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Rainfall Variability Effects on Aggregate Crop Model Predictions

Permanent Link: http://ufdc.ufl.edu/UFE0044578/00001

Material Information

Title: Rainfall Variability Effects on Aggregate Crop Model Predictions
Physical Description: 1 online resource (276 p.)
Language: english
Creator: Dzotsi, Kofikuma A
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: correlation -- cotton -- dssat -- georgia -- gist -- maize -- mcmc -- metropolis-hastings -- modeling -- peanut -- rainfall -- salus -- simulation -- variability -- weather
Agricultural and Biological Engineering -- Dissertations, Academic -- UF
Genre: Agricultural and Biological Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Crop production operates in a highly heterogeneous environment. Space-time variability in weather and spatial heterogeneity in soil and management generate variability in crop yield. While it is practically unfeasible to thoroughly sample the variability of the crop environment, quantification of the associated uncertainties in crop performance can provide vital information for decision-making. The present study used rainfall data collected in southwestern Georgia at scales ranging from 1 km to 60 km to assess the effect of weather variability (in particular rainfall) on crop predictions aggregated over soil and management variations. The simple SALUS (System Approach to Land Use Sustainability) crop model was integrated in DSSAT (Decision Support System for Agrotechnology Transfer) then parameterized and tested for maize, peanut and cotton for use in obtaining the crop predictions. Analysis of the rainfall data indicated that variability in storm characteristics depends upon the season. Winter rainfall was more correlated at a mean distance of 54 km between locations than summer rainfall was at a mean distance of 3 km. The pairwise correlation between locations decreased with distance faster in the summer than in the winter. This rainfall variability translated into crop yield variability in the study area (about 3100 km2). It was found that weather variability explained 60% and 49% of maize yield variability respectively in 2010 and 2011 when heterogeneity in weather, soil, cultivar and planting dates were accounted for simultaneously. Uncertainties in crop predictions due to rainfall spatial uncertainty decreased as the number of sites where weather data were collected increased. Expressed in terms of maize yield coefficient of variation, this uncertainty decreased exponentially from 27% to approximately 4% at a sampling density of 20 weather locations. Based on 30 years of generated weather data, it was concluded that the general form of the relationship between maize yield distribution and density of weather network was not affected by long-term seasonal weather variability; however, year-to-year weather variability appeared to be an additional source of uncertainty in aggregating crop yield when less than 10 weather locations were used.
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 Kofikuma A Dzotsi.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Jones, James W.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044578:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044578/00001

Material Information

Title: Rainfall Variability Effects on Aggregate Crop Model Predictions
Physical Description: 1 online resource (276 p.)
Language: english
Creator: Dzotsi, Kofikuma A
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: correlation -- cotton -- dssat -- georgia -- gist -- maize -- mcmc -- metropolis-hastings -- modeling -- peanut -- rainfall -- salus -- simulation -- variability -- weather
Agricultural and Biological Engineering -- Dissertations, Academic -- UF
Genre: Agricultural and Biological Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Crop production operates in a highly heterogeneous environment. Space-time variability in weather and spatial heterogeneity in soil and management generate variability in crop yield. While it is practically unfeasible to thoroughly sample the variability of the crop environment, quantification of the associated uncertainties in crop performance can provide vital information for decision-making. The present study used rainfall data collected in southwestern Georgia at scales ranging from 1 km to 60 km to assess the effect of weather variability (in particular rainfall) on crop predictions aggregated over soil and management variations. The simple SALUS (System Approach to Land Use Sustainability) crop model was integrated in DSSAT (Decision Support System for Agrotechnology Transfer) then parameterized and tested for maize, peanut and cotton for use in obtaining the crop predictions. Analysis of the rainfall data indicated that variability in storm characteristics depends upon the season. Winter rainfall was more correlated at a mean distance of 54 km between locations than summer rainfall was at a mean distance of 3 km. The pairwise correlation between locations decreased with distance faster in the summer than in the winter. This rainfall variability translated into crop yield variability in the study area (about 3100 km2). It was found that weather variability explained 60% and 49% of maize yield variability respectively in 2010 and 2011 when heterogeneity in weather, soil, cultivar and planting dates were accounted for simultaneously. Uncertainties in crop predictions due to rainfall spatial uncertainty decreased as the number of sites where weather data were collected increased. Expressed in terms of maize yield coefficient of variation, this uncertainty decreased exponentially from 27% to approximately 4% at a sampling density of 20 weather locations. Based on 30 years of generated weather data, it was concluded that the general form of the relationship between maize yield distribution and density of weather network was not affected by long-term seasonal weather variability; however, year-to-year weather variability appeared to be an additional source of uncertainty in aggregating crop yield when less than 10 weather locations were used.
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 Kofikuma A Dzotsi.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Jones, James W.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044578:00001


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1 RAINFALL VARIABILITY EFFECT S ON AGGREGATE CROP MODEL PREDICTIONS By KOFIKUMA ADZEWODA DZOTSI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012

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2 2012 Kofikuma Adzewoda Dzotsi

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3 To my wife, Pascaline, for renewing my endurance everyday throughout this work and m y parents for the initial impetus that gave me the love to explore science

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4 ACKNOWLEDGMENTS This dissertation represents one of the most exciting journeys I have ever embarked on and attracted th e support of a number of people whose roles converged into making this work a successful one. The most important academic support came from my advisor Dr. James W. Jones who initially gave me the opportunity to pursue advanced degrees in the U.S. He has considerably increased my confidence in conducting a research study, developing innovative thinking and publishing results. M y professional improvement over the past eight years can be directly or indirectly related to his excellent mentoring and inspirational guidance I would like to thank my Committee members for their invaluable contributions to this study : Dr. Jud ge for her proactive pieces of advice related to academic procedures and the overall quality and validity of the research ; Dr. Baigorria for contributing his extensive knowledge in the area of geo spatial analysis of weather data even if this meant leaving a conference to Skype connect to one of our meetings; Dr. Matyas for challenging my understanding of atmospheric science and its relationship with my research study; Dr. Erickson for enhancing my understanding of the quantitative relationship between the crop and its environment and how this relationship can be affected by climate change. I thank Dr. Kenneth Boote for accepting to participate in the committee meeting following my dissertation defense and making useful comments. I would like to express my s pecial appreciation to Fred Wayne Williams for his incredible assistance with the design and implementation of the field work. He not only recognized the importance of this type of research but also provided the necessary expertise to guarantee that the data collected meet the highest quality standards. I wish to thank Dr. Gerrit Hoogenboom (now at Washington State University) and county

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5 extension agents Rad Yager, Jordan Lanier and Ivey Griner for tremendously facilitating contacts with farmers, which wa s a major prerequisite to finding the 46 locations where rain gauges were installed. I thank farmers who participated in the study for providing the rain gauge locations and assisting with maintenance activities These farmers valued our research and were very cooperative. I would like to acknowledge the special role played by Dr. Bruno Basso who provided the original codes of the SALUS models and made important recommendations for improving the model. I wish to express my gratitude to Cheryl Porter for h er critical assistance with integrating the simple SALUS model into DSSAT. I thank my former advisor, Dr. Tjark Struif Bontkes, for guiding my first steps into systems analysis and strengthening my motivation through encouragement letters every year. I am gr East and Southern Africa Division for helping arrange for me an opportunity to pursue graduate studies in the United States. Special thanks to my lab mates and friends, in particular Osvaldo Gargiulo for his encouragement and pertinent recommendations on several informal occasions ; Tapan Pathak, Prem Woli, Jawoo Koo, Victoria Keener and McNair Bostick for their guidance with finding appropriate courses. I will particularly miss McNair Bostick for his thoughtfu lness and great personality. Most importantly, I would like to thank my family in Togo and in the United States: my parents for their unconditional love and spiritual support; my beautiful wife Pascaline for her patience attention and profound love ; my son, Robert and my daughter, Joanna for creating a relaxing atmosphere full of fun

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ .......... 10 LIST OF FIGURES ................................ ................................ ................................ ........ 13 LIST OF ABBR EVIATIONS ................................ ................................ ........................... 17 ABSTRACT ................................ ................................ ................................ ................... 19 CHAPTER 1 BACKGROUND TO PRECIPITATION VARIABILITY EFFECTS ON CROP MODEL PREDICTIONS ................................ ................................ .......................... 21 Importance of the Pr ecipitation Crop Relationship ................................ .................. 21 Precipitation Variability ................................ ................................ ............................ 22 Crop Models as Tools in Agricultural Assessments ................................ ................ 24 Effects of Rainfall Variability on Crops ................................ ................................ .... 25 Research Question and Objectives ................................ ................................ ........ 29 2 INTEGRATING THE SIMPLE SALUS CROP MODEL IN DSSAT .......................... 32 Introduction ................................ ................................ ................................ ............. 32 Materials and Methods ................................ ................................ ............................ 37 Overvi ew of the SALUS Crop Model ................................ ................................ 37 Description of the SALUS Crop Model ................................ ............................. 38 Plant development ................................ ................................ ..................... 38 Light interception ................................ ................................ ........................ 39 Leaf area index ................................ ................................ .......................... 39 Radiation use efficiency and total dry matter ................................ ............. 41 Dry matter partitioning and yield ................................ ................................ 42 Effect of cold temperatures ................................ ................................ ........ 43 Root dynamics ................................ ................................ ........................... 43 Integrating SA LUS in DSSAT ................................ ................................ ........... 44 Uncertainty and Sensitivity Analysis ................................ ................................ 45 Sites and analysis settings ................................ ................................ ......... 45 Methods of uncertainty and sensitivity analysis ................................ ......... 47 Synthetic data ................................ ................................ ............................ 53 Statistical distributions of crop parameters ................................ ................. 55 Results and Discussion ................................ ................................ ........................... 55 Modifications to the SALUS Model ................................ ................................ ... 55 Results of Synthetic Data and Ranges of Parameters ................................ ..... 57 Statistical Distributions of Crop Parameters ................................ ..................... 61

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7 Sample Size Selection for Uncertainty and Sensitivity Analysis ....................... 62 Uncertainty Analysis ................................ ................................ ......................... 63 Maize ................................ ................................ ................................ ......... 63 Peanut and cotton ................................ ................................ ...................... 66 Sensitivity Analysis ................................ ................................ ........................... 68 Effect of year on parameter ranking ................................ ........................... 68 Sensitivity to maize biomass and grain yield ................................ .............. 69 Maize season length ................................ ................................ .................. 70 Peanut a nd cotton ................................ ................................ ...................... 71 Discussion of sensitivity analysis results ................................ .................... 71 Conclusions ................................ ................................ ................................ ............ 73 3 PARAMETER ESTIMATION OF THE SALUS CROP MODEL FOR MAIZE, PEANUT, AND COTTON USING A MARKOV CHAIN MONTE CARLO APPROACH ................................ ................................ ................................ ............ 98 Introduction ................................ ................................ ................................ ............. 98 Bayesian Approach to Parameter Estimation ................................ ....................... 101 Markov C hain Monte Carlo ................................ ................................ ............. 102 The Metropolis Hastings Algorithm ................................ ................................ 103 Materials and Methods ................................ ................................ .......................... 104 Method s of Parameter Estimation ................................ ................................ .. 104 Detailed case parameter estimation ................................ ......................... 105 Limited case parameter estimation ................................ .......................... 106 Application of the Metropolis Hastings Algorithm ................................ ........... 107 Prior parameter distribution ................................ ................................ ...... 107 Likelihood function ................................ ................................ ................... 108 Characterizing the posterior parameter distribution ................................ 109 Datasets for Parameter Estimation and Model Testing ................................ .. 111 Maize datasets ................................ ................................ ......................... 111 Peanut datasets ................................ ................................ ....................... 113 Cotton datasets ................................ ................................ ........................ 114 Crop Growth Models ................................ ................................ ...................... 116 The simple SALUS model ................................ ................................ ........ 116 Th e DSSAT crop models ................................ ................................ ......... 11 7 Evaluation of model performance ................................ ............................ 118 Comparison among DSSAT SALUS and DSSAT Models .............................. 120 Results and Discussion ................................ ................................ ......................... 120 Stab ility Analysis of the Chains ................................ ................................ ...... 120 Posterior Distributions ................................ ................................ .................... 122 Prediction of LAI, Biomass and Yield ................................ ............................. 124 Overall performance of SALUS ................................ ................................ 124 Prediction of in season maize LAI and biomass ................................ ...... 126 Prediction of in season peanut LAI and biomass ................................ ..... 127 Prediction of in season cott on LAI and biomass ................................ ...... 128 Independent Testing of SALUS and Comparison with DSSAT ....................... 129 Further Discussion ................................ ................................ ......................... 132

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8 Conclusi ons ................................ ................................ ................................ .......... 134 4 SPATIAL AND TEMPORAL VARIABILITY OF RAINFALL IN SOUTHWEST GEORGIA ................................ ................................ ................................ ............. 159 Introduction ................................ ................................ ................................ ........... 159 Materials and Methods ................................ ................................ .......................... 163 Study Area ................................ ................................ ................................ ...... 163 Tipping Bucket Rain Gauge ................................ ................................ ............ 164 The Rainfall Data ................................ ................................ ............................ 165 Analysis of the Spatial Variability of Storms ................................ ................... 165 Analysis of the Spatial Variability of Rainfall Correlations .............................. 167 Analysis of Spatial Dependence for Rainfall In terpolation .............................. 168 Results and Discussion ................................ ................................ ......................... 172 Spatial and Temporal Variability of Storms ................................ ..................... 172 All regional storm events ................................ ................................ .......... 172 Large regional storm events ................................ ................................ ..... 175 Dry duration between regional storms ................................ ..................... 176 Local storm analysis ................................ ................................ ................ 177 Correlations of Daily and Hourly Rainfall Amounts and Events ...................... 179 Modeling the Spatial Dependence for Rainfall Interpolation ........................... 182 Conclusions ................................ ................................ ................................ .......... 185 5 UNCERTAINTIES IN CROP MODEL PREDICTIONS RESULTING FROM RAINFALL VARIABILITY AT DIFFERENT AGGREGATION SCALES ................. 208 Introduction ................................ ................................ ................................ ........... 208 Materials and Methods ................................ ................................ .......................... 212 Characterization of Spatial Heterogeneity ................................ ...................... 212 Overview of the Simple SALUS Crop Model ................................ .................. 213 Global Sensitivity Analysis ................................ ................................ .............. 215 Effect of Weather Network Density ................................ ................................ 217 Effect of Long term Rainfall Variability ................................ ........................... 219 Results and Discussion ................................ ................................ ......................... 221 Global Sensitivity Analysis ................................ ................................ .............. 221 Variability in simulated crop yield and season length ............................... 221 Partitioning of model prediction variance ................................ ................. 222 Network Density Analysis ................................ ................................ ............... 225 Long term Seasonal Effects ................................ ................................ ........... 228 Conclusions ................................ ................................ ................................ .......... 231 6 SUMMARY AND CO NCLUSIONS ................................ ................................ ........ 249 Main Results of Chapter 2: Integrating SALUS in DSSAT ................................ .... 249 Main Results of Chapter 3: Estimating Crop Parameters for DSSAT SALUS ....... 251 Main Results of Chapter 4: Rainfall Variability ................................ ...................... 252

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9 Main Results of Chapter 5: Uncertainties in Crop Model Predictions Resulting from Rainfall Variability ................................ ................................ ...................... 253 Fi nal Conclusions ................................ ................................ ................................ 254 APPENDIX: SOME CHARACTERISTICS OF THE WEATHER LOCATIONS ......... 257 LIST OF REFERENCES ................................ ................................ ............................. 261 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 276

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10 LIST OF TABLES Table page 1 1 Percentage of selected land cover types in the three counties ........................... 30 2 1 List of variables used to describe the SALUS model ................................ .......... 76 2 2 List of SALUS crop model parameters and definitions ................................ ....... 77 2 3 Characterization of the locations of the uncertainty and sensitivity analysis ....... 77 2 4 Specification of treatments and total number of runs required for the uncertainty and sensitivity analysis ................................ ................................ ..... 78 2 5 Specification of treatments used for generating the simulated data ................... 78 2 6 Growth and development coefficients for the four maize cultivars used in producing the synthetic data ................................ ................................ ............... 79 2 7 Growth and development coefficients for the four peanut cultivars used in producing the synthetic data ................................ ................................ ............... 79 2 8 Growth and development coefficients for the four cotton cultivars used in producing the synthetic data ................................ ................................ ............... 80 2 9 Pear son correlation coefficients between crop parameters derived from synthetic data for maize, peanut, and cotton ................................ ...................... 81 2 10 Statistical distributions of SALUS crop parameters for maize ............................. 82 2 11 Statistical distributions of SALUS crop parameters for peanut ........................... 83 2 12 Statistical distributions of SALUS crop parameters for cotton ............................ 84 2 13 Top down correlation coefficients for comparing numbers of model runs ........... 85 2 14 Minimum and maximum values of mean biomass, grain yield and season length for maize, peanut, and cotton ................................ ................................ .. 86 2 15 Minimum and maximum values of standard deviation of biomass, grain yield and season length for maize, peanut, and cotton ................................ ............... 87 2 16 PRCC between total maize biomass and significant crop model parameters at four locations ................................ ................................ ................................ .. 88 2 17 PRCC between total peanut biomass and significant crop model parameters at four locations ................................ ................................ ................................ .. 88

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11 2 18 PRCC between total cotton biomass and significant crop model parameters at four locations ................................ ................................ ................................ .. 89 3 1 List of SALUS crop parameters estimated ................................ ........................ 137 3 2 Potential growth and development characteristics of different maturity groups of maize used in estimating parameters for SALUS ................................ ......... 137 3 3 Potential growth and development characteristics of different maturity groups of peanut used in estimating parameters for SALUS ................................ ........ 138 3 4 Potential growth and development characteristics of different maturity groups of cotton used in estimating parameters for SALUS ................................ ......... 138 3 5 Parameters with fixed values during model calibration ................................ ..... 138 3 6 Prior information on the parameter expressed in the form of ranges ................ 139 3 7 Description of datasets used in model calibration and testing .......................... 140 3 8 Means and standard deviations of the posterior distributions of maize parameters for two methods of parameter estimation ................................ ...... 141 3 9 Means and standard deviations of the posterior distributions of peanut parameters for two methods of parameter estimation ................................ ...... 142 3 10 Means and standard deviations of the posterior distributions of cotton parameters for two methods of parameter estimation ................................ ...... 143 3 11 Summary statistics used to measure the ability of the SALUS model to predict in season biomass during detailed parameter estimation ..................... 143 3 12 Summary statistics used to measure the ability of the SALUS model to predict in season LAI during detailed parameter est imation case .................... 144 3 13 Summary statistics used to measure the performance of the SALUS model during limited parameter estimation case ................................ ......................... 144 3 14 Summary statistics used to measure the performance of the SALUS model during independent testing ................................ ................................ ............... 145 4 1 Parameters for performing and tuning the analysis of spatio temporal variability of storms ................................ ................................ ........................... 189 4 2 Characteristics of all storms identified during the period analyzed ................... 190 4 3 Characteristics of large storms identified during the period analyzed ............... 191

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12 4 4 Numb er of storms and ranges of location specific means of all storms identified in the local analysis ................................ ................................ ........... 1 92 4 5 Spearman correlation of daily rainfall amount and gauge separation distances ................................ ................................ ................................ .......... 193 4 6 Spearman correlation of daily rainfall event and gauge separation distances .. 193 4 7 Geostatistical model parameters and comparison of observed and predicted rainfall using IDW and kriging with and without trend removal ......................... 194 5 1 Characteristics of observed total seasonal rainfall (mm) at gauge locations during 2010 and 2011 over the study area ................................ ....................... 234 5 2 Some properties of soils used in characterizing spatial soil variations ............. 234 5 3 Definition of SALUS crop parameters ................................ ............................... 235 5 4 Values of crop parameters of the three cultivars used to characterize spatial variations in maize cultivar ................................ ................................ ............... 236 5 5 Main effect and interaction sensitivity indices representing the partitioning of crop prediction variance into different sources of variation ............................... 237 5 6 Total sensitivity indices and ranking of the sources of variability involved in the partitioning of crop prediction variance ................................ ....................... 237 A 1 Geographic coordinates of the weather locations, total summer rainfall and simulated maize yield aggregates in 2010 and 2011 ................................ ........ 257

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13 LIST OF FIGURES Figure page 1 1 Google Earth im age of the study area ................................ ................................ 31 2 1 Diagram of the SALUS model showing the main crop growth and development processes ................................ ................................ ...................... 90 2 2 Generic LAI curve and effect of water stress on leaf senescence and RUE as modeled in SALUS. ................................ ................................ ............................ 91 2 3 Cumulative distribution function of maize, peanut and cotton potential and water limited biomass over the 10 years of the study ................................ ........ 92 2 4 Cumulative distribution function of maize, peanut and cotton potential and water limited season length over the 10 years of the study. ............................... 93 2 5 Partial rank correlation coefficients between grain yield and significant SALUS crop parameters in the first year of the study ................................ ........ 94 2 6 Partial rank correlation coefficients between season length and significant SALUS crop parameters in the first year of the study ................................ ........ 95 2 7 Logic diagram of the most sensitive SALUS model parameters for a warmer climate ................................ ................................ ................................ ............... 96 2 8 Logic diagram of the most sensitive SALUS model parameters for a cooler climate ................................ ................................ ................................ ............... 97 3 1 Diagram of the limited and detailed case parameter estimation procedures .... 146 3 2 LAI and maximum RUE calibrated using the detailed dataset .......................... 147 3 3 maximum LAI and maximum RUE calibrated using the detailed dataset ......... 148 3 4 LAI and maximum RUE calibrated using the detailed dataset .......................... 149 3 5 Posterior distribution of maximum LAI for three maize maturity groups under limited and detailed dataset calibration ................................ ............................. 150 3 6 Posterior distribution of maximum RUE for three maize maturity groups under limited and detailed dataset calibration ................................ ............................. 150 3 7 Posterior distribution of maximum LAI for three peanut maturity groups under limited and detailed dataset calibration ................................ ............................. 151

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14 3 8 Posterior distribution of maximum RUE for three peanut maturity groups under limited and detailed dataset calibration ................................ .................. 151 3 9 Posterior distribution of maximum LAI and maximum RUE using the limited and detailed datasets for cotton ................................ ................................ ........ 152 3 10 Calibration: comparison of observed and simulated biomass and grain yield based on mean parameter values ................................ ................................ .... 152 3 11 Calibration: maize medium irrigated biomass and LAI simulated by DSSAT and SALUS based on the detailed and limited cases ................................ ....... 153 3 12 Calibration: maize medium rainfed biomass and LAI simulated by DSSAT and SALUS based on the detailed and limited cases ................................ ....... 153 3 13 Calibration: peanut medium irrigated biomass and LAI simulated by DSSAT and SALUS based on the detailed and limited cases ................................ ....... 154 3 14 Calibration: peanut medium rainfed biomass and LAI simulated by DSSAT and SALUS based on the detailed and limited cases ................................ ....... 154 3 15 Calibration: cotton medium irrigated biomass and LAI as simulated by DSSAT and SALUS based on the detailed and limited cases .......................... 155 3 16 Calibration: cotton medium rainfed biomass and LAI as simulated by DSSAT and SALUS based on the detailed and limited cases ................................ ....... 155 3 17 season biomass and LAI ................................ ................................ ............................... 156 3 18 Validation: observed and simulated biomass and grain yield using mean parameter values from the detailed and limited cases ................................ ...... 156 3 19 Validation: independent testing of maize medium maturity groups with parameters from the detailed and limited cases ................................ ............... 157 3 20 Validation: independent testing of peanut medium maturity groups with parameters from the detailed and limited cases ................................ ............... 157 3 21 Validation: independent testing of peanut long maturity groups with parameters from the detailed and limited cases ................................ ............... 158 3 22 Validation: independent testing of cotton medium maturity groups with parameters from the detailed and limited cases ................................ ............... 158 4 1 Study area with locations where rainfall was collected and interpolated total rainfall from June 2010 to May 2011 (12 months) ................................ ............ 195

