil type and assuming fixed soil transport parameters Hanson et al. (2006) ex tended this work for urea-ammonium-nitrate fertilizer, but neither st udy presented field measurements beneath a fertigation system. In the laboratory, Li et al. (2005) assumed a longitudinal dispersivity of 0.1 cm to predict NO3 transport through a soil core and reported good co rrelation to laboratory measurements. Yet, Ajdary et al. (2007) wa s the only study found that applied H2D to a fertigation system with nutrient data collected in-season. They used tabulated values for soil hydraulic parameters and fixed soil transport para meters to validate predictions against soil sample data that was collected periodically following fertigation events. Inverse optimization can help alleviate uncer tainty from using mean parameter values within distributions of soil parameters. Duri ng inverse optimization soil parameters are bounded by a known range that can be dete rmined through field measurements or previously established parameter distributions. The inverse optimization process attempts several parameter

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85 combinations until the error between model prediction and measurement is minimized. Simulating furrow irrigation with H2D, Abbasi et al. (2003) employed an inverse optimization soil parameter estimation reporting a two-step ap proach, first soil hydraulic parameters then transport parameters, to better predict SMC compar ed to a single-step optimization approach, but little difference in concentration estimates was observed between approaches. Uncertainty in measured values can also be accounted for through improved goodness-of-fit indicators (Harmel and Smith, 2007). For a technology that carries high resource conservation potentia l, it speaks to the difficulty of obtaining measurements that only one study to date has c oupled detailed in-season monitoring of fertigation with th e two-dimensional modeling of nut rient transport available with H2D. The objective of this study was to strengt hen the existing data se t in the literature by collecting in-situ measurements of SMC a nd nutrient distributions following in-season fertigation of a raised bed vegetable production system covered with plastic mulch and compare H2D predictions to the measurements while co nsidering soil parameter estimation uncertainty through inverse optimization of soil parameters and measurement uncer tainty using improved goodness-of-fit indicators. Materials and Methods Measurement Methods SMC was measured at 15 minute intervals by the CS616 (Campbell Scientific Inc., Logan, Utah) water content reflectometer (WCR) calibrated to volumetric water content calculated from gravimetric soil sampling at the field site (Cha pter 2). Soil water conductivity (K) was also measured at 15 minute intervals by the Hydra Prob e II (Stevens Water Mon itoring Systems, Inc., Portland, Oregon), commonly referred to as a Vi tel Probe. A matrix c ontaining eight WCRs was installed in a representative s ection of the bed (Figure 4-1). An approximately 40 cm long section

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86 of the entire bed width was removed from the installation location. Th e section provided enough space for horizontal WCR installation parallel to the surface. A matrix containing eight Vitel probes was installed on the opposite trench face. An alysis of a similar field setup revealed the opposite trench face locations can be considered re plicates (Chapter 2). Af ter installation of each matrix, the section was repacked and covered with plastic mulch. Each matrix was configured in a 2 X 4 (Vertical X Transverse) formation, with the top row buried at 8 cm and a bottom row at 23 cm below the surface of the bed. The four columns were spaced on center 16 cm apart centered directly under the drip tape. Tomato plan ts were located near the interface of the probe rods and the portion cont aining the electronics. Due to difficulties experienced at the field si te the actual Vitel matrix location placed the center of the probe measurement volumes approximately 3 cm away from the nearest emitter, measured along the drip line. Al so the probe measured K (S m-1) represents the combined effect of all the fertigation constituents; however, it has previously been observed that non-adsorbing, non-transforming ions such as NO3 and chloride (Cl) exhibit similar relationships between concentration and K (Muoz-Carpena et al., 20 05a). Considering this and assuming that NO3 was the most influential ion, since it represen ted 79% of the fertigat ion anion weight, probe measured K was transformed to NO3 concentrations using the equa tion presented by Neve et al. (2000). Still the probe location and combined concentration assumption introduce measurement uncertainty that was not quantified here. A weather station located w ithin 500 m of the experime ntal site provided hourly temperature, relative humidity, solar radiation and wind speed data that was used to calculate reference evapotranspiration (ET0) according to FAO-56 (A llen et al., 1998). Crop evapotranspiration (ETc) was calculated base d on the product of ET0 and the crop coefficient

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87 (Kc) for a given crop growth stage (Simonne et al., 2004) and values were reduced by 30% to account for the effect of plastic mulched vegetable beds on overall ETc values (Amayreh and AlAbed, 2005). ETc averaged 0.26 cm day-1 with a standard deviation of 0.01 cm day-1 for the period surrounding the fertigat ion events of interest. To determine the root distribution, root samp les were collected with a 5 cm diameter soil auger at 0-15, 15-30, 30-60, and 60 to 90 cm dept h layers and in three positions: 0, 12.5, and 25 cm distance on a transverse line perpendicular to the plant row. Root samples were collected 66 days after transplanting to ensure full root growth and can be c onsidered a reasonable estimate of the root distribution for Experiment 3 and Experi ment 4. Immediately after collection, samples were put in plastic bags and refrigerated at 4C until cleaning. The samples were washed on a 2 mm sieve and organic debris was cleaned manually. Roots were then placed in Petri dishes and frozen until further analysis. The root samples were scanned and the root length and diameter was measured by WINRHIZO software (Rgent Instrument, Inc., Canada). Experimental Site The experimental site was located at the Univer sity of Florida, Plant Science Research and Education Unit, near Citra, Florid a. Buster (1979) classi fied the soil at the research site as a Tavares sand and Candler sand. These soils cont ain >97% sand-sized particles and have a field capacity of 0.05-0.07 cm3 cm-3 in the upper 100 cm of the pr ofile (Carlisle et al., 1978). Two distinct data sets were used in this study, one collect ed in-season and one collected post-season, previously summarized in Tabl e 2-1 as Experiment 3 and Experiment 4 respectively. The Experiment 3 setup was previo usly described (Chapter 2) with additional relevant information provided here. Experiment 3 SMC and K measurements transformed to NO3 concentrations were used for solute predicti ons, focusing on fertigation events that occurred on May 30, June 6, and June 14, 2006. The three fertigation events were chosen due to their

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88 similar applications, associated evapotranspiration (0.26 cm day-1), and associated root distribution. Fertigation events were applied manually inline and o ccurred in the early afternoon. Fertilizer for the three fertigation events fo cused on in this study was composed of 71.7% Ca(NO3)2H2O, 21.5% KCl, and 6.8% Mg(SO4)7H2O. Experiment 4: 2006 Post-Season Experiment 4 involved the collection of pos t-season WCR SMC measurements to account for any in-season modifications to the soil hydraulic parameters, but eliminate the influence of transpiration. To accomplish this, following harv est on July 5 the tomato plants surrounding the Experiment 3 monitoring sites were clipped near the soil surface. Data was collected until July 14. The data collected from July 8 to July 14 thus represents a bed modified by root growth (or other in-season processes), but under no transpiration influence. Experiment 4 SMC was used for calibration of soil hydraulic parameters. Similar to Experiment 3, irrigation occurred daily from 0600 to 0800 hrs with a nominal emitter flow rate of 0.76 L hr-1 at 69 kPa. Model Description The H2D program numerically solves the mixe d formulation of Rich ards' equation, as proposed by Celia et al. (1990), for saturated-un saturated water flow using Galerkin-type linear finite element schemes (Equation 3-1) and th e convection-dispersion equation for solute transport as well as incorporating a sink term to account for water uptake by plant roots. An accurate soil moisture release cu rve is also required to model the system. Accordingly, the van Genuchten-Mualem model (van Genuchten, 1980) wa s calibrated to the system (Equations 4-1 to 4-3). 0 0 1h h h hs m n r s r (4-1)

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89 2 /1 1m m l e l e sS S K h K (4-2) where m = 1 1/n, n > 1 (4-3) The van Genuchten-Mualem equations are defined where r is residual water content [L3L-3], s is saturated water content [L3L-3], h is pressure head [L], is soil water retention coefficient [L-1], n and m are scaling factors [-], Se is degree of saturation [-], and Ks is saturated hydraulic conductivity [LT-1]. The van Genuchten-Mualem model within H2D requires a poreconnectivity parameter l [-] that was estimated to be 0.5 for all scenarios and also contains five soil dependent input parameters (r s n, and Ks). The water content tolerance was set at 0.001 [L3L-3] representing the absolute magnitude of change allowed for unsaturated nodes between two iterations within a time step. For solute transport, the Crank-Nicholson implicit scheme was used along with a Galerkin spatia l weighting scheme (Simunek et al., 1999). Initial and Boundary Conditions For all model runs, only half of the bed ar ea was considered with calibration performed under the assumption that water flow is symmetrical across the vertical plan e directly beneath the emitter (Wooding, 1968; Warrick, 1974). The nominal emitter flow rate of 0.76 L hr-1 was used in all simulations. The defined simulation area had the general shape of a rectangle, representing a soil half-section below the surface, bounded by the bed center and bed edge, and located to the right of an emitter. A two-dimensional simulation domain, semi-spherical soil wetting geometry, and 0.50 cm boundary radius (water entry boundary) was chosen to represent the system due to the superior performance prior to uncertainty consideration previously observed for similar systems (Chapter 3). The water en try boundary was located at the inte rsection of the left vertical boundary and the upper boundary. During irrigation, the water entry boundary was assigned as a

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90 variable flux boundary. During fe rtigation, the water entry bounda ry was set as a third-type boundary, representing a concentration influx (Sim unek et al., 1999). The left vertical boundary and upper boundary were assigned as no flux, re presenting the symmetry across the vertical plane and plastic mulch covering the surface, re spectively. The lower boundary of the profile was assigned as a free drainage boundary located 60 cm subsurface. The right vertical boundary, which represents the boundary be tween the soil half-s ection and the inter-row area, was also assigned as a free drainage boundary below 25 cm subsurface. Between 0 and 25 cm subsurface, the right vertical boundary was assigned as a no flux boundary, again due to the plastic mulch covering. For soil transport parameter calibration, the ar ea assigned as rooted was estimated from the root distribution data, with rela tive distributions equivalent to root concentrations. The van Genuchten S-shaped model (van Genuchten, 1987) was used for root water uptake, with the p exponent [-] set to the recommended value of 3 a nd the 50% pressure head uptake coefficient, h50 [L], set to -800 cm. It was assumed that th e potential evapotranspi ration was equal to the potential crop transpiration calculated for the si te. All soil transport parameter calibrations began the morning of (prior to irrigation) the fertigati on event and lasted for f our days (four irrigation events) following fertigation. Since probe K measurements were transformed to NO3, the fertigation concentration was simulated as the combined NO3 and Cl concentration and is also represented by a single constituent, NO3. The combined concentration assumpti on is reasonable for our study since the combined NO3 and Cl concentration was over 95% of the total anion concentration and these anions exhibit similar impacts on K (Muoz-Carpe na et al., 2005a). Following this assumption and using fertilizer weight, composition, and flow data, the inline fertigation concentration used

