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High Frequency Irrigation Simulation (HFIS) Model: Development and Analysis
Jason Icerman
INTRODUCTION
Population growth in the U.S. continues to burden our water resources. Though improvement in water
consumption rates has been seen since the early 1980s, rates in the U.S. remain at about 408 billion gallons of
water per day, with irrigation consuming the most freshwater at 137 billion gallons per day (USGS, 2004). Hence,
an important issue in agriculture is irrigation management coupled with water conservation. With irrigation being
the primary use of developed water supplies, in many areas the irrigation water demand exceeds the available
supply at current costs (Pitts et al., 1996). In agriculture, the goal is higher crop yield (higher profits).
Water conservation, while preferred, will often be sacrificed to obtain higher yields in the belief that the profit
gains will outweigh the extra water costs. This quandry perpetuates the never ending search for maximum profit
from minimal water usage.
Optimizing irrigation scheduling can increase water use efficiency (Howell et al., 1975). Water requirements
become even more important when water consumption is regulated, such as under the Water Management
Districts in the State of Florida. Irrigation models are a useful tool for managing and scheduling irrigation when
water is limited or regulated (Santos et al., 2000). Though users still request a water allotment based on
crop requirements, often models are used by governing bodies to determine an appropriate figure. The goal of
the consumptive use program in the State of Florida is to provide water for reasonable-beneficial uses
while protecting the water resources of the Districts (SJRWMD, 2004). Currently, Consumptive Use Permits (CUPs)
do not incorporate effective rainfall into their water limitations. Effective rainfall describes precipitation neither
lost through runoff nor deep percolation. The inclusion of an accurate representative of effective rainfall in CUPs
will aid in water conservation by creating the most precise crop water requirement possible. If permit
allowances reflect the true requirement of a user, a more precise distribution of available water can occur - in
effect allowing more access to more users. The creation of a model with the ability to determine crop water
need throughout the growing season, using the most efficient and effective irrigation scheduling possible
while focusing on accurate accounting of effective rainfall, should enhance the regulatory success of CUPs.
The objectives of this study were to first create a one-dimensional model capable of simulating crop water
use, irrigation, drainage, and effective rainfall at hourly and daily time steps. Second, a sensitivity analysis
was conducted to determine the effect of input changes on key outputs.
MATERIALS AND METHODS
Model Logic
The model, High Frequency Irrigation Simulation (HFIS), utilizes the Microsoft Excel spreadsheet interface to
simulate crop water need throughout the growing season. The model receives a spreadsheet input along with
19 quantitative inputs from the user (Figure 1).
Figure 1. User input parameters as displayed in model, Kc Break Down, Root Zone Function, and
Other Inputs tab displays can be seen in Figures Al, A2, and A3 in the Appendix.
The required spreadsheet input from the user had to meet the following format: contain date and time information
in the first column, evapotranspiration (ET) data in millimeters in the second column, and rain data in millimeters
in the third column, with the three columns of data left justified and beginning at row one. Once all input data
were entered correctly, the data were stored in arrays and as single variables.
In general, the model is governed by a balance of the water in the crop root zone as follows:
CropHOreq = ET, - El,'ecaveRam
(Equation 1)
where:
CropH2Oreq is the water required by the crop (mm)
ETc is the crop evapotranspiration (mm)
EffectiveRain is the depth of rain entering the root zone (mm)
semwoa am S( retft ,& L'U PDOC ZCn~Pricf I-' 1 .VWt, Ju f
SesnraPropertkhs
Fkild Capdty (%) [W
Pernamnt WMlling
DPat (%)
Deoutin (%) I
lSeaM Lh Fii4
(daV,-
Mioto MuWtrof rawmmnWAw
AS - Rain + Irrigation - ET - (RunOff + Drainage)
(Equation 2)
where:
AS is the change in storage at a given time (mm)
Rain is the rain occurring at a given time (mm)
Irrigation is the scheduled irrigation at a given time (mm)
ET is the evapotranspiration at a given time (mm)
RunOff + Drainage is water unable to be stored in the root zone (mm)
However, these equations are broken into several functions in the model logic. The first function run by the
model was the creation of a crop coefficient (Kc) function for the entire specified season. A simple step-function
was assumed to represent the change in the crop coefficient over the season similar to the function defined in FAO
- 56 (Allen et al., 1998). At time zero, the Kc function returns a value equal to the first entered threshold
and continues to return that value until the first seasonal fraction is reached. Seasonal fractions are input by the
user as decimals. They represent a break point in the season similar to ranges defining a combination
function (Figure 2). Returning to the Kc function, from the first seasonal fraction to the second seasonal fraction,
the second threshold is returned; from the second seasonal fraction to the third seasonal fraction, the third
threshold is returned; and from the third season fraction to the end of the season, the fourth and final threshold
is returned. A representative crop water need could then be calculated by Equation 3.
ETc, Kc * REFET.
(Equation 3)
where:
ETc is the crop evapotranspiration (mm)
REFET is the ET data from the spreadsheet input (mm)
Kc is the crop coefficient determined by the step function (mm)
The root zone function was developed by the summation of two linear functions and two thresholds.
The representative equation returns a root zone depth output equal to the initial depth at time zero. The return
value then increases linearly until it reaches a value equal to the first threshold at a time equal to the first
threshold seasonal fraction. The return value remains at this threshold until the time equals the second
threshold seasonal fraction, at which point the return value again begins increasing linearly until maximizing
the output root zone depth at the second threshold, with a time equal to the third threshold seasonal fraction.