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15 4 2 Distribution of pairwise distances between rain gauges with estimated kernel density ................................ ................................ ................................ .............. 196 4 3 Long term variability of the Palmer Drought Severity Index (PDSI) over the study area in winter, spring, summer and fall ................................ ................... 197 4 4 Number of storms by month ................................ ................................ ............. 198 4 5 Empirical cumulative distribution functions of various characteristics of the regional storm analysis ................................ ................................ ..................... 199 4 6 Profiles of 50 0 mb daily composite mean geopotential heights for selected ra infall events ................................ ................................ ................................ ... 200 4 7 Empirical cumulative distribution functions of various characteristics of the local storm analysis ................................ ................................ .......................... 201 4 8 Kernel density estimates of location mean storm characteristics and storm beginning and end times at any location ................................ .......................... 202 4 9 Relationship between correlation of daily rainfall amount and separation dis tance ................................ ................................ ................................ ............ 203 4 10 Relationship between correlation of daily rainfall event and separation distance ................................ ................................ ................................ ............ 203 4 11 Spatial variability of daily rainfall amount correlation between location in red and the remaining sites ................................ ................................ .................... 204 4 12 Sample variograms of daily rainfall with and without trend removal and corresponding fitted spherical variogram models ................................ ............. 205 4 13 Comparison of the performance of ordinary kriging, universal kriging and IDW interpolation of daily rainfall aggregated to seasonal level ....................... 206 4 14 Comparison of ordinary kriging, universal kriging and IDW map of interpolated total rainfall for summer 2010 and winter 2011 ............................. 207 5 1 Land use and annual rainfall variability in stu dy area ................................ ...... 238 5 2 Spatial variability of observed summer rainfall in 2010 and 2011. The points show the locations where rainfall data were collected. ................................ ..... 239 5 3 Spatial variability of simulated maize grain yield in 2010 and 2011. ................. 239 5 4 Uncertainty in simulated maize yield and season length due to spatial variations of soil, cultivar, and planting date. ................................ .................... 240

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16 5 5 Ma in effect and interaction sensitivity indices for describing sources of variability in maize grain yield and season length ................................ ............. 241 5 6 Effect of increasing the density of weather locations on the distribution on simulated aggregate maize yield and season length ................................ ........ 242 5 7 Variability in the coefficient of variation of the distribution of simulated aggregate crop predictions as a function of the density of weather locations ... 243 5 8 Effect of increasing the density of weather locations on the distribution of simulated aggregate yield of a maize cultivar ................................ .................. 244 5 9 Variability in simulated aggregate crop prediction by weather location for generated years 1 with and without the effect of cold temperatures. ................ 245 5 10 Influence of year on the spatial distribution of simulated aggregate maize yield and season length ................................ ................................ .................... 246 5 11 Effect of long term seasonal variability of weather on simulated aggregate maize yield and season length ................................ ................................ ......... 246 5 12 Influence of year on the distribution of simulated aggregate maize yield for selected weather network densities. ................................ ................................ 247 5 13 Effect of weather network density on the coefficient of variation of the distributions of simulated aggregate maize yield and season length ................ 248 A 1 Locations of rain gauges and weather stations in the study area ..................... 259 A 2 Elevation and annual rainfall variability in the study area. Source of elevation data ................................ ................................ ................................ .................. 260

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17 LIST OF ABBREVIATION S ALMANAC Agricultural Land Management Alternatives with Numerical Assessment Criteria CDF Cumulative Density Function CERES Crop Environment Resource Synthesis CROPGRO A DSSAT crop template module simulating legumes and some non legume crops CSM Cropping System Model CV Coefficient of Variation DM Dry Matter DSSAT Decision Support System for Agrotechnology Transfer ECDF Empirical Cumulative Distribution Function EPIC Erosion Productivity Impact Calc ulator FACE Free Air CO 2 Enrichment FAST Fourier Amplitude Sensitivity Test GAEMN Georgia Automated Environmental Monitoring Network GiST Geospatial and Temporal ( weather generator ) GLUE Generalized Likelihood Uncertainty Estimation IDW Inverse Distance Weighted IPAR Intercepted P hotosynthetically A ctive R adiation KSB Kellogg Biological Station LAI Leaf Area Index LH Latin Hypercube MCMC Markov Chain Monte Carlo MH Metropolis Hastings MSE Mean Squared Error

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18 NCAR National Center for Atmospheric Research NC DC National Climatic Data Center NCEP National Centers for Environmental Prediction NRCS National Resources Conservation Service NRMSE Normalized R oot M ean S quared E rror PAR Photosynthetically Active Radiation PDF Probability Density Function PDSI Palmer D rought Severity Index PRCC Partial Rank Correlation Coefficient RMSE Root Mean Squared Error RUE Radiation Use Efficiency SALUS System Approach to Land Use Sustainability SECC Southeast Climate Consortium SIRP Stripling Irrigation Research Park SSURGO Soil Survey Geographic STATSGO State Soil Geographic (now U.S. General Soil Map) SWAT Soil and Water Assessment Tool TDCC Top Down Concordance Coefficient TSI Total Sensitivity Index TSR Total Seasonal Rainfall UGA University of Georgia USDA United States Department of Agriculture VIF Variance Inflation Factor WI Willmott Index WOFOST World Food Studies

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19 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy RAINFALL VARIABILITY EFFECT S ON AGGREGATE CROP MODEL PREDICTIONS By Kofikuma Adzewoda Dzotsi August 2012 Chair: James W. Jones Major: Agricultural and Biological Engineering Crop production operates in a highly heterogene ous environment. Space time variability in weather and spatial heterogeneity in soil and management generate variability in crop yield While it is practically unfeasible to thoroughly sample the variability of the crop environment, quantification of the a ssociated uncertaint ies in crop performance can provide vital information for decision making. The present study used rainfall data collected in s outhwest ern Georgia at scales ranging from 1 km to 60 km to assess the effect of weather variability (in parti cular rainfall) on crop predictions aggregated over soil and management variations The simple SALUS (System Approach to Land Use Sustainability) crop model was integrated in DSSAT (Decision Support System for Agrotechnology Transfer) then parameterized and tested for maize, peanut and cotton for use in obtaining the crop predictions. Analysis of the rainfall data indicated that variability in storm characteristics depend s upon the season. Winter rainfall was more correlated at a mean d istance of 54 km between locations than summer rainfall was at a mean distance of 3 km The pairwise correlation between locations decreased with distance faster in the summer than in the winter. This rainfall variability translated into crop yield variabi lity in the study

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20 area (about 3100 km 2 ) It was found that weather variab ility explained 60% and 49% of maize yield variability respectively in 2010 and 2011 when heterogeneity in weather, soil, cultivar and planting dates were accounted for simultaneously U ncertainties in crop predictions due to rainfall spatial uncertainty decreased as the number of sites where weather data were collected increased. Expressed in terms of maize yield coefficient of variation, this uncertainty decreased exponentially from 27% to approximately 4 % at a sampling density of 20 weather locations Based on 30 years of generated weather data, it was concluded that the general form of the relationship between maize yield distribution and density of weather network was not affected by long term seasonal weat her variability; however, year to year weather variability appeared to be an additional source of uncertainty in aggregating cro p yield when less than 10 weather locations were used.

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21 CHAPTER 1 BACKGROUND TO PRECIPITATION VAR IABILITY EFFECT S ON CROP MODEL PREDICTIONS Importance of the Precipitation Crop Relationship Precipitation and crops interact in various ways as two components affecting feedbacks between the atmosphere and the land surface It is widely documented that croplands through their eff ects on heat and moisture exchanges within the planetary boundary layer contribute to modifying precipitation patterns at regional scales (Pielke and Avissar, 1990; Pielke, 2001; Sud et al., 2001) Precipitation originates in moisture fluxes from the land surface to low er atmospheric boundary layers. M oist air is mixed upward s and transported to greater heights through convection. Vertical motion in the atmosphere stimulates rising of air parcels l eading to cloud formation. P recipitation received at the land surface can be partitioned to a horizontal flow of water that does not enter the soil profile (runoff) a vertical downward flux (infiltration or drainage), and a vertical upward flux in the for m of latent heat (evaporation) Virtually every step of the water cycle is affected by land cover that is mostly composed of crops in agricultural systems. Vegetative cover and particularly crops have specific properties that modify the water cycle through a bi directional exchange of energy and moisture. Additionally, exchange of momentum and carbon are integral components of the interactions between the atmosphere and the land surface (Bonan, 1995) Crops modify the albedo, roughness and the leaf area index (LAI) of the land surface Their rooting system constitutes the means by which water is conducted from the soil to the plant. Water is an important plant constituent (about 50 to 80% by mass ) and is used for maintenance of turgidity and evaporative cooling. Plants respond to short term water deficit s through the regulation of their stomates. Prolonged deficit s can result in loss of green leaf area

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22 and inhibition of photosynthesis (Taiz and Zeiger, 2002) Complementing agricultural water deficits with irrigation constitutes an additional input to the soil plant atmosphere water balance that is characteristic of agricultural systems. Agric ultural interactions with the atmosphere have also been documented in the form of regional alteration s of temperature resulting from a modification to latent heat fluxes (Loarie et al., 2011) Seasonal variations of crop cover in agricultural systems imply that interactions between crops and the atmosphere are dynamic in nature. These interactions do not occur on non vegetated lands which generally have a reduced aerodynamic roughness and higher soil evaporation (Betts, 2001) Observational and modeling studies have demonstrated that the timing and intensity of cloud development is influenced by a gricultural land use (Pielke, 2001; Adegoke et al., 2007) Precipitation Variability Precipitation ranks among the most variable components of the climate system and rep resents the most recurrent meteorological variable in variability studies (Hubbard, 1994; Willmott et al., 1996) Although the processes that contribute to the formation of precipitation are well understood and mostly deterministic, the timi ng and occurrence of precipitation remain essentially a stochastic process (Ward and Robinson, 2000) This inherent variability makes precipitation one of the most difficult atmospheric variable s to predict (Guenni and Hutchinson, 1998) Precipitation variability has been emphasized at all scales, ranging from farm to global levels (Brunetti et al., 2012) including watershed (Bosch et al., 1999) state (Boone et al., 2012) and regional levels (Baigorria et al., 2007) General characteristics of precipitation spatial variability around the globe and in the U.S. are well documented in the literature. These characteristics are season dependent In some regions like the

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23 s outheastern U.S., precipitation received is essenti ally in the form of rainfall. Daily rainfall tends to exhibit high variations due to local weather conditions These variations are caused by storm characteristics. Statistical distributions of spatial variation in daily rainfall amount s tend to be skewed with a peak at zero. Monthly totals tend to approach a Gaussian distribution as they absorb the day to day variations and reflect the large scale behavior of storms and the organization of climates (Grimes and Pardo Iguzquiza, 2010) Winter rainfall has been characterized as dominated by the effect of synoptic scale fronts, with long durations, moderate rainfall amounts and intensities and lower frequency of occurrence (Bosch et al., 1999) These types of rainfall accommodate a large stratiform component and have stron g spatial gradients and correlations. In contrast to winter summer rainfall tend s to be more intense with rapid correlation decay around a point and occur s more frequently within localized cells (B aigorria et al., 2007) Locations within the same area may experience high rainfall amounts while others escape completely. This type of system is usually the result of the influence of local convections that may be organized within a large scale system Spatial variability of precipitation has been found to be more important than temporal variability in long term climatology means of precipitation (Willmott et al., 1996) Although large scale variations in precipitation constitute an important factor in defining small scale variability defines the local climate and influence s related decisions (Brunetti et al., 2012) Measurement of regional rainfall variability is widespread and use sys tematic weather networks (Bosch et al., 2007; Boone et al., 2012) The importance of dense weather networks f o r captur ing local rainfall variations has been long recognized and emphasized in numerous studies

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24 (McConkey et al., 1990; Bosch et al., 1999; Changnon, 2002; van de Beek et al., 2011) So me of these applications include crop production on which we concentrate in the present study. Since the analysis of the effect of rainfall variability on crop production involve s spatial and temporal scales that are often beyond the possibility of measure ments for practical reasons, quantitative tools that correctly represent the soil plant atmosphere relationship are needed. Crop Models as Tools in Agricultural Assessments A crop model describes mathematically the growth and yield of a crop in a dynamic way. This means that the relationship between the crop and its environment is described using equations that mimic relevant pro cesses over a homogeneous area. Characteristics of the crop are defined using genetic coefficients that represent the p otential performance of the crop in the absence of environmental stresses. Characteristics of the environment are described for soil, weather and management. Typical states of the crop growth and development simulated are phenology and evolution of biomass LAI and grain yield. Integration of the state variables is performed numerically typically using the Euler method and a daily time step. A range of approaches has been used to represent evolution in biomass, LAI and grain yield (Hoogenboom, 2003) Biomass accumulation can be estimated using a radiation use efficiency (RUE) and the intercepted photosynthetically active radiation (Kiniry et al., 1989) A more mechanistic approach to modeling biomass involves the use of carbo n uptake from the atmosphere to calculate photosynthesis and respiration based on work by Penning de Vries and van Laar ( 1982) Leaf area index can be modeled using a generic function that mimic s typical LAI variations in crops growing at potential production level (Kiniry et al., 1992) A more complex approach to modeling

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25 LAI involves the simulation of leaf growth, expansion and senescence (Boote et al., 1998) Grain yield can be determined using a harvest index that may be modified in the presence of environmental stresses. Some models specifically describe fruit growth and partitioning of assimilates to reproduct ive organs (Boote et al., 1998) At one end of the spectrum simple crop models combine simple, generic, empirical description s of crop growth, development and yield (Kiniry et al., 1992) More complex crop models include a large number of para meters to represent crop growth based on a detailed approach to biomass and LAI simulation s While each modeling philosophy has its own advantages and disadvantages, the appropriate choice of complexity depends upon the intended use (Boote et al., 1996) Crop models have enjoyed worl dwide use in a wide range of agricultural applications However, they are limited in simulating spatial variation in crop yield because they are designed to operat e over homogeneous fields Effects of Rainfall Variability on Crops The surface of the land is highly heterogeneous Spatial variability in crop yield emanates primarily from variability in weather (especially rainfall ), soil and management. Variability in soil has been characterized to occur largely in space (NRCS, 2010) Variability in weather has a strong temporal compone nt as well that crop models must account for to accurately represent spatial and temporal variations in crop yield. While fertilizers and other management practices are used to correct changes in soil properties (Brady and Weil, 2002) variability in weather, especially rainfall is less predictable and constitute the primary driver of inter seasonal crop yield variability in rainfed production systems (Hansen and Jones, 2000) Irrigated crop production systems also rel y on weather variability, in particular the average weather, for a number

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26 of management decisions (Royce et al., 2011) It has been reported that up to 80% of the variability in agricultural production was attributable to weather variability in some cases (Hoogenboom, 2000) Most traditional crop models are not designed to simulate variation in crop yield in a tw o dimensional space. Accounting for spatial heterogeneity in model inputs involve s specific modeling of emerging processes such as fluxes of water and nutrients between fields (Faivre et al., 2004) Other approaches include sampling the spatial heterogeneity in geographic or probability space (Hansen and Jones, 2000) and us ing geostatistical method s to represent the continuous variation over space. Crop models can also be adapted based on large scale empirical observations to operate over large areas (Challinor et al., 2004) and even integrated into regional scale land surface models (Osborne et al., 2007 ) However, modeling the effect of atmospheric feedbacks on crops is not considered in the present discussion and research. Only the uni directional effect of rainfall (and other crop model inputs) used as external factors to the cropping system are con sidered. Rainfall variability accommodates significant stochastic contributions that are driven by local variability. These stochastic variations are propagated to crop production in a non linear manner (Hansen and Jones, 2000) Since crop production oc curs at local scales the agricultural risks associated with changing rainfall pattern and magnitude are likely to be felt first at these scales. As a consequence, understanding of the spatial and temporal variability of rainfall as well as its effects on crop production at localized scales that are compatible with cropping systems is key to understanding large scale patterns. Several studies recommended using high resolution weather data to simulate the

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27 effect s of rainfall variability o n crops and sediment transport (Goodrich et al., 1995; The present study was designed to provide a quantitative understanding of the spatial and temporal variability of rainfall over a range of scales in a way that contributes to aggregation and disaggregation of rainfall and the implications of these scale changes on crop predictions. One of the major problems associated with rainfall spatial variability is the effects of its incomplete knowledge on crop yield. Numerous modeling studies rely on one or a limited number of weather stations to simulate aggregate crop yield over an area ) Other studies assume that rainfall is uniform over a given area and use a neighboring weather station to model crop growth on a field. However, the assumption of spatial homogeneity of rainfall is not valid (Goodrich et al., 1995; Hoogenboom, 2000) Incomplete knowledge of the spatial variability of rainfall can result in uncertainties in predicted yield. A number of studies have shown that uncertainties in crop yield and nutrient loads decrease d as the number of weather sites used to account for rainfall variability increased et al., 2002; Cho et a l., 2009) In this study, uncertainties in simulated crop yield due to rainfall uncertainty were also evaluated, using the simple and generic SALUS (System Approach to Land Use Sustainability) crop model. The SALUS model is simple in the sense that the two most important aspects of crop growth, biomass accumulation and LAI evolution, were represented in a summarized form based on empirical relationships. The model is generic in the sense that it can potentially be parameterized to simulate a wide range o f crops and grasses (Kiniry et al., 1992) Using a crop model at a large scale (for example for climate change

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28 impact assessments or evaluating the importance of the feedback between the crops and the atmosphere) wo uld usually involve simulating several crops or evaluating the productivity of grasses present over the region of interest. Accounting for this variability in land cover implies, if using a detailed crop model, developing parameter sets for each crop or gr ass, which may be demanding and even lead to extensive model modifications. In addition, this intensive parameterization may not necessarily result in a significant gain in accuracy (Monteith, 1996) because some crop processes may lose their importan ce at a larger scale (Challinor et al., 2004; Adam et al., 2011) A good modeling practice entails incorporating major crop growth processes while keeping their representation as simple as needed (Monteith, 1996) Studies have shown that simple crop models have the potential to perform as well as detailed models, especially over larger areas where individual plant variations tend to have little influence on the average productivity (Kiniry et al., 1997; Adam et al., 2011) The simple SALUS crop model was selected for testing simple approaches to simulating crop yield in DSSAT Further research may involve using SALUS at regional scales to understand feedbacks between croplands and the at mosphere as an integrated part of a land surface model. The area selected to study at a high resolution the variability in rainfall and its effects on crop model predictions was composed of Dougherty, Baker and Mitchell counties in southwestern Georgia (Fi g ure 1 1). This area is located within the s outheastern U S the focus region of the Southeast Climate Consortium (SECC) under the auspices of which this research was conducted. These counties have a significant coverage of cultivated areas and forests wi th a relatively low proportion of developed

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29 areas (Table 1 1). Therefore, they are suitable for studying the relationship between rainfall variability and crop model predictions. Research Question and Objectives This research concentrates on the overall qu from the spatial variability of rainfall affect crop performance at different aggregation To answer this question the following objectives were evaluated: Objective 1 : Conduct a global uncertainty and sensit ivity analysis of the simple SALUS model after integrating it in DSSAT Objective 2 : Estimate parameters for simulating maize, peanut and cotton using the DSSAT SALUS crop model Objective 3 : Understand the spatial and temporal variability of rainfall in sou thwest Georgia over a range of scales Objective 4 : Evaluate the effect s of rainfall spatial and temporal variability and spatial variations in soil, cultivar, and planting date on aggregate crop model predictions at different scales

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30 Table 1 1. Percentage of selected land cover types in the three counties Land cover type Dougherty Baker Mitchell Cultivated areas 9 30 36 Forests 38 34 34 Developed areas 18 4 6 Others 35 32 24 Source: C alculated us ing reclassified data from the National Land Cover D atabase (USDA, 2001)

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31 Figure 1 1. Google Earth image of the study area showing the locations of the rain gauges and weather sta tions. The several small circles represent annual crop fields. The ir circular shapes are due to the center pivot based irrigated system common in the area Note that Dougherty county has a small number of crop fields due to the city of Albany and a larger number of plantations

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32 CHAPTER 2 INTEGRATING THE SIMP LE SALUS CROP MODEL IN DSSAT I ntroduction Recent interest in applying crop models at scales larger than field levels ha s motivated the ir adaptation for assessing bi directional feedbacks between the atmosphere and croplands A daptations have included crop model simplification to enable estimation of biomass, grain yield and leaf area index (LAI) for a range of crops and grasses (Osborne et al., 2007) and to avoid intensive parameterization that may, at the scales considered, contribute more noise than numerical precision to the simulations (Monteith, 1996; Stehfest et al., 2007) Some studies have suggested that when operating at larger scales, crop models may be less sensitive to detailed crop growth processes that were designed for simulating individual plants ; therefore such processes may lose their importance only at those scales (Adam et al., 2011; Ewert et al., 2011) In addition, gaps in knowledge of detailed crop parameters for many crops and grasses prevent the application of detailed crop models in global assessment studies (Stehfest et al., 2007) Existing models range in com plexity from simple, canopy level, and field scale using a Radiation Use Efficiency (RUE) simplification to quantify growth, to complex, leaf level, plant scale simulating growth and development of leaf, reproductive organs and different yield components (Kiniry et al., 2002) While the need for simpler models depends upon t he intended application (Boote et al., 1996) and is not the subject of consensus (Faivre et al., 2004) many modeling commun ities agree that accommodating a wide range of crops in generic models will not only increase the applicability of the models but also contribute to structuring knowledge common to these crops (Wang et al., 2002; Jones et al., 2003)

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33 Indeed, t he realization that most plant growth and development processes can be described using a set of functions common to multiple species forms the basis for generic pl ant modeling. This approach to plant modeling represents growth aspects specific to each plant using species specific parameters. Generic plant modeling allows for a quick addition of a new crop or grass without extensive model modifications to account for specific growth aspects. It also provides an appropriate framework for rapid model adaptations to simulate intercropping between species. Further, applications requiring estimation of the productivity of different vegetation covers in large areas may be r easonably resolved. Major crop modeling communities have implemented this approach to potentially benefit from these features (Wang et al., 2002; Jones e t al., 2003) However, while these generic models have enjoyed worldwide applications, many of them, including the CERES family (Jones and Kiniry, 1986) the CROPGRO family (Boote et al., 1998) and WOFOST (Supit et al., 1994) exhibit a significant level of details and therefore restrict their use in situations where required inputs and parameters are not readily available. Integration of a simple and generic crop model in the widely used Decision Support System for Agrotechnology Transfer (DSSAT) was undertaken to provide a simpler alternative to existing models for applications where detailed parameterizations are not desirable or compariso n between simple and complex approaches are informative. The crop model is the simple version of SALUS (System Approach to Land Use Sustainability, Basso et al., 2006 ) based on modeling approaches used by EPIC ( Erosion Productivity Impact Calculator, Williams et al., 1989 ) and ALMANAC (Agricultural Land Management Alternatives with Numerical Assessment Criteria, Kiniry

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34 et al., 1992 ) for representing changes in canopy level LAI RUE, and estimating field scale plant biomass during the season. Th e model i s simple in the sense that approaches used to describe the two most important aspects of crop growth (LAI and biomass) were implemented in a summarized form when compared to other more elaborated crop models. A number of crop models estimate bioma ss based on the RUE approach but most of these models use detailed process based equations to represent LAI. A limited number of crop models use a summarized approach to describe LAI (Kiniry et al., 1992) This sim plified LAI approach has recently received some attention as modelers have been exploring different methods of using crop models at large scale in climate impact assessments (B ondeau et al., 2007; Adam et al., 2011) In combining simplifications in the estimation of both biomass and LAI, the SALUS model propose s a simple modeling approach to crop growth while harnessing the power of DSSAT in terms of crop environment modeling The current version of the simple SALUS model describes water limited production with 20 plant parameters and can in principle be parameterized for a range of plants from literature or available data Comparison between ALMANAC (on which the simple SALUS was based) and CERES showed that the two models had similar capabilities to simulate variability of maize grain yield across nine U.S. locations (Kiniry et al., 1997) However, limited applicability of the simpl e SALUS model was found in the literature (Basso et al., 2006) The implementation of SALUS in DSSAT l ed to a number of specific questions: 1. Does the model behave as expected under different environments? 2. What plant parameters exert the largest influence on major model outputs?