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91 during simulation was determined to be 13.78 g NO3 L-1. The applied concentration was assumed to be non-adsorbing and non-transforming. Th e diffusion coefficient was set at 0.001 cm2 min-1, again representing NO3 in free water (Robinson and Stokes, 1968). The diffusion coefficient was not varied during this study as such a small value w ill have little impact relative to dispersivity effects on predicted concentrations in a high velocity regime. In fact, diffusion effects have been ignored in previous studies focusing on NO3 (Ajdary et al., 2007; Gardenas et al., 2005); moreover, smaller values have been reported for saturated soils compared to free water due to soil matrix impedance (Gardner et al., 2001). The time-series of model prediction comparisons to measured data are presented as day of simulation (DOS). The entire model domain was initialized four days prior to the beginning of this comparison (DOS -4). From DOS -4 to 0 model variables were allowed to reach a quasistatic state by applying the same irrigation ev ents as between DOS 0 and 8 for soil hydraulic parameter calibration and DOS 0 and 5 for soil tr ansport parameter calibration. Fertigation was applied between DOS 0 and DOS 1 depending on the ac tual application time at the site. For soil hydraulic parameter calibration the simulation domain was initialized at 0.10 cm3 cm-3 SMC. For soil transport parameter calibration the simulation domain was initialized at 0.10 cm3 cm-3 SMC and 0.50 g NO3 L-1 soil water. The initial NO3 concentration was established to match background measurements observed at the bed ed ge, but it was observed during the calibration process that only a few irrigation events were required to leach all the concentration from the bed center. So at DOS 0 for the soil transport para meter calibrations, monito ring location C8 and C23 always predicted 0.0 g NO3 L-1. The finite element dimensions were generated automatically by H2D MESHGEN. Smaller elements were create d around the water entry boundary to account for rapid variable changes, increasi ng model stability. Generally elem ent size increased as the lower

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92 and right vertical boundary intersection was appr oach, with MESHGEN de nsities 200% greater at the lower and right vertical boundary intersection as compar ed to around the water entry boundary. Calibration and Optimization Procedure As suggested by Abbasi et al. (2003), soil pa rameters were determined by a two-step calibration, soil hydraulic parameters followed by soil transport parameters. In addition, during both steps in the calibration process uncertainty of estimated parameters was accounted for through an inverse optimization pro cess. Inverse optimization was util ized in this study as it had been previously reported to impr ove H2D predictions (Chapter 3). Three different hydraulic parame ter distribution sets were ex amined for their ability to match measured SMC: Carsel and Parrish (1988 ) parameters for sand (1), the ROSETTA model (Schaap et al., 1998) parameters for sand (2), and the measured soil moisture release curve (Chapter 3; Figure 3-5) determined from undisturbed soil cores collected nearby (3). Inverse optimization during soil hydraulic parameter ca libration was performed within two standard deviations range of the soil hydraulic parameters: r s n, and Ks. For parameter set 3, no bounds were placed on Ks during calibration as it was not estimated from the undisturbed soil cores (Chapter 3). Also although soil hydraulic parameters are known to follow log-normal distributions, for parameter set 3 all measured parameters were f it to normal distributions for simplicity and due to the small sample size. The set of hydraulic parameters yielding th e best SMC prediction following the soil hydraulic parameter calibration was used for soil transport parameter calibration. The range for soil transport parameters was derived from previ ously reported values for field studies in sandy soils (Vanderborght and Vereecken, 2007). Longitudinal dispersivity (DL) and transverse

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93 dispersivity (DT) were optimized to NO3 concentrations obtain ed from Vitel probe K measurements following th e May 30 fertigation. Each inverse optimization was based on the nu merical solutions of Richards equation for soil hydraulic parameters and the convection-disp ersion equation for soil transport parameters. All optimizations were performed using the built-in Levenberg-Marquardt nonlinear minimization method in H2D. During the invers e optimization process, the unknown parameters are determined by the minimization of an esta blished objective functi on (Simunek et al., 1999). All weighing coefficients were set to 1. Multiple optimizations were performed for each calibration simulation using different initial values for the parameters to be determined in order to increase the probability of finding the global minimum. To validate model predictions, the combined parameter set resulting from soil hydraulic and transport parameter calibrations was used to simulate two more fertigation events: June 6 and June 14. Prediction Evaluation Two goodness-of-fit indicators ar e reported by H2D following a given simulation, sum of squares (SSQ) and the coefficient of determination (R2) (Simunek et al., 1999). Both indicators simply use the squared residual to represent the deviation between paired measured and predicted data. n i i n i i i effO O P O C1 2 1 20 1 (4-4) The NashSutcliffe (1970) co efficient of efficiency (Ceff) uses a similar approach, where iO is measured data; iP is predicted data; and O is the mean of the measured data (Equation 4-

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94 4). The range of Ceff lies between 1.0 (p erfect fit) and When Ceff is lower than zero the mean value of the measured time series would have be en a better predictor than the model (Nash and Sutcliffe, 1970). Ceff is the reported goodness-of-fit indicator in this study because it is better suited to evaluate model goodness-of-fit compared to SSQ or R2 (Legates and McCabe, 1999). In the presence of measurement un certainty, it is also valuable to evaluate paired measured and predicted data against the uncertainty boundar ies of the measured data instead of against individual data values. When the uncertainty boundary, but not the distribution of uncertainty around each measured data point is known, Harmel and Smith (2007) proposed that the chosen goodness-of-fit indicator can be improved by a modi fication that accounts for this uncertainty, summarily described here. n i nE E E E PER1 2 2 3 2 2 2 1... (4-5) The probable error range (PER), where n is the number of potential e rror sources and En is the uncertainty associated with each potential er ror source (%), was used to establish an upper and lower bound for the measured SMC and NO3 concentrations at a given time (Equation 4-5). If iP fell within the established boundary, the residual used in Ceff calculation is changed to zero. If iP fell outside the established bound ary, the residual used in Ceff calculation is changed to the difference between iP and the nearest boundary value (Harmel and Smith, 2007). To account for the measured uncertainty, the modified Ceff is also reported, designated in this document as Ceff*. For SMC measurements in this study, three so urces of error were considered. The first was the reported WCR accuracy, 0.025 cm3 cm-3 (Campbell Scientific, Inc. 2002). Recall the WCR measurements were further calibrated to the fiel d site (Chapter 2) usi ng measured gravimetric data that was converted to volumetric soil mois ture by using bulk density measurements. The

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95 WCR error (E1) was calculated as the reported accuracy divided by the average SMC for all probes used in model calibration ove r the time-series of interest, 19.7%. The errors for the soil samples were calculated by dividi ng the standard error of the m easurements by the mean of the measurements, resulting in a gravimetric error (E2) of 10.3% and a bulk density error (E3) of 2.0%. The three error sources result in a PER of 22.3% for SMC measurements. For NO3 concentrations obtained from K measurem ents in this study, the only source of error considered was the Vitel K measurement. K errors have been reported to be 20% (Stevens Water Monitoring Systems, Inc., 2007) yielding a PER of 20.0% for NO3 measurements. This PER can be considered low as possible errors resulting from the Vitel probe location and combined concentration assumption were unable to be quantified. Results and Discussion Field Results Since symmetry across the half-bed was assume d, probe locations (WCR and Vitel) at similar locations on each half-bed were averaged After averaging, the probes as labeled in Figure 3-1 were renamed with resp ect to their location, center of the bed (C) or edge of the bed (E), and their depth, 8 cm (8) or 23 cm (23) subs urface. Therefore, E8 is the average of probe 1 and 4; C8 is the average of probe 2 and 3; E23 is the average of probe 5 and 8; and C23 is the average of probe 6 and 7. Averaging also minimizes errors associated with the drip tape lying away from the exact bed center. Since the expe riment site required separate irrigation and fertigation drip lines (Chapter 2), locations are never truly symme trical, but averaging yields a representative measurement for the locat ion of interest (Figure 4-2 and 4-3). WCR SMC measured at the bed edge differed s ubstantially at the E8 location, probe 1 and 4. Differences between the probe 1 and 4 were observed to be as high as 0.09 cm3 cm-3. The observed difference could be due to a number of factors; however, SMC at these locations was

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96 only minimally impacted by irrigation events, with the average SMC for the location (E8) ranging from 0.05 cm3 cm-3 to 0.08 cm3 cm-3. Due to these differences a three location data set (C8, C23, and E23) was used for soil hydraulic parameter calibration. Large differences were also observed for the C23 location, with consis tent deviations in SMC between probe 6 and 7 near 0.04 cm3 cm-3 and as high as 0.13 cm3 cm-3, but the range of average SMC from 0.10 cm3 cm-3 to 0.23 cm3 cm-3 made the location important to retain in the data set (Figure 4-2). Measurement variability was also observed in the soil core data (Chapter 3; Table 3-2), with only s having a standard error less than 10 % of the parameter average (3.2%). Figure 4-3 displays the in-season Vite l K measurements transformed to NO3 concentrations, with fertigation leaving the syst em after only a few subsequent irrigation events. No physical explanation exists fo r the trend observed at the E8 location and for consistency E8 was not included in soil transport parameter calibration. In general, the root distribution measured at the peak of plant de velopment agrees with previously reported distributions (Scholberg, 1996) with the highest density near the emitter. But, as seen in Figure 4-4, roots have penetrated much deeper than the bed depth. For more detail on root distribution at the site, th e reader is referred to Zotarelli et al. (2007b). For soil transport parameter calibration, the area assigned as rooted was estimated from the root distribution data (Figure 4-4), with relative distributions equivalent to input root concentrations. Soil Hydraulic Parameter Calibration The three different soil hydraulic parameter se ts were used during inverse optimization to predict SMC from Experiment 4. The C23 location, where large differences were observed between probes, was the driving force behind cali bration. To predict the C23 location a large parameter was required (Table 4-1); however, large parameters result in large drainage

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97 predictions from the center of the bed and thus little impact is predicted at the E23 location following irrigation events (Figure 4-5). While the measured data does reveal a relatively dry bed edge, SMC increases were observe d following irrigation events (Fig ure 4-2). In fact, prior to considering SMC measurement uncertainty no repr esentative fit was observed with only Set 1 (Ceff = 0.266) yielding a Ceff value greater than 0.0. Recall Ceff values below 0.0 imply the location average measured SMC over the entire time-series acts as a better predictor than H2D results. Following uncertainty consideration, all three parameter sets provide a good fit (Ceff* > 0.9). Again focusing on the E23 location, one could even make the argument that parameter Set 2 and 3 provide a better visual ma tch of all three locations (Figur e 4-5), regardless of their poor predictions prior to uncertainty consideration (Table 4-1). The inability to achieve a very accurate fit (Ceff) of all three monitoring locations prior to measurement uncertainty considerati ons could be an artifact of the site setup. Since separate drip lines for irrigation and fertigation were required at the site, the drip emitter was not located in the exact center of the bed, but monitoring locations were installed relative to the bed center. The probes on each side of the bed center were subseq uently averaged to alleviate this concern; however, with only two monitoring locations per average, the linea r interpolation is admittedly simple. Also micro-heterogeneity at the mon itoring location could be responsible. Since SMC data collected at a near-by location (Chapter 3) by similar methods was predicted well (Ceff > 0.9), site specific characteris tics are likely the cau se not measurement methods. Even so, such errors are not egregious for field monitoring a nd once accounted for representative fits were achieved (Ceff* > 0.9; Table 4-1). To proceed with the soil tran sport parameter calibration, a representative set of hydraulic parameters had to be selected. While Set 1 pr eformed best prior to measurement uncertainty