The function returns the second threshold value until the end of the season (Figure 2).
Threshold
Fracbtn r.3
T. h Threshold #2
Threshold #1 Threshold
h Threshood
X OThreshold Frachon #2
,",,al C.,nrn Fracbon 1
DAP
Figure 2. Sample root zone function representation.
The available water storage was quantified at each time interval by multiplying the root zone function at that
interval by the difference between the field capacity and permanent wilting point as entered by the user
(Equation 4).
- AWS - (FC - PWP 7
WS 100 Z
(Equation 4)
where:
AWS is the available water storage (mm)
FC is the field capacity (mm/mm)
PWP is the permanent wilting point (mm/mm)
RZ is the root zone depth (mm)
Now that a water storage volume and a crop water need at each time interval had been calculated according to
user specifications, the soil moisture saturation depth was modeled through the season.
The model had two logical sequences at this stage, one for daily irrigation routines and one for hourly
irrigation routines. The daily soil moisture logic, including irrigation and drainage events, will be described first due
to the relative simplicity. For the daily simulations, the model compared the current day's (for daily scheduling
time steps were in days) parameters, as shown in Equation 5.
IF 61-1 - ET7_1 + I + R < A WS,
@i = .e_, - ET,., + I_, + R,_
6, = AWS,
(Equation 5)
THEN
ELSE
where:
0 is the soil moisture content (mm)
ET is evapotranspiration (mm)
I is irrigation (mm)
R is rain (mm)
AWS is available water storage (mm)
The logic statement above accounts for possible drainage, with i representing the current time step. If the addition
of water depth on the previous day exceeds the water storage capacity on the current day, drainage occurs and
the soil moisture depth (0) equals the available water storage. If the soil moisture level falls below the
maximum depletion threshold, as input by the user, an irrigation event would take place at that time
interval (Equation 6).
IF , < (1 - MAD)* A WS,
I, = AWS, -O
THEN
ELSE
I= 0
(Equation 6)
where:
0 is the soil moisture content (mm)
MAD is maximum allowable depletion (mm/mm)
AWS is available water storage (mm)
I is irrigation (mm)
Added into the above logic is the ability to specify a minimum irrigation depth. If the difference between the
available water storage and soil moisture on day i is less than the specified minimal irrigation, no irrigation would
be scheduled for day i and the drop below the minimal soil moisture level would be ignored.
IF R- - ETc, + It.> A WSi THEN
Di = R, - ETc, + I, - A WSi ELSE
(Equation 7)
where:
R is rain (mm)
ETc is crop evapotranspiration (mm)
I is irrigation (mm)
AWS is available water storage (mm)
If all the water present could not be stored in a given time interval, the excess water was represented as
drainage (Equation 7). Calculation of drainage allowed for a calculated effective rainfall is shown in Equation 8.
EF =R. - D
(Equation 8)
where:
REF is effective rain (mm)
R is rain (mm)
D is drainage (mm)
The hourly scheduling simulation of soil moisture, and the associated irrigation and drainage, is complicated by
the introduction of a user input drainage delay. In general, the above logic remained, but a drainage event no
longer lasted for a single interval, but lasts as long as specified by the user. The time extension retains more water
in the soil profile overall, since the soil moisture depth was at a maximum as long as drainage was occurring.
The amount of drainage per time interval was determined by dividing the drainage depth equally among the
time intervals (for example a drainage event of 3 mm with a 2 hr delay had a model output of three 1 mm
drainage events, time i, time i + 1, time i + 2). If a second drainage event occurred during the delayed response of
a previous event, the remaining drainage volume depth from the previous event was added to the depth of the
new event and the "delay clock" was reset to zero. Accruing the drainage surplus in a storage variable separate
from the drainage array allowed the model to time-release given amounts as stated above.
The model then prompts the user to select a high frequency or a daily irrigation simulation. Upon selection, the
model output a new workbook containing three worksheets. The first worksheet displays a summary of the
events scheduled according to the simulation selected, irrigation depths and event times. The second
worksheet contains a table summary of parameters calculated during the simulation. The third worksheet is
a graphical summary of parameters calculated during the simulation.
Sensitivity Analysis
After completion, the model was verified against an accepted irrigation scheduling spreadsheet. The model
showed similar output values for both the daily and hourly simulations. Verification complete, sensitivity analysis
was performed for all the user input variables over a compilation of almost two years (544 days) of rain
and evapotranspiration data.
To find the impact of each variable on model calculations, a baseline simulation was created. The baseline
values were changed in increments of 25% from -100% to 100%, with the baseline values representing a 0%
change (Figure 3). The six variables compared for each input were the average soil water content over the
season, total irrigation, drainage, and effective rainfall over the season, and the number of irrigation and
drainage events over the season.
ROOT ZONE FUNCTION
Frac f Frac2 Frac 3 d Threshod
I (mm) 2 (mm)
25 50 75 20 40
NC NC NC 0 0
NC NC NC 5 10
NC NC NC 10 20
NC NC NC 15 30
NC NC NC 25 50
NC NC NC 30 60
NC NC NC 35 70
NC NC NC 40 80
CROP COEFFICIENT FUNCTION
kc2 ke3 kc4 fcI flkc2
0.4 1.1 1 0-2 0A4
0 0 0 NC NC
0.1 0.275 0.25 NC NC
0.2 0.55 0.5 NC NC
0.3 0.825 0.75 NC NC
0.5 1.375 1.25 NC NC
0.6 1.65 1-5 NC NC
0.7 1.925 1.75 NC NC
0.8 2.2 2 NC NC
Figure 3. Sensitivity analysis parameters and values.