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35 3. How do uncertainties in plant parameters translate into variability in these model outputs? 4. Do all the parameters in SALUS ne ed to be estimated for each maturity group in a species ? A global uncertainty and sensitivity analysis c an help answer these questions as it trans lates uncer tainties in crop parameters into uncertainties in model outputs. Further, a global uncertainty and sensitivity analysis h as not been performed on the simple SALUS model previously, so little was known about how input plant parameters were mapped to key model outputs. The use of global uncertainty and sensitivity analysis in assessing effects o f uncertainties in inputs on cro p models outputs is widely accepted and has been used for various objectives including verifying model behavior (Confalonieri et al., 2010 b) identifying important crop parameters (Pathak et al., 2007) and ranking model parameters with respect to their importance in yield formation (Richter et al., 2010) A detailed review of uncertainty and sensitivity analysis methods was provided by Saltelli et al. ( 2004 ) Helton ( 1993) and He lton et al. ( 2005) A comparison of the most common sensitivity analysis methods was recently discussed by Confalonieri et al. ( 2010a) The incorporation of the dependence of model outputs on time in global sensitivity analysis method s has been recently proposed (Campbell et al., 2006) and applied to a crop model (Lamboni et al., 2009) However, inter dependence between crop param eters is an aspect of global uncertainty and sensitivity analysis frequently unaccounted for probably because many authors obtain information on parameter ranges from different, not necessarily related sources in the literature Moreover, common sensitivi ty analysis methods like the Fourier Amplitude Sensitivity Test (FAST, Cukier et al., 1973, 1978) the extended FAST or the method of Sobol (Saltelli et al., 2004) do not account for correlations between variables For the DSSAT

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36 SALUS model, it was possible to determine and account for the correlation structure for some of the parameters studied because a method for generating synthetic data using DSSAT crop models was used to find ranges and distributions for parameters with limited information in the literature. The primary objective of this paper was to describe the simple SALUS crop model integrated in DSSAT and investigate outputs to crop parameter uncertainty. Specific objectives were to : 1. Quantify the effect of changes in crop parameters within their range of uncertainty, on final biomass, final grain yield and season length of maize, peanut and cotton; 2. Identify parameters in SALUS that have the most influential effect s on model outputs, a nd hence need to be estimated with high accuracy; 3. Quantify the effect of locations (soil and weather ) and inter annual weather variability of rainfall on model output uncertainty and crop parameter ranking; 4. Determine how the uncerta inty and sensitivity a nalysis a re affected by production levels (potential and water limited); 5. Determine if the uncertainty and ranking of crop parameters were affected by the crop modeled. This paper is organized as follows: 1. The materials and methods section provides a descri ption of the SALUS crop model and the procedure for integrating it in DSSAT. This section also presents the methodology used for the uncertainty and sensitivity analysis, including the generation of synthetic data needed to obtain the ranges, distributions and correlations among the crop parameters; 2. In the results and discussion section, modifications to the SALUS model during the integration in DSSAT are presented. The synthetic data obtained are also discussed in combination with information from the lite rature to determine the crop parameter distributions. Finally, uncertainty and sensitivity analysis results are presented and discussed 3. The conclusion section highlights the main results and findings related to the SALUS model development.

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37 Materials and M ethods Overview of the SALUS C rop M odel The crop growth modules in SALUS are largely based on the DSSAT family of crop models (Jones et al., 2003) Each model simulate s specific characteristics of a particular crop using weather, soil a nd management information from common modules. However, the simple version of SALUS (simply denoted SALUS or SALUS crop model hereafter) d oes not describe a particular crop but i s rather designed to be simple, generic and easily parameterized. The approach used in this version of SALUS i s based on the ALMANAC simulation model (Kiniry et al., 1992) The simple SALUS model can simulate the potential production of a plant using fewer than 20 plant parameters with additi onal parameters required for water and nutrient limited production. The crop development and growth processes simulated in SALUS a re summarized in Figure 2 1. Germination, emergence and maturity a re predicted using plant specific parameters based on the growing degree day approach. Simulation of LAI growth and decline use s a generic sigmoid function whose shape i s dependent on plant specific parameters. Biomass production from Photosynthetically Acti ve Radiation (PAR) absorbed by the leaf canopy i s based on a RUE approach (Hoogenboom, 2003) Accumulated biomass i s partitioned betwe en aboveground dry matter and root biomass using an inverse exponential function. Variables and crop parameters used to describe the SALUS model in the following sections a re summarized respectively in Table s 2 1 and 2 2 All rate equations appearing in th e description of the model are integrated numerically using the Euler method.

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38 Description of the SALUS C rop M odel Plant development Because many plant development stages are dependent on temperature, it is appropriate to model the development stages based on the daily accumulation of a certain amount of heat units above a threshold temperature. This concept, known as thermal time, has been popular in crop growth modeling (Ritchie and NeSmith, 1991) In SALUS, plant germi nation i s predicted using a fixed thermal time from planting to germination (a crop parameter called TTGerminate ). Although other models have described germination to occur in one day provided soil water conditions are adequate (Muchow and Carberry, 1989) the thermal time app roach was assumed to be appropriate (Birch et al., 2003) This assumption i s later evaluated in a sensitivity analysis (in this paper). Emergence is but dependent on planting depth. Several studies have confirmed the relationship between thermal time from germination to emergence (called TTEmerge in SALUS) and planting depth (Alessi and Power, 1971; Gupta et al., 1988; Kiniry and Bonhomme, 1991) In the SALUS model, a linear relationship i s used to predict TTEmerge according to Equation 2 1. (2 1) where EmgInt and EmgSlp are crop parameters defined in Table 2 2 The variables TTEmerge and PlantingDepth are defined in Table 2 1. Time to m aturity is also coupled with thermal environ ment and varie s with genotype and maturity group. For example, there is a large variability in maize total thermal time from planting to maturity ( TTMature in SALUS) (Kiniry et al., 1997; Lindquist et al., 2005) In SALUS, progress towards maturity is normalized to the

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39 TTMature using the relative thermal time ( RelTT ) whic h represents a fraction of the growing season between planting ( RelTT equals 0.00) and maturity ( RelTT equals 1.00). Light interception The model simulate s the interception o aw. First, the PAR i s defined as 50% of the incomi ng solar radiation. Second, the intercepted PAR by the canopy (IPAR) i s approximated using an extinction coefficient ( KCan ) and canopy (2 2) where the subscript represents the current day of simulation. Row spacing has a significant effect on the extinction coefficient KCan Flenet et al. ( 1996 ) reported that an increase in maize row spacing from 0.35 to 1.00 m resulted in a 29% decrease in the canopy extinction coefficient. The effect of row spacing and plant population i s modeled in SALUS using an equation that takes the form (2 3) Leaf area i ndex Accurate simulation of the LAI profile is critical because light interception directly depends upon the value of LAI. The model use s five parameters to describe the evolution of LAI up to the maximum LAI and one additional parameter to determine the shape of LAI decline after the beginning of leaf senescence. Both parts of the generic LAI curve use the concept of relative LAI ( RelLAI ) which is equivalent to a given fraction of maximum LAI under non stressed conditions.

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40 During the part of the season where LAI increase s relative LAI i s determined using a sigmoid curve (Figure 2 2 A ). To simulate the appropriate shap e, the model generate s two parameters ( LAIP1 and LAIP2 ) as inputs to the sigmoid curve (Kiniry et al., 1992) These two parameters represent respectively a point on the curve near emergence (at RelTT = 0.15) and a p oint near flowering (at RelTT = 0.50), which correspond s approximately to the first and second inflexion points on the LAI growth curve (Figure 2 2 A ). The equation for this curve takes the form (2 4) where represents the relative LAI on day prior to the beginning of leaf senescence To solve Equation 2 4 on any day that growth occur s between emergence and the beginning of leaf senescence, the values of the parameters LAIP1 and LAIP2 must be known. Since these two parameters represent points located on the LAI curve described in Equation 2 4, their values can be calculated from their c oordinates. The x coordinates represented by RelTT were set to 0.15 (near emergence) for LAIP1 and 0.50 (near flowering) for LAIP2 Values of the x coordinates are needed to calculate LAIP1 and LAIP2 These x coordinates correspond to break points where the slope of the relative LAI function changes. The y coordinates (denoted respectively RelLAIP1 and RelLAIP2 ) were defined as crop parameters. The equations for the parameters LAIP1 and LAIP2 follow from Equation 2 4 (2 5) with

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41 (2 6) The LAI decline occur s after the relative thermal time to senescence ( RelTTSn ) i s reached. This i s described using the LAI decline parameter denoted SnParLAI (2 7) where is now the relative LAI on day after the beginning of leaf senescence. The shape of the LAI decline function (linear, concave or convex) i s species dependent and controlled by the value of the parameter SnParLAI The ra te of LAI increase (prior to the beginning of leaf senescence) is computed as (2 8) After the beginning of leaf senescence, LAI is directly calculated based on the relative LAI as follows: (2 9) No stress factors are applied to the LAI after t he beginning of leaf senescence. Only natural senescence (as modeled in RelLAI ) is accounted for. Radiation use efficiency and total dry matter The model use s species specific maximum RU E to compute actual RUE values during the season. Radiation use efficiency i s maintained at a maximum value during LAI growth until the beginning of leaf senescence. During LAI decline, RUE decrease s according to a function identical to the LAI decline function with a corresponding decline

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42 parameter denoted SnParRUE Like for the LAI, this parameter define s the shape and rate of RUE decline. Potential total plant dry matter including roots i s calcula ted for each species from their RUE and intercepted PAR. (2 10 ) where is the potential simulated total dry matter including roots on day Water and nutrient stress factors a re applied daily to reduce the rate of potential biomass growth in the presence of moisture and nutrient deficits. Dry matter partitioning and yield The SALUS model partitions the d aily accumulat ion of dry matter between the aboveground plant part and the roots using a dynamic partitioning coe fficient that change s with crop age. The formulation of this coefficient was based on work by Swinnen et al. ( 1994 ) who used 14 C pulse labeling to determine that the proportion of net assimilated carbon in wheat shoot increased from 61% at elongation to 85% at dough ripening with a corresponding decrease from 15 to 2% in roots. This dynamic partitioning was adapted using an expone ntial decrease function to calculate a root partitioning coefficient (fraction of total dry matter present in roots) as follow s : (2 1 1 ) The RootPartCoef coefficient reduce s exponentially the fraction of dry matter partitioned to roots, from 0.45 at planting ( RelTT = 0.0) to 0.067 at maturity ( RelTT = 1.0). Using the RootPartCoef the rate of root biomass growth i s calculated as (2 1 2 )

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43 The model assume s a RootFracLive (fraction of root dry matter in live roots) of 0.90, meaning that 90% of the root mass remain in live roots with the remaining 10% allowed to participate in soil organic matter formation. The aboveground biomass ( Tops ), i s the remaining portion of total dry matter not partitioned to roots (2 13 ) Crop yield i s calculated as the product of the aboveground dry matter and a crop dependent parameter, the harvest index ( HrvIndex ). The reduction in harvest index due to water nutrient or heat stress i s not directly accounted for. Ongoing improvement of SALUS will inc lude introduction of a factor that reduces the harvest index if a stress condition prevents the crop from accumulating a certain amount of biomass between the beginning of leaf senescence and maturity. Effect of cold temperatures Plant growth st op s in col d environments if any of the following conditions are met: 1. T he daily thermal time reache s a value smaller than 0.10 o C for 20 consecutive days; 2. After the beginning of leaf senescence, the minimum temperature drops to a value smaller or equal to 10 o C Root dynamics The model simulate s the dynamics of root growth in different soil layers using three main processes: (i) the root front growth, (ii) the root distribution in different soil layers, and (iii) soil impeding factors that modify root front growth and root distribution. The progression of the rooting front from the depth of planting at germination to a (Jones et al., 1991) The SALUS crop model calculate s the potential daily root depth

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44 increment as 10% of the daily thermal time accumulated that controls plant growth. Numerous studies have shown that the actual r oot penetration in soil layers was modified by soil strength, soil aeration and soil temperature (Jones et al., 1991) In SALUS, the potential root depth increase i s reduced by impeding factors that include saturated soil, dry soil, low soil temperature and a soil hospitality factor. The effect of these stress factors i s pooled to modify and determine the fraction of dai ly root dry matter that must be present in each soi l layer where root growth occur s Integrating SALUS in DSSAT The SALUS model was implemented in the DSSAT Cropping System Model (CSM) to make a generic, easily parameterized crop model available to users w hile enhancing the capability of DSSAT to potentially simulate other crops. The integration of the generic SALUS crop model in the DSSAT CSM was based on the same approach used to implement other crop models in DSSAT and required structural adaptations to ensure desired communication between the CSM and the new crop model These modifications included the translation of SALUS from Microsoft Visual Basic to FORTRAN, the creation of a new SALUS parameter file in DSSAT and the update of modules to recognize SALUS as a new crop model. Simulation of potential plant growth, development and yield i s now performed by SALUS within DSSAT as described earlier. This type of simulation i s executed using a standard DSSAT experiment file (file X) w ith the cultivar and model name specified for the SALUS model T o simulate the effect of water stress on plant growth SALUS primary module s in the following way: 1. D aily root growth and distribution a re computed in the root dynamic s subroutine of SALUS and root dry matter i s converted into root length volume for each soil layer using a root length to weight ratio (RLWR Table 2 2 ) ;

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45 2. The daily root length volume and the daily LAI calculated by SALUS are used in plant at mosphere module to calculate root water uptake and potential plant transpiration; 3. This latter information is received and used by SALUS to compute plant water stress as the ratio of total root water uptake to potential plant transpiration. Therefore, the interface between SALUS and DSSAT consist s of the exchange of information on root growth and distribution root water uptake, plant LAI and the surface energy balance. The integration of SALUS in DSSAT required the introduction of the RLWR as a new SALUS crop parameter. The RLWR is used by other DSSAT crop models as well. O ther modifications to the SALUS model during integration in DSSAT are described in the results section. Uncertainty and Sensitivity A nalysis An uncertainty and sensitivity analy sis was conducted using the improved version of SALUS to assess the behavior of selected model outputs in the face of uncertainty in crop parameters defined in Table 2 2 The analysis included the original SALUS crop parameters and the new parameters intro duced as the model was modified during integration in DSSAT. In this study, u ncertainty analysis is concerned with assessing the uncertainty in model predictions resulting from uncertainty in crop parameters, and sensitivity analysis involves quantifying t he contribution of specific crop parameters to the uncertainty in model predictions (Helton, 1993; Saltelli et al., 2004) Uncertainty and sensitivity analysis are closely related and based on similar method s. Sites and analysis settings The uncertainty and sensitivity analysis was performed using three crops, maize ( Zea mays L.), peanut ( Arachis hypogaea L. ) and cotton ( Gossypium hirsutum L. ) at

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46 four locations (Table 2 3 ) per crop for 10 years and at potenti al and water limited production levels This resulted in 80 treatments (combinations of location, year and production level) for each crop (Table 2 4 ). The four locations were selected to account for variations in model sensitivity due to location dependen t combinations of soi l, solar radiation, temperature and rainfall. For maize, they were Gainesville, Florida (latitude 29.63 o longitude 82.37 o ), Clayton, North Carolina (latitude 35.65 o longitude 78.46 o ), Ames, Iowa (latitude 42.02 o longitude 93.63 o ), and Kellogg Biological Station (KBS) in Michigan (latitude 42.41 o longitude 85.41 o ). For peanut and cotton, Ames and KBS were replaced by Camilla, Georgia (latitude 31.28 o longitude 84.28 o ) and Suffolk, Virginia (latitude 36.72 o longitude 75.40 o ) because peanut and cotton are not grown in the northern part of the U S Specific soil and weather characteristics at these locations a re summ arized in Table 2 3 which indicates a gradient of decreasing maximum and minimum temperatures with increasing lati tude. Mean daily solar radiation in Gainesville and Camilla was similar and higher than values observed at upper latitudes (Table 2 3 ). The order of magnitude of total annual rainfall was also similar at nearby locations and matche d closely the gradient of temperatures (Table 2 3 ). The planting dates used were publication of usual planting dates in the United States (USDA, 1997) Maize plant population was chosen to be the average of two common plant populations, which was 6.0 plants m 2 (Kiniry et al., 1992) P l ant populations of peanut and cotton were 12.9 and 14.0 plants m 2 respectively obtained from Boote ( 1982 ) and Ortiz et al. ( 2009 ) Soil properties and daily weather data were available from the DSSAT database for Gainesville, Camilla, Ames and KBS S oil survey information from the National

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47 Soil Survey Geographic ( SSURGO ) database (NRCS, 2010) was used to create DSSAT soil prof iles for Clayton and Suffolk. Daily rainfall and temperature for these two locations were obtained from the National Climatic Data Center (NCDC, available online at www.ncdc.noaa.gov). Solar radiation at the two locations was estimated using an improved Br istow Campbell method (Thornton and Running, 1999) Methods of uncertainty and sensitivity analysis The uncertainty and sensitivity analysis was implemented us ing a Monte Carlo approach, which i s based on studying the relati onships between probabilistically selected model inputs or crop parameters and their corresponding model outputs (Helton, 1993) This analysis involved four steps that were repeated for each crop. T he first step consisted of defining a probability distribution for each cro p parameter. The definition and characterization of these distributions can be done from the literature, available data, or expert opinion (Monod et al., 2006) In the present study, a methodology for generating synthetic data from which the ranges and probability distributions of the crop parameters were derived, was developed and described in the following section. The synthetic data was used in combination with information from the literature. The correlations among the crop parameters obtained through the synthetic data were also calculated. In the second step, a Latin H ypercube (LH) sample of the crop parameters was obtained based on the ir statistical distributions and the correlation structure defined in the first ste p. The LH sampling approach ensures a thorough coverage of the probability space of each parameter and has been found to yield more stable results than simple random sampling (Stein, 1987; Helton, 1993) Here, stable results means that there was

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48 only a small variation between sets of model output values calculated from different independ ent samples. For uncorrelated and uniformly distributed crop parameters cumulative probability distribution s were divided into equiprobable intervals and one value was selected randomly from each interval (McKa y et al., 1979) Using the inverse of the distribution functions of the crop parameter s the values selected were transformed into samples. For normally distributed and correlated crop parameters, ariables was used (Stein, 1987) Based on this approach, simple random samples were initial ly obtained from a multivariate normal distribution with covariance matrix reflecting the correlation between the crop parameters. To transform these initial samples into LH sample s while preserving the correlations between pairs of crop parameters the following procedure was used: 1. Let the sample ( ) from the crop parameter ( ) be represented by There were crop parameters and samples for each crop parameter; 2. We obtain ed as the vector of ranks of corre sponding to the crop parameter. This vector is nothing but a random permutation of in a specific order; 3. N ext we obtained independent random variates from a uniform distribution on ; 4. The LH samples were obtained using the cumu lative distribution functions (CDFs) of the crop parameters as (Pebesma and Heuvelink, 1999) (2 1 4 ) This procedure yielded for each crop a sample matrix of size Each row vector in this matrix represents a sample of crop parameters in a specific combination.