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98 considerations, the prediction wa s poor and after measurement un certainty considerations, all three parameter sets predicted SMC well (Ceff* > 0.9). And while parameter Set 1 was yielded the highest goodness-of-fit indicators, the prediction failed to visually match the E23 SMC timeseries. Regardless, since it was previously obser ved (Figure 4-3) that most fertigation is transported through the center of the bed, Se t 1 was chosen for soil transport parameter optimization since Set 1 also has the largest parameter, again an indica tor of vertical drainage. Set 1 should provide the most re presentative water transport in the bed center, allowing for accurate soil transport parameter calibration. Soil Transport Parameter Calibration As previously discussed, the fertigation c oncentration was determined to be 13.78 g NO3 L-1 and in-situ K measurements were transformed to NO3 concentrations. Using the optimized soil hydraulic parameter Set 1 and the transformed NO3 concentrations, the soil transport parameters DL and DT were calibrated using in verse optimization. Since it had been previously observed that soil hydrau lic parameter Set 1 does not predict much water transport to the outer regions of the bed and in preliminary simulations initial concentrations had an unfair impact on goodness-of-fit indicators due to the small range of concentrations measured at the E23 location, the build-up of NO3 concentrations in the bed edge obs erved in the field (Figure 4-3) was ignored. As such, the reported Ceff and Ceff* values are related to the C8 and C23 monitoring sites only. The soil transport paramete r calibration yielded a DL of 2.38 cm and a DT of 0.01 cm, best representing the system (Figure 4-6) with Ceff = 0.562 and Ceff* = 0.799. While prior to considering measurement uncertainty the calibration may seem poor (Ceff = 0.562) when compared to the soil hydraulic parameter calib ration prior to uncertainty considerations (Ceff = 0.266) the soil transport parameter calibration results are impressive. When measurement

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99 uncertainty is considered, a decrease in Ceff* is observed from the prior calibration. Still the soil transport parameter calibration predicts measured NO3 concentrations well after measurement uncertainty is considered (Ceff* = 0.799). The soil transport parameters determined in this study are also within the range of compiled data reported by Vanderborght and Vereecken (2007) and near their mean value of ~3.0 cm (DL). But while the values are within the ra nge established by previous studies using H2D (Table 4-2), the values are higher than t hose reported for the laboratory sand study (Li et al., 2005). The increase in DL from a laboratory experiment to the field is a trend that has previously been observed (Vanderborght and Vereecken, 2007) and lends further credence to the importance of obtaining strong fi eld measurement data sets. Upon further examination of Figure 4-6, dist inct differences were observed between the predicted and observed NO3 concentration time-series at both the C8 and C23 location. Concentrations at the C8 locat ion are under predicted immediatel y following the first irrigation event (after DOS 1), while the C23 site is predicted fairly accurately. Similar results were also reported by Ajdary et al. (2007) with under pr edictions between 10 and 15 cm subsurface and more accurate predictions reported for deeper dept hs. Further examination of the C8 location in Figure 4-6 reveals the simulated concentrations arriving at the C8 location powered only by fertigation. Where as, it takes the followi ng irrigation event before the measured NO3 concentration arrive at the location. Both observations could be a product of the two-dimensional simulation domain assumption, which states that all irrigation and fertigation enters the bed evenly across the distance between two emitters as a line sour ce. While the line source assumptions have previously been shown to predict well SMC unde r drip irrigation (Chapt er 3), the assumption

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100 may not hold for Vitel probe measurements. The WCR probe has a 30 cm (150% emitter spacing) collection length within the bed, much larger than the 5.7 cm (28.5% emitter spacing) length collected associat ed with the Vitel probe (Chapter 2). Though both probes were located at similar normal distances for each monitoring locati on (C8, C23, and E23) the smaller collection length of the Vitel probe causes measured concen tration values to be more susceptible to variations created by the radial distance from the emitter. The difference immediately following fertigation could also be a product of H2D nutrient uptake pr ediction. During simulation, NO3 concentration uptake occurs only with root water uptake (Simunek et al., 1999). The process could be more complicated in our system, especially when the relatively low SMCs following fertigation are considered. As previously stated, the center of the 5.7 cm measurement length was located ~3 cm from the nearest emitter. At this location, if wate r applied during fertigation is enough to allow transport to the C8 location some impact, though perhaps mitigated, should still be observed by the Vitel probe. Considering this, the difference observed immediately following fertigation also draws into question the optimized DT value (2.38 cm). A lower value as assumed in previous studies (Table 4-2) will allevi ate the deviation between predic ted and observed concentrations immediately following fertigation, but will not ma tch the remainder of the time-series as well. Such curve-fitting as compared to finding values representing the physical system is one of the possible drawbacks that have been previously reported for inverse optimization techniques (Ritter et al., 2003). Validation Simulations During the validation simulations similar fertigation concentration was applied, but different fertigation timing and different amounts of water applied as irrigation. For example, the site scheduled irrigation DOS -1 and 0 for the June 14 fertigation even t did not occur due to

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101 electrical problems. Even so, the model continued to predict the events reasonably well. Prior to uncertainty consideration, values were again low yet relatively high compared to the soil hydraulic parameter calibration with Ceff values of 0.635 and 0.432 for the June 6 and 14 events respectively. After considering measurement un certainty, validation simulations were observed to predicted measured values well with Ceff* values of 0.854 and 0.684 for the June 6 and 14 events respectively. As before prediction improvement was observed after measurement uncertainty was accounted for and the C8 locat ion was again under pred icted while the C23 location was more accurately simulated. Summary and Conclusions A representative data set of SMC and NO3 concentrations was colle cted in-situ beneath a plastic mulch covered, raised bed vegetable prod uction system. The data collected was complete enough to apply inverse optimization methods for simulating the site. Soil hydraulic parameters were obtained through inverse op timization of SMC measured on site. The optimization process was limited by the van Genuchten model parameter. A large parameter was required to match SMC reported by monitoring locations in th e center of the bed (C8 and C23). Since the large parameter prevented water from reaching the bed edge (E23) during simulation, a representative parameter set could not be dete rmined until uncertainty in SMC measurements was considered. The soil hydraulic parameter dist ribution reported by Cars el and Parrish (1988) for sand provided the best fit as the dist ribution provided the largest range for the parameter. Soil transport parameters were also calibrated to the system by inverse optimization to NO3 concentration data using the best results of the soil hydraulic pa rameter calibration. The inverse optimization process revealed DL of 2.38 cm and DT of 0.01 cm to best represent the system (Ceff = 0.562). Prediction results were again improved after measurement uncertainty was considered (Ceff* = 0.799). Similar improvements were obser ved for both validation simulations with

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102 goodness-of-fit indicators increasing from 0.635 to 0.854 and 0.432 to 0.684 for the June 6 and June 14 fertigation simulations respectively, once measurement uncertainty was considered. The soil transport parameters reported here are higher than those reported for a laboratory sand study that used H2D (Li et al., 2005), but within the range of previously reported field sites (Vanderborght and Vereecken, 2007). This supports the optimization results and further confirms the value of field measurements compared to la boratory or theoretical estimations. Also as reported by Ajdary et al. (2007) in our study H2D under predicte d concentrations at shallow monitoring location (C8), while more accurate predictions were observed at the deeper monitoring location (C23). The difference between m easured and predicted concentrations at the location nearest the fertigation emitter (C8) was observed between the simulated fertigation event and following day irrigation event. In shor t, predicted concentrations arrived at the monitoring location several hours before any rise in concentration was measured. It is unclear from the results in this study whether this obser ved difference is a byprodu ct of the line source assumptions used for simulation or errors associ ated with root nutrient uptake simulated by the model.

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103Table 4-1. Results from soil hydraulic parameter calibrations to Experiment 4 soil moisture content at C8, C23, and E23 Parameter source Set r (cm3 cm-3) s (cm3 cm-3) (cm-1) n (-) Ks (cm min-1) Ceff Ceff* Carsel and Parrish 1 0.035 0.370 0.174 2.390 0.235 0.266 0.991 ROSETTA 2 0.072 0.370 0.063 3.882 0.169 -0.145 0.989 Measured 3 0.052 0. 383 0.035 2.838 0.276 -0.089 0.958 r is residual water content; s is saturated water content; and n are fitting parameters for the van Genuchten (1980) model. Ks is saturated hydraulic conductivity. Ceff is Nash and Sutcliffe (1970) coefficient of efficiency. Ceff* is Nash and Sutcliffe (1970) coefficient of efficiency with measurem ent uncertainty (Harmel and Smith, 2007).

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104 Table 4-2. Reported dispersivity values used in previous HYDRUS-2D fertigation studies Dispersivity Parameter source Soil type DL (cm) DT (cm) Li et al. (2005) Sand 0.10 0.001 Li et al. (2005) Loam 0.32 0.003 Gardenas et al. (2005) & Hanson et al. (2006) Sandy loam, loam, silty clay, anisotropic clay 5.00 0.500 Ajdary et al. (2007) Sandy clay loam, sandy loam, loam, silty clay loam, silt 0.30 0.030 DL is longitudinal dispersivity and DT is transverse dispersivity. Figure 4-1. Experiment 3 and 4 WC R matrix configuration centered in bed. Numbering of probes used in results discussion also shown.

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105 0.05 0.10 0.15 0.20 0.25 7/87/97/107/117/127/13 DATE (2006)SMC (cm3 cm-3) E8 C8 E23 C23 Figure 4-2. Experiment 4 WCR soil mo isture content (SMC) measurements. 0.0 0.5 1.0 1.5 4/135/35/236/127/2 DATE (2006)CONCENTRATION g NO3 L-1 E8 C8 E23 C23 Figure 4-3. Experiment 3 V itel determined nitrate (NO3) concentrations.

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106 0510152025 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5LATERAL DISTANCE FROM DRIP (cm)DEPTH (cm) ROOT DENSITY (cm cm-3)10 30 20 40 50 80 60 70 90 0510152025 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5LATERAL DISTANCE FROM DRIP (cm)DEPTH (cm) ROOT DENSITY (cm cm-3)10 30 20 40 50 80 60 70 90 Figure 4-4. Root distribution co llected during full canopy, 66 DAT.

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107 0.05 0.10 0.15 0.20 0.25 0.30 0.01.02.03.04.05.0 DAY OF SIMULATIONSMC (cm3 cm-3) PER BOUNDS 1 2 3C8 0.05 0.10 0.15 0.20 0.25 0.30 0.01.02.03.04.05.0 DAY OF SIMULATIONSMC (cm3 cm-3) PER BOUNDS 1 2 3C23 0.05 0.10 0.15 0.20 0.25 0.30 0.01.02.03.04.05.0 DAY OF SIMULATIONSMC (cm3 cm-3) PER BOUNDS 1 2 3E23 Figure 4-5. Parameter Sets 1, 2, and 3 soil hydraulic parame ter calibration, soil moisture content (SMC), DOS 0 to 5.

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108 0.0 0.5 1.0 1.5 0.01.02.03.04.05.0 DAY OF SIMULATIONCONCENTRATION g NO3 L-1 PER BOUNDS SIMULATEDC8 0.0 0.5 1.0 1.5 0.01.02.03.04.05.0 DAY OF SIMULATIONCONCENTRATION g NO3 L-1 PER BOUNDS SIMULATEDC23 Fertigation Fertigation Figure 4-6. Nitrate (NO3) concentration predictions for May 30 fer tigation. Soil hydraulic parameter set 1, DL = 2.38 cm, and DT = 0.01 cm.

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109 0.0 0.5 1.0 1.5 0.01.02.03.04.05.0 DAY OF SIMULATIONCONCENTRATION g NO3 L-1 PER BOUNDS SimulatedC8 0.0 0.5 1.0 1.5 0.01.02.03.04.05.0 DAY OF SIMULATIONCONCENTRATION g NO3 L-1 PER BOUNDS SimulatedC23 Figure 4-7. Nitrate (NO3) concentration predictions for June 6 fer tigation. Soil hydraulic parameter set 1, DL = 2.38 cm, and DT = 0.01 cm.

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110 0.0 0.5 1.0 1.5 0.01.02.03.04.05.0 DAY OF SIMULATIONCONCENTRATION g NO3 L-1 PER BOUNDS SimulatedC8 0.0 0.5 1.0 1.5 0.01.02.03.04.05.0 DAY OF SIMULATIONCONCENTRATION g NO3 L-1 PER BOUNDS SimulatedC23 Figure 4-8. Nitrate (NO3) concentration predictions for June 14 fer tigation. Soil hydraulic parameter set 1, DL = 2.38 cm, and DT = 0.01 cm.