The comparison results were then graphed for each of the input changes. For the root zone function and
crop coefficient function the seasonal fractions were not changed and the thresholds were treated as a single
variable when changed.
DISCUSSION
Model Results
%CHANGE
-100%
-75%
-50%
-25%
25%
50%
75%
100%
Drainage
Delay
4
0
1
2
3
6
7
a
Depth
(mm)
1
0
0.25
0.5
0.75
1-25
1.5
1.75
2
A notable observation seen during model runs was the consistently higher irrigation sums from the high
frequency irrigation simulations (HFIS) relative to the daily irrigation simulations (DIS), 621mm to 582mm for
the baseline simulations used in the sensitivity analysis. One would expect hourly simulations to conserve
water; however, the reason this is not seen in the model is the presentation of irrigation as a depth (see the
baseline simulations of Table Al through Table A7). Upon further inspection, the relatively smaller
percentage difference of 6.7% between the HFIS and DIS cumulative irrigation depths is outweighed by a
larger difference in average soil moisture content over the season, 7.31 mm and 6.54 mm, respectively, for HFIS
and DIS baseline simulations (see the baseline simulations of Table Al through Table A7). The 11.8% change
in average soil moisture content is almost double the change in irrigation depth applied in the two simulations, with
a higher soil moisture level creating a more crop-friendly environment. It can be inferred that the DIS simulation
with the lower average soil moisture content induces more crop stress, though crop stress is not accounted for
or quantified in the model.
Sensitivity Analysis
As discussed in the Materials and Methods section, sensitivity analysis was performed on the quantitative inputs.
The model output values of the soil water content average, irrigation sum, drainage sum, effective rain
sum, irrigation count, and drainage count were measured at 25% intervals from a -100% to 100% increase.
Visual representations of the sensitivity analyses can be seen in Figure 4 through Figure 10 and are discussed below.
Sensitivity of maximum allowable depletion (MAD) in the model calculations is best seen through the change
in irrigation events and effective rain magnitude from both the daily and hourly simulations (Figure 4 & Table
AS). Increasing irrigation events with decreasing MAD percentages is seen in both simulation figures. Rising
event counts is explained by the shrinking root zone associated with a decreasing MAD, a shallow root zone will
dry out faster than a deeper root zone. A root zone that dries more rapidly needs more frequent irrigation events
of smaller magnitudes. This increase in events coupled with a marginal increase in irrigation depth is exhibited
in Figure 4. Associated with the higher irrigation counts is the decrease in effective rainfall. With a quicker
demand on irrigation events, and subsequent increase in events, there is less opportunity for infiltrating rain to
be effective. Also, deeper root zones accompanied by larger time intervals between events allow for more rainfall
to infiltrate the soil, resulting in more effective rainfall.
300
HFIS
200
5 " 100
-100 -50 0 50 1 -l00
- 100
0. -200
-300
Percent Change MAD
* SWCAVG IRRSUM
EFF RAIN SUM < I.RCNT
DRAIN SUM
* DRAIN CT
300
DIS
200
a 100
-100 -50 0 5b 190
-100
-200
-300
Percent Change MAD
DRAIN SIUM
* RAIN CNT
4 SWC AVG m IRR SIM
EFF RAI SUM IRR CNT
Figure 4. Sensitivity analysis of the Maximum Allowable Depletion parameter where DIS represents
the Daily Irrigation Simulation and HFIS represents the High Frequency Irrigation Simulation.
Note: Maximum allowable depletion simulations were extrapolated from a baseline simulation with no
minimum irrigation depth (minimum irrigation depth = 0). The reason for the change lies in the model logic.
A minimum irrigation depth too large eliminated describable effects of the maximum allowable depletion
percentage. All other input parameter analyses were developed from a baseline simulation having a
minimum irrigation depth of 10 mm (see Materials and Methods section).
The effect of the crop coefficient function is quite opposite of the MAD on the model. For both the high
frequency simulations and daily simulations, a clear increase in irrigation events and summation can be seen as
the Kc values increase (see Figure 5 & Table A7). Also seen, though on a smaller magnitude, is an increase
in effective rainfall as Kc values increased. Both aforementioned observations can be attributed to a higher crop
water demand created by the increasing Kc thresholds. Since the baseline simulation had a relatively small root
zone compared to the increasing Kc thresholds, it holds that a larger increase would be seen in irrigation events
and depth. A larger root zone coupled with increasing crop water demand would take longer to deplete and allow
for more effective rainfall to occur relative to required irrigation. Also seen in Figure 5 is a small decrease
in drainage and average soil water content as Kc values increase. On the other side of the graphs, an increase is
seen drainage and soil water content larger in magnitude than the decrease seen as Kc values increased.
The difference in magnitude is most likely due to the Kc values approaching zero, causing the root zone to
remain near saturation for longer periods of time.
300
200
100
*. . 0 -10
-200
-300
Percent Change KCF
* SWCAVG IRRSUM
EFF RAIN SUM - *Af CNT
DRAIN SUM
* DRAIN CWTT
-100
IL
300
200
t100
a-
10 50
-100
-200
-300
Percent Change KCF
* SWC AVG m IRR SLU
EFF RAWN SUM IRR CNT
DRAIN SUM
* ORAIN NT
Figure 5. Sensitivity analysis of the Crop Coefficient Function where DIS represents the Daily
Irrigation Simulation and HFIS represents the High Frequency Irrigation Simulation.