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49 In the third step, the model was evaluated for each row vector in the matrix (that is a total number of model evaluations). This propagation of the sampled crop parameters through the model yield ed output vectors of size as well. In this study, three model outputs were selected for further analysis namely, the final aboveground biomass, the final grain yield and the season length. For example, solving the crop model represented by using the matrix of samples produce s the corresponding vector of model output s as follows: (2 1 5 ) where can be biomass, grain yield o r season length and repr esent s a stochastic implementation of the SALUS model with variability in due to the variability in the matrix In the fourth step, the uncertainty in the model outputs was assessed, and their sensitivity to each contributing crop parameter quantified. In th is study uncertaint ies in biomass, grain yield and season length w ere characterized by computing the mean and variance of their distributions and estimating their CDFs (Helton et al., 2005) For the sensitivity analysis, the contribution of each crop parameter to the variability in the model outputs was quantified using the method of partial correlation (Johnson and Wichern, 2002) that ha s proven to be among the most reliable and efficient regression based global sensitivity analysis methods (Helton, 1993; Marino et al., 2008; Confalonieri et al., 2010a) Since the relationship between the model outputs and the crop parameters was nonlinear, a partial ra nk correlation coefficient (PRCC), which is the sample partial correlation coefficient computed on the rank of the data, was used. If

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50 we define t he correlation coefficient between a given crop parameter and a specific model output as (2 1 6 ) then the partial correlation coefficient (PCC) between and is the correlation coefficient in E quation 2 1 6 calculated between the two residuals and where and are respectively predicted model output and predicted crop parameter based on the regression models and (2 1 7 ) The PCC can therefore be written as follows: (2 1 8 ) The PRCC is the PCC computed on the rank of the data. Since some crop parameters were not normally distributed us ing the rank of the data to compute the PRCC was appropriate. In addi tion, using the residuals from Equation 2 1 7 to compute the PRCC removes any linear effects of the remaining crop parameters on and (Marino et al., 2008) The PRCC provide s a quantitative measure of the strength of the sensitivity of the model outputs to the crop parameters. The highe r the absolute value of the PRCC the more sensitive the model output i s to the parameter considered

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51 The significance of the PRCC values was tested using the statistic (Johnson and Wichern, 2002) (2 1 9 ) where is the sample size and is the number of crop parameters whose effects are removed during the PRCC calcula tion. The statistic follows a standard normal distribution with degrees of freedom. The null hypothesis tested using was that the PRCC value was not different from 0. This hypothesis was rejected when the calculated p value was smaller than = 0.01. The variance inflation factor (VIF) was used to measure and control the effect of collinearity between crop parameters that were highly correlated prior to computing the PRCC With the proportion of variance in the crop parameter that i s explained by the remaining crop parameters, the VIF for parameter can be defined as It represent s the degree to which the variance of a can the presence of correlations with other variables in the m odel (Fox and Monette, 1992) To prevent flu ctuations in the PRCC estimates not related to the model outputs, some plant parameters ( RelTTSn TTMature and SnParRUE for maize, TTMature and SnParRUE for peanut and cotton) were removed from the partial rank correlation analysis This allowed a recommended VIF value that was smaller than 4.0 (Craney and These crop parameters removed from the PRCC analysis were considered to have the same effect on the model outputs as the parameters they

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52 had the highest positive correlations with. For maize for example, this means that any inference for MaxLAI would be valid for Rel TTSn and TTMature ; likewise, any conclusion for SnParLAI was valid for SnParRUE The number of model executions ( that is sample size ) was determined by running the model for maize at one location (Gainesville, Florida) for several sample sizes between 5 00 and 50,000 runs and examining the stability of final aboveground biomass, final grain yield, and season length. The 50,000 mode l runs was used as a reference f or testing f or any statistically significant differences. This means that the agreement among parameter ranking at 50,000 runs and increasing number of runs between 500 and 50,000 was tested using the top down concordance coefficient (TDCC). In the sample size choice analysis performed here, each pertain s to a specific sample size ( for example 500 model runs) and a specific parameter Denoting by ( with the total number of parameters ranked according to the PRCC values ), the ranking assigned to the TDCC was based on S avage scores (Savage, 1956) calculated as follow s : (2 20 ) For example if parameters ranked, the three savage scores for rankings at = 500 runs are ; ; (Iman and Conover, 1987) If only two sets of rankings were compared (as in this study, for example at = 500 and 50,000 runs), the TDCC i s simpl y the sam ple correlation coefficient in Equation 2 1 6 computed on savage scores. According to Theorem 1 in Iman and Conover ( 1987) the asymptotic distribution of is the standard

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53 normal distribution for two sets of rankings. This provide d the statistic for testing the si gnificance of the TDCC under the null hypothesis of independence between the two sets of rankings. The two rankings were considered identical in a top down sense (that is the null hypothesis was rejected) if the p value resulting from the test was smaller than an alpha level of 0.05. The method of TDCC was originally proposed by Iman and Conover ( 1987) to emphasize agreement among important parameters (top ranked) while allowing low ranked parameters to carry less weight The TDCC has been recently used by Helton et al. ( 2005 ) to compare sensitivity analysis rankings using random and LH sampling methods, and by Confalonieri et al. ( 2010a) to compare multiple rankings resulting from different sensitivity analysis methods. Marino et al. ( 2008) suggested the use of the TDCC for sample size selection in Monte Carlo type studies. S ynthetic data A computer experiment was created to determine the uncertainty ranges and correlations of selected crop parameters that were not readily measured in agronomic experiments. This computer experiment generated synthetic data that contributed to finding the probability distributions for the following crop parameters: HrvIndex LAIMax RelLAIP1 RelLAIP2 RelTTSn SnParLAI SnParRUE TTMature (Table 2 2 ). This methodology was designed for simulating maize, peanut and cotton species in SALUS without concentrating on the specificity of a cultivar, planting date, plant population or location. The computer experiment used location, culti var, plant population and planting date as experimental factors (Table 2 5 ) to account for the variability in corresponding crop parameters reported in the literature. This variability was shown to be attributable

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5 4 to cultivar differences (Narwal et al., 1986) plant population variations (Kiniry et al., 1992) planting date changes (Muchow and Carberry, 1989) and site conditions (Lindquist et al., 2005) The simulations were conducted at the potential production level using CERES Maize and CROPGRO peanut and cotton models in DSSAT. The genetic coefficients of the cultiv ars were obtained from the DSSAT database (Table s 2 6 to 2 8 ). The computer experiment was ended at simulated maturity as prescribed by the genetic coefficients of the cultivars. Daily relative thermal time was obtained for each combination of crop, cultiv ar, planting date, plant population and location by dividing the daily thermal time by the cumulative thermal time at maturity ( TTMature Table 2 2 ). The relative thermal time to senescence ( RelTTSn ) was taken as the relative thermal time at which the maxi mum LAI was simulated. The maximum LAI ( MaxLAI ) and harvest index ( HrvIndex ) were direct outputs from the synthetic data. The parameters LAIP1 and LAIP2 were obtained by fitting Equation 2 4 to the simulated LAI curve for each of the 432 combinations of cr op, cultivar, plant population, planting date and location, prior to the beginning of leaf senescence. Next the parameters RelLAIP1 and RelLAIP2 were calculated from the values of LAIP1 and LAIP2 using Equations 2 5 and 2 6. Similar to LAI growth parameters, the LAI senescence parameter SnParLAI was estimated from the simulated LAI curve after the beginning of leaf senescence using Equation 2 7. The correlation s among crop parameters obtained from the synthetic data were calculated and used in the LH sampling (Table 2 9 ). The highest correlation coefficients were found between MaxLAI and TTMature for maize and peanut, and MaxLAI and HrvIndex for cotton (Table 2 9 ).

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55 Statistical distributions of crop parameters Eighteen of t he 20 SALUS parameters were used in the uncertainty and sensitivity analysis ( SeedWt and TFreeze were fixed and not used in the analysis) The ranges and statistical distributions of crop parameters were derived from the synthetic data and the literature. The distributions of the parameters were assumed to be either uniform or square test for assessing normality based on skewness and kurtosis of data (Zar, 1999) was used to test the assumption of normality in crop parameters entirely or partially derived from synthetic data. The parameters or their transformed versions were consider ed normal if the p Pear Results and Discussion Modifications to the SALUS Model A number of modifications to the original SALUS model were implemented during integration in DSSAT. These modifications resulted in the introduction of a total of five new SALUS crop parameters In the original version of SALUS, the LAI growth rate on day can be interpreted as the increase in LAI from the current to the potential level. Stress factors are applied after this growth rate is computed (E quation 2 8). It was found that t his approach was only appropriate in unstressed conditions. T est runs in wa ter limited conditions using rainfed maize data from Gainesville, FL showed that LAI growth was consistently overestimated as the approach constantly forced the LAI to return to an equilibrium position (which is the potential level). In particular, recover y from stress was immediate, meaning that after a period of water stress, a large LAI rate allowed LAI growth to Another consequence of this approach is

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56 that the LAI growth rate on a day following a severe wa ter stress can be larger than the corresponding potential LAI growth rate. In the modified version of the model, LAI growth on any day (prior to any reduction in growth due to stress) is assumed to occur at potential level even after a period of stress T his is reflected in Equation 2 21: (2 21) where is the slope of the RelLAI versus RelTT function described in Equations 2 4 and 2 5 on day ; is the change in relative thermal time from day to day Calculation of LAI decline rate after the beginning of leaf senescen ce used the same relationship (E quation 2 21) without the stress factor term ( ). Modeling of t he effect of water stress after the beginning of leaf senescence on biomass and LAI decline involved the introduction of the parameters RelTTSn2 StresLAI and StresRUE (Table 2 2) to mimic observed responses to w ater stress (Brisson et al., 2003) This implies that after the beginning of leaf senescence the plant is affected by water stress only between the two points RelTTSn and RelTTSn2 (Figure 2 2B). At minimum stress level (water stress = 1), the actual LAI decline factor between these two points is equal to SnParLAI (Table 2 2); at maximum stress level (water stress = 0), the actual LAI decli ne factor is where is an LAI senescence acceleration coefficient at maximum water stress level (Figure 2 2B). Between minimum and maximum water stress levels, the LAI senescence factor is linearly interpo lated between and A similar approach was used for the reduction in RUE using StresRUE (Table 2 2). Combined with changes in the computation of LAI growth and decline rates, t hese modifications produced a

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57 drastic improvement in the simulation of LAI and dry matter after the beginning of leaf senescence in rainfed conditions as shown using maize data from Gainesville, FL (Figure 2 2C D). Test runs of the uncertainty and sensitivity analysis showed that in c ooler environments (Iowa and Michigan), the combination of low temperature s and minimum temperature s larger than 10 o C after the beginning of leaf senescence imposed unusually long season durations and prolonged the accumulation of biomass. Therefore, the effect of cold temperature s on growth was reviewed with the addition of a new parameter TFreeze (Table 2 2). In the modified version of SALUS, p lant growth stop s in cold environments when the daily minimum temperature drop s below the TFreeze temperature (Table 2 2). Initialization of plant weight at emergence was added to the model following the This modification involved the introduction of SeedWt (seed weight, Table 2 2) as a new crop parameter. The see d weight was used in combination with the plant population t o estimate plant weight at emergence. Results of Synthetic Data and Ranges of Parameters Values of the emergence intercept ( EmgInt ) and slope ( EmgSlp ) were obtained from data published in the literature. Data on maize emergence response to planting depth provided by Alessi and Power ( 1971) and Gupta et al. ( 1988) were used to estimate EmgInt and EmgSlp (Table 2 10 ). The values of EmgInt and EmgSlp used by the cereal crop models in DSSAT were within the selected ranges (45 o C and 6 o C cm 1 respectively). For peanut and cotton thermal time to emergence and sowing depth

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58 reported by Ketring and Wheless ( 1989) and Angus et al. ( 1981) were used to calculate these parameters (Tables 2 11 and 2 12 ). The range of harvest index ( HrvIndex ) obtained fro m the synthetic data was 0.25 to 0.63 for maize, 0.27 to 0.47 for peanut and 0.30 to 0.55 for cotton. Values of harvest indices reported in the literature fell within these ranges for maize (Kin iry et al., 1992, 1995) and cotton (Ko et al., 2009) D ata provided by Bell and Wright ( 1998) was used as the upper range of harvest index for peanut The maximum leaf area index ( MaxLAI ) obtained from the synthetic data varied between 0.40 and 6.22 m 2 m 2 for maize, 2.52 and 8.11 m 2 m 2 for peanut, and 1.22 to 5.49 m 2 m 2 for cotton. While many author s have observed LAI values within these ranges for peanut (for example Kiniry et al., 2005) most st udies on maize and cotton reported values larger than simulated potential LAI using DSSAT (for example Lindquist et al., 2005; Ko et al., 2009) Therefore uncertainty range s used for maize and cotton were wider than obtained from the synthetic data The first parameter describing the potential LAI curve ( LAIP1 ) varied between 2.38 and 5.06 for maize, 2.88 to 5.05 for peanut and 3.55 to 7.08 for cotton. The second parameter ( LAIP2 ) ranged from 9.58 to 20.37 for maize, 11.14 to 15.63 for peanut and 10.11 to 22.10 for cotton. The corresponding relative thermal time to senescence ( RelTTSn ) varied from 0.36 to 0.62, 0.26 to 0.50, and 0.67 to 0.99 respectively for the three crops. A value close to the maximum of t he range for maize (0.70) was used by Kiniry et al. ( 1995) to parameterize EPIC. The root length to weight ratio (RLWR) was probably the parameter with the highest uncertainty among the crop paramete rs analyzed, suggesting that more

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59 consistent measurements are needed to confirm the true variability of this parameter (Jones et al., 1991) Plants (species and growth stage) and soil (depth physical and chemical properties) are known sources of variability in RLWR (Jones et al., 1991) The variability in RLWR reported here was primarily due to sampling depth and site (soil type) differences. The largest range was measured by Allmaras et al. ( 1 975) who observed increasing RLWR with maize sampling depth (1950 cm g 1 to 6340 cm g 1 ) consistent with findings by Follett et al. ( 1974) and Barber ( 1971) The largest measured value of RLWR for maize was r eported by Grant ( 1989) (12000 cm g 1 ) while the cereal crop models in DSSAT currently use a value of 9800 cm g 1 (Jones and Kiniry, 1986) For peanut and cotton, the variabili ty found in the literature was smaller. Robertson et al. ( 2002) reported the lowest RLWR value (6500 cm g 1 ) for modeling APSIM leg umes while Boote et al. ( 1985) used a value of 9500 for peanut and Van Noordwijk and Brouwer ( 1991) reported a value of 9600 for cotton. The DSSAT models currently use the same value for peanut and cotton (7500 cm g 1 ). The selected ranges covered this variability found in the literature. The range of maize RUE published in Kiniry et al. ( 1989) was in close agreement with the variability of RUE across maize ecotypes in CERES Maize of DSSAT. Maize RUE varied with cultivars and locations between 2.1 g MJ 1 and 4.5 g MJ 1 IPAR (Kiniry et al., 1989) whi ch was consistent with other studies on maize (Lindquist et al., 2005) Peanut and cotton had smaller ranges of 1.2 (Robertson et al., 2002) to 3 .0 0 (Kiniry et al., 2005) and 2 to 3 (Gallagher and Biscoe, 1978; Ko et al., 2009) respectively Estimated SnParLAI from the simulated data ranged from 0.22 to 0.50 for maize, 0.05 to 0.14 for peanut, and 0.01 to 0.11 for cotton. The values of SnParLAI observed

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60 for pea nut and cotton (indeterminate crops) were more characteristic of a slower leaf senescence ( SnParLAI of 0.15) than a rapid LAI decline curve ( SnParLAI of 2.0, Kiniry et al. 1995 ). We assumed that the sha pe of the decline in RUE after the beginning of leaf senescence (described by SnParRUE ) could be modeled identically to the LAI decline. Hence, the same range was used for both SnParLAI and SnParRUE A wealth of experimental and modeling studies have meas ured or used base temperature ( TBase ) and optimum temperature ( TOpt ) values for maize (Warrington a nd Kanemasu, 1983; Narwal et al., 1986; Kiniry and Bonhomme, 1991) peanut (Boot e et al., 1985; Bell and Wright, 1998) and cotton (Reddy, 1994; Roussopoulos et al., 1998) Based on t he diversity and similarity of v alues reported in these studies, the uncertainty range of (i) base temperature was determined to be between 7 o C and 10 o C for maize, 9 o C and 14 o C for peanut, and 10 o C and 15 o C for cotton; (ii) optimum temperature was determined to be between 25 o C and 34 o C for maize, 29 o C and 36.5 o C for peanut, and 27 o C and 35 o C for cotton. There was limited information in the literature on the thermal time to germination ( TTGermination ) probably because most modeling studies were interested in measuring or predicting crop emergence instead. The maize crop models described by Muchow and Carberry ( 1989) and Kiniry and Bonhomme ( 1991) assumed that germination occurred in 1 day if soil moisture conditions were adequate similarly to Robertson et al. ( 2002) for peanut. Birch et al. ( 2003) assumed a thermal time from planting to germination of 20 o C in their model rather than prescribing 1 day after planting. Hayhoe et al. ( 1996) observed that with soil moisture limiting at planting only, germination was delayed and occurred on the third day after planting. This latter information was

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61 combined with the 1 day prescription used by some crop models a nd the base temperature ranges to determine the range of uncertainty for TTGermination The range of total thermal time from planting to maturity ( TTMature ) obtained from the simulated data was 993 to 2093 o C for maize, 1473 to 1961 for peanut, and 1718 to 2075 for cotton. Maximum values of TTMature found in the literature were slightly outside of these ranges for maize and cotton (for example, Wanjura and Supak, 1985; Narwal et al., 1986) Therefore the upper ranges of TTMature were larg er than obtained from the synthetic data. Statistical Distributions of Crop Parameters SnParLAI was found to have a Cauchy distribution and was transformed into a normal distribution by multiplication with an arbitrary normal distribution. A root s quared transformation was applied to Max LAI to obtain a normal distribution. Likewise square root and squared transformations were applied to obtain a normal distribution for some crop parameters (Tables 2 10 to 2 12 ). The LAIP1 and LAIP2 equivalents of R elLAIP1 and RelLAIP2 were used for sampling purposes because they were normal. MaxRUE TBase and TOpt were assigned a normal distribution based on information from the literature (Kiniry et al., 1989; Confalonieri et al., 2010a) The mean and variance of the normal distribution were estimated from the synthetic data or the range from the literatur e. For the remaining model parameters derived essentially from the literature, a uniform distribution was used for one or a combination of the following reasons 1) different values of the same crop parameter worked for different authors (for example, RLWR) 2) the lack of consensus in measurements reported in the literature motivated the hypothesis of equal weight in the uncertainty range of the parameter (for example, EmgSlp ), 3) the statistical distribution of the crop parameter could not be

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62 determined so lely based on the range derived from the literature (for example, TTGerminate ). Seed weight ( SeedWt ) was set at a constant value of 0.309 g for maize and cotton and 0.655 g for peanut. Likewise, freezing temperature ( TFreeeze ) was set at a value of 0 o C for all crops. Sample S ize Selection for Uncertainty and Sensitivity Analysis The calculated TDCC values using 50,000 model runs as reference were all close to 1 with associated p values smaller than 0.05 for biomass, season length and grain yield, at pote ntial and water limited levels (Table 2 1 3 ). This result indicated that there was no significant difference between the ranking of model parameters at 500, 1000, PRCC at 500 and 50,000 runs indicated that the magnitude of these coefficients was preserved between the two numbers of runs. The stability of sensitivity analysis results using a small sample size was an advantage of LH sampling indicated in the study by Helton et al. ( 2005) With regard to uncertainty analysis, the variability of mean biomass, mean season length, and mean grain yield with increasing number of model runs was hardly noticeable for all combinations of model outputs and production levels. For example, water limited mean biomass increased by 7% from 500 runs to 5000 runs. The corresponding increase in standard deviation was 5%. Slight changes in th e mean and standard deviation were noted between 5000 runs and 10000 runs. The coefficient s of variation at water limited production level was 1.58% for mean biomass, 0.30% for mean season length, and 1.14% for mean grain yield; for the standard deviation, the coefficient of variation was 1.23%, 1.12%, and 0.78% respectively, still at water limited production level. Although these results indicated that even a small sample size (for

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63 example 500 runs) would be sufficient, a more conservative sample size of 1 0,000 runs was chosen to account for the beginning of the true stability o f the means and standard deviation s Hence, each treatment in Table 2 4 was run 10,000 times, which resulted in a total of 800,000 model evaluations ( for all 80 treatments ) per crop. For the three crops, the total computing time used on a Windows 7 machine with a 2.20 Ghz Intel core2 duo processor was approximately 14 days. Uncertainty A nalysis Maize Variability in crop parameters over their plausible ranges of uncertainty resulted i n a maize total biomass range from 1.2 to 38 t ha 1 all locations and years considered. For grain yield and season length, this range was respectively 0.7 to 18 t ha 1 and 62 to 185 days. Differences among the four locations were small as shown for Florida and North Carolina in Figure 2 3. Maximum biomass and grain yield were respectively 3 t ha 1 and 1 t ha 1 lower in North Carolina than at other locations, however some years were cooler and produced longe r growth duration s at this location. When water limitation was accounted for, maximum biomass and yield levels strictly increased with latitude. Water limited maximum biomass reached 21 t ha 1 28 t ha 1 34 t ha 1 and 35 t ha 1 respectively in Florida, No rth Carolina, Iowa and Michigan. A similar pattern was observed for water limited grain yield. This was despite the lower mean annual rainfall in Iowa and Michigan, which suggested that the distribution of rainfall as well as the soils probably carried mor e weight in the determination of water stress. I nter annual differences in the individual distributions of potential biomass were hardly noticeable in Florida with the 25 th to 75 th percentile biomass values ranging between 10 and 20 t ha 1 The mean of th e potential biomass distributions varied

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64 between 12 t ha 1 (North Carolina) and 18 t ha 1 (Michigan) depending on the location (Table 2 1 4 ). For the standard deviations of the distributions of biomass, this range was between 4.8 t ha 1 and 7.5 t ha 1 at th e same respective locations (Table 2 1 5 ). Differences among the years were more pronounced at higher latitudes. For example, the mean potential biomass in the mo st productive year differed from the mean potential biomass in the least productive year by 2.1, 1.6, 2.9 and 3.9 t ha 1 with increasing latitude (Table 2 1 4 ). Uncertainties in the distributions of biomass associated with parameter uncertainty (as measured b y the standard deviations) were also larger at higher latitudes meaning that biomass levels, although lower in the south, were also more stable. The year with highest variability differed from the most stable year in standard deviation of potential biomas s by 0.7, 0.9, 1.2 and 2.5 t ha 1 respectively in Florida, North Carolina, Iowa and Michigan (Table 2 1 5 ). While inter annual differences in the mean and standard deviations of the distribution of potential biomass were clearly dependent on latitude, the shapes of the distributions were less affected by location (Figure 2 3). Regardless of the year considered, the coefficient of variation (CV) of potential biomass was approximately 40% in Florida, North Carolina and Iowa. Michigan exhibited the most drama tic CV range, 33 to 43% (depending on the year). As expected the addition of water stress resulted in a significant redu ction in overall biomass levels and higher variability among the different years (Figure 2 3C D) At all locations potential CDFs we re more similar than water limited CDFs suggesting that in the presence of water stress, the uncertainty in final biomass was more dependent on the year of study than when water stress was not simulated. Just like in the case of potential production, the m ean biomass gap among the years increased with

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65 latitude meaning that water stressed biomass was equally more stable across years in Florida and more variable in Michigan. Differences in mean biomass between the driest and the wettest year were up to 4 tim es larger than at potential production. The individual distributions exhibited higher variability as well (Figure 2 3C D). Coefficients of variations of up to 85% were observed in Florida. Most CVs in water stressed biomass were larger than the 40% reporte d at potential production. The CDFs shown in Figure 2 3 could also be used to provide a measure of the uncertainty in final biomass expressed in terms of agricultural risk assessment (Thornton and Wilk ens, 1998) because they represent the probability that the biomass is less than or equal to a specified value. For example, if a threshold of 10 t ha 1 was defined in Figure 2 3A as the minimum level of maize biomass that must be exceeded for a profitab le decision making to engage then the probability that the biomass would exceed the threshold given uncertainty in crop parameters would vary with year s approximately between 0.75 and 0.80 at potential level and 0.20 and 0.30 at water limited level in Flor ida (Figure 2 3 A and C ). To demonstrate that water stress introduced more uncertainty in annual biomass distribution at other locations, this same probability ranged between 0.25 and 0.40 for potential production, and 0.40 to 0.90 at water limited production lev el in North Carolina (Figure 2 3 B and D ). In conclusion biomass levels were significantly reduced when the effect of rainfall was accounted for in the model. With respect to the inter annual variability, the distribution of biomass was more stable at potential production level than at water limited level, suggesting that inter annual variability of rainfall was a major factor to consider when determining the uncertainty in biomass. The effect of the interaction

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66 between production level and lo cation on biomass may be due to the degree of rainfall variability at each location and soil variability among locations. Similar trends in uncertainty results were obtained for maize grain yield at all locations (Tables 2 1 4 and 2 1 5 ) However, for season length, there was no effect of production level on uncertainty results because the effect of water stress on growth duration was not modeled for any of the crops studied Further, uncertainty in season length was more pronounced in Iowa and Michigan than in Florida and North Carolina where crop duration was more stable both within and across years In terms of mean of the distribution of season length shown in Figure 2 4, the shortest season differed from the longest season by 6 days in Florida and North C arolina In contrast, this difference was 18 and 30 days respectively in Iowa and Michigan (Table 2 1 4 ) The yearly distributions were also characterized by CVs ranging from 15 to 17% in Florida and North Carolina and 8 to 21% in Michigan. Peanut and co tton Peanut biomass and yield levels were generally lower than those of maize Ranges from 4.0 to 26.5 t ha 1 at potential level and 1.6 to 20 t ha 1 at water limited level were observed. While potential peanut biomass tended to be similar across locations the highest water stressed biomass levels were attained in Georgia, North Carolina and Virginia (Table 2 1 4 ). Cotton biomass was more location dependent. For example, maximum potential biomass in any year was highest in Georgia (29 t ha 1 ) and lowest in North Carolina (23 t ha 1 ). Maximum water stressed cotton biomass was still highest in Georgia (22 t ha 1 ) and lowest at other locations (19 to 20 t ha 1 ).