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111 CHAPTER 5 RESEARCH SUMMARY AND FUTURE WORK Research Summary In Florida, intensive bed management systems are commonly used for vegetable production. These systems consist of raised beds for planting covered with plastic mulch, with water and nutrients commonly applied via drip i rrigation and fertigation. Currently available dielectric soil moisture sensors provide inexpensive alternatives when compared to Time Domain Reflectometry (TDR) and the labor co sts of soil sampling. The CS616 water content reflectometer (WCR) and the Hydra Probe II (V itel), operating on time-domain and capacitance methods respectively, were installed beneath drip irrigated tomatoes in an intensively managed vegetable production system. The monitoring capab ility of each probe was examined through one-to-one and time-series comparisons. The probes were installed in a two-dimensional grid to capture the soil moisture content (SMC) distribu tion beneath drip irriga tion. It was observed during one-to-one comparisons that SMC measured using the factor y calibration provided with each probe failed to match volumetric water content (VWC) determined from gravimetric soil samples. However, the longer measurement dist ance of the WCR probe (150% emitter spacing) allowed for relatively good calibration to VWC data (R2 = 0.74) since soil samples were collected at like normal distances from the bed ce nter as probe locations, but without regard to emitter location. Accordingly, the short measurement distance of the Vitel probe (28.5% emitter spacing) resulted in a poor calibra tion for to SMC measurements (R2 = 0.26) and soil water salinity measurements (R2 < 0.10). More importantly, time-seri es observations were observed to provide accurate description of the system, as both probes matched the season-long SMC trends well. And the Vitel probe was observed to match soil water salinity trends during time-series

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112 following two different fertigation events. The abili ty to capture descriptive time-series allowed for the probe measurements to be used during model calibration (Chapter 2). The HYDRUS-2D program (H2D) has previo usly been used for drip irrigation management forecasts. A review of the simulatio ns reported in the literature revealed an assortment of techniques for defining the model simulation space. To examine the effectiveness of these techniques, H2D was calibrated to SMC data collected from a non-planted bed section with soil moisture release curve (SMRC) paramete rs determined from un disturbed soil cores and saturated hydraulic conductiv ity determined by inverse opt imization. The goodness-of-fit indicator (Ceff) was also modified to account for measurement uncertainty (Ceff*). Semi-spherical (SC) soil wetting geometries proved superior to th eir surface-radius counterparts in convergence and simulation time, but nearly identical in SMC prediction. Both the axis-symmetrical and twodimensional SC approaches predicted the SMC data well, Ceff ~ 0.77 and ~0.91 respectively. Goodness-of-fit indicators obtained near perfect values after un certainty in the SMC and SMRC measurements was considered (Ceff* = 1.0). This means SMC measurement uncertainty at the site was greater than any water entry bounda ry condition impact on SMC (Chapter 3). It was also observed that most previous studi es of fertigation using H2D used mean values for soil parameter estimation. The determinatio n of appropriate soil hydraulic and transport parameters is essential to accurately simulate distributions beneath fertigation. To account for soil parameter uncertainty, inverse optimization methods were applied for soil hydraulic and transport parameter calibration. Calibration of the soil hydraulic parameters revealed high bubbling pressure (~0.17 cm-1) was required to obtain even mode st predictions in the bed center (Ceff = 0.27). Calibration of soil transport paramete rs yielded a longitudina l dispersivity of 2.38 cm and a transverse dispersivity of 0.01 cm (Ceff = 0.56). As before, accounting for measurement

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113 uncertainty improved the results of both calibrations, Ceff* = 0.99 and 0.80, respectively. Observations made following the soil transport parameter calibration question the applicability of line source assumptions for comparis on to Vitel measurements (Chapter 4). Future Work As is often the case with scientific research, as many questions were raised as were answered. The adage is especially true in this case as the experimental site was managed for a larger project. Each experimental design had to a ccount for the often differe nt goals of the larger project. The results presented in this documen t are not weakened by this fact, but the door remains open for experiments with more goal sp ecific designs. Some suggestions for these projects are presented in the following paragrap hs and are intended to both direct and inspire. More work is needed to specifically addr ess any parameter impacts or other modeling needs for sensor-based drip irrigation. From re sults obtained at the experiment site but not addressed in this document, sensor-based irri gation should greatly enha nce agricultural water conservation. As such, monitoring and modeling these systems will become a need and may be more complex than applying models developed for low frequency, timed irrigation. In our case, modeling a sensor-based system was complicat ed by measurement errors resulting from consistently low SMC. If in-situ probes are to be used for data collections beneath these systems, additional calibration to lo w SMC may be necessary. As was most evident beneath the sensor-based treatment if the WCR is to be used for monitoring drip irrigation system s, experiments need to be conduc ted to determine the extent of the fertigation impact on SMC measurements. Similar experiments could be replicated on different soils or using different fertigation constituents. For these experiments, a lab setup would likely prove superior.

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114 As evident by replication in the final summary the most important take home message that impacted all the works documented here is th e impact of measuremen t volumes on monitoring drip systems. To properly calibrate the Vitel, or any monitoring device with a measurement length less than the emitter spacing used on site, the benchmark measurements, be it gravimetric samples or TDR, must be collected at the sa me normal distance and radial distance from the emitter. The benchmark measurements should also have a similar measurement volume to the probe being calibrated. Calibrations in a lab se tting can easily eliminate this need, but would likely struggle to account for ot her impacts inherent to intensiv e bed management systems, such as soil structure and temperature. Concurrently, model selection should also consider whether the measured data set consists of true point measur ements or measurements averaged over several emitters. One question that loomed over this work from beginning to end was th e influence of root growth on hydraulic parameters. Hindered by the need to monitor distributions at different sites within the field to find areas un-impacted and im pacted by root growth, th e results obtained in our study could neither confirm nor deny root growth impacts. The need in this work to have two monitoring sites was a result of the setup method required for such a large field, both construction and planting. Though some discussion is provided in the appe ndix, a more specific experiment should allow for one m onitoring location and further isol ate root growth effects. An experimental design to address ro ot effects on hydraulic parameters in intensive bed management systems is detailed below. Probes need to be installed and monitor dist ributions of interest for several days irrigation events prior to plan ting. An appropriate model such as H2D should then be calibrated to the data set collected prior to planting. After fruiting, plants should be clipped near the surface

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115 to eliminate as much transpiration as possible. Monitoring should continue for several days after the plants are clipped, and the previously calibrated model could then be applied to the data set collected after clipping. A simple forecast shou ld be enough to test the root growth impact hypothesis. Further analysis c ould involve a comparison of so il moisture retention curves optimized or measured prior to planting and after clipping. If a time dependent relationship between r oot growth and soil hydraulic parameter modification is to be developed, several monitori ng sites should be initiated at the same time. Each site would again require data collected prior to planting for ca libration and should be assigned a different length of the growing season to allow plant growth. For example if three sites are monitored, plants could be clipped at one site at 1/3, 1/2, and 2/ 3 the season. Each site should continue to monitor distributions after cli pping, with similar analysis used to determine the relative impact seen throughout the season. A time dependent relationship between root growth and hydraulic parameter modification woul d enhance the ability to model a season long data set. Similar experiments could be replicat ed on different soils or beneath different crops. The analysis could be repeated for soil transport parameters. Another question raised that could no be addr essed through the data co llected in this study is the impact of bed construc tion techniques on soil parameters. Different bed compaction levels may be used for different crops, soil s, or even from year to year at the same site. No work to date has quantified impacts from different bed construc tion techniques. A simple experiment could be designed to compare measured distributions be neath drip irrigation in beds of varying compaction. Though H2D was observed to be a powerful tool and quite applicable to drip systems in this study, due to the amount of data needed to properly calibrate H2D, a simpler, analytical

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116 model specifically designed for drip irrigation and intensive bed management systems would be ideal. The model should account for all the uniqu e aspects associated with intensive bed management systems, while requiring minimal i nputs such as soil type and emitter flow rate. Such a model is currently under development at th e University of Florida. The 3DMGAR model, which will be fully described in a dissertation yet to be published by Leslie Gowdish, should provide easy computations of SMC beneath drip irri gation; however, if solute transport is desired 3DMGAR needs to be coupled w ith another model or else, H2D is again required. To validate 3DMGAR, experiments similar to those documente d here should be performed and replicated across different soil types and different flow rates. Finally for all future works addressed here or not, if the goal of collected data is the eventual use in model calibration due to the symme try often assumed in drip irrigation modeling, a single drip line should be us ed for both irrigation and fertig ation at the experiment site.

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117 APPENDIX A SELECT HYDRUS-2D INPUT FILES Initial Calibration of 2DSC1.0 The following input files were from the 2D SC1.0 simulation used during the initial calibration process in Chapter 3, where only Ks was included in the inverse optimization process. The files are generally representative of a ll two-dimensional, semi-spherical simulations. *** BLOCK I: ATMOSPHERIC INFORMATION ********************************** MaxAL (MaxAL = number of atmospheric data-records) 31 hCritS (max. allowed pressure head at the soil surface) 0 tAtm Prec rSoil rRoot hCritA rt ht 360 0 0 0 10000 0 0 480 0 0 0 10000 -0.200822 0 1800 0 0 0 10000 0 0 1920 0 0 0 10000 -0.200822 0 3240 0 0 0 10000 0 0 3360 0 0 0 10000 -0.200822 0 4680 0 0 0 10000 0 0 4800 0 0 0 10000 -0.200822 0 6120 0 0 0 10000 0 0 6240 0 0 0 10000 -0.200822 0 7560 0 0 0 10000 0 0 7680 0 0 0 10000 -0.200822 0 9000 0 0 0 10000 0 0 9120 0 0 0 10000 -0.200822 0 10440 0 0 0 10000 0 0 10560 0 0 0 10000 -0.200822 0 11880 0 0 0 10000 0 0 12000 0 0 0 10000 -0.200822 0 13320 0 0 0 10000 0 0 13440 0 0 0 10000 -0.200822 0 14760 0 0 0 10000 0 0 14880 0 0 0 10000 -0.200822 0 16200 0 0 0 10000 0 0 16320 0 0 0 10000 -0.200822 0 17640 0 0 0 10000 0 0 17760 0 0 0 10000 -0.200822 0 19080 0 0 0 10000 0 0 19200 0 0 0 10000 -0.200822 0 20520 0 0 0 10000 0 0 20640 0 0 0 10000 -0.200822 0

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118 21000 0 0 0 10000 0 0 *** END OF INPUT FILE 'ATMOSPH.IN' ************************************* *** BLOCK ?: BOUNDARY INFORMATION ********************************************* NumBP NObs SeepF FreeD DrainF qQWLF 29 3 f t f f Node Number Array 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 66 67 68 69 70 71 72 73 74 75 76 Width Array 0.0461842 0.0923672 0.092366 0.092366 0.0923677 0.0923675 0.0923662 0.0923666 0.092367 0.0923665 0.0923664 0.0923677 0.0923673 0.0923668 0.0923668 0.0923668 0.0923672 0.0461837 2.1875 4.66667 5.25 5.83333 6.41667 7 7.39583 7.33333 7 6.66667 3.25 Length of soil surface associated with transpiration 0 Observation nodes. Node(1,....NObs) 121 122 123 *** End of input file 'BOUNDARY.IN' ******************************************* *** BLOCK A: BASIC INFORMATION ***************************************** Heading Welcome to HYDRUS-2D LUnit TUnit MUnit (indicated uni ts are obligatory for all input data) cm min mmol Kat (0:horizontal plane, 1:axisymmetric vertical flow, 2:vertical plane) 2 MaxIt TolTh TolH InitH/W (max. number of iterations and tolerances) 200 0.0001 0.1 t lWat lChem lSink Short Flux lScrn At mIn lTemp lWTDep lEquil lExtGen lInv t f f f t t t f f t t t *** BLOCK B: MATERI AL INFORMATION ************************************** NMat NLay hTab1 hTabN 1 1 0 0 Model Hysteresis 0 0 thr ths Alfa n Ks l 0.061 0.393 0.0249 2.286 0.8 0.5 *** BLOCK C: TIME INFORMATION ****************************************** dt dtMin dt Max DMul DM ul2 ItMin ItMax MPL 0.5 0.0001 15 1.3 0.7 3 7 10