Changing the root zone function thresholds had little effect on any model variables besides average soil water
content (Figure 6 & Table A6). The average soil water content for both simulation methods increases as root
zone function thresholds increased. The lack of differentiation seen in the other output variables may be explained
by the relatively high minimum irrigation requirement. The high irrigation depth requirement would maintain a
stable irrigation pattern through the simulations. The deeper root zone allows for more water accumulation in
the soil, hence the rise in soil water content, with little change in irrigation events as discussed there would be
a negligible effect on output parameters outside of average soil water content.
a -100
-y0 50 100oo
-100
-200
-300
Percent Change RZF
* SWCAVG RR SUM
EFF RAINSLAM RRCNT
DRAIN SUM
* DRAIN CNT
a
0 -11o
8
* *
* 0 50 100
-100
-200
-300 -
Percent Change RZF
* SWC AVG m IRR SUM
EFF RAW SUM . IRR CNT
DRAIN SUM
* RAIN ONT
Figure 6. Sensitivity analysis of the Root Zone Function where DIS represents the Daily
Irrigation Simulation and HFIS represents the High Frequency Irrigation Simulatio
Unlike other user inputs, the drainage delay only affected high frequency irrigation simulations and,
accordingly, sensitivity analysis for the drainage delay variable were only performed for hourly simulations.
The largest change, as to be expected, was the rise in drainage events as the delay is increased. As written in
I -
U. --
100
100 t
100
the model code, the drainage delay creates more events through the delay at each time interval, so it follows
an increase in drainage events occurs with the increasing delay (Figure 7 & Table A4). Using similar logic,
an increase in effective rainfall is expected and again is observed. There is little change seen in the other variables.
A proportional decrease in irrigation depth would be anticipated assuming an increase in effective rainfall;
however, since analyses were performed on a percentage basis, the decrease in irrigation depth, while equal in
depth to the increase in effective rainfall, was proportionally less.
200
t100
No Data for DIS
Drainage Delay
Figure 7. Sensitivity analysis of the Drainage Delay parameter where DIS represents the Daily
Irrigation Simulation and HFIS represents the High Frequency Irrigation Simulation.
The most dramatic changes in model output were observed during the sensitivity analysis performed on the
minimum irrigation input (Figure 8 & Table A3). First, as predicted, decreasing the minimum irrigation
requirement greatly increased the number of irrigation events scheduled for both daily and hourly
simulations. Conversely, since increasing the minimum irrigation requirement effectively bypasses irrigation
events, an increase in effective rainfall is expected and observed (Figure 8). The extended time between
irrigation events, due to the increasing minimum irrigation depth, is reason for both observations reported above.
-50
-100
0 50 l0
-100
-200
-300
Percent Change MIN IRR
SSWC AVG R RR SUM
EFF RAIN SUM O r RoT
DRAIN SUM
* DIRAIH C4T
-50
100
0 so - i11
-100
-200
-300
Percent Change MIN IRR
DRAIN SLIUM
* RAIN NT
* SWCAVG 1 IRR SUM
IFF RA SUM IRR CNT
so 0 so 100
-100
-200
-300
Percent Change Drainage Delay
-- SWC AVG -- IRR SUM DRAIN SLIM
EFF RAIN SLIM � IRR CNT -4- DRAIN CNT
Figure 8. Sensitivity analysis of Minimum Irrigation Depth parameter where DIS represents the
Daily Irrigation Simulation and HFIS represents the High Frequency Irrigation Simulation.
Similar to results obtained from the root zone function sensitivity tests, permanent wilting point (PWP) and
field capacity (FC) analyses affected only one variable significantly, average soil water content (Figure 9, 10
& Table Al, A2); however, the individual results vary inversely. As field capacity increased through the analyses,
so did the average soil water content as compared to increasing the permanent wilting point, which decreased
the average soil water content. The increase in average soil water content observed with increasing FCs showed
a differential around twice the magnitude of the decrease observed with increasing PWPs. The inverse
relationship between the two input variables is expected, due to their opposite effect on the root zone
depth. Increasing the FC yields a deeper usable root zone while increasing the PWP shrinks the root zone.
Little change is seen in irrigation and drainage events since there was no change in crop water demand over
the simulations.
HFIS
a.
* SWCAVG RR SUM
EFFRAINSU1 IRRACT
* 100
100 -50 0 90 100
-100
-200
-300
Percent Change PWP
DRAIN SUM
* DRXAN C T
300
200
100
-50 0 50
-100
-200
-300
Percent Change PWP
* SWC AVG l IRR SUM
EFF RAIN SUM IRR ONt
Figure 9. Sensitivity analysis of the Permanent Wilting Point parameter where DIS represents the
Daily Irrigation Simulation and HFIS represents the High Frequency Irrigation Simulation.
300
200
8100
-100 -50 a 0
-100
-200
-300
Percent Change FC
* SWCAVG m RRSUM
EFF RAIN SLOA I RO CT
HFIS
50 100
DRAIN SUM
* DRAJN 'NT
* A0C A. �, a IRR Lm
I EFF RAN SUM - IRRCNT
DRAIN SUM
* RAIN CNT
300
DIS *
200 *
100
-1 00 -50 0 50 100
-100
*
a. -200
-300
Percent Change FC
* RAIN CNT
, o
*6
Figure 10. Sensitivity analysis of the Field Capacity parameter where DIS represents the Daily
Irrigation Simulation and HFIS represents the High Frequency Irrigation Simulation.