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67 Differences among the means of peanut biomass distributions were smaller in Florida than other locations indicating that as found for maize, potential and water limited biomass was more stable under changes in weather across years. For cotton, Georgia was the location with the highest stability in mean biomass (Table 2 1 4 ). Georgia demonstrated also the narrowest range of standard deviation of biomass distribution for both peanut and cotton (Table 2 1 5 ). The yearly dis tributions of potential biomass were less variable when compared to maize (CVs of approximately 20% Rainfall had the same effect of increasing the variability among years without modify ing the shape of peanut and cotton dry matte r distribution (Figure 2 3C D) The CVs ranged from 19 to 33%, which was approximate ly the same at each location. This result suggested that despite observed differences in biomass, location had little effect on the ratio of standard deviation to mean biom ass. Biomass uncertainty results were similar to those of grain yield (Tables 2 1 4 an d 2 1 5 ). Peanut and cotton season length distributions shared similar characteristics although growth duration was larger for cotton (Figure 2 4). Mean season length incr eased from south to north (Table 2 1 4 ). Standard deviation also increased in the same direction but only for peanut (Table 2 1 5 ) because i n addition to longer crop durations, cotton was often affected i n cooler environments (Figure 2 4B and D). Therefore, u ncertainties in cotton (and peanut to a lesser extent) season length in cooler environments were compounded by the slow accumulation of thermal time (due to a larger base temperature Tables 2 11 and 2 12 ) that increased the crop duration and resulted in multimodal season length

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68 distributions. The yearly distributions of season length were characterized by CVs of These C Vs ranged from 8 to 15% for peanut and 0.4 to 14% for cotton. Sensitivity A nalysis Figure s 2 5 and 2 6 show PRCC values corresponding to the most frequently statistically significant parameters for biomass and season length for the first year of the simul ation at both production levels and two locations. These results indicated that regardless of the location and production level RLWR SnParLAI SnParRUE and TOpt were negatively related to grain yield while TBase MaxRUE MaxLAI TTMature RelTTSn and HrvIndex were positively related to grain yield Likewise, TOpt and HrvIndex were negatively related to season length while TBase and MaxLAI were positively related to season length. Biomass showed a relationship similar to that of grain yield except for H rvIndex that was weakl y negatively related (Table 2 1 6 ). The consistency of these relationships across locations was an indication that they reflected the model structure rather than a specific location The strength of these relationships varied, however, depending on location, production level and model output (Table s 2 1 6 to 2 18 ), and determined the importance of each parameter in the sensitivity analysis treatments. Effect of year on parameter ranking Ranking of model parameters was not significantly different among years at all locations and for all model outputs examined (biomass, grain yield and season length). The TDCC test of differences between parameter rankings in different years for each combination of location and production level produced a p value consistently smaller than 0.05. This result implied that inter annual variation in PRCC was not significantly

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69 large to translate into different order s of parameter ranking s among the years. Solar radiation, temperatures and rainfall were the weathe r variables that characterized the variability among years. The stability of the parameter rankings across years suggested that the relationships between the important model parameters and the model outputs studied were consistently maintained when these weather variables were varied from one year to another. Sensitivity to maize biomass and grain yield At all four locations, EmgInt EmgSlp and TTGerminate were not significant (p value from PRCC test smaller than 0.01) at both potential and wa ter limited levels By design RelTTSn2 StresLAI and StresRUE were not expected to be significant at pote ntial production because they a re used only when water stress occur s In Florida and North Carolina, the order of importance of the parameters for pot ential production was MaxLAI TTMature RelTTSn MaxRUE SnParLAI SnParRUE RelLAIP1 TOpt TBase RelLAIP2 and HrvIndex (Figure 2 7) A similar ranking was observed i n Iowa and Michigan (Table 2 1 6 ). For the water limited results RLWR became an import ant parameter for biomass at all locations (with PRCC values as high as 0. 77 in Florida) for two main reasons. First, the RLWR determined how much root length was produced and available for crop water uptake, hence played a major role in the calculation of plant water stress. Second, the uncertainty range of this parameter, as determined from the literature was relatively wide ( Jones et al. 1991) MaxLAI TTMature RelTTSn MaxRUE RLWR SnParLAI and SnParRUE were consistently ranked (in this order) as the most influential parameters except in Florida where RLWR was ranked first. The order of the remaining parameters, RelLAIP1 RelLAIP2 TOpt TBase StresLAI StresRUE RelTTSn2 and

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70 HrvIndex varied with location but generally TBase seemed to be more influential at higher latitudes (Iowa and Michigan) while TOpt was more important in Florida and North Carolina (see complete rankings in Figures 2 7 and 2 8) Rankings for biomass and grain yield were similar. The major difference between these two model outputs was that for grain yield, a new influential parameter, HrvIndex emerged with PRCC values as high as 0.70 in Florida (Figure 2 5) which is an obvious result since the portion of biomass in gr ain yield i s the harvest index. Maize season length The most striking feature of the sensitivity to season length was t hat it did not respond to some parameters that were the most influential factors of biomass and grain yield (Figure 2 6). Production level did not influence season length sensitivity because as mentioned earlier for uncertainty analysis, SALUS d oes not acc ount for the effect of water deficit on growth duration. Although the sensitive parameters were not affected by location, their ranking was. Only a few parameters were significant for season length and had a PRCC value larger or equal to 0.10 because in th e model, the duration of growth is not affected by some parameters that are the major determinant s of biomass and yield ( MaxRUE SnParRUE and RLWR ) They were TTMature RelTTSn MaxLAI TOpt RelLAIP1 TBase RelLAIP2 HrvIndex in this order (in Florida). In Iowa and Michigan, TBase was ranked second instead underlining the higher influence of TBase in cooler climates. For example, in Florida, TBase had a PRCC of 0.34 while TOpt had a PRCC of 0.42. In Michigan, the order of impo rtance of the PRCC was reversed to 0.36 (for TBase ) and 0.10 (for TOpt ).

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71 Peanut and cotton The major drivers of crop growth and development namely MaxLAI TTMature MaxRUE HrvIndex LAI parameters and temperature parameters were also significant for peanu t and cotton biomass and grain yield. The main differences with maize could be summarized as follows: i) the significant parameters had either large or small PRCC values suggesting that only a few parameters were truly influential on growth and developmen t of these two crops. T op ranked parameters were MaxLAI TTMature MaxRUE TBase TOpt and HrvIndex with their relative importance varying with location and model output (Figures 2 7 and 2 8); ii) the RLWR did not appear to be a major determinant of water limited biomass and grain yield. Values of PRCC as low as 0.13 were obtained in Virginia (Table s 2 1 7 and 2 18 ) ; iii) peanut season length variation was essentially dominated by TBase MaxLAI and TTMature with PRCC values of 0.8 0 0. 62 and 0.62 respectively in Florida (all other parameters had PRCC values equal to or smaller than 0. 40 in absolute value); iv) cotton season length variation could be essentially attributed to TBase and TOpt (in Florida) and TBase alone (in Virginia) with respective PRCC values of 0.87, 0.72 and 0.57. All other significant parameters had PRCC values smaller than 0.30. Specific rankings can be found in the logic diagram in Figures 2 7 and 2 8. Discussion of sensitivity analysis results Three parameters were consiste ntly found to be either non significant or significant with a weak relationship with the model outputs analyzed: EmgSlp EmgInt and TTGerminate These parameters were used in the model to predict germination and emergence dates. The results of the sensiti vity analysis suggested that at any of the locations of the study, these parameters did not play a significant role in the prediction

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72 of biomass, grain yield or season length within their ranges of uncertainty. These findings were in agreement with the mod eling philosophy of some authors who d id not predict germination explicitly based on a thermal time approach (Muchow and Carberry, 1989) Among the parameters the model was sensitive to, three categories can be distinguished: parameters directly related to biomass accumulation ( MaxRUE SnParRUE ), LAI parameters ( MaxLAI RelLAIP1 RelLAIP2 RelTTSn SnParLAI ), and temperature parameters ( TOpt and TBase ). In addition, some parameters, because of the specific role they play ed in determining targeted model outputs or production levels, were always significant in those situations: HrvIndex directly determined the fraction of biomass in grain yield; RLWR directly influenced crop water uptake and hence water limited production; TT Mature directly defined the season length (not valid for cotton) Parameters that modified LAI and RUE in the presence of water stress ( RelTTSn2 StresLAI and StresRUE ) were often significant when water stress was simulated but with relatively low PRCC val ues. For this group of parameters, the highest PRCC value (0.52) was obtained for StresRUE for peanut biomass in North Carolina. Biomass and grain yield were highly sensitive to MaxRUE that was used in the model to convert intercepted light into dry matte r. Biomass and grain yield were also highly sensitive to LAI parameters because they defined the maximum capacity of the canopy to capture light ( MaxLAI ), determined how fast this capacity could be reached ( RelTTSn RelLAIP1 and RelLAIP2 ), or lost ( SnParL AI ). The sensitivity of season length to MaxLAI was mainly due to the high correlation between MaxLAI and TTMature for maize and peanut. Season length in crop models has been found to be generally

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73 sensitive to crop duration parameters (for example, as foun d in the study by Pathak et al. 2007 ), however this was only observed for maize and peanut in this study. For cotton, uncertai nties in TBase and TOpt were sufficiently influential to mask the sensitivity of season length to the remaining parameters. Optimum temperature and RUE have been found ( in other studies using RUE based crop models ) as the most influential crop parameters (Confalonieri et al., 2010a) The high sensi tivity of TBase was also underlined in the sensitivity analysis by Richter et al. ( 2010) who reported it as a parameter of considerable importance for a wheat model. The variability in the ranking of most influential parame ters motivated the design of a logic diagram to summarize the results (Figures 2 7 and 2 8). Conclusion s Integration of the simple SALUS model in DSSAT involved the implementation of a number of modifications. The original version of SALUS appeared to be adequate for simulating potential production. However, response of LAI and biomass growth to water stress was hardly noticeable. Modifications to the model that has now become DSSAT SALUS included an improvement to the LAI growth rate computation, an account for the effect of water stress on LAI sene scence and RUE decline, the initialization of total dry matter at emergence, and a change in the response of crop growth to cold temperatures. These improvements produced a more robust model for studying the relationships between crop parameters and model outputs across a range of environments. Results of the u ncertainty analysis showed that yearly cumulative distribution functions ( CDFs ) were more stable at potential production than at water limited production level for maize, peanut and cotton. The year t o year variability in these CDFs

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74 was smaller at lower latitudes and warmer climates (Florida and Georgia) and greater at higher latitudes and cooler climates (North Carolina, Virginia, Iowa, and Michigan). The simulation of water stress decreased biomass a nd yield but increased the uncertainty associated with them. Uncertainty in season length was not affected by water stress because the SALUS model did not modify the accumulation of daily thermal time in the presence of water deficits. At higher latitudes, cooler temperatures resulted in longer season duration s and more variability in model ou tputs, hence higher uncertainty. R anking of important model parameters was not affected by the year under consideration. In general, the model was not sensitive to pa rameters related to prediction of the timing of germination ( TTGerminate ) and emergence ( EmgInt and EmgSlp ). Regardless of location, production level, and model output examined, the most influential parameters were related to LAI growth ( MaxLAI RelTTSn R elLAIP1 and RelLAIP2 ), crop duration ( TTMature ), and temperature ( TBase and TOpt ). Biomass accumulation parameters ( MaxRUE SnParRUE and SnParLAI ) were particularly influential on biomass and grain yield, harvest index ( HrvIndex ) was particularly important for grain yield, and TTMature was the primary determinant of season length (except for cotton where TBase and TOpt were the main drivers of season length). The main site effect was base temperature, which was more influential tha n the optimum temperature in cooler environments (Iowa and Michigan for maize, North Carolina and Virginia for peanut and cotton). The primary effect of production level was that the RLWR was influential for water limited maize biomass and grain yield beca use of the role of this parameter in root water uptake. Similarly to uncertainty analysis, sensitivity of crop parameters to season length was not affected by water stress.

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75 Variability in crop yield, biomass and season length was strongly dependent on cro p parameter uncertainty. A large number of the parameters were influential on the model outputs, only their relative importance varied with specific situations (combinations of crop, production level, location, and model output). Since common applications of crop models involve one or a combination of these situations, it is adequate to infer that all 15 parameters that were regularly significant are important for accurate crop predictions. Additionally, v ariability in model outputs may be dependent on how well the distributions of the crop parameters represent the true parameter uncertainty. Obtaining parameter uncertainty ranges is usually complicated by the variability in measurement methods used in the literature that may inflate measurement errors thems elves. Results from this study confirmed the efficiency of the LH sampling method through the stability of model results at small sample sizes. Result stability at low sample sizes will be even more critical in reducing computational costs as the number of parameters involved in the analysis increases. Findings reported in this study assisted with identify ing parameters that require accurate estimation, and those that may be viewed as candidates in model simplification. In particular, since RUE decline and LAI senescence were modeled similarly, it was not necessary to specify two different crop parameters to characterize their shape. Additionally, ongoing model improvement involves the implementation of a dynamic harvest index to reflect the response of grai n growth in the presence of water stress. The next step in the integration of SALUS in DSSAT will consist of estimating parameters for a number of annual crops.

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76 Table 2 1. List of variables used to describe the SALUS model No. Variable Type Unit Definition 1 Rate g m 2 day 1 Rate of total dry matter growth 2 Rate m 2 m 2 day 1 Rate of LAI growth or decline 3 DM State g m 2 Mass of t otal dry matter 4 Rate day 1 Change in RelLAI relative to the previous day 5 Rate g m 2 day 1 Rate of root growth 6 Rate g m 2 day 1 Rate of aboveground dry matter growth 7 IPAR Input MJ m 2 day 1 Intercepted P hotosynthetically A ctive R adiation 8 KCan Parameter Canopy extinction coefficient 9 LAI State m 2 m 2 Leaf area index 10 LAIP1 Parameter Point on generic LAI curve with coordinates (RelTT = 0.15, RelLAI = RelLAIP1) 11 LAIP2 Parameter Point on generic LAI curve with coordinates (RelTT = 0.50, RelLAI = RelLAIP2) 12 PAR Input MJ m 2 day 1 Photosynthetically active radiation 13 PlantingDepth Input cm Planting depth 14 PlantPop Input plant m 2 Plant population 15 RelTT Auxiliary Relative thermal time 16 RelLAI Auxiliary Relative leaf area index 17 RootFracLive Parameter Fraction of root dry matter in live roots 18 Roots State g m 2 Mass of roots 19 RootPartCoef Auxiliary Root partitioning coefficient (fraction of total dry matter present in roots) 20 RowSpacing Input cm Row spacing 21 StressFactors Auxiliary Water and nutrient stress factors 22 Tops State g m 2 Mass of aboveground dry matter 23 TTEmerge Auxiliary o C Thermal time from germination to emergence

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77 Table 2 2 List of SALUS crop model parameters and definitions No. Parameter Unit Definition 1 EmgInt o C Intercept of emergence thermal time calculation 2 EmgSlp o C cm 1 Slope of emergence thermal time calculation 3 HrvIndex Crop harvest index 4 MaxLAI m 2 m 2 Maximum expected Leaf Area Index 5 RelLAIP1 Parameter for shape at point 1 on the potential LAI curve 6 RelLAIP2 Parameter for shape at point 2 on the potential LAI curve 7 RelTTSn Relative thermal time at beginning of senescence 8 RelTTSn2 Relative thermal time beyond which the crop is no longer sensitive to water stress 9 RLWR cm g 1 Root length to weight ratio 10 RUEMax g MJ 1 Maximum expected Radiation Use Efficiency 11 SeedWt g seed 1 Seed weight 12 SnParLAI Parameter for shape of potential LAI curve after beginning of senescence 13 SnParRUE Parameter for shape of potential RUE curve after beginning of senescence 14 StresLAI Factor by which LAI senescence due to water stress is increased between RelTTSn and RelTTSn2 15 StresRUE Factor by which RUE decline due to water stress is accelerated after the beginning of leaf senescence 16 TBaseDev o C Base temperature for development 17 TFreeze o C Threshold temperature below which crop development and growth stop 18 TOptDev o C Optimum temperature for development 19 TTGerminate o C Thermal time from planting to germination 20 TTMature o C Thermal time from planting to maturity Table 2 3 Characterization of the locations of the uncertainty and sensitivity analysis Soil Average solar radiation (MJ m 2 ) Average maximum temperature ( o C) Average minimum temperature ( o C) Total annual rainfall (mm) Gainesville FL Millhopper Fine Sand, Typic Paleudults 16.11 27.58 14.66 1271 Camilla GA Loamy sand Thermic Arenic Paleudult 16.75 25.76 12.84 1266 Clayton NC Norfolk Sandy, Clay Loam 13.93 21.67 9.55 1124 Suffolk VA Suffolk Loamy sand 13.99 20.99 9.62 1183 Ames IA Typic Hapludoll, Clarion Loam 13.55 15.45 3.54 804 KB S MI Typic Hapludalf, Kalamazoo Loam 13.68 14.5 0 4.11 908

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78 Table 2 4 Specification of treatments and total number of runs required for the uncertainty and sensitivity analysis Maize Peanut Cotton Locations (states) (4 levels) Florida, North Carolina, Iowa, Michigan Florida, Georgia, North Carolina, Virginia Florida, Georgia, North Carolina, Virginia Years (10) 10 years 10 years 10 years Production level (2) Potential and water limited Potential and water limited Potential and water limited Total number of treatments 80 80 80 Number of model runs per treatment 10,000 10,000 10,000 Total number of model runs 800,000 800,000 800,000 Table 2 5 Specification of treatments used for generating the simulated data Maize Peanut Cotton Cultivars (4 levels) Generic long, medium, short, and very short season (DSSAT database) Spanish type, Early Bunch, Florunner, Southern Runner (Bell et al., 1991) Acala, Deltapine 77, Deltapine 555, Georgia King (Grimes et al., 1975; Ortiz et al., 2009) Locations (states 4 levels) Florida, North Carolina, Iowa, Michigan Florida, Georgia, North Carolina, Virginia Florida, Georgia, North Carolina, Virginia Planting dates (3 levels) Early, medium, late Early, medium, late Early, medium, late Plant population (plants m 2 3 levels ) 4, 6, 8 (Kiniry et al., 1992) 5.6 (Bell et al., 1991) 8.8 (Bell et al., 1987) 12.9 (Boote, 1982) 5 (Fye, 1984) 10.5 (Reddy and Baker, 1988) 14 (Ortiz et al., 2009) Total number of treatments 144 144 144

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79 Table 2 6 Growth and development coefficients for the four maize cultivars used in producing the synthetic data Definition DSSAT ID Very short Short Medium Long Degree days (base 8 o C) from emergence to end of juvenile phase ( o C) P1 5 110 200 320 Photoperiod sensitivity (day hr 1 ) P2 0.30 0.30 0.30 0.52 Degree days (base 8 o C) from silking to physiological maturity ( o C) P5 680 680 800 940 Potential kernel number (plant 1 ) G2 820 820 700 620 Potential kernel growth rate (mg day 1 ) G3 6.60 6.60 8.50 6.00 Phyllochron ( o C ) PHINT 38.90 38.90 38.90 38.90 Table 2 7 Growth and development coefficients for the four peanut cultivars used in producing the synthetic data Definition DSSAT ID Spanish type Early Bunch Florunner Southern Runner Photothermal days from emergence to first flower EM FL 17.40 21.90 21.20 22.90 Photothermal days from first flower to first pod FL SH 7.00 7.60 9.20 8.20 Photothermal days from first flower to first seed FL SD 17.50 16.50 18.80 18.20 Photothermal days from first seed to physiological maturity SD PM 62.00 72.40 74.30 82.60 Photothermal days from first flower to end of leaf expansion FL LF 67 77 85 88 Maximum leaf photosynthesis rate, mg CO 2 m 2 s 1 LFMAX 1.28 1.34 1.40 1.30 Specific leaf area, cm 2 g 1 SLAVR 245 270 260 265 Maximum size of full leaf, cm 2 SIZLF 16 20 18 17 Maximum fraction of d aily growth partitioned to seed and shell XFRT 0.84 0.93 0.92 0.84 Maximum weight per seed (g) WTPSD 0.36 1.10 0.68 0.63 Photothermal days for seed filling per individual seed SFDUR 29 44 40 40 Average seed number per pod SDPDV 1.65 1.65 1.65 1.65 Photothermal days to reach full pod load PODUR 15 22 24 30 Maximum ratio of seed/(seed and shell) at maturity THRSH 78 75 80 79

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80 Table 2 8 Growth and development coefficients for the four cotton cultivars used in producing the synthetic data Definition DSSAT ID Acala Deltapine 77 Deltapine 555 Georgia King Photothermal days from emergence to first flower EM FL 29 34 40 45 Photothermal days from first flower to first pod FL SH 8 8 12 11 Photothermal days from first flower to first seed FL SD 12 15 17 17 Photothermal days from first seed to physiological maturity SD PM 46 49 45 45 Photothermal days from first flower to end of leaf expansion FL LF 52 75 75 75 Maximum leaf photosynthesis rate, mg CO 2 m 2 s 1 LFMAX 1.1 1.1 1.1 1.1 Specific leaf area, cm 2 g 1 SLAVR 250 170 170 170 Maximum size of full leaf, cm 2 SIZLF 270 280 300 300 Maximum fraction of daily growth partitioned to seed and shell XFRT 0.75 0.9 0.65 0.75 Maximum weight per seed (g) WTPSD 0.18 0.18 0.18 0.18 Photothermal days for seed filling per individual seed SFDUR 22 35 35 35 Average seed number per boll SDPDV 27 27 27 27 Photothermal days to reach full boll load PODUR 8 8 10 8 Maximum ratio of seed/(seed and shell) at maturity THRSH 74 74 74 74