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119 tInit tMax 0 21000 TPrint(1),TPrint(2),...,TPrint(MPL) 2100 4200 6300 8400 10500 12600 14700 16800 18900 21000 *** END OF INPUT FILE 'SELECTOR.IN' ************************************ Welcome to HYDRUS-FIT Parameter Estimation of Soil Hydraulic Properties NOBB MIT iWeight 2904 20 0 lWatF lChemF NMat lTempF t f 1 f Model Hyster Aniz 0 0 f thr ths Alfa n Ks l 0.061 0.393 0.0249 2.286 0.8 0.5 0 0 0 0 1 0 0 0 0 0 0.4 0 0 0 0 0 2 0 HO(N) FOS ITYPE(N) POS WTS 5760 0.119884 2 3 1 5775 0.12061 2 3 1 5790 0.12061 2 3 1 5805 0.119158 2 3 1 5820 0.118433 2 3 1 5835 0.119884 2 3 1 5850 0.118433 2 3 1 5865 0.116981 2 3 1 5880 0.117707 2 3 1 5895 0.116981 2 3 1 5910 0.117707 2 3 1 5925 0.116981 2 3 1 5940 0.116255 2 3 1 5955 0.116255 2 3 1 5970 0.11553 2 3 1 5985 0.116255 2 3 1 6000 0.114804 2 3 1 [Remainder of file not included to save space] end*** END OF INPUT FILE 'FIT.IN' **********************************

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120 Figure A-1. Boundary conditions for 2DSC1.0 simu lation. Pink is variable flux and represents the water entry boundary. Red is fr ee drainage. White is no flux.

PAGE 121

121 1 2 3 Figure A-2. Numerical node st ructure for 2DSC1.0 simulation. Red dots represent monitoring locations. Location 1 corresponds to C8, location 2 to C 23, and location 3 to E23 from the field. Initial Calibration of 3DSC1.0 The following input files were from the 3D SC1.0 simulation used during the initial calibration process in Chapter 3, where only Ks was included in the inverse optimization process. The files are generally represen tative of all three-dimensiona l, semi-spherical simulations. *** BLOCK I: ATMOSPHERIC INFORMATION ********************************** MaxAL (MaxAL = number of atmospheric data-records) 31 hCritS (max. allowed pressure head at the soil surface) 0 tAtm Prec rSoil rRoot hCritA rt ht 360 0 0 0 10000 0 0 480 0 0 0 10000 -2.00822 0 1800 0 0 0 10000 0 0 1920 0 0 0 10000 -2.00822 0 3240 0 0 0 10000 0 0 3360 0 0 0 10000 -2.00822 0

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122 4680 0 0 0 10000 0 0 4800 0 0 0 10000 -2.00822 0 6120 0 0 0 10000 0 0 6240 0 0 0 10000 -2.00822 0 7560 0 0 0 10000 0 0 7680 0 0 0 10000 -2.00822 0 9000 0 0 0 10000 0 0 9120 0 0 0 10000 -2.00822 0 10440 0 0 0 10000 0 0 10560 0 0 0 10000 -2.00822 0 11880 0 0 0 10000 0 0 12000 0 0 0 10000 -2.00822 0 13320 0 0 0 10000 0 0 13440 0 0 0 10000 -2.00822 0 14760 0 0 0 10000 0 0 14880 0 0 0 10000 -2.00822 0 16200 0 0 0 10000 0 0 16320 0 0 0 10000 -2.00822 0 17640 0 0 0 10000 0 0 17760 0 0 0 10000 -2.00822 0 19080 0 0 0 10000 0 0 19200 0 0 0 10000 -2.00822 0 20520 0 0 0 10000 0 0 20640 0 0 0 10000 -2.00822 0 21000 0 0 0 10000 0 0 *** END OF INPUT FILE 'ATMOSPH.IN' ************************************* *** BLOCK ?: BOUNDARY INFORMATION ********************************************* NumBP NObs SeepF FreeD DrainF qQWLF 35 3 f t f f Node Number Array 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 Width Array 0.289557 0.576635 0.569237 0.556991 0.540003 0.518396 0.49236 0.462133 0.427963 0.390138 0.348986 0.304861 0.25813 0.209196 0.158479 0.10641 0.0534333 0.0133869 20.0434 133.979 314.281 552.308 854.474 1227.19 1570.7 1612.64 1539.33 1466.03 1392.73 1319.43 1246.13 1172.83 1099.53 1026.22 494.786 Length of soil surface associated with transpiration 0 Observation nodes. Node(1,....NObs) 121 122 123

PAGE 123

123 *** End of input file 'BOUNDARY.IN' ******************************************* *** BLOCK A: BASIC INFORMATION ***************************************** Heading Welcome to HYDRUS-2D LUnit TUnit MUnit (indicated uni ts are obligatory for all input data) cm min mmol Kat (0:horizontal plane, 1:axisymmetric vertical flow, 2:vertical plane) 1 MaxIt TolTh TolH InitH/W (max. number of iterations and tolerances) 200 0.001 0.1 t lWat lChem lSink Short Flux lScrn At mIn lTemp lWTDep lEquil lExtGen lInv t f f f t t t f f t t t *** BLOCK B: MATERI AL INFORMATION ************************************** NMat NLay hTab1 hTabN 1 1 0 0 Model Hysteresis 0 0 thr ths Alfa n Ks l 0.061 0.393 0.0249 2.286 0.88 0.5 *** BLOCK C: TIME INFORMATION ****************************************** dt dtMin dt Max DMul DM ul2 ItMin ItMax MPL 1 0.0001 15 1.3 0.7 3 7 100 tInit tMax 0 21000 TPrint(1),TPrint(2),...,TPrint(MPL) 210 420 630 840 1050 1260 1470 1680 1890 2100 2310 2520 2730 2940 3150 3360 3570 3780 3990 4200 4410 4620 4830 5040 5250 5460 5670 5880 6090 6300 6510 6720 6930 7140 7350 7560 7770 7980 8190 8400 8610 8820 9030 9240 9450 9660 9870 10080 10290 10500 10710 10920 11130 11340 11550 11760 11970 12180 12390 12600 12810 13020 13230 13440 13650 13860 14070 14280 14490 14700 14910 15120 15330 15540 15750 15960 16170 16380 16590 16800 17010 17220 17430 17640 17850 18060 18270 18480 18690 18900 19110 19320 19530 19740 19950 20160 20370 20580 20790 21000 *** END OF INPUT FILE 'SELECTOR.IN' ************************************

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124 Welcome to HYDRUS-FIT Parameter Estimation of Soil Hydraulic Properties NOBB MIT iWeight 2904 20 0 lWatF lChemF NMat lTempF t f 1 f Model Hyster Aniz 0 0 f thr ths Alfa n Ks l 0.061 0.393 0.0249 2.286 0.26 0.5 0 0 0 0 1 0 0 0 0 0 0.1 0 0 0 0 0 0.6 0 HO(N) FOS ITYPE(N) POS WTS 5760 0.119884 2 3 1 5775 0.12061 2 3 1 5790 0.12061 2 3 1 5805 0.119158 2 3 1 5820 0.118433 2 3 1 5835 0.119884 2 3 1 5850 0.118433 2 3 1 5865 0.116981 2 3 1 5880 0.117707 2 3 1 5895 0.116981 2 3 1 5910 0.117707 2 3 1 5925 0.116981 2 3 1 5940 0.116255 2 3 1 5955 0.116255 2 3 1 5970 0.11553 2 3 1 5985 0.116255 2 3 1 6000 0.114804 2 3 1 [Remainder of file not included to save space] end*** END OF INPUT FILE 'FIT.IN' **********************************

PAGE 125

125 Figure A-3. Boundary conditions for 3DSC1.0 simu lation. Pink is variable flux and represents the water entry boundary. Red is free drainage. White is no flux

PAGE 126

126 1 2 3 Figure A-4. Numerical node st ructure for 3DSC1.0 simulation. Red dots represent monitoring locations. Location 1 corresponds to C8, location 2 to C 23, and location 3 to E23 from the field. Full Calibration of 2DSC1.0 The following input files were from the 2DSC1.0 simulation used during the full calibration process in Chapter 3, where all soil hy draulic parameters were included in the inverse optimization process. Boundary conditions and th e node distribution were similar to Figure A-1 and A-2. Atmospheric, boundary, ba sic, material, and time inform ation are identi cal to initial calibration of 2DSC1.0. Welcome to HYDRUS-FIT Parameter Estimation of Soil Hydraulic Properties NOBB MIT iWeight 2904 20 0 lWatF lChemF NMat lTempF t f 1 f Model Hyster Aniz

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127 0 0 f thr ths Alfa n Ks l 0.061 0.393 0.04 2.286 0.7 0.5 1 1 1 1 1 0 0.01 0.329 0.0158 1.586 0.1 0 0.15 0.46 0.044 4.57 0.8 0 HO(N) FOS ITYPE(N) POS WTS 5760 0.119884 2 3 1 5775 0.12061 2 3 1 5790 0.12061 2 3 1 5805 0.119158 2 3 1 5820 0.118433 2 3 1 5835 0.119884 2 3 1 5850 0.118433 2 3 1 5865 0.116981 2 3 1 5880 0.117707 2 3 1 5895 0.116981 2 3 1 5910 0.117707 2 3 1 5925 0.116981 2 3 1 5940 0.116255 2 3 1 5955 0.116255 2 3 1 5970 0.11553 2 3 1 5985 0.116255 2 3 1 6000 0.114804 2 3 1 [Remainder of file not included to save space] end*** END OF INPUT FILE 'FIT.IN' ********************************** Full Calibration of 3DSC1.0 The following input files were from the 3DSC1.0 simulation used during the full calibration process in Chapter 3, where all soil hy draulic parameters were included in the inverse optimization process. Boundary conditions and th e node distribution were similar to Figure A-3 and A-4. Atmospheric, boundary, ba sic, material, and time inform ation are identi cal to initial calibration of 3DSC1.0. Welcome to HYDRUS-FIT Parameter Estimation of Soil Hydraulic Properties NOBB MIT iWeight 2904 20 0 lWatF lChemF NMat lTempF t f 1 f