CONCLUSION
The study illustrated that even a simple one-dimensional model could incorporate effective rainfall into
irrigation scheduling. Extrapolating from this, future regulation can be drafted to include effective rainfall
into allotment considerations, which would in turn encourage growers to reduce water usage. Further research
is needed to determine all the implications of effective rainfall inclusion.
REFERENCES
1. Allen, R. G., L. S. Pereira, D. Raes, and M. Smith. (1998). Crop Evapotranspiration Guidelines for computing
crop water requirements. FAO - Food and Agriculture Organization of the United Nations, Irrigation and
Drainage Paper 56.
2. Clemmens, A. J., T. S. Strelkoff, and E. Playan. (2003). Field Verification of Two-Dimensional Surface
Irrigation Model. Journal of Irrigation and Drainage Engineering, 6, 402-411.
3. George, B. A., N.S. Raghuwanshi, and R. Singh. (2004). Development and testing of a GIS integrated
irrigation scheduling model. Agricultural Water Management, 66, 221-237.
4. Howell, T. A., E. Hiler, and D. Reddell. (1975). Optimization of water use efficiency under high frequency irrigation-
II. System
5. simulation and dynamic programming. Transactions of the ASAE, 18, 879-887.
6. Pitts, D., K. Peterson, G. Gilbert, and R. Fastenau. (1996). Field Assessment of Irrigation System
Performance. Applied Engineering in Agriculture, ASAE, 12 (3), 307-313.
7. Santos, A. M., M. Cabelguenne, F. L. Santos, M. R. Oliveira, R. P. Serralheiro, and M. A. Bica. (2000). EPIC-PHASE:
a Model to explore Irrigation Strategies. Journal of Agricultural Engineering Research, 75, 409-416.
8. SJRWMD, St. Johns River Water Management District. (2004). Program Overview, Consumptive Use Permitting.
http://sjr.state.fl.us/programs/regulation/cup/overview.html. Last Modified October 1, 2004.
9. Tilahun, K., and D. Raes. (2002). Sensitivity analysis of optimal irrigation scheduling using a dynamic
programming model. Australian Journal of Agricultural Research, 53, 339-346.
10. USGS, United States Geological Survey. (2004). Trends in Water Use.
http://ga.water.usgs.gov/edu/totrendbar.html. Last Modified May 6, 2004.
APPENDIX
Sasfw md SSaoprpsU c treakDowm Root Zone Function Othw kfut
Season VC
FraCton '/Vakes
Note: Fracton Inputs
shoW abe*Ao arwhi i FMtxcWte 9 fr rsldiay's
Figure Al. Kc Break Down tab input display.
SeaWtoW and 500 Mopertie I Kc reak Domn Root Z-n Function IothMlnput
Root z me Amtion
(OB) |(ch) | (o re
Threshold 0[ ,25
Fraction I
TreishodI o,5
Fraction 2
tllrshokl 075
Fraction 3
otW: Fracton
be m DC.'L
Threshoak
- Fracdon #3
rL \ Threshold T2
Threshold 01
1--- --ThresoId
S-/' ----Thmeshoj Fraction #2
h FractionP1
DAP
Figure A2. Root Zone Function tab input display.
Semwi d Sol Propmti I k D9c mak Do RootZw Fution Othe Inp |L
Min (ram)
Drahiage 4
Delay (hr)
MadrE Coded by ,3a~o It
unvewrSadhars Progam 20UH Rohby .Krd co~tweyf
COaea ckohta Cent
Mntar: MK. D, Was, PtO
Figure A3. Other Inputs tab input display.
PERCENT CHANGE
H DIS PWP (% SWC rrigation Diranage fflctIve Ilgon Droinag PWP SW Irlrigatn Drlnage EffStlWv Irrngaln Dralneag
HFUIDIS rP (f Average Sum Sun Rain Sum Count Count (%) Average Sum Sum Rain Sum Count Count
1362 583.16 1679.15 454.45 50
11-86 5S2.79 1679.93 453.67 50
1003 58336 18142 45218 50
8.29 82,93 1682 16 451 44 50
6 4 58Z50 152 g0 450 7U 50
4,80 57319 157477 45~ e3 49
3.05 573.04 1675.79 457.81 49
1.30 572.68 1676.81 456.79 49
-045 572.73 1677.B3 455.77 49
14-39 621.34 1712.64 42B.79 61
1263 l s 1714 75 425 4 61
108l 621.53 171830 42274 61
906 621 41 1719 7 42131 61
7,31 62139 172133 41958 61
5.55 621.28 1722.75 418.28 61
3.8D 621.45 1724.55 416.50 61
2.04 611.44 1716.34 424.94 60
0.29 611.30 1717.67 423.34 60
129 -100 108.32 011 -0.22
129 -75 81.51 0.05 -0.18
127 - 3533 015 -0,09
127 -25 26577 007 -0.04
127 0 000 000 0.00
127 25 -266.0 -1.i: -0,48
127 50 -53.31 -1.62 -0.42
127 75 -80.12 -1.65 -0.36
127 10,1 -106.91 -1.68 -0.30
1285 -100 96.77 -0.01 -0.50
1295 -75 7273 02 -0.36
1295 -50 4379 002 -0.18
12U8 -25 232 000 -0.09
1289 0 000 000 000
129D 26 -24.07 -0.02 0.08
1290 50 -48.09 0,01 0.19
1281 75 -72.05 -1.wo -0.29
1283 100 -9S.9B -1.62 -0.21
083 000 1.57
0-66 0O00 1.57
033 000 000
016 000 0.00
000 000 000
S80 -2.00 000
1.58 -2.00 D.00
1.35 -2.00 0.00
1. 13 -2.00 D0OO
2-17 000 -0.31
164 000 047
073 000 070
039 000 -0.D0
000 000 000
-0.33 0.00 0.08
-0.76 0.00 D0.08
1-25 -1.64 -0.62
0-87 -1.64 -0.47
Table Al. Sensitivity analysis of the Permanent Wilting Point parameter.