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81 Table 2 9 Pearson correlation coefficients between crop parameters derived from synthetic data for maize, peanut, and cotton HrvIndex MaxLAI RelLAIP1 RelLAIP2 RelTTSn SnParLAI TTMature Maize HrvIndex 1 0.70 0.64 0.38 0.67 0.10 0.74 MaxLAI 0.70 1 0.72 0.43 0.81 0.10 0.91 RelLAIP1 0.64 0.72 1 0.20 0.52 0.08 0.75 RelLAIP2 0.38 0.43 0.20 1 0.78 0.43 0.55 RelTTSn 0.67 0.81 0.52 0.78 1 0.22 0.87 SnParLAI 0.10 0.10 0.08 0.43 0.22 1 0.07 TTMature 0.74 0.91 0.75 0.55 0.87 0.07 1 Peanut HrvIndex 1 0.19 0.33 0.05 0.33 0.33 0.31 MaxLAI 0.19 1 0.65 0.57 0.10 0.59 0.85 RelLAIP1 0.33 0.65 1 0.65 0.30 0.18 0.49 RelLAIP2 0.05 0.57 0.65 1 0.72 0.06 0.50 RelTTSn 0.33 0.10 0.30 0.72 1 0.38 0.11 SnParLAI 0.33 0.59 0.18 0.06 0.38 1 0.51 TTMature 0.31 0.85 0.49 0.50 0.11 0.51 1 Cotton HrvIndex 1 0.83 0.28 0.73 0.59 0.70 0.54 MaxLAI 0.83 1 0.33 0.70 0.53 0.60 0.45 RelLAIP1 0.28 0.33 1 0.01 0.06 0.09 0.19 RelLAIP2 0.73 0.70 0.01 1 0.81 0.54 0.26 RelTTSn 0.59 0.53 0.06 0.81 1 0.30 0.06 SnParLAI 0.70 0.60 0.09 0.54 0.30 1 0.49 TTMature 0.54 0.45 0.19 0.26 0.06 0.49 1

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82 Table 2 10 Statistical distributions of SALUS crop parameters for maize Parameter a Distribution Parameter 1 b Parameter 2 b Source c EmgInt Uniform 22 47.43 (Alessi and Power, 1971; Gupta et al., 1988) EmgSlp Uniform 2.6 7.6 (Alessi and Power, 1971; Gupta et al. 1988) HrvIndex Normal 0.46 0.09 Simulated data; (Kiniry et al., 1992) (MaxLAI) 0.5 Normal 1.67 0.53 Simulated data; (Lindquist et al., 2005) LAIP1 Normal 3.47 0.61 Simulated data LAIP2 Normal 14.89 2.43 Simulated data RelTTSn Normal 0.48 0.06 Simulated data; (Kiniry et al., 1995) RelTTSn2 Uniform 0.55 0.90 RLWR Uniform 798 12000 (Follett et al., 1974; Grant, 1989) MaxRUE Normal 3.50 0.70 (Kiniry et al., 1989; Lindquist et al., 2005) SnParLAI* N(10,2) Normal 3.12 0.67 Simulated data; (Kiniry et al., 1995) SnParRUE* N(10,2) Normal 3.12 0.67 Simulated data; (Kiniry et al., 1 995) StresLAI Uniform 1 10 StresRUE Uniform 1 10 TBaseDev Normal 8.50 0.50 (Warrington and Kanemasu, 1983; Hatfield et al., 2008) TOptDev Normal 29.50 1.50 (Kiniry and Bonhomme, 1991; Kiniry et al., 1992) TTGerminate Uniform 7 30 (Muchow and Car berry, 1989; Hayhoe et al., 1996) TTMature Normal 1508 344 (Narwal et al., 1986; Kiniry et al., 1992) a sqrt( MaxLAI) is root squared transformation of MaxLAI; SnParLAI*N(10,2) is the SnParLAI multiplied by an arbitrary normal distribution with mean 10 and standard deviation 2 (see text). b Parameter 1 and Parameter 2 are lower and upper bounds if distribution is u niform; mean and standard deviation if distribution is normal. c See text for a full discussion of all sources used.

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83 Table 2 1 1 Statistical distributions of SALUS crop parameters for peanut Parameter a Distribution Parameter 1 b Parameter 2 b Source c EmgInt Uniform 15 59.5 (Ketring and Wheless, 1989; Robertson et al., 2002) EmgSlp Uniform 5.5 7.6 (Angus et al., 1981; Gupta et al., 1988) HrvIndex Normal 0.43 0.05 Simulated data; (Bell and Wright, 1998) (MaxLAI) 2 Normal 31.30 14.12 Simulated data; (Kiniry et al., 2005) LAIP1 Normal 3.84 0.42 Simulated data LAIP2 Normal 13.10 0.97 Simulated data (RelTTSn) 2 Normal 0.38 0.50 Simulated data RelTTSn2 Uniform 0.55 0.90 RLWR Uniform 6500 9500 (Boote et al., 1985; Robertson et al., 2002) MaxRUE Normal 2.10 0.30 (Robertson et al., 2002; Kiniry et al., 2005) SnParLAI Normal 0.10 0.02 Simulated data SnParRUE Normal 0.10 0.02 Simulated data StresLAI Uniform 1 10 StresRUE Uniform 1 10 TBaseDev Normal 11.50 0.83 (Boote et al., 1985; Hatfield et al., 2008) TOptDev Normal 32.75 1.25 (Ong, 1985; Bell and Wright, 1998) TTGerminate Uniform 9 42 (Robertson et al., 2002) TTMature Normal 1743 138 Simulated data; (Ketring and Wheless, 1989) a The parameter or its transformed version that is normal is specified. b Parameter 1 and Parameter 2 are lower and upper bounds if distribution is uniform; mean and standard deviation if distribution is normal. c See text for a full discussion of all sources used.

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84 Table 2 1 2 Statistical distributions of SALUS crop parameters for c otton Parameter a Distribution Parameter 1 b Parameter 2 b Source c EmgInt Uniform 15 59.5 (Ketring and Wheless, 1989; Robertson et al., 2002) EmgSlp Uniform 5.5 7.6 (Angus et al., 1981; Gupta et al., 1988) HrvIndex Normal 0.41 0.06 Simulated data; (Ko et al., 2009) MaxLAI Normal 3.86 0.88 Simulated data; (Ko et al., 2009) LAIP1 Normal 4.97 0.78 Simulated data LAIP2 Normal 15.38 2.66 Simulated data (RelTTSn) 0.5 Normal 0.83 0.09 Simulated data RelTTSn2 Uniform 0.55 0.90 RLWR Uniform 6500 9600 (Van Noordwijk and Brouwer, 1991; Robertson et al., 2002) MaxRUE Normal 2.50 0.17 (Gallagher and Biscoe, 1978; Ko et al., 2009) SnParLAI Normal 0.05 0.03 Simulated data SnParRUE Normal 0.05 0.03 Simulated data StresLAI Uniform 1 10 StresRUE Uniform 1 10 TBaseDev Normal 12.50 0.83 (Reddy, 1994; Ko et al., 2009) TOptDev Normal 31.00 1.33 (Reddy, 1994; Roussopoulos et al., 1998) TTGerminate Uniform 10 45 (Robertson et al., 2002) TTMature No rmal 1995 277 Simulated data; (Wanjura and Supak, 1985) a The parameter or its transform ed version that is normal is specified. b Parameter 1 and Parameter 2 are lower and upper bounds if distribution is uniform; mean and standard deviation if distribution is normal. c See text for a full discussion of all sources used.

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85 Table 2 1 3 Top down correlation coefficients (TDCC) with corresponding p values resulting from the comparison between rankings at 50,000 runs and the indicated number of runs Number of Biomass Duration Grain yield model runs Potential Water limited Potential Water limited Potential Water limited 1000 TDCC 0.999 0.992 0.973 0.961 0.996 0.992 p value 0.003 0.002 0.004 0.002 0.003 0.002 5000 TDCC 0.996 0.982 0.991 0.981 0.999 0.986 p value 0.003 0.002 0.003 0.002 0.003 0.002 10000 TDCC 1 0.993 0.986 0.981 0.999 1 p value 0.003 0.002 0.003 0.002 0.003 0.002 30000 TDCC 1 1 0.998 0.998 0.998 1 p value 0.003 0.002 0.003 0.002 0.003 0.002 40000 TDCC 1 1 0.999 0.997 0.998 1 p value 0.003 0.002 0.003 0.002 0.003 0.002

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86 Table 2 1 4 Minimum and maximum values of mean biomass, grain yield and season length (based on 10000 simulations) over the 10 years of the study for maize, peanut and cotton Biomass (kg ha 1 ) Grain yield (kg ha 1 ) Season length (days) Location Potential Water limited Potential Water limited Potential Water limited Maize Gainesville FL 14180 2905 6173 1229 101 101 16327 5738 7129 2493 107 107 Clayton NC 12372 3802 5374 1647 107 107 13948 10071 6084 4399 114 114 Ames IA 14712 7437 6411 3260 112 112 17618 14905 7688 6483 130 130 KBS MI 14537 6719 6390 2873 117 117 18448 14968 8077 6532 147 147 Peanut Gainesville FL 12257 5844 5227 2491 119 119 13796 8701 5886 3715 124 124 Camilla GA 13058 6234 5563 2670 118 118 14971 9433 6394 4034 125 125 Clayton NC 11312 4852 4826 2069 131 131 13829 9931 5908 4252 149 149 Suffolk VA 12402 6859 5289 2937 133 133 14591 11701 6239 5000 163 163 Cotton Gainesville FL 11846 6156 4839 2517 152 152 14028 9870 5720 4018 158 158 Camilla GA 14336 6832 5854 2766 156 156 15779 9433 6445 3825 171 171 Clayton NC 11574 5605 4723 2285 162 162 13972 10393 5723 4240 197 197 Suffolk VA 10524 7296 4286 2962 163 163 14361 11017 5884 4498 212 212

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87 Table 2 1 5 Minimum and maximum values of standard deviation of biomass, grain yield and season length (computed based on 10000 simulations) over the 10 years of the study for maize, peanut and cotton Biomass (kg ha 1 ) Grain yield (kg ha 1 ) Season length (days) Location Potential Water limited Potential Water limited Potential Water limited Maize Gainesville FL 5743 2466 2143 945 17 17 6460 3642 2401 1390 17 17 Clayton NC 4843 2044 1822 762 17 17 5747 4589 2129 1702 19 19 Ames IA 5933 3566 2244 1405 17 17 7088 7059 2645 2764 24 24 KBS MI 5003 4085 2004 1534 11 11 7468 7012 2803 2780 30 30 Peanut Gainesville FL 2377 1517 1053 670 10 10 2652 2294 1170 971 10 10 Camilla GA 2671 1463 1189 635 10 10 2816 2247 1256 976 12 12 Clayton NC 2585 1201 1136 520 12 12 2967 2161 1300 924 22 22 Suffolk VA 2304 1564 1033 675 10 10 3082 2876 1340 1219 24 24 Cotton Gainesville FL 2392 1444 873 505 14 14 2949 2353 1067 832 16 16 Camilla GA 2929 1812 1067 671 12 12 3440 2799 1245 990 24 24 Clayton NC 2162 1257 873 453 1 1 2654 2317 1006 817 16 16 Suffolk VA 1986 1836 808 626 1 1 2786 2511 1057 894 13 13

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88 Table 2 1 6 PRCC between total maize biomass and significant crop model parameters at four locations Gainesville FL Clayton NC Ames IA KBS MI Potential Water Potential Water Potential Water Potential Water HrvIndex 0.16 0.09 0.16 0.13 0.15 0.08 0.13 0.15 MaxLAI 0.93 0.65 0.94 0.74 0.93 0.75 0.92 0.79 TTMature 0.93 0.65 0.94 0.74 0.93 0.75 0.92 0.79 RelTTSn 0.93 0.65 0.94 0.74 0.93 0.75 0.92 0.79 RelLAIP1 0.44 0.2 0.44 0.27 0.42 0.21 0.4 0.33 RelLAIP2 0.18 0.23 0.17 0.33 0.16 0.16 0.15 0.37 SnParLAI 0.54 0.26 0.53 0.33 0.53 0.33 0.5 0.4 SnPar RUE 0.54 0.26 0.53 0.33 0.53 0.33 0.5 0.4 MaxRUE 0.81 0.5 0.81 0.57 0.81 0.65 0.81 0.6 TBaseDev 0.21 0.13 0.21 0.17 0.21 0.07 0.22 0.24 TOptDev 0.32 0.15 0.32 0.17 0.26 0.1 0.09 0.1 RLWR 0 0.77 0 0.68 0 0.67 0 0.53 RelTTSn2 0.01 0.10 0.01 0.09 0.01 0.16 0.01 0.15 StresLAI 0.00 0.16 0.00 0.17 0.00 0.19 0.01 0.20 StresRUE 0.01 0.23 0.01 0.26 0.01 0.27 0.02 0.29 Table 2 1 7 PRCC between total peanut biomass and significant crop model parameters at four locations Gainesville FL Camilla GA Clayton NC Suffolk VA Potential Water Potential Water Potential Water Potential Water HrvIndex 0.22 0.17 0.2 0.23 0.24 0.2 0.21 0.21 MaxLAI 0.73 0.71 0.72 0.66 0.72 0.73 0.7 0.69 TTMature 0.73 0.71 0.72 0.66 0.72 0.73 0.7 0.69 RelLAIP1 0.03 0.09 0.02 0.21 0.09 0.06 0.06 0.22 RelLAIP2 0.23 0.22 0.22 0.16 0.23 0.12 0.2 0.13 RelTTSn 0.02 0.07 0.02 0.13 0.01 0.12 0.01 0.08 SnParLAI 0.12 0.11 0.12 0.18 0.11 0.19 0.11 0.18 SnParRUE 0.12 0.11 0.12 0.18 0.11 0.19 0.11 0.18 MaxRUE 0.91 0.89 0.93 0.93 0.88 0.93 0.9 0.89 TBaseDev 0.61 0.45 0.58 0.59 0.7 0.53 0.68 0.61 TOptDev 0.3 0.18 0.35 0.36 0.25 0.19 0.1 0.11 RLWR 0 0.19 0 0.3 0 0.24 0 0.13 RelTTSn2 0.01 0.00 0.02 0.13 0.01 0.16 0.01 0.16 StresLAI 0.03 0.01 0.03 0.08 0.03 0.09 0.03 0.07 StresRUE 0.00 0.06 0.01 0.48 0.01 0.52 0.01 0.44

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89 Table 2 1 8 PRCC between total cotton biomass and significant crop model parameters at four locations Gainesville FL Camilla GA Clayton NC Suffolk VA Potential Water Potential Water Potential Water Potential Water HrvIndex 0.14 0.07 0.14 0.1 0.02 0.05 0.03 0.01 MaxLAI 0.66 0.71 0.63 0.6 0.65 0.62 0.68 0.66 TTMature 0.66 0.71 0.63 0.6 0.65 0.62 0.68 0.66 RelLAIP1 0.23 0.26 0.21 0.29 0.19 0.13 0.22 0.06 RelLAIP2 0.16 0.08 0.15 0.22 0.17 0.14 0.2 0.13 RelTTSn 0.05 0.18 0.03 0.29 0.15 0.31 0.18 0.29 SnParLAI 0.2 0.15 0.2 0.28 0.12 0.25 0.09 0.14 SnParRUE 0.2 0.15 0.2 0.28 0.12 0.25 0.09 0.14 MaxRUE 0.9 0.93 0.89 0.9 0.9 0.91 0.91 0.91 TBaseDev 0.61 0.25 0.65 0.31 0.07 0.04 0.35 0.26 TOptDev 0.47 0.2 0.42 0.17 0 0.05 0.11 0.05 RLWR 0 0.31 0 0.29 0 0.26 0 0.15 RelTTSn2 0.01 0.02 0.01 0.12 0.01 0.13 0.01 0.05 StresLAI 0.00 0.01 0.00 0.10 0.01 0.09 0.01 0.04 StresRUE 0.00 0.12 0.01 0.26 0.01 0.28 0.01 0.14

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90 Figure 2 1. Diagram of the SALUS model showing the main crop growth and development processes

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91 A B C D Figure 2-2. Generic LAI curve and effect of water stress on leaf senescence and RUE as modeled in SALUS. A) Generic LAI function showing various parameters from Table 2-2 used to characterize the curve, B) Relationship between senescence parameter and water stress, C) Effect of wa ter stress on LAI decline, and D) Effect of water stress on biomass accumulation. Simulations in C) and D) are compared with data collected in a maize rainfed experiment in Gainesville, FL in 1982. 0.00.20.40.60.81.0 0.0 0.2 0.4 0.6 0.8 1.0 Relative thermal timeRelative Leaf Area Index LAIP1 LAIP2 RelTTP1RelTTP2 RelLAIP1 RelLAIP2 RelTTSn2 y = x x + eLAIP1 LAIP2x y = 1.001 x 1 RelTTSn SnParLAI 0.00.20.40.60.81.0 0 00 51 01 5 Water stress (0 = maximum stress, 1 = no stress)Senescence parameter (accelerates senescence) 2SnParLAI SnParLAI StresLAI = 2 StresLAI = 5 0.00.20.40.60.81.0 01234 Relative thermal timeMaize LAI (m2 m 2) RelTTSn RelTTSn2 Modified SALUS Original SALUS Observed, Rainfed 0.00.20.40.60.81.0 0200040006000800010000 Relative thermal timeMaize biomass (kg ha 1) RelTTSn RelTTSn2 Modified SALUS Original SALUS Observed, Rainfed

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92 A B C D Figure 2 3 Cumulative distribution function of maize, peanut and cotton potential and water limited biomass over th e 10 years of the study at A and C ) Gainesville, B and D ) Clayton, North Carolina

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93 A B C D Figure 2 4 Cumulative distribution function of maize, peanut and cotton potential and water limited season length over the 10 years of the study at A and C ) Gainesville, B and D ) Clayton, North Carolina

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94 A B C D Figure 2 5 Partial rank correlation coefficients between potential and water limited maize, peanut and cotton grain yield and significant SALUS crop parameters in the first year of the study at A and C ) Gainesville, Florida, B and D ) Clayton, North Carolina

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95 A B C D Figure 2 6 Partial rank correlation coefficients between potential and water limited maize, peanut and cotton season length and significant SALUS crop parameters in the first year of the study at A and C ) Gainesville, Florida, B and D ) Clayton, North Carolina

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96 Figure 2 7 Logic diagram of the most sensitive SALUS model parameters ( statistically significant with PRCC absolute value larger or equal to 0.10) as dependent on crop, model output and production level for a warmer climate (Florida). Biomass and grain yield had the same rankings except for harvest index that was regularly ranked higher fo r grain yield as shown in parenthesis.

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97 Figure 2 8. Logic diagram of the most sensitive SALUS model parameters ( statistically significant with PRCC absolute value larger or equal to 0.10) as dependent on crop, model output and production level for a coo ler climate (Michigan for maize and Virginia for peanut and cotton). Biomass and grain yield had the same rankings except for harvest index that was regularly ranked higher for grain yield as shown in parenthesis.

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98 CHAPTER 3 PARAMETER ESTIMATION OF THE SALUS CROP MO DEL FOR MAIZE, PEANU T, AND COTTON USING A M ARKOV CHAIN MONTE CA RLO APPROACH Introduction A crop model relies on a number of parameters to calculate the development stages and growth characteristics of crops. While the model describes t he functional relationships between a crop and its environment, these parameters supply the necessary information for characterizing variation in physiological responses to the crop environment across species, ecotypes and cultivars. The ability of a crop model to capture cultivar and species differences therefore depends largely on the quality of parameters used to model these differences. Parameter estimation is one of the critical components in model development, improvement and simplification. In partic ular, estimation of the most influential parameters identified through a sensitivity analysis is necessary to establish the responses of different genotypes to a range of environments. Parameters can be estimated from literature, data, expert knowledge or a combination of all these sources depending on the approach used. In the frequentist approach to parameter estimation, the parameter is considered to have a true, fixed value that can be estimated by obtaining a random sample of data from an experiment (Ellison, 1996) This approach is solely based on ava ilable data and since the true value of the parameter is unknown, a confidence interval constructed about the estimated parameter value captures the true value in of all possible samples. A more transferrable result would be an interval that contains of all possible parameter values (Ellison, 1996) or better a probability distribution of the parameter that quantifies the uncertainty about the parameter given the data: this is the typical methodology of a Bayesian approach (Makowski et al., 2002)

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99 The Bayesian approach integrates s everal sources of information about the parameter treated as a random variable for which a posterior distribution can be derived by combining prior knowledge (range, distribution) with observed data. Prior to collecting data, a n uncertainty range can be de fined, for example based on the variability in the parameter values found in the literature. A distribution may also be obtained from expert knowledge or synthetic data. This prior knowledge is inevitably associated with some level of uncertainty attributa ble to the variability inherent to disagreement in literature values or expert opinions. This variability is precisely what is captured through a prior probability distribution. Because this approach does not seek to calculate a fixed value, prior uncertai nty is not lost and can be used to evaluate the consequences of incorrect assumption s about the parameter on model predictions (Makowski et al., 2002) The Bayesian approach further associates a likelihood function to the data, which is t he probability of observing the data conditional upon the parameter. In theory, the posterior parameter distribution can be calculated using Bayes theorem. In practice, it is not possible to calculate analytically the posterior distribution due to the comp lexity involved in solving multidimensional integrals generated by multiple observations a high number of parameters, and a non linear model. Numerical techniques based on Monte Carlo simulations whose success was largely dependent on the advance of compu ters are the most efficient way of actually implementing a Bayesian parameter estimation. One of the most recognized methods originally used by physicists is the Metropolis algorithm (Metropolis et al., 1953) later generalized as the Metropolis Hastings (MH) algorithm (Hastings, 1970) The purpose of this method is to

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100 generate parameter samples that would converge to the target, posterior distribution of interest. The Metropolis Hastings algorithm is a Markov Chain Monte Carlo (MCMC) method because it relies on the current value of the parameter to determine the next sample in the sequence. The Bayesian approach based on the MCMC MH has been increasingly popular in the literature and applications in various fields including hydrology (Bates and Campbell, 2001) forestry (Ceglar et al., 2011) large scale crop modeling (Iizumi et al., 2009) astrophysics (Putze et al., 2010) and field scale crop modeling (Makowski et al., 2002) have been reported. Accounting for prior information in Bayesian parameter estimation provide s a means for detecting complicated patterns in massive datasets or experimental outcomes influenced by multiple variables (Malakoff, 1999) A comprehensive description and analysis of the MH algorithm can be found in Chib and Greenberg ( 1995) This paper use s the Metropolis Hastings algorithm as a parameter estimation t echnique to answer a number of questions related to the SALUS model development and testing 1. Can the Metropolis Hastings algorithm be used to derive parameter sets for different maturity groups in maize, peanut and cotton using prior knowledge on the param eters and available data? 2. Does the availability of detailed, in season data improve the accuracy of estimated parameters over the use of limited, end of season data only? 3. Can a simplified, generic model like SALUS perform similarly to more complex models To answer the questions stated above, this paper examine d the following objectives 1. D evelop and apply a parameter estimation procedure for simulating maize, peanut and cotton in the SALUS crop model based on a Bayesian approach;

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101 2. C ompare two methods of parameter estimation, one based on detailed, in season data and another based on limited, end of season data, and determine if reliable parameter estimates could be obtained in the case of the availability of on ly limited data; 3. E valuate the performance of two types of crop models, a complex model (from DSSAT, CERES and CROPGRO) and a simple model (SALUS) and assess if the simple SALUS model regarded as a simplification of the DSSAT models has a comparable perfor mance; 4. T est the validity of estimated parameters using independent data. Bayesian Approach to P arameter E stimation The original question that gave rise to Bayesian statistics was how would one update existing information (say, about a parameter) when pres ented with new evidence (e.g. data from an experiment). The answer was a theorem, proposed by Bayes in the 1760s, and was based on conditional probability theory (Malakoff, 1999) The Bayesian approach to parameter estimation is a method for finding the posterior distribution of a parameter by combining the prior parameter distribution and the likelihood of the data. For a crop model with parameters to estimate (3 1) the Bayesian approach cons iders each of these parameters as a random variable that has a probability distribution ( termed prior distribution, ) which encapsulates information about the parameter prior to observing the data. Because the true value of the parameter is unknown, th described with a certain degree of uncertainty characterized by a range or a statistical distribution. Each sample of with the prior dis tribution one can generate several samples of resulting in several realizations of model outputs with equivalent model errors computed relative to the data. The distribution of this error (between model predictions and experimental observations)

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102 can be thought of as the probability of the data given the parameter values, which is denoted Bayesian parameter estimation allows one to integrate into a posterior distribution, the new distribution of after observing the data, th e extent to which the initial knowledge about the parameter has been improved in light of the data. Bayes theorem provides a useful expression for making this inference (3 2) where the probability of the data does not depend on the parameters and hence can be treated as a constant of proportionality for the integral in Equation 3 2 and the likelihood of the data is A major difficulty in applying Bayes theor em lies in the determination of the marginal probability density functions (PDF) for the posterior distributions, which requires the calculation of high dimensional integrals over the whole parameter space. The mathematics become intractable when consideri ng that, the normalization constant must be known as well in a complex parameter space of a nonlinear crop model, if the posterior distribution was to be calculated analytically. The MH algorithm, based on constructing Markov chains in Monte Car lo simulations, is one of these practical methods that provide a convincingly stable solution to the problem. Markov Chain Monte Carlo The Monte Carlo method was invented in the 1930s by physicists working in the Los Alamos Scientific Laboratory in New Mex ico who realized that solutions to complex neutron diffusion problems (that could not be solved analytically) could be approximated through repeated random sampling.