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128 Model Hyster Aniz 0 0 f thr ths Alfa n Ks l 0.061 0.393 0.0249 2.286 0.26 0.5 1 1 1 1 1 0 0.01 0.329 0.0158 1.586 0.1 0 0.15 0.46 0.044 4.57 0.8 0 HO(N) FOS ITYPE(N) POS WTS 5760 0.119884 2 3 1 5775 0.12061 2 3 1 5790 0.12061 2 3 1 5805 0.119158 2 3 1 5820 0.118433 2 3 1 5835 0.119884 2 3 1 5850 0.118433 2 3 1 5865 0.116981 2 3 1 5880 0.117707 2 3 1 5895 0.116981 2 3 1 5910 0.117707 2 3 1 5925 0.116981 2 3 1 5940 0.116255 2 3 1 5955 0.116255 2 3 1 5970 0.11553 2 3 1 5985 0.116255 2 3 1 6000 0.114804 2 3 1 [Remainder of file not included to save space] end*** END OF INPUT FILE 'FIT.IN' ********************************** Calibration Bounded by Carsel and Parrish Distributions The following input files were from the Ca rsel and Parrish soil hydraulic parameter calibration in Chapter 4. Boundary conditions and the node distribution were similar to Figure A1 and A-2. *** BLOCK I: ATMOSPHERIC INFORMATION ********************************** MaxAL (MaxAL = number of atmospheric data-records) 31 hCritS (max. allowed pressure head at the soil surface) 0 tAtm Prec rSoil rRoot hCritA rt ht 360 0 0 0 10000 0 0 480 0 0 0 10000 -0.401644 0 1800 0 0 0 10000 0 0

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129 1920 0 0 0 10000 -0.401644 0 3240 0 0 0 10000 0 0 3360 0 0 0 10000 -0.401644 0 4680 0 0 0 10000 0 0 4800 0 0 0 10000 -0.401644 0 6120 0 0 0 10000 0 0 6240 0 0 0 10000 -0.401644 0 7560 0 0 0 10000 0 0 7680 0 0 0 10000 -0.401644 0 9000 0 0 0 10000 0 0 9120 0 0 0 10000 -0.401644 0 10440 0 0 0 10000 0 0 10560 0 0 0 10000 -0.401644 0 11880 0 0 0 10000 0 0 12000 0 0 0 10000 -0.401644 0 13320 0 0 0 10000 0 0 13440 0 0 0 10000 -0.401644 0 14760 0 0 0 10000 0 0 14880 0 0 0 10000 -0.401644 0 16200 0 0 0 10000 0 0 16320 0 0 0 10000 -0.401644 0 17640 0 0 0 10000 0 0 17760 0 0 0 10000 -0.401644 0 19080 0 0 0 10000 0 0 19200 0 0 0 10000 -0.401644 0 20520 0 0 0 10000 0 0 20640 0 0 0 10000 -0.401644 0 21000 0 0 0 10000 0 0 *** END OF INPUT FILE 'ATMOSPH.IN' ************************************* *** BLOCK ?: BOUNDARY INFORMATION ********************************************* NumBP NObs SeepF FreeD DrainF qQWLF 20 3 f t f f Node Number Array 1 2 3 4 5 6 7 8 9 63 64 65 66 67 68 69 70 71 72 73 Width Array 0.0490088 0.098017 0.0980174 0.0980175 0.0980161 0.0980171 0.0980174 0.0980169 0.0490087 1.66667 3.83333 4.83333 5.83333 6.83333 7.83333 8.45238 8.28572 7.71428 7.14285 3.42857 Length of soil surface associated with transpiration 0 Observation nodes. Node(1,....NObs) 121 122 123 *** End of input file 'BOUNDARY.IN' *******************************************

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130 *** BLOCK A: BASIC INFORMATION ***************************************** Heading Welcome to HYDRUS-2D LUnit TUnit MUnit (indicated uni ts are obligatory for all input data) cm min mmol Kat (0:horizontal plane, 1:axisymmetric vertical flow, 2:vertical plane) 2 MaxIt TolTh TolH InitH/W (max. number of iterations and tolerances) 200 0.001 0.1 t lWat lChem lSink Short Flux lScrn At mIn lTemp lWTDep lEquil lExtGen lInv t f f f t t t f f t t t *** BLOCK B: MATERI AL INFORMATION ************************************** NMat NLay hTab1 hTabN 1 1 0 0 Model Hysteresis 0 0 thr ths Alfa n Ks l 0.04 0.4 0.03 2.3804 0.4 0.5 *** BLOCK C: TIME INFORMATION ****************************************** dt dtMin dt Max DMul DM ul2 ItMin ItMax MPL 0.5 0.0001 15 1.3 0.7 3 7 10 tInit tMax 0 21000 TPrint(1),TPrint(2),...,TPrint(MPL) 2100 4200 6300 8400 10500 12600 14700 16800 18900 21000 *** END OF INPUT FILE 'SELECTOR.IN' ************************************ Welcome to HYDRUS-FIT Parameter Estimation of Soil Hydraulic Properties NOBB MIT iWeight 1731 50 0 lWatF lChemF NMat lTempF t f 1 f Model Hyster Aniz 0 0 f thr ths Alfa n Ks l 0.04 0.4 0.03 2.3804 0.4 0.5 1 1 1 1 1 0 0.025 0.31 0.087 2.1 0 0 0.065 0.55 0.203 3.26 1.015 0 HO(N) FOS ITYPE(N) POS WTS 5760 0.119884 2 3 1

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131 5775 0.119884 2 3 1 5790 0.119158 2 3 1 5805 0.119158 2 3 1 5820 0.119158 2 3 1 5835 0.118433 2 3 1 5850 0.118433 2 3 1 5865 0.118433 2 3 1 5880 0.117707 2 3 1 5895 0.117707 2 3 1 5910 0.117707 2 3 1 5925 0.117707 2 3 1 5940 0.116981 2 3 1 5955 0.116981 2 3 1 5970 0.116255 2 3 1 5985 0.116255 2 3 1 6000 0.116255 2 3 1 [Remainder of file not included to save space] end*** END OF INPUT FILE 'FIT.IN' ********************************** Calibration Bounded by ROSETTA Distributions The following input files were from the RO SETTA soil hydraulic para meter calibration in Chapter 4. Boundary conditions and the node dist ribution were similar to Figure A-1 and A-2. Atmospheric, boundary, basic, material, and time information are identi cal to the calibration bounded by Carsel and Parrish (1988) distributions. Welcome to HYDRUS-FIT Parameter Estimation of Soil Hydraulic Properties NOBB MIT iWeight 1731 50 0 lWatF lChemF NMat lTempF t f 1 f Model Hyster Aniz 0 0 f thr ths Alfa n Ks l 0.04 0.4 0.03 2.3804 0.4 0.5 1 1 1 1 1 0 0 0.265 0.011 1.387 0.029 0 0.111 0.485 0.111 7.277 6.755 0 HO(N) FOS ITYPE(N) POS WTS 5760 0.119884 2 3 1 5775 0.119884 2 3 1

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132 5790 0.119158 2 3 1 5805 0.119158 2 3 1 5820 0.119158 2 3 1 5835 0.118433 2 3 1 5850 0.118433 2 3 1 5865 0.118433 2 3 1 5880 0.117707 2 3 1 5895 0.117707 2 3 1 5910 0.117707 2 3 1 5925 0.117707 2 3 1 5940 0.116981 2 3 1 5955 0.116981 2 3 1 5970 0.116255 2 3 1 5985 0.116255 2 3 1 6000 0.116255 2 3 1 [Remainder of file not included to save space] end*** END OF INPUT FILE 'FIT.IN' ********************************** Calibration Bounded by Measured Distributions The following input files were from the meas ured soil hydraulic parameter calibration in Chapter 4. Boundary conditions and the node dist ribution were similar to Figure A-1 and A-2. Atmospheric, boundary, basic, material, and time information are identi cal to the calibration bounded by Carsel and Parrish (1988) distributions. Welcome to HYDRUS-FIT Parameter Estimation of Soil Hydraulic Properties NOBB MIT iWeight 1731 50 0 lWatF lChemF NMat lTempF t f 1 f Model Hyster Aniz 0 0 f thr ths Alfa n Ks l 0.04 0.4 0.03 2.3804 0.4 0.5 1 1 1 1 1 0 0 0.311 0.009 0.733 0.1 0 0.147 0.478 0.043 4.605 2 0 HO(N) FOS ITYPE(N) POS WTS 5760 0.119884 2 3 1 5775 0.119884 2 3 1 5790 0.119158 2 3 1

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133 5805 0.119158 2 3 1 5820 0.119158 2 3 1 5835 0.118433 2 3 1 5850 0.118433 2 3 1 5865 0.118433 2 3 1 5880 0.117707 2 3 1 5895 0.117707 2 3 1 5910 0.117707 2 3 1 5925 0.117707 2 3 1 5940 0.116981 2 3 1 5955 0.116981 2 3 1 5970 0.116255 2 3 1 5985 0.116255 2 3 1 6000 0.116255 2 3 1 [Remainder of file not included to save space] end*** END OF INPUT FILE 'FIT.IN' ********************************** Calibration bounded by Vanderborght and Vereecken distributions The following input files were from the soil transport parameter calibration in Chapter 4. Boundary conditions and the node distribution were similar to Figure A-1 and A-2. *** BLOCK I: ATMOSPHERIC INFORMATION ********************************** MaxAL (MaxAL = number of atmospheric data-records) 30 hCritS (max. allowed pressure head at the soil surface) 0 tAtm Prec rSoil rRoot hCr itA rt ht cValue1 cValue2 cValue3 360 0 0 0 10000 0 0 0 0 0 480 0 0 0.00036 10000 -0.401644 0 0 0 0 1080 0 0 0.00036 10000 0 0 0 0 0 1800 0 0 0 10000 0 0 0 0 0 1920 0 0 0.00036 10000 -0.401644 0 0 0 0 2520 0 0 0.00036 10000 0 0 0 0 0 3240 0 0 0 10000 0 0 0 0 0 3360 0 0 0.00036 10000 -0.401644 0 0 0 0 3960 0 0 0.00036 10000 0 0 0 0 0 4680 0 0 0 10000 0 0 0 0 0 4800 0 0 0.00036 10000 -0.401644 0 0 0 0 5400 0 0 0.00036 10000 0 0 0 0 0 6120 0 0 0 10000 0 0 0 0 0 6240 0 0 0.00036 10000 -0.401644 0 0 0 0 6630 0 0 0.00036 10000 0 0 0 0 0

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134 6640 0 0 0.00036 10000 -0.401644 0 0 13.78 0 6840 0 0 0.00036 10000 0 0 0 0 0 7560 0 0 0 10000 0 0 0 0 0 7680 0 0 0.00036 10000 -0.401644 0 0 0 0 8280 0 0 0.00036 10000 0 0 0 0 0 9000 0 0 0 10000 0 0 0 0 0 9120 0 0 0.00036 10000 -0.401644 0 0 0 0 9720 0 0 0.00036 10000 0 0 0 0 0 10440 0 0 0 10000 0 0 0 0 0 10560 0 0 0.00036 10000 -0.401644 0 0 0 0 11160 0 0 0.00036 10000 0 0 0 0 0 11880 0 0 0 10000 0 0 0 0 0 12000 0 0 0.00036 10000 -0.401644 0 0 0 0 12600 0 0 0.00036 10000 0 0 0 0 0 13000 0 0 0 10000 0 0 0 0 0 *** END OF INPUT FILE 'ATMOSPH.IN' ************************************* *** BLOCK ?: BOUNDARY INFORMATION ********************************************* NumBP NObs SeepF FreeD DrainF qQWLF 24 3 f t f f Node Number Array 1 2 3 4 5 6 7 8 9 63 64 65 66 67 68 69 70 71 72 73 86 87 88 89 Width Array 0.0490088 0.098017 0.0980174 0.0980175 0.0980161 0.0980171 0.0980174 0.0980169 0.0490087 1.66667 3.83333 4.83333 5.83333 6.83333 7.83333 8.45238 8.28572 7.71428 7.14285 3.42857 0.955681 1.8125 1.61477 0.757954 Length of soil surface associated with transpiration 5.14091 Observation nodes. Node(1,....NObs) 121 122 123 *** BLOCK ?: Solute trans port boundary conditions ***************************** KodCB(1),KodCB(2),.....,KodCB(NumBP) -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 *** End of input file 'BOUNDARY.IN' ******************************************* *** BLOCK A: BASIC INFORMATION ***************************************** Heading Welcome to HYDRUS-2D LUnit TUnit MUnit (indicated uni ts are obligatory for all input data) cm min