PERCENT CHANGE
DI FC % WC krIgation Drain o Eftiw ilg ton Orinr FC SWC IrCgutkm DraInage Effectfle InWgall, DraInagp
HJDIS FC Average Sum Sun Rain Sum Count Count Avrage Sum Saum Rain Sum Count Count
0 -10.95 585.B7 1684.96 448.64 50
2.5 -6.59 572.19 1681.37 452.23 49
5 -220 572.58 15786 454 T 49
75 2,17 57296 167630 45730 49
10 6.S4 5WZ W 168290 450 0 s0o
12.5 10 9 58261 158033 45328 50
15 1537 583.52 1678.37 455.23 50
17.5 19-77 583.39 1675.38 4586.22 50
20 2415 584.27 1673.33 460.27 50
0 -10.19 611.29 1726.92 414.31 60
25 -582 611.30 1722,93 41797 60
5 -145 61133 171933 42170 60
7.5 2.92 621.38 1725 29 41578 61
10 7.31 521 38 1721.33 419,68 61
12.5 11-76 621.32 1717.28 423.75 61
15 16-15 621.50 1713.43 427.93 61
17.5 20.55 621.41 1709.31 432.19 61
20 2494 621.34 1704.95 436.36 61
128 -100 -26749 0.58
127 -75 -20078 -1.77
127 -w5 -13373 -1.70
U? -25 -66.74 -1.613
127 0 000 000
129 25 6311 002
129 50 135.12 018
129 75 202.43 0-15
129 100 269.44 030
1306 -100 -239-35 -1.63
1292 -7S -17951 -1,62
1285 -50 -11982 -1.62
1iZ -Z5 -V.07 000
1289 0 000 000
1296 25 60.74 -0.01
1294 50 120.83 0-02
1291 75 180.89 0.00
1272 100 240.95 -0.01
-0.46 0.00 0.79
0-34 -2.00 0.00
0Do -2.00 0.00
1 46 -2.00 000
000 000 000
057 000 157
1-01 0-00 1.57
1U67 000 1.57
212 0.00 1.57
-1.28 -1.64 147
-0.41 -1.-A 0.23
048 -1.64 -0.31
-0.93 000 S08
000 000 0.00
0-97 0-00 0.70
197 000 0.39
298 0.00 0.16
397 0-00 -1.32
Table A2. Sensitivity analysis of the Field Capacity parameter.
Table A3. Sensitivity analysis of the Minimum Irrigation Depth parameter.
PERCENT CHANGE
MIN IM SWC Irrlgaton Drainage EffctrAive IrrDlgo rioni.* MIN SWC IrrguKm Oralneg Eftctlve IrrTngak Dralnea
1%) Average Sum Su Rain Sum Count Count IRR (%) Average Sum Sum Rain Sum Count Count
DIS 0 8.37 752.29 1850.16 283.44 167 142 -100 21.11 29.15 9.94 -37.11 234.00 11.81
DIS 2.5 8.35 741.08 138.76 294.84 155 139 -75 27.74 27.23 9.26 -34.58 210.00 9.45
DIS 5 7.8 567226 177163 361 97 100 13 -5 2061 15.41 527 -19.69 100.00 946
DIS 7.5 7.22 5~B55 1701 31 431 79 66 131 -25 10,46 276 1.12 -4.19 32.00 315
DIS 10 6.54 MZ50 1,2 Z 450670 50 127 0 0000 000 0.00 000 000 000
DIS 12.5 6.13 M80 9 167 59 45501 42 13o 25 -6.20 -0.26 -0.26 096 -16.00 236
DIS 15 5.45 4WO.D4 1577.81 555.79 29 123 50 -16.57 -17.59 -6.25 23.32 -42.00 -3.15
DIS 17.5 4.86 457.17 1570.82 562.78 24 121 75 -25.67 -21.52 -6.66 24.87 -52.00 -4.72
DIS 20 4.10 437.98 1551.47 582.13 20 11l 100 -37.33 -24.81 -7.61 29.16 -60.00 -8.68
HFIS 0 9.32 799.39 1192.B0 249.58 240 1418 -100 27.36 28.65 9.96 -40.53 293.44 10.01
HFIS 2 5 9,2 784 48 1577 ? 26454 211 1412 -75 265 7 26.25 909 -36.94 245.90 954
HFIS 5 8.81 75531 1852 39 24.46S 146 1405 -w 2044 21.55 7561 -9.84 139.34 900
HFtS 75 7.94 54 18 1750 O Z62 s5 1330 -25 58 528 1 f7 -6,45 39.34 318
HFIS 10 7,31 62139 1721 33 41958 61 1289 0 000 000 0. 000 000 000
HFIS 12.5 6.71 557.18 1653.99 47.19 44 1223 25 -8.22 -10.33 -3.91 16.09 -27.87 -5.12
HFMS 15 6.00 533.16 1628.43 512.78 35 1231 50 -17.92 -14.20 -5.40 22.18 -42.62 -4.50
HFIS 17.5 5.35 495.51 1584.18 556.71 26 1193 75 -26.85 -20.26 -7.97 32.65 -54.10 -7.45
HFIS 20 4.71 465.61 1577.70 562.66 23 1156 100 -35.63 -25.07 -8.34 34.07 -62.30 -10.32
Table A4. Sensitivity analysis of the Drainage Delay parameter.