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103 The Markov Chain Monte Carlo (MCMC) method does not provide an analytical equation for th e posterior PDF but rather a set of parameter samples, which can be used to compute useful properties (mean, mode, median, and variance) to summarize the target distribution. In most applications however, these properties would be sufficient to make infere nces and the convenience of not dealing with prohibit ive ly expensive complex integrals makes up for the inability to obtain a closed form solution. The approach is based on repeatedly generating a random sample (hence the name Monte Carlo) whose value at s tate depends only on the previous value at in the sequence. The chain obtained from such a Monte Carlo simulation is Markovian in the sense that the current sample is entirely determined by a distribution defined about the value of the previous sam ple (Putze et al., 2009) The implementation of a MCMC requires the specification of crit eria for proposing subsequent samples and deciding which samples should be accepted or rejected for the chain to evolve efficiently over repeated trials, i.e. converge towards the target distribution. The salient features of the MH algorithm, an MCMC imple mentation of Bayesian parameter estimation are presented next. The Metropolis Hastings A lgorithm In the MH algorithm, we wish to approximate a target density that can be written in the form where is an unknown constant of normalization. Using an auxiliary distribution to propose subsequent samples in the chain, a jump from the current state to a new state requires the evaluation of the ratio (the constant cancels out because we

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104 are taking a ratio). Bayes theorem applied to the MH algorithm (i.e. ) reads (3 3) The specific steps of the algorithm consist of the following (Hastings, 1970) : 1. Generate from a proposal distribution where is the current state; 2. Evaluate 3. If then accept the candidate as the new state, i.e. If the candidate can still be accepted with some probability: d raw from a uniform distribution over the interval If then accept the candidate with probability else reject the candidate with probability and stay at the previous state, i.e. 4. Return to step (1 ) and repeat times where is the number of trials required for the Markov chain to be stationary. Here, stationary means that the chain has converged to the posterior distribution. Relevant moments such as expected values and variance can therefore be computed to summarize the distribution. Materials and Methods Methods of Parameter E stimation A total of 13 parameters were estimated (Table 3 1) following two distinct procedures to study the effect of limited availability of data on the estimated parame ters. The case of availability of a detailed dataset (hereafter denoted by detailed case ) based the parameter estimation (also referred to as model calibration in the paper) procedure on observed in season biomass and LAI, measured planting and harvest dat es and measured final grain yield. The second parameter estimation procedure used a reduced version of the detailed dataset (hereafter denoted by limited case ) that include d only

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105 measured planting and maturity dates, final biomass and final grain yield. Th e different steps used in the two estimation procedures were depicted i n Figure 3 1. Parameters were estimated for three maturity groups of maize, peanut and cotton. These maturity groups were identified by simulating potential season length, maximum LAI, grain yield and harvest index at six locations (Florida, Georgia, North Carolina, Virginia, Iowa and Michigan) based on the field experiments that generated data for them (Table s 3 2 to 3 4 ). Detailed case parameter estimation In the detailed case, EmgInt EmgSlp and TTGerminate were set to constant values because a global sensitivity analysis showed that these parameters did not affect model predictions of biomass, grain yield, LAI and season length. Unit seed weight ( SeedWt ) and freezing temperature ( TFreeze ) were also set to fixed values (Table 3 5 ). TBase (base temperature) and TOpt (optimum temperature) were not estimated and s et to the mean s of their distributions (Table 3 5 ) because sufficient information was not available to reliably estimate the m. Moreover, these parameters were needed to estimate the remaining 13 parameters. The next steps are summarized as follow s ( see Figure 3 1) : 1. Using an irrigated treatment, estimate TTMature based on reported planting and maturity dates. Calculate daily thermal time based on TBase TOpt and daily maximum and minimum temperature and convert days from planting to maturity into relative thermal time; 2. Using in season LAI data, derive RelTTSn as the relative thermal time at which maximum LAI was observed ; 3. Using in season LAI data and corresponding relative thermal time obtained in step (1 ), estimate LAIP1 and LAIP2 through nonlinear regression based on the relationship Compute corresponding RelLAIP1 and RelLAIP2 used by the model as

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106 and wh ere 0.15 and 0.50 in the equations are the relative thermal times at which the respective RelLaiP1 and RelLaiP2 were calculated; 4. Similarly to step ( 3 ), estimate SnParLAI using nonlinear regression with relative thermal time and LAI data Set SnParRUE = SnParLAI ; 5. Estimate the remaining parameters, MaxRUE MaxLAI RLWR and HrvIndex with a Bayesian approach, the MCMC MH algorithm using in season d ata (biomass and LAI ) and final biomass and grain yield; 6. Similarly to step ( 5 ), using observed in season biomass and LAI, and final biomass and grain yield in a rainfed treatment, and setting parameters estimated in the previous steps to the means of their distributions, estimate the following parameters essentially driven by water stress: RelTTSn2 StresLAI StresRUE HrvIndex and RLWR When the dataset did not contain distinct irrigated and rainfed treatments, all in season data, final grain yield and fi n al biomass were used in steps (1 ) to ( 4 ) above and the MH algorithm was applied to estimate MaxRUE MaxLAI RLWR HrvIndex RelTTSn2 StresLAI and StresRUE simultaneously. Limited case parameter estimation For each detailed procedure there was a matching limited case variant that used a reduced form of the detailed dataset. As in the detailed case, EmgInt EmgSlp TTGerminate TBase TOpt TFreeze and SeedWt were set to fixed values throughout the estimation procedure that involved three main steps (Figure 3 1): 1. Estimate TTMature using observed season length (planting and maturity dates); 2. Use measured final biomass and grain yield in the irrigated treatment to estimate, based on the MH algorithm, MaxLAI RelLAIP1 RelLAIP2 RelTTSn SnParLAI SnParRUE MaxRUE RLWR and HrvIndex ; 3. Repeat the previous step (2 ) using a rainfed treatment to estimate RelTTSn2 StresLAI StresRUE HrvIndex and RLWR ;

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107 When irrigated and rainfed treatments were not present in the dataset all 12 parameters in steps (2 ) and ( 3 ) a bove were estimated simultaneously using the MH algorithm. Datasets used in the parameter estimation are described in a later section. Application of the Metropolis Hastings A lgorithm Prior parameter distribution The prior information used for estimating p arameters of the DSSAT SALUS model was derived from synthetic data and literature (Table 3 6 a comprehensive analysis of these ranges was provided in chapter 2). Although a few parameters in Table 3 6 originally had normal distributions, uniform prior s we re used because the ranges in Table 3 6 cover ed different maturity classes for which the crop parameters had to be estimated. The expression of the ratio in Equation 3 3 implies that the sample of parameters accepted in the chain depends not only on the da ta (likelihood function) but also on the prior distribution of the parameter. In the case of a parameter assuming a uniform distribution, the decision to move from a particular state to another will only be based on the ratio of the likelihood of the data given the new candidate to the likelihood value at the existing parameter sample since the PDF of a uniform distribution is a constant (i.e. the ratio of the priors, is always equal to 1) In this case, E quation 3 3 simplifies to (3 4) The uniform distribution does not supply information to contribute to the posterior distribution and hence is referred to as non informative (Harmon and Challenor, 1997) On the other hand, when a normal distribution is used the ratio of the priors can be

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108 different from 1 and modify the likelihood ratio In particular, the location of the mean of the normal distribution in the uncertainty range has a critical effect on the results Likelihood function At each step in the chain, the likelihood of the data given the corresponding model prediction was eva luated to compute the ratio in Equa tion 3 4 The likelihood function was modeled as Gaussian with mean which, calculated at state for observations can be written as (3 5) where is the standard deviation associated with the data calculated as The coefficient of variation (CV) was taken to be 0.22 (Kiniry et al., 1997) ; is the number of model executions; is the number of observations of the same type. When estimating parameters using observations of different types (e.g. grain yield biomass and LAI simultaneously ) the likelihood must be combined into one functi on. Aggregation of the likelihood function by multiplication which was found to reduce uncertainties in posterior distributions estimated from the Generalized Likelihood Uncertainty Estimation (GLUE, Beven and Binley, 1992; He et al., 2010 ) was used. Applied to observatio n types (e.g. for grain yield, biomass and LAI, ), E quation 3 5 becomes

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109 (3 6) where are the number of observations in the respective data types. Characterizing the p osterior parameter distribution A number of candidate generating distributions (the ) are available for implementing the MH algorithm and their choice determines the type of chain that is produced [ a review of familie s of candidate generating densities was provided by Chib and Greenberg ( 1995) ] In the present study, candidates were generated from uniform distributions obtained by adding some controlled noise to the current sample. This means that, emerging from the current st ate, the chain could freely evolve in any directions with equal probability and this is referred to in the literature as a uniform random walk (Chib and Greenberg, 1995) When the candidate generating density is symmetric or uniform, the MH decision ratio simplifies to (3 7) since It follows that the ratio in Equation 3 7 now depends only on the likelihood of the data. In practice, the uniform proposal distribution was centered on the current sample position and the variance of this distribution was adjusted to obtain a chain that explored the parameter space efficiently (Bates and Campbell, 2001) If the variance of the proposal distribution was chosen to be too small, candidate samples would have a higher probab ility of acceptance because they would tend to be similar to current samples. This would result in high acceptance rate and the chain would diffuse slowly through the posterior distribution while low probability regions (i.e. the tails of the

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110 posterior dis tribution) would be under sampled. On the other hand, if the variance was too large, the chain would explore the posterior distribution quickly but would jump often too far from the current state resulting in high rejection rates. The variance of the prop osal distribution could be viewed as a tuning parameter used to achieve a compromise between chain mixing and acceptance rate (Geyer, 1992) There was no specific guidance in the literature regarding the value of the acceptance rate and the calibration of this critical parameter should probably depend on the nature of study. For random walk chains, acceptance rates of 0.5 have been reported to deliver optimal results (Chib and Greenberg 1995) while other studies have aimed for a value of 0.25 in the context of a multivariate normal proposal (Harmon and Challenor, 1997) We aimed for a broader interval of 0.30 to 0.70 (Bates and Campbell, 2001; Makowski et al., 2002) In a small number of limited case calibrations however, the acceptance rate exceeded 0.70. Another critical aspect of implementing the MH algorithm was determining the number of model runs (i.e. iterations) required for the chain to converge to the target distribution. Some authors outlined the benefit of running multiple chains with different s tarting values (e.g. Geyer, 1992) while others adopted one chain (Marshall et al., 2004) Regardless of the number of chains, it is undeniable that the number of model runs must be high to ensure that the chain fully explores the posterior distribution (Harmon and Challenor, 1997) We experimented briefly with different starting points but found no difference in the behavior of the chain. One chain of length 50,000 was found to be suitable.

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111 By construction, the random walk MH has a high degree of dep endence at the beginning of the chain and this is because each sample is directly taken from a distribution centered on the value of the previous sample. The autocorrelation normally decays over a few hundred runs as the chain escapes from its initial tran sient state to (Van Oijen et al., 2005) to 50% (Ceglar et al., 2011) of the chain. We discarded the first half of the chains and based the summary of the posterior distributions on the last 25,000 samples. The converge nce of the chain was verified graphically based on the chain sample path (Iizumi et al., 2009) autocorrelation (Putze et al., 2009) and the variability in the chain mean and variance. Datasets for Parameter Estimation and Model T esting Datasets used for parameter estimation and testing were obtained for three crops from DSSAT (version 4.5) to facilitate comparison of SALUS and DSSAT models (CERES and CROPGRO). The data w ere categorized into three maturity groups (short, medium and long) for each crop (Table 3 2) and further into parameter estimation and model testing uses (Table 3 7 ). Since nutrient limitations and plant disease effects were not yet implemented in the current version of SALUS in DSSAT, only high nitrogen and control treatments were used. Maize datasets The short duration maize dataset came from a study conducted in Florence, South Carolina in 1981 (file FLSC8101), where the effect of irrigation on maize cultivar Pioneer 3382 was investigated (Table 3 7 ). Two irrigated treatments (irrigated and rainfed) were used with a total of 200 kg ha 1 of nitrogen (N) supplied in three equal applications in both treatments The soil was a Norfolk loamy sand. The crop was planted on April 7,

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112 1981 at a depth of 4 cm, in 50 cm between rows to a plant population of 7.1 plants m 2 Data collected included final grain yield, total biomass, LAI, maturity date and unit grain weight available for the irrigated treatment only. In season sampling was not conducted. The irrigate d treatment was used for model calibration with the end of season data provided. The medium duration maize dataset was a study conducted at the University of Florida in Gainesville, Florida in 1982 (file UFGA8201) to study the interactive effects of nitrog en and water on maize (Bennett et al., 1986) Maize variety McCurdy 84AA was planted on February 26, 1982 in 61 cm rows to achieve a plant population of 7.2 plants m 2 at eme rgence. The soil was of type Millhopper fine sand classified as loamy, siliceous, Hyperthe r mic Grossarenic Paleudults (Ma et al ., 2006) Six treatments resulting from a combination of two factors were implemented. The first factor consisted of irrigation management with three levels, no irrigation (rainfed), full irrigation (optimal irrigation) and vegetative stress irrigation (partial irrigation). The difference between the last two levels was that in the partial irrigation treatment, a 10 day water stress period was allowed to develop immediately prior to 50% silking (Bennett et al., 1986) The second factor was nitrogen fertilizer with two levels (low at 62, and high at 275 kg ha 1 ). Data collected included in season growth (biomass, LAI and grain yield) and physiological maturity grain weight. T he optimal irrigation and rainfed treatments (high N) were used for calibration and the partial irrigation treatment was used for testing. The long duration cultivar dataset was a study conducted in 1983 in Waipio, Hawaii on the effect of nitrogen fertiliz er on maize cultivars Pioneer 304 and UH610 (file IBWA8301). The crop was planted on November 30, 1983 in 75 cm row spacing with a

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113 plant population of 5.8 plants m 2 at emergence. The soil was a Wahiawa silty clay classified as Clayey, kaolinitic, isohyper thermic, Tropeptic Eutrustox (Ma et al., 2006) All treatments were irrigated with a total of 304 mm of water supplied. Three levels of N (0, 50 and 200 kg ha 1 ) were applied to each cultivar resulting in six treatments. Observed data included in season growth (biomass, LAI and grain yield), maturity dates and final grain weight (Singh, 1985) The measurements showed little to no difference between the two cultivars in terms of biomass, LAI, grain yield and season length. The 200 level N treatments were selected for parameter estimation in DSSAT SALUS Peanut datasets The short duration culti var represented by Chico (Table 3 2) was used in a varietal experiment involving seven other peanut cultivars and conducted in 1989 at Green Acres, Newberry, Florida (file UFGR8901). The cultivars were planted on May 5, 1989 in 91 cm rows at 4 cm depth wit h a plant density of 13.5 plants m 2 at emergence. The soil was a Millhopper fine sand of the same classification as that of Gainesville ( loamy, siliceous, Hyperthe r mic Grossarenic Paleudults ). A total of 103 mm of water was supplied in three applications between June 4 and August 1, 1989. Measurements included in season growth, physiological maturity and grain weight. The Chico treatment from this experiment was used for calibrating the short duration maturity class. The medium duration dataset used for ca libration was a field experiment with the cultivar Florunner in 1984 at the University of Florida Agronomy Farm in Gainesville (file UFGA8401). The crop was planted on June 13, 1984 at a depth of 3.5 cm in 76 cm rows resulting in a plant population of 12.9 plants m 2 Two treatments were tested i) limited irrigation (with a total water application of 243 mm) and ii) full irrigation (with a total of 365 mm of water application). The main difference between the two treatments

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114 in addition to the quantity of ad ditional water supplied was that the limited irrigation treatment did not receive any water applications between June 15 and September 19, 1984. The soil was the Gainesville Millhopper fine sand Measurements of in season growth, maturity date and grain we ight were available for both treatments. The experiment that provided data for calibrating the long duration maturity group was also a varietal study involving four cultivars (file UFGA9001) from which Southern Runner was used to represent the long duratio n maturity class (Table 3 2). The experiment was conducted on the University of Florida Agronomy Farm in 1990. The cultivars were planted on May 15, 1990 at a 4 cm depth and in 61 cm rows corresponding to a 15.2 plants m 2 plant population. A total of 273 mm of water was applied throughout the season. Detailed growth analysis was conducted and maturity dates and grain weight data were also available for all treatments. The treatment with the Southern Runner cultivar was used for calibration purposes. The da taset used for independent model testing was taken from an experiment conducted in Marianna, Florida in 1983 to study the effect of leaf spot disease control on four cultivars of peanut (file UFMA8301). The cultivars were planted on May 5, 1983 at a 4 cm d epth and in 91 cm rows for a plant population of 11 plants m 2 at emergence. The soil was a Norfolk sandy loam classified as loamy, siliceous T hermic Typ ic Paleudults The crop was irrigated intermittently from planting to August 29, 1983 providing a tota l of 201 mm of water. Detailed growth analysis and yield for the Florunner and Southern Runner treatments were used for testing the crop models. Cotton datasets Datasets on cotton were limited in DSSAT. Two experiments on a medium maturity cultivar, Deltap ine, were used for calibration and testing.

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115 The calibration dataset was from an experiment conducted at the Stripling Irrigation Research Park (SIRP) in Camilla, GA in 2004 to evaluate the performance of a new cotton model using two treatments, rainfed and fully irrigated. The cotton cultivar Deltapine 555 BG/RR was planted on May 6, 2004 in 90 cm rows resulting in a plant population of 11 plants m 2 at emergence. The soil had a loamy sand texture characterized as loamy, siliceous, T hermic Arenic Paleudult s The water supply in the irrigated treatment was automatic when the available water was below 60% of the maximum capacity A total of 90 kg ha 1 of N in the form of ammonium nitrate was banded beneath the surface to control any N limitations. Available co tton growth data were collected every two weeks. The dataset used for independent testing was the free air CO 2 enrichment (FACE) experiment conducted in 1989 at the University of Arizona Maricopa Agricultural Center to quantify the effect of CO 2 enrichment on cotton growth and yield. The cultivar used was Deltapine 77 planted on April 17, 1989 in 102 cm rows to achieve a plant population of 10 plants m 2 at emergence. A control treatment (350 ppm CO 2 ) and a CO 2 enriched treatment (550 ppm) were t ested. The soil was of texture Trix clay loam and classified as Fine, loamy, mixed (calcareous) hyperthermic Typic Torrifluvent (Mauney et al., 1994) Subsurface drip irrigation was started on April 24 and ended on September 11, 1989 provid ing a total of 1270 mm of water to the plant during the season (Mauney et al., 1994) A total 133 kg ha 1 of N was applied to both treatments. Replicated in season growth data were available from this experiment, which permitted the assessm ent of errors on measurements. Only the control treatment was used for testing the crop models.