PAGE 135

135 mg Kat (0:horizontal plane, 1:axisymmetric vertical flow, 2:vertical plane) 2 MaxIt TolTh TolH InitH/W (max. number of iterations and tolerances) 200 0.001 0.1 t lWat lChem lSink Short Flux lScrn At mIn lTemp lWTDep lEquil lExtGen lInv t t t f t t t f f t t t *** BLOCK B: MATERI AL INFORMATION ************************************** NMat NLay hTab1 hTabN 1 1 0 0 Model Hysteresis 0 0 thr ths Alfa n Ks l 0.065 0.31 0.203 3.0809 0.077401 0.5 *** BLOCK C: TIME INFORMATION ****************************************** dt dtMin dt Max DMul DM ul2 ItMin ItMax MPL 0.5 0.0001 15 1.3 0.7 3 7 100 tInit tMax 0 13000 TPrint(1),TPrint(2),...,TPrint(MPL) 130 260 390 520 650 780 910 1040 1170 1300 1430 1560 1690 1820 1950 2080 2210 2340 2470 2600 2730 2860 2990 3120 3250 3380 3510 3640 3770 3900 4030 4160 4290 4420 4550 4680 4810 4940 5070 5200 5330 5460 5590 5720 5850 5980 6110 6240 6370 6500 6630 6760 6890 7020 7150 7280 7410 7540 7670 7800 7930 8060 8190 8320 8450 8580 8710 8840 8970 9100 9230 9360 9490 9620 9750 9880 10010 10140 10270 10400 10530 10660 10790 10920 11050 11180 11310 11440 11570 11700 11830 11960 12090 12220 12350 12480 12610 12740 12870 13000 *** BLOCK G: SOLUTE TRANSPORT INFORMATION ***************************************************** Epsi lUpW lArtD lTDep cTolA cTol R MaxItC PeCr Nu.of Solutes Tortuosity 0.5 f f f 0 0 1 2 1 t Bulk.d. DisperL. DisperT Frac ThImob (1..NMat) 1.5 0.5 0.1 1 0 DifW DifG n-th solute 0 0

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136 Ks Nu Beta Henry SnkL1 SnkS1 SnkG1 SnkL1' SnkS1' SnkG1' SnkL0 SnkS0 SnkG0 Alfa 0 0 1 0 0 0 0 0 0 0 0 0 0 0 cTop cBot 0 0 0 0 30 0 0 0 0 tPulse 13000 *** BLOCK G: ROOT WATE R UPTAKE INFORMATION ***************************** Model (0 Feddes, 1 S shape) 1 h50 P3 -800 3 Solute Reduction f *** END OF INPUT FILE 'SELECTOR.IN' ************************************ Welcome to HYDRUS-FIT Parameter Estimation of Soil Hydraulic Properties NOBB MIT iWeight 962 20 0 lWatF lChemF NMat lTempF f t 1 f NS 1 Bulk.d. DisperL. Frac ThImob DifW DifG Ks Nu Beta Henry SnkL1 SnkS1 SnkG1 SnkL1' S nkS1' SnkG1' SnkL0 SnkS0 SnkG0 Alfa 1.5 1.2 0.01 1 0 0.001 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 HO(N) FOS ITYPE(N) POS WTS 5760 0.180045 4 3 1 5775 0.180318 4 3 1 5790 0.174323 4 3 1 5805 0.177593 4 3 1 5820 0.178138 4 3 1 5835 0.177048 4 3 1 5850 0.17732 4 3 1 5865 0.185223 4 3 1 5880 0.17405 4 3 1

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137 5895 0.186312 4 3 1 5910 0.182225 4 3 1 5925 0.18277 4 3 1 5940 0.184678 4 3 1 5955 0.177865 4 3 1 5970 0.185495 4 3 1 5985 0.178683 4 3 1 6000 0.18931 4 3 1 [Remainder of file not included to save space] end*** END OF INPUT FILE 'FIT.IN' **********************************

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138 APPENDIX B POSSIBLE IN-SEASON IMPACTS ON CALIBRATION Introduction As previously discussed in this document, the H2D program has become a popular tool for modeling drip irrigation systems due to its two-dimensional capab ilities. While the model has been validated across many sites, commonly only a few irrigation events are chosen or reported in the calibration and validation process (Cha pter 3 and Chapter 4). The question remains whether soil hydraulic properties beneath these in tensive management systems are truly static throughout the growing season. Notably no study to date has accounted for the im pact soil structure modifications, such as root development, on numerical simulations of dr ip irrigation (Gardenas et al. 2005). If drip systems undergo significant hydrau lic modification from in-season impacts, it is essential to quantify these shifts if season long si mulations are to be successful. The most likely catalyst of in-season hydrauli c parameter modification is root growth. Previous studies have focused on root distribu tions under drip irrigated crops (Scholberg, 1996), but to date no work has been reported speci fically focusing on the soil hydraulic parameter impact of root growth within intensive management systems. Comparing the results of these studies, independent of crop select ion, root development in drip systems is concentrated around the emitter. Mmolawa and Or (2003) reported H2D to pred ict SMC distributions well when no plants were present, but to consistently over predic t water extraction from roots when a crop was present; moreover, while H2D matched the total so il profile water distribution fairly well, most of the error was located near the drip emitter. Erro rs observed in this area are likely either the

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139 result of poor root uptake simulation or an inab ility to account for root zone modification of soil hydraulic parameters. Outside of drip irrigation, Whalley et al. ( 2004) analyzed the change in physical soil properties and the SMRC differences between rhiz osphere soil and bulk soil, with bulk soil defined as soil located over 10 mm from the roots. The study showed SMRCs to remain relatively constant before and af ter root growth. Similarly, Wh alley et al. (2005) reported no significant shift in SMRCs, but did find a noticeabl e increase in macro-pores in the rhizosphere soil. The results are comparable with Gish et al (1998), where dye tracers were used to visually observe the water movement through cropped root system and it was concluded that roots are a major contributor to preferential flow paths. With roots concentrated around the emitter unde r drip irrigated crops, it was hypothesized that the concentrated root growth creates a highly dynamic zone of so il hydraulic properties around the emitter that in-turn requi res time specific data for calib ration. The objective of this study was to examine any impacts of root grow th on soil hydraulic parameters by using H2D to determine representative sets of hydraulic parame ters for different seas onal periods by inverse optimization. Results All results observed during this study were influenced by the two site design of the experiment. Experiment 2 and Experiment 4 were performed at different locations within the same field and homogeneity of so il properties was assumed; howev er, after reviewing the results of this study it is clear at the emitter scal e the field was not homogeneous thus voiding all observation of root growth impact Interestingly, the heterogene ity was not observed at the C8 location, possibly due to the tillage method thoroughly mixing the top most soil layer.

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140 0.05 0.10 0.15 0.20 0.25 10/1310/1410/1510/1610/1710/18 DATESMC E8 C8 E23 C23 No Crop Data 0.05 0.10 0.15 0.20 0.25 7/87/97/107/117/127/13 DATESMC E8 C8 E23 C23 End of Season Data Figure B-1. Averaged data used in calibrations. Representative five days displayed for each. No Crop Data was taken from Experiment 2 and End of Season Data was taken from Experiment 4. SMC is soil moisture content (cm3 cm-3).

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141 0.05 0.10 0.15 0.20 0.25 0.001.002.003.004.005.00 DAYSMC NP EOS C8 0.05 0.10 0.15 0.20 0.25 0.001.002.003.004.005.00 DAYSMC NP EOS C23 0.05 0.10 0.15 0.20 0.25 0.001.002.003.004.005.00 DAYSMC NP EOS E23 Figure B-2. Location by location comparison for measured soil moisture content (cm3 cm-3) (SMC) from each experiment. NP is Experiment 2 and EOS is Experiment 4. 0.05 0.10 0.15 0.20 0.25 22.22.42.62.83 DAY OF SIMULATIONSMCC8 0.05 0.10 0.15 0.20 0.25 22.22.42.62.83 DAY OF SIMULATIONSMCC23 0.05 0.10 0.15 0.20 0.25 22.22.42.62.83 DAY OF SIMULATIONSMCE23 Figure B-3. Results of Experiment 2 calibra tion (line) and measured data during Experi ment 4 (data points). SMC is soil moistur e content (cm3 cm-3)

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142 Summary More work is needed to verify the existen ce or absence of in-seas on root impacts on soil hydraulic parameters within bedded systems. Th e drastic difference between the two monitored SMC distributions inhibited any efforts of isol ating in-season changes to saturated hydraulic conductivity. Human impacts such as staking, tig htness of bed constructi on, or the use of a tractor-pulled rolling hole-punch dur ing planting could also be th e cause of the heterogeneity effects observed in this study. If these man-made impacts are the culprit, results from soil sampling performed prior to these seasonal modi fications would be rend ered useless. A study that maintains one monitoring loca tion after bed construction, but prior to seasonal preparations and through the growing season is ideal.

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143 LIST OF REFERENCES Abbasi, F., D. Jacques, J. Simunek, J. Feyen, M.Th. Van Genuchten. 2003. Inverse estimation of soil hydraulic and solute transport paramete rs from transient field experiments: Heterogeneous soil. Transactions of the ASAE 46, 1097-1111. Ajdary, K., D.K. Singh, A.K. Singh, M. Khanna 2007. Modelling of nitrogen leaching from experimental onion field under drip fertigati on. Agricultural and Water Management 89, 15-28. Allen R.G., L.S. Pereira, D. Raes, M. Smith 1998. Crop evapotranspiration. Guidelines for computing crop water requirements. FAO Irri gation and Drainage Paper No. 56, Rome. Al-Yahyai, R., B. Schaffer, F.S. Davies, R. Munoz-Carpena. 2006. Charact erization of soil-water retention of a very gravelly loam soil varied with determin ation method. Soil Science 171, 85-93. Amayreh, J., N. Al-Abed. 2005. Developing crop coefficients for field-grown tomato (Lycopersicon esculentum Mill.) under drip irrigation with black plastic mulch. Agricultural Water Management 73, 247-254. Buster, T.P. 1979. Soil survey of Marion Count y, Florida. Soil Conservation Service, Washington, D.C. Campbell Scientific, Inc. 2002. CS616 Water C ontent Reflectometer. User guide. Campbell Scientific, Inc., Logan, Utah. Carlisle, V.W., R.E. Caldwell, F. Sodek, L.C. Hammond, F.G. Calhoun, M.A. Granger, H.L. Breland. 1978. Characterization data for sele cted Florida soils. Soil Science Research Report 78-1. University of Florida, Ins titute of Food and Agricultural Sciences, Gainesville, Florida. Carsel R.F., R.S. Parrish. 1988. Developing joint probability distributions of soil water retention characteristics, Water Resources Research 24, 755-769. Celia, M.A., E.T. Bououtas, R.L. Zarba. 1990. A general mass-conservative numerical solution for the unsaturated flow equation, Water Resources Research 26, 1483-1496. Cook, F.J., P. Fitch, P.J. Thorburn, P.B. Char lesworth, K.L. Bristow. 2006. Modelling trickle irrigation: Comparison of analytical and numer ical models for estimation of wetting front position with time. Environmental Modelling and Software 21, 1353-1359. Cote, C.M., K.L. Bristow, P.B. Charlesworth, F.J. Cook, P.J. Thorburn. 2003. Analysis of soil wetting and solute transport in subsurface tric kle irrigation. Irrigati on Science 22, 143-156. Dukes, M.D. and R. Muoz-Carpena. 2006. Soil water sensor-based automatic irrigation of vegetable crops. In: Encyclopedia of Water Scie nce. S.W. Trimble, B.A. Stewart and T.A. Howell (eds). Marcel-Dekker, Inc ., New York, New York. pp. 1-5.