PERCENT CHANGE
iHFlsIDI M ~AD M WC Irrigation Drainag Effective Iirdgaon Drfinage MAD SWC Irnigaton Drainage Effectve Inrlwalck Drainag
FS MAD Average Sum Sum Rain Sum Count Couit (%) Avrage Sum Sum Rain Sum Count Count
DIS 0 9.07 812.54 1909.53 224.07 392 154 -100 1133 1.01 3.21 -20.94 134.73 .45
DIS 7.5 902 802.74 1699.73 233.67 330 152 -75 7.72 671 2.68 -17.49 97.60 7.04
DIS 15 8.86 792,46 1689 34 244 26 266 149 -5M 585 534 2.12 -13.82 59.28 4.93
DIS 22.5 865 ?74 34 167243 26117 214 145 -25 329 293 1 20 -7.I6 28.14 211
DIS 30 837 75229 15016 2M344 157 142 0 000 000 0.00 000 000 000
DIS 37.5 8.07 703.23 1799 6 333 95 124 137 25 -3.61 -6.52 -2.73 17.62 -25.75 -3.52
DIS 45 7.76 677.60 1776.18 358.72 102 135 50 -7.09 -9.93 -3.96 25.865 -38.92 -4.93
DIS 52.5 7.56 634.36 1732.11 401.49 86 132 75 -9.76 -15.66 -6.38 41.65 -48.50 -7.04
DIS 60 7.36 604.77 1707.94 425.66 75 129 100 -12.16 -19.61 -7.69 50.18 -55.09 -9.15
HFIS 0 1050 975.77 2057.33 95.06 7467 1756 -100 12.69 22.0 6.69 -61.90 301125 23.84
HAS 7.5 1021 925,98 2007 47 14141 993 1625 -75 962 15,4 506 -43.34 313.75 14.67
HFAS 15 9191 5 51 1958 54 185 57 503 153 -50 36 8 28 3,47 -25.25 109.8 6 3
HFS 22,5 9.64 26 32 192152 224 31 327 1490 -25 3 45 337 152 -10,13 3625 508
HFAS 30 9.32 79939 159260 249 58 240 1416 0 000 000 0 00 000 000 0 00
HFIS 37.5 9.03 770.42 1686.79 275.80 16 1404 25 -3.12 -3.62 -1.27 10.51 -22.50 -0.99
HFS 45 8.73 726.72 1624.56 318.51 145 1377 50 -6.29 -9.09 -3.61 27.62 -39.5B -2.06
HFIS 52.5 8.40 695.89 1792.63 349.03 118 1356 76 -9.78 -12.95 -6.29 39.85 -50.83 -4.37
HFIS 60 8,15 705.48 1800.50 342.01 10 1327 100 -12.49 -11.75 -4.88 37.03 -55.83 -6.42
Table A5. Sensitivity analysis of the Maximum Allowable Depletion parameter.
Table A6. Sensitivity analysis of the Root Zone Function.
PERCENT CHANGE
DRAIN SWC I riation Drainage Ectlw Irdgaoo Drainage, DRAIN SWC Iigaton Dralnae Effective Intgaon Drainage
HFSJMDIS DELAY Aerage Ssum Sum Rain Sum Count Court DELAY Averge Sum Sum Rain Sum Count Count
HFIS 0 696 669.70 1444.92 66.93 66 425 -100 -4.88 7.78 -16.06 64.16 120 -67.03
HFIS 1 7.22 611.60 1700.26 433.64 60 780 -75 -1.28 -1.58 -1.22 3.33 -1.64 -39.49
HFS 2 7.25 621 53 1713 " 42031 61 972 -SO -0.82 002 -0.43 015 000 -24.59
HFAS 3 7,26 621 56 1716 8 41970 6 1 1140 -25 -045 003 -026 001 000 -11.55
HFtS 4 7.31 62139 1721 33 41956 61 1289 0 000 000 0.00 00 000 0 00
HAFS 5 7.32 611,64 171506 432 S 60 1419 25 003 -1.5 -0.36 316 -1.64 10.09
HFIS 6 7.32 611.56 1718.66 436.14 60 1546 50 0.08 -1.58 -0.16 3.92 -1.64 20.09
HFIS 7 7.34 611.42 1721.16 441.56 60 1671 75 0.40 -1.60 -0.01 521 -1.64 29.64
HFIS 8 7.36 610.54 1722.74 446.06 60 1807 100 0.58 -1.75 0.DB 6-29 -1.64 40.19
PERCENT CHANGE
HFi SDIS RZF SWC lirgation Dralage Effectiv Iirlgailon Drinageo SWC IrrtgaltKn Dralnage Effeive imgiulko Dralnage
Average Sum Sum Rain Sum Count Count Aveage Sum Sum Rain Sum Count Count
DIS 0 -3-2 506.68 1675.66 457.74 49 127 -100 -158-50 -2.37 -0.42 156 -2.00 D00
DIS 0-25 -133 572.65 1678.34 455.26 49 127 -75 -12032 -1.69 -0.27 1.01 -2.00 D00