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116 Crop G rowth M odels The parameters were estimated for the SALUS (System Approach to Land Use Sustainability) crop model in DSSAT (Decision Support System for Agr otechnology Transfer). C alibration and independent testing results were compared to more complex crop models from DSSAT. The DSSAT models integrate information on the crop environment (soil and weather), management and physiological potentials to simulate growth, development and yield of annual plants. The SALUS and DSSAT models differ essentially in the way those physiological characteristics are coupled to the environment. Comparisons of CERES and ALMANAC (on which the simple SALUS model was based) showed that both models accurately simulated mean maize grain yield under different climate and soil regimes across nine U.S. states (Kiniry et al., 1997) and at different sites in Texas (Kiniry and Bockholt, 1998) The simple SALUS model The simple version of SALUS is a generic model designed to simulate a wide range of annual plant species, including grasses, and the impact of different environments. Within species variation may be confined to maturity groups. While the model can be parameterized for specific cultivar s, it was not designed to capture detailed differences among plant cultivars. The SALUS crop model uses the concept of relative thermal time to represent the development of the crop. The duration of crop growth between planting and maturity i s expressed a s the cumulative degree days between the two phases ( TTMature Table 3 1) and the relative thermal time i s the fraction of TTMature such that 0 represent planting and 1 corresponds to maturi ty. Germination and emergence a re predicted based on the cumulative degree days approach T he beginning of leaf senescence that

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117 marks th e end of the vegetative phase i s a species dependent fixed fraction of the total thermal time. Simulation of LAI growth i s based on a general sigmoid function, the shape of whic h i s controlled by two plant parameters. Similarly the shape of the LAI decline function i s defined by a plant parameter that could be tuned to accelerate or slow LAI senescence depending on the species. Total dry matter i s calculated daily based on the R adiation Use Efficiency (RUE) approach and partitioned to roots and aerial plant parts using a dynam ic partitioning function that i s dependent upon the relat ive thermal time. Grain yield i s considered to be a fixed fraction of aboveground biomass. The rate of total dry matter accumulation and LAI growth or loss may be affected by water and nutrient stresses depending on the production level. The current version of SALUS use s 19 parameters to model potential production and an additional parameter, the root l ength to weight ratio (RLWR) in water limited conditions. The DSSAT crop models The DSSAT crop models used (CERES, Crop Environment Resource Synthesis for cereals, and CROPGRO for legumes) have the ability to simulate cultivar variations within the same s pecies using ecotype, cultivar and species parameters to describe their differences (Jones et al., 2003) These models were designed to represent detailed growth, development and yield characteristics of a crop, including phenology even ts (emergence, tasseling, silking and physiological maturity), mass accumulation organ expansion and yield components (grain weight and grain number). Simulation of phenological stages is based on the growing degree days approach, i.e. the beginning and e nd of a growth stage is controlled by a cultivar specific heat sum above a base

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118 temperature, which can be modified by photoperiod sensitivity. Unlike SALUS, LAI simulation in CERES and CROPGRO is based on individual leaf growth and senescence. Leaf develop ment between emergence and flowering (vegetative phase) is degree day dependent. Leaf senescence may occur as a result of natural abscission and mobilization of carbohydrates to reproductive organs but may be accelerated by stress as in SALUS. Photosynthes is is computed based on the daily canopy RUE approach in CERES (Ritchie, 1998) or the hourly leaf level approach in CROPGRO (Boote and Pickering, 1994; Boote et al., 1998) Gross photosynthesis is converted into tiss ue growth after accounting for maintenance respiration, following the approach developed by Penning de Vries and van Laar ( 198 2) During the reproductive phase, partitioning of assimilates to seeds takes priority over partitioning to leaf and stem, a process which increases leaf senescence. In CERES maize, the seed number, determined prior to the grain filling period, is combined w ith the average seed mass to calculate grain yield (Ritchie, 1998) These two grain yield components are influenced by cultivar specific coefficients, the potential kernel numbe r per plant and the potential grain filling rate respectively. Both models (CERES and CROPGRO) have been extensively tested and applied under a wide range of environmental conditions and cropping systems (Jones et al., 2003) Evaluation of model performance Agreement between model outputs and observations were quantified using a number of statistics selected to capture different facets of the overall simulation measurement discrepancies. The root mean squared error (RMSE) was used to mea sure the average distance between simulations and observations (Wallach, 2006)

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119 (3 8) where is observation i, is prediction i, and the number of pairs. An ideal model (i.e. a model such that for all values of which only exist s in theory) would have an RMSE of zero. Generally, RMSE will have similar interpretations as a standard deviation computed on a set of model predictions given a vector of means (represented by the corresponding observations). Large RMSE values imply a higher average deviation of the simulations from the observations. When comparing RMSEs for different variables (e.g. biomass at emergence and biomass at maturity), a normalized value where is the mean of observations, similar to a coefficient of variation, may be useful to account for the difference in order of magnitude when is smaller than The second measure of agreement was the Willmott index (WI; Willmott, 1992) which involved the ratio of the mean square error (MSE) to a term that measured the variability of the simulations and observations around the mean of observations. (3 9) where the new term is the mean of observations. The WI measured the extent to which the deviation between the simulations and observations was different from the combined deviations of the simulations and observations from the mean of observations. It will have a value close to 1 (indicating good model performance) if the simulations and observations are more similar than the simulations and the mean of observations, and the observations and the mean of

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120 extent of linear ass ociation between simulations and measurements. The bias was used to assess the degree of under or over prediction by the model (Kobayashi and Salam, 2000) Compar ison among DSSAT SALUS and DSSAT Models The performance of DSSAT SALUS (based on calibration and testing datasets) after parameter estimation was compared to DSSAT CERES Maize (for maize) and DSSAT CROPGRO (for peanut and cotton) to evaluate agreement betw een the two classes of models We did not calibrate CERES Maize or CROPGRO but based the comparisons on parameters in the DSSAT database for the cultivars used in the datasets described earlier. Results and Discussion Stability Analysis of the Chains The a utocorrelation between successive samples, trace plot, variability of parameter mean and parameter distribution for the medium maturity class of maize, peanut and cotton were presented in Figures 3 2 to 3 4 for diagnostic analysis of the MH chain. Only the first and last 1000 samples were shown on the trace plots with a moving average computed based on half of the corresponding number of iterations, to facilitate detection of possible trends. The distributions as well as their means were also based on the l ast 50% of all samples that is the last 25000 values. Diagnostics for the medium maturity group and two influential parameters, maximum LAI and maximum RUE, were shown but other maturity class parameter combinations presented similar chain stability prope rties. The serial correlation decay with lags was variable among parameters (subplots A and B in Figures 3 2 to 3 4) and its pattern could consistently be predicted using the

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121 shape of the resulting distribution (subplots G and H). When the posterior distr ibution was mostly Gaussian, the number of lags required for the serial correlation to reach a value of zero was smaller than in situations of skewed distributions. This could be easily observed by comparing Figures 3 2A and 3 2G for the case of a near Gau ssian distribution where approximately a lag of 50 was required for the autocorrelation to drop to about 0.05. When the posterior was skewed (Figures 3 2B and 3 2H) the correlation was around 0.25 for the same lag value. Similar analyses could be derived f rom Figures 3 3 (for Gaussian posteriors) and 3 4 (for a positively skewed posterior). This result is to be interpreted as the skewness of the posterior was caused by the chain persistently searching for the optimum parameter value in a region not centered on the prior range. It was unclear just looking at the trace plots (subplots C and D) if there was an intuitive difference between the earliest and latest iteration histories. However, when a smoothed average was superimposed, the underlying trend emerge d to a mere visual inspection. The first 1000 iterations were mostly characterized by somewhat erratic exploration of the parameter space while the last 1000 runs defined a s table, asymptotic property. Projected to the broader scale of 50,000 iterations (subplots E and F), this behavior unveiled the ultimate conclusion of the stability analysis of the chain: after an initial transient variation corresponding to a burn in perio d of 10,000 iterations, the chain converged to its limiting distribution, which is the posterior. Discarding the first 25,000 iterations therefore appeared to be even more protective.

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122 Posterior D istribution s The Gaussian kernel density estimates for maxi mum LAI and maximum RUE were displayed for all maturity groups and all crops in Figures 3 5 to 3 9. The corresponding expected values and standard deviations were presented in Tables 3 8 to 3 10 The most striking aspect of the posterior densities was that not considering a few exceptions, the distributions of MaxLAI and MaxRUE for the detailed calibration were essentially Gaussian. These two parameters were generally the most influential on biomass, LAI and grain yield as indicated by sensitivity analyses reported in Chapter 2. An example of exceptions to this overall observation could be seen in Figure 3 6B where the distribution of MaxRUE was slightly skewed. Another striking case of negative skewness was shown in Figure 3 7B, for peanut long maturity cl ass. These cases of strong asymmetry were the result of the data (mostly in season LAI and biomass) driving the samples to the extremes in an effort to match the measured patterns. This type of behavior i s a reflection of the MCMC design used The decision criterion in Equation 3 7 depends only upon the likelihood of the data (due to using a non informative prior distribution) Therefore, the data carried more weight than this prior distribution in the estimation of the posterior distribution. We note that although the modes of these posteriors were closer to the extremes of the prior ranges, results of the MH algorithm were distributions with low probability regions corresponding to the tails. Although the limited case calibrations presented asymmetric and elongated tail distributions as well, their dominant feature was rather a distinctly higher variance regardless of the crop, maturity class or parameter considered. For maize medium maturity class maximum LAI (Figure 3 5A), the standard deviation for the limited case was 1.56 m 2 m 2 while for the detailed case it was only 0.67 m 2 m 2 (Table 3 8 ). This

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123 translated into a CV of 30% compared to 14% respectively. While the order of magnitude of the standard deviations were comparable for maize and peanut (Table s 3 8 and 3 9 ), the relationship to their respective expected values (quantified through the CV) was not stable. For example, strong cases of high variance posteriors in the limited calibration (as in Figure 3 7A) were characterized by CV values ranging fr om 32% to 38%, with corresponding detailed calibration CV between 6% and 16% (Table 3 9 ). These findings suggested that although the MH algorithm may in theory be used to estimate a large number of parameters from only a few data points, such configuration s would result in higher uncertainties in the posteriors. In the present study this effect was produced by ratios of number of parameters estimated to number of data points used for estimation as high as 12 to 2, i.e. six. Despite the larger uncertaintie s associated with the limited case parameter estimation results some of the point estimates obtained (expected values of the distributions) were fairly close to those of the detailed case. This was remarkable given the limited data and the high parameter to data ratio the algorithm was constrained to work with. Comparison of mean parameter estimates for maize medium maturity group, limited and detailed cases in Table 3 8 showed that except for RelLAIP1 the limited case estimates were within 3 to 14% of th e detailed estimates. However, for a few peanut and cotton parameters, wide differences were observed between the two methods (Tables 3 9 and 3 10 ) Mean parameter estimates were generally in close agreement for HrvIndex RelTTSn RelTTSn2 StresLAI Stres RUE and in some cases SnParLAI SnParRUE and MaxRUE (Tables 3 8 to 3 10 ) The limited calibration failed

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124 to capture the pattern of variation across maturity groups, of two critical peanut parameters MaxRUE and MaxLAI Prediction of LAI, Biomass and Yield The expected values of the parameters shown in Tables 3 8 to 3 10 were used as inputs to the crop models to assess the degree of agreement between data used for calibration and simulations using parameter estimates from the same calibration. In other words this procedure was the inverse of the parameter estimation. Perf ormance statistics of the degree of agreement between measurements and simulations are given in Tables 3 11 and 3 12 for the detailed case and Table 3 13 for the limited case. Overall performance of SALUS A comparison of observed and simulated aboveground dry matter and grain yield for all crops and maturity classes was presented in Figure 3 10. The detailed case calibration used in season dry matter; hence more data were plotted on Figure 3.10A. There was a general tendency of the model to under predict peanut biomass, especially in the range 5000 to 15000 kg ha 1 but the model captured the variation in biomass values smaller than 5000 kg ha 1 (detailed case calibration, Figure 3 10A). This was reflected in the bias values for peanut which were negative f or all maturity classes with the largest value corresponding to the medium rainfed combination (Table 3 11 ). Peanut RMSEs for biomass ranged from 657 to 1867 kg ha 1 The NRMSEs ranged from 14 to 28% (Table 3 11 ). By contrast in the limited case calibrati on, peanut biomass bias, RMSE and NRMSE were the smallest of the three crops (Table 3 1 3 ). The WI had the highest value as well, indicative of good model performance. Simulated biomass was in close agreement with observations for maize and cotton. The biom ass RMSE values for the detailed case calibration (irrigated and

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125 rainfed) were 718 and 780 kg ha 1 (for maize) and 734 and 1589 kg ha 1 (for cotton). These values represented 7% and 16%, and 14% and 24% of the corresponding mean observations. Based on the limited case calibration, the model had a tendency to under predict biomass for maize and over predict biomass for cotton (Table 3 1 3 ). The small value of biomass WI for cotton in Table 3 1 3 was caused essentially by an over prediction of biomass in the ir rigated treatment. This was a common problem in both calibration methods (Table 3 11 cotton irrigated). Maize biomass under prediction in the limited case calibrated was more pronounced in the short maturity group that had an observed final biomass of 23. 8 t ha 1 (outlier in Figure 3 10B). This biomass level could not be achieved in the simulation mainly due to a combination of short growth duration and low estimated MaxRUE. Peanut yield was predicted with a higher accuracy than peanut biomass for the deta iled calibration (Figure 3 10C). Despite differences in estimates of key parameters between the limited and the detailed calibrations, both methods seemed to agree well with observed grain yield. In fact, there is little difference between Figure 3 10C (yi eld, detailed case ) and Figure 3 10D (yield, limited case ). Peanut yield RMSE was only 270 kg ha 1 in the limited case calibration with a bias of 114 kg ha 1 (Table 3 1 3 ). The highest bias for this calibration method was 435 kg ha 1 (cotton), which represented 12% of the mean observation (Table 3 1 3 ). The highest RMSE value was 771 kg ha 1 (maize), which was equivalent to an NRMSE of 10%. Thus, in general, prediction of final grain yield based on the limited case calibration was sens itive to crops and in convincing agreement with measurements.

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126 Prediction of in season maize LAI and biomass We r ecall that only the detailed case calibration used in season data but in the series of Figures 3 11 to 3 16, we consider simulations of in seaso n biomass and LAI based on calibrated parameters from the limited method as well for comparison purposes. The corresponding performance statistics for the detailed case calibration were given in Table s 3 11 and 3 12 Figure 3 11 provides convincing evidenc e that prediction of irrigated maize biomass and LAI time series by the SALUS model was in agreement with measurements. Parameters that controlled the shape of LAI (in Figure 3 11C) were fitted using in season LAI data as part of the detailed parameter est imation case; therefore a good reproduction of this time series was expected. The replication of the LAI time series in this figure was sufficiently congruent with measurements to yield WI and correlation coefficient values of 1.0, an RMSE of 0.13 m 2 m 2 (NRMSE of 4%) and a bias of 0.05 m 2 m 2 (Table 3 12 ). On the other hand, prediction of biomass (Figure 3 11A) resulted in an RMSE of 780 kg ha 1 (NRMSE of 7%) and a WI of 1.0. In contrast to Figure 3 11C, LAI parameters used in Figure 3 11D (limited case c alibration ) were not fitted but rather estimated using final biomass and grain yield only. Nonetheless, the performance of the SALUS model in this configuration was again congruent with the data. On the basis of Figure 3 12, an analogous analysis could be conducted for the maize non irrigated treatment. Simulation of water stressed biomass and LAI appeared to be less accurate. It was felt that the limited case calibration (Figures 3 12B and D) was slightly more concordant with observations than the detailed case calibration (Figures 3 12A and C). Both LAI and biomass after the beginning of leaf senescence

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127 were over predicted, especially in the detailed calibration (subplots A and C), which was confirmed by a bias of 0.33 m 2 m 2 and 397 kg ha 1 respectively. The WI was 0.98 for biomass and 0.91 for LAI (Table s 3 11 and 3 12 ). It was evident from Figures 3 11 and 3 12 that regardless of the calibration method, SALUS predictions of biomass and LAI were closer to measurements than CERES maize predictions. Leaf Ar ea Index was over predicted by CERES maize during the period preceding maximum LAI (Figures 3 11C and 3 12C) which did not however translate into a poor biomass prediction (Figures 3 11A and 3 12A). CERES maize failed to accurately describe the timing of maximum LAI in the rainfed treatment as well as change s in LAI beyond day 80 after planting (Figure 3 12C). However, we reiterate that parameters used to produce CERES Maize predictions were not estimated in this study but obtained from the DSSAT database Prediction of in season peanut LAI and biomass SALUS predictions of peanut LAI and biomass time series in the detailed calibration firmly fitted the observations (Table 3 1 2 and Figure 3 13C, medium maturity class shown). However, degradation in the perfo rmance of the model was observed with the limited case calibration (Figures 3 13B and D). This evolution towards a poorer performance could in essence be attributed to the incorrect estimation of two important parameters, MaxLAI and MaxRUE. Indeed, the val ues obtained for these parameters were respectively 22% and 6% lower in the limited than in the detailed case calibration (Table 3 9 ). Discrepancies between SALUS simulations and observations were particularly large in the rainfed treatment (Figure 3 14). Error measures were as high as 1867 kg ha 1 (RMSE) and 1317 kg ha 1 (bias) for biomass in the detailed case (Table 3 11 ). The

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128 limited case failed to capture appropriately the rate of LAI decline and the overall evolution in biomass growth. Despite a relati vely poor accuracy in predicting non irrigated LAI and biomass case was consistent with CROPGRO 14A and C). It is appropriate to assert that the models had some difficulties p redicting peanut growth and yield probably because peanut is an indeterminate crop In SALUS based on the detailed case calibration, the highest error was associated with the medium duration cultivar rainfed combination (Table 3 11 and Figures 3 14A and C ). However, plotting the distribution of biomass and LAI (using values calculated by the SALUS model during the detailed case calibration) showed that practically all (irrigated treatment) and a few (rainfed treatment) of the data points fell within the di stributions (Figure 3 17). Prediction of in season cotton LAI and biomass Cotton growth based on parameters estimated in the detailed case (subplots A and C in Figures 3 15 and 3 16) was predicted with some mixed success. Prediction of LAI was coherent wi th measurements under well watered conditions (Figure 3 15C). Rainfed biomass was equally concordant with observations (Figure 3 16A). Irrigated biomass was in agreement with the data prior to the beginning of leaf senescence (period before 100 days after planting). After the initiation of LAI decline however, an abrupt increase in biomass was noted (Figure 3 15A). This sudden deviation from the observed growth curve resulted in an RMSE of 1589 kg ha 1 (NRMSE of 24%) and a bias of 971 kg ha 1 (Table 3 11 ). It was unclear what caused this end of season over estimation. In the rainfed treatment, the inflation in LAI prediction errors was due to the

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129 model failing to capture a water stress induced reduction in LAI around 100 day after planting (Figure 3 16C). On the basis of crop parameters derived from the limited case calibration, the ability of the SALUS model to simulate cotton growth became categorically weak (subplots B and D in Figures 3 15 and 3 16). The fact that the shapes of the growth curves matched t ypical seasonal variations in LAI and biomass suggested that this weak performance was primarily attributable to a small value of the MaxLAI parameter. Indeed, MaxLAI was approximately 40% lower in the limited case calibration than in the detailed case cal ibration (Table 3 10 ). CROPGRO s of LAI and biomass w ere slightly more concordant with observations than th ose of SALUS based on the detailed calibration case Final biomass (Figure 3 15A) and LAI decline (Figure 3 16C) were more accurat ely predicted in CROPGRO cotton than SALUS detailed case calibration However, like for CERES Maize, parameters used in CROPGRO predictions were not estimated in this study. Independent Testing of SALUS and Comparison with DSSAT An independent test of SALU S was conducted using the mean parameter estimates from both calibration methods (limited and detailed cases). Results a re presented in Figures 3 18 to 3 22 and Table 3 1 4 Results of the independent test suggested that the simple SALUS model was sufficiently stable for simulating maize growth. The WI reached its maximum value of 1.0 for biomass and a value of 0.97 for LAI based on the detailed case Other error statistics in dicated agreement between model and data for this crop (Table 3 1 4 ). As shown in Figure 3 19, the independent evaluation results for maize were essentially insensitive to the calibration method used, particularly later in the season. This

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130 independent test was based on the vegetative stress treatment from the Gainesville maize dataset. Accurate simulation of this treatment without any further parameter calibration or model modification was critical because it supports the argument that the model may be able to simulate different water regimes. This was not trivial since crop model responses t o different irrigation levels a re not expected to be linear. Over prediction of LAI prior to the beginning of LAI decline and inaccurate representation of the point in th e season when this decline actually began were two major problems found in CERES maize. The independent test ing of peanut used a medium (Figure 3 20 and a long duration treatment (Figure 3 21), both from the 1983 Marianna peanut dataset. For the medium mat urity group based on the detailed case calibration the independent testing errors were larger than the calibration errors in the irrigated treatment, and similar to calibration errors in the rainfed treatment (Table 3 1 4 ). In the long maturity group, the biomass RMSE value was reduced by 50% compared to its calibration counterpart but the LAI RMSE, the bias and the WI were similar (Table 3 1 4 ). For this peanut maturity group, the NRMSE was as small as 10% for biomass but was higher for LAI (26%) due an ina ccurate prediction of LAI decline (Figure 3 21C). Thus, the prominent characteristics of peanut independent testing were i) generally reasonable predictions of biomass and LAI in the detailed case calibration with bias that were in essence inherited from t he calibration; ii) accurate predictions of final biomass and maximum LAI based on the detailed case calibration in both long and medium maturity groups, with exceptionally low errors for biomass, (RMSE was 567 kg ha 1 NRMSE was 10%, WI and correlation had a value of 1.0); iii) substantial under

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131 predictions of biomass and LAI in the limited case calibration with the only exception being the final biomass in the medium maturity class that was predicted accurately (Figure 3 20B); iv ) the performance of CROPGRO peanut was mostly close to, but sometimes poorer than that of the SALUS detailed case calibration Both models exhibited a consistent tendency of under predicting peanut growth. Differences in cotton LAI and biomass predictions between the limited and the detailed cases were not discernible during the season. In both cases, simulations of biomass were within one standard deviation of measurements (Figures 3 22A and B) but their predictions of LAI were distinctly affected by nega tive bias (Figures 3 22 C and D). As illustrated in Table 3 1 4 for the detailed case this bias represented 44% of the mean observation. Cotton LAI suffered from the lowest correlation (smaller than 0.50) and lowest WI as well (Table 3 1 4 ). In the limited case LAI predictions improved towards the end of the season but were not closer to observations than CROPGRO limited case (compared to the detailed case ) probably originat ed in this attenuation in LAI prediction errors (Figure 3 22B). CROPGRO extended to one standard deviation above measurements during the season but final biomass was slightly under predicted (Figure 3 22A). This profi le was arguably closer to SALUS detailed case CROPGRO cotton until the beginning of LAI decline around 100 days after planting where an unexpected departure from measurements became distinct (Figure 3 22C). The dataset used in this testing came from the 1989 Arizona FACE experiment which was sufficiently irrigated to the point that water stress was neither observed nor

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132 predicted. It seem s therefore likely that a too rapid natural rate of LAI senescence that was not observed in the experiment may have been predicted by the CROPGRO cotton model. Further Discussion The choice of the prior and proposal distribution used in the MH algorithm has a strong influence on the characteristics of the poste rior distribution (Chib and Greenberg, 1995) because the proposal distribution determines the sampling pattern and the prior is an integral part of the posterior approximation. In this study, some key parameters ( MaxRUE and MaxLAI ) were determined to have a normal distribution but using this normal distribution could provide the wrong information to the MH algorithm, in essence because the three maturity groups calibrated have different characteristics with regard to those parameters. For example, a normal distribution for maize MaxLAI that cover s v ariability in MaxLAI values in all three maize maturity groups is representative of the species but not of any particular maturity groups. This broad species distribution underestimates the MaxLAI distribution for the long duration maturity group but overe stimates the MaxLAI distribution for the short duration maturity group. When we experimented briefly using this normal distribution as a prior distribution to calibrate each maturity group, mean MaxLAI was under estimated for the med ium and long durations a nd over estimated for the short duration. This effect was produced by the influence exerted by the expected value of the prior distribution as one of the major contributors (with the data) to the approximation of the posterior distribution In other words, taking the example of the short maturity group