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144 Fernandez-Galvez, J. L.P. Simmonds. 2006. M onitoring and modelling the three-dimensional flow of water under drip irrigation. Ag ricultural Water Management 83, 197-208. Feyen, J., D. Jacques, A. Ti mmerman, J. Vanderborght. 1998. Mode lling water flow and solute transport in heterogeneous soils: A review of recent approaches. Journal of Agricultural Engineering Research 70, 231-256. Gardenas, A.I., J.W. Hopmans, B.R. Hanson, J. Simunek. 2005. Two-dimensional modeling of nitrate leaching for various fertigation scenar ios under micro-irrigation. Agricultural Water Management 74, 219-242. Gardner, P.J., N. Flynn, E. Maltby. 2001. A simple method for the determination of ionic diffusion coefficients in flooded soils. Hydrological Processes 15, 511-518. Gish, T.J., D. Gimenes, W.J. Rawls. 1998. Im pact of roots on ground water quality. Plant and Soil 200, 47-54. Goldberg, S.D., Gornat, B., Bar, Y. 1971. The di stribution of roots, wa ter and minerals as a result of trickle irrigation. Journal of Amer ican Society Horticultural Science 96, 645-648. Hanson, B.R., J. Simunek, J.W. Hopmans. 2006. Evaluation of ureaammoniumnitrate fertigation with drip irrigation using numeri cal modeling. Agricultural Water Management 86, 102-113. Harmel, D.R., P. Smith. 2007. Consideration of measurement uncertainty in the evaluation of goodness-of-fit in hydrologic and water qual ity modeling. Journal of Hydrology, doi:10.1016/j.jhydrol.2007.01.043. Hochmuth, G.J., and A.G. Smajstrla. 1998. Fert ilizer application and management for micro (drip)-irrigated vegetables in Florida. Florid a Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida. Circ. 1181. Kennedy, J.R., Keefer, T.O., Paige, G.B., Barnes E. 2003. Evaluation of dielectric constantbased soil moisture sensors in a semiarid rangeland. Proceedings First Interagency Conference on Research in the Watersheds. October 27-30, 2003. Benson, Arizona, 503508. Li, J., J. Zhang, M. Rao. 2005. Modeling of wa ter flow and nitrate transport under surface drip fertigation. Transactions of the ASAE 48, 627-637. Legates, D.R., G. J. McCabe Jr. 1999. Evalua ting the use of goodness-of-fit measures in hydrologic and hydroclimatic model validati on. Water Resources Research 35, 233. Lubana, P.P.S., N.K. Narda. 2001. Modelling soil water dynamics under trickle emitters A review. Journal of Agricultural E ngineering Research 78, 213-232. Marella, R.L. 2004. Water withdrawals, use, di scharge, and trends in Florida, 2000. U.S. Geological Survey Scientific Inves tigations Report 2004-5151, pp. 136.

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145 Maynard, D.N., G.J. Hochmuth, S. M. Olson., C. S. Vavrina, W.M. Stall, T.A. Kucharek, S.E. Webb, T.G. Taylor, S.A. Smith, E.H. Simonne 2003. Tomato producti on in Florida. In: Vegetable Production Guide for Florida, 2003-20 04. S.M. Olsen and D.N. Maynard (eds.) Florida Cooperative Extension Service, Univer sity of Florida, Gainesville, Florida, pp. 271-283. Mmolawa, K., D. Or. 2003. Experimental and Numerical Evaluation of Analytical Volume Balance Model for Soil water Dynamics under Drip Irrigation. Soil Science Society of America Journal 67, 1657-1671. Mulvaney, R.L. 1996. Nitrogen-Inorganic forms. In Methods of soil analysis. Part 3. Chemical methods. D. L. Sparks et al., (Eds.). SSSA Book Ser. 5. SSSA, Madison, WI. pp. 11231184. Muoz-Carpena, R., C.M. Regalado, A. Ritter, J. Alvarez-Bened A.R. Socorro. 2005a. TDR estimation of electrical conductiv ity and saline solute concen tration in a volcanic soil. Geoderma 124, 399-413. Muoz-Carpena, R., M.D. Dukes, J. Icerman. 2005b. Expand soil water balance capabilities of the DSSAT model for simulating yields under intensive bed management systems. Best Management Practices Modeli ng Project, FDACS UF/IFAS. Deliverable 4. August, 31. Muoz-Carpena, R., M.D. Dukes, Y.C. Li, W. Klassen. 2006. Design and evaluation of a new controller for soil water-based irrigation cont rol. Applied Engineering in Agriculture. Manuscript no. SW-06008-2005. Nash, J.E., J.V. Sutcliffe. 1970. River flow for ecasting through conceptual models part I A discussion of principles. J ournal of Hydrology 10, 282-290. Neve, S.D., J.V.D. Steene, R. Hartmann, G. Hofman. 2000. Using time domain reflectometry for monitoring mineralization of n itrogen from soil organic matt er. European Journal of Soil Science 51, 295-304. Pitts, D.J., A.G. Smajstrla, D.Z. Haman, G.A. Clark. 1990. Irrigation Costs for Tomato Production in Florida. Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida. AE74. Reviewed July, 2002. Plauborg, F., V.B. Iversen, P.E. Laerke. 2005. In situ comparison of three dielectric soil moisture sensors in drip irrigated sandy so ils. Vadose Zone Journal 4, 1037-1047. Ritter, A., F. Hupet, R. Muoz-Carpena, S. Lambot, M. Vanclooster. 2003. Using inverse methods for estimating soil hydraulic properties from field data as an al ternative to direct methods. Agricultural Water Management 59, 77-96 Robinson, R.A., R.H. Stokes. 1968. Electrolyte Solutions. Butterworths: London; Appendix 11.1 and pp. 286.

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146 Schaap, M.G., F.J. Leij, M.Th. van Genucht en. 1998. ROSETTA: a co mputer program for estimating soil hydraulic properties with hierar chical pedotransfer functions. Journal of Hydrology 251, 163-176. Scholberg, J.M. 1996. The Adaptive use of Crop Gr owth Models to Simulate the Growth of Field-Grown Tomato. Doctoral Dissertati on, University of Florida. 131-155. Schroder, J. 2006. Soil moisture ba sed drip irrigation for efficient use of water and nutrients and sustainability of vegetables cr opped on coarse soils. Masters Th esis, University of Florida. Seyfried, S.M., M.D. Murdock. 2004. Measurem ent of Soil Water Conten t with a 50-MHz Soil Dielectric Sensor. Soil Science Soci ety of America Journal 68, 394-403. Simonne, E.H., M.D. Dukes, D.Z. Haman. 2004. Principles and Practices of Irrigation Management for Vegetables. In: Vegetable Production Guide for Florida, 2003-2004. S.M. Olsen and D.N. Maynard (eds.) Florida Coope rative Extension Service, University of Florida, Gainesville, Florida, pp. 33-39. Simunek, J., M. Sejna, M.Th. van Genucht en. 1999. The HYDRUS-2D software package for simulating two-dimensional movement of water, heat, and multiple solutes in variably saturated media. Version 2.0, IGWMC-T PS-53, International Ground Water Modeling Center, Colorado School of Mines, Golden, Colorado. Simunek, J., N.J. Jarvis, M.Th. van Genuchten A. Gardenas. 2003. Review and comparison of models for describing non-equilibrium and pref erential flow and transport in the vadose zone. Journal of Hydrology 272, 14-35. Skaggs, T.H., T.J. Trout, J. Simunek, P.J. Shouse. 2004. Comparison of HYDRUS-2D simulations of drip irrigation with experimental observati ons. Journal of Irrigation and Drainage Engineering 130, 304-310. Stevens Water Monitoring Systems, Inc. 2007. Comprehensive Stevens Hydra Probe Users Manual. Stevens Water Monitoring Systems, Inc., Portland, Oregon. Topp, G.C., J.L. Davis, A.P. Annan. 1980. Elect romagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resources Research 16, 574-582. USDA. 2006. Census, US State Data Table 35. Vegetables and Melons Harvested for Sale: 2002. http://www.nass.usda.gov:8080/ Census/Pull_Data_Census Last accessed 03/14/2006. van Genuchten, M.Th. 1980. A closed-form equation for predicting the hydr aulic conductivity of unsaturated soils, Soil Science Soci ety of America Journal 44, 892-898. van Genuchten, M.Th., 1987. A numerical model for water and solute movement in and below the root zone. Research Report No 121, U.S. Salinity laboratory, USDA, ARS, Riverside, California.

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147 van Genuchten, M.Th., F.J. Leij, S.R. Yate s. 1991. The RETC Code for Quantifying the Hydraulic Functions of Unsaturated Soils. U.S. Salinity Laboratory, U.S. Department of Agriculture, Agricultural Research Service. http://www.scisoftware.com/products /retc_details/retc_details.html Last accessed 02/15/2007. Vanderborght, J., H. Vereecken. 2007. Review of dispersivities for transport modeling in soils. Vadose Zone Journal 6, 29-52. Vazquez, N., A. Pardo, M.L. Suso, M. Quemada. 2006. Drainage and nitrate leaching under processing tomato growth with drip irri gation and plastic mu lching. Agriculture, Ecosystems, and Environment 112, 313-325. Warrick, A. W. 1974. Time-dependent linearized infiltration, I: point -sources. Soil Science Society of America Proceedings 38, 383-386. Whalley, W.R., P.B. Leeds-Harrison, P.K. Leech B. Riseley, N.R.A. Bird. 2004. The hydraulic properties of soil at root-soil interface. Soil Science 169, 90-99. Whalley, W.R., B. Riseley, P.B. Leeds-Harrison, N R.A. Bird, P.K. Leech, W.P. Adderley. 2005. Structural differences between bulk and rhizos phere soil. European Journal of Soil Science 56, 353-360. Wooding, R.A. 1968. Steady infiltration from a shallow circular pond. Water Resources Research 4, 1259-1273. Zotarelli L., J.M. Scholberg, M.D. Dukes, R. Muoz-Carpena. 2007a. Monitoring of Nitrate Leaching in Sandy Soils: Comparison of Three Methods. Journal of Environmental Quality 6, 953-962. Zotarelli L., M.D. Dukes, J.M. Scholberg, J. Ic erman, K. Le Femminella, R. Muoz-Carpena. 2007b. Tomato and pepper root distribution asso ciated to different ir rigation management and N-leaching under plastic mulch conditions. In: Proceedings of the ASA-CSSA-SSSA International Annual Meeting, Nov 4-8, 2007, New Orleans, Louisi ana. ASA CDROM.

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148 BIOGRAPHICAL SKETCH Born in Tallahasse, Florida on July 4th, 1982, Jason Icerman started his academic career at Timberlane Preschool. From there, he attended Gilchrist Elementary, Desoto Trail Elementary, and Augusta Raa Middle School before finishing his grade school educat ion at Maclay School. Staying as involved in athletics as natural ability would allow, Jason also managed to achieve high marks in the classroom passing seven AP exam inations. In August 2000, he enrolled at the University of Florida as an el ectrical engineering major. Afte r trying his hand at pre-law, premed, and mechanical engineeri ng, Jason settled on land and water resource engineering and graduated summa cum laude with a Bachelor of Sc ience degree in December 2004. It was at this time that he accepted an offer to study under Dr. Michael Dukes and pursue a Master of Engineering degree.