DIS 05 1.30 57288 167661 45579 49 127 -50 -80,12 -1.65 -0.36 135 -2.00 000
DIS 075 3.92 57311 157528 458 32 49 127 -25 -3l9S -1.61 -0.45 169 -2.00 0.00
DIS 1 6.54 58250 1682 90 450 t0 50 127 0 0 00 000 0.00 000 000 0 00
DIS 125 9.165 316 1681 79 45161 50 127 25 4015 011 -0.07 025 000 000
DIS 1.5 11-86 582.79 1679.93 453.67 50 129 50 81.51 0-05 -0.18 0.66 000 1.57
DIS 1.75 14.49 583.34 1678.76 454.84 50 129 75 121.72 0.14 -0.25 D092 0.00 1.57
DIS 2 1712 583.88 1677.59 456.01 50 129 100 161.93 0-24 -0.32 118 000 1.57
HFIS 0 -3.07 611.21 1720.56 420.49 60 1286 -100 -141-99 -1.64 -0.04 0-19 -1.64 -0.23
HFAS 025 -057 611 40 171659 42443 60 1284 -75 -107 6 -1.61 -0.28 113 -1.54 -0,38
HFAS 05 2.04 61144 1716 34 424894 60 1251 -50 -7205 -1.60 -0.29 125 -1.64 -0.62
HFS 0175 4.67 52137 172361 41739 61 1290 -25 -36,17 000 013 -0.54 000 008
HFAS 1 7,31 62139 172133 41968 61 1289 0 000 000 0.00 000 000 000
HFIS 125 10.01 621.35 1718.94 422.12 61 1299 25 36.80 -0.01 -0.14 0-58 0-00 0.78
HFIS 1.5 1263 621.50 1714.75 426.54 61 1295 50 72.73 *.02 -0.38 164 000 0.47
HFIS 175 1526 621.45 1714.19 427.19 61 1294 75 108.63 0-01 -0.41 179 0-00 0.39
HFIS 2 17-90 621.38 1711.55 429.82 61 1293 100 144.78 0-00 -0.57 242 000 0.31
PERCENT CHANGE
HFleDIS KCF Owc W1igat.on DraInage Effctolve IlrigRaoo Drlinage KCF Irrgatiom Dralng Eiffclve* Irrlgale Drainaig
AH rage Sum Sum Rain Sum Count Coult Aveag Sum Sum Rain Sum Count Count
DIS 0 1054 0.00 2128.32 5.28 0
DIS 005 895 52.49 1926.35 207.25 5
DIS 0 1 779 13 01 1102 28 31 32 17
DIS 015 7.20 317591 1731 01 40256 34
DIS 0 2 6.54 z2 1 r2 W 450 7 so0
DIS 025 614 78421 113140 Z 20 67
DIS 0.3 5.75 956.53 1537.1 595.99 78
DIS 035 5.29 119.91 1524.44 609.16 93
DIS 0A 4.85 1475.77 1546.58 587.02 111
HFIS 0 10-54 0.00 2124.56 9.29 0
HFtS 00 8"S 60.20 192B 39 207 90 6
HFiS 01 7.96 20232 118 18 319 83 20
HFAS 015 1 61 415 29 16T 51 37199 41
HFIS 02 7.31 62139 172133 41956 61
HFIS 0.25 7.13 BB9.57 1839.57 505.14 79
HFIS 0.3 7.05 1054.83 1636.34 507.80 1C3
HFIS 035 6.86 1312.27 1838.17 505.51 127
HFIS 0.4 6.89 1574.55 1638.62 508.34 152
223 -100 61.19 -100.O0 26.47 -M8.83 -100-00 75.59
164 -75 36.88 -0.99 14.47 -54.01 -90.0D 29.13
137 -W 1921 -6855 7.09 -26.49 -6.,00 7a7
130 -25 10,12 -35.46 2.86 -10.67 -32.00 236
127 0 000 0 00 0,0 0 o 000 OOO
124 25 -6.08 34.53 -3,06 11.43 34.00 -2.36
121 50 -t2.05 64.21 -8.63 32.24 56.1X -4.72
117 75 -19.12 105.82 -9.42 35.16 86.M -7.87
110 100 -25.79 153.35 -8.10 30.25 122.00 -13.39
1 02 -100 44.08 -10000 23.43 -97.79 -101-00 47.56
151 -75 22 16 -90.31 12.03 -M0.45 -90,16 15.45
1344 -50 82 -67.44 5.63 -23.79 -67.21 4,27
1319 -25 467 -33 1?T 274 -11,36 -32.79 233
1289 0 000 0 00 000 000 000 000
1222 25 -2.55 30.2 -4.75 20.36 29.51 -5.20
1224 50 -3.59 69.75 -4.94 21.00 68.B5 -5.04
1197 75 -6.18 111.18 -4.83 2045 1C8.20 -7.14
1152 100 -5.M 153.39 -4.81 21.13 149.18 -10.63
Table A7. Sensitivity analysis of the Crop Coefficient Function.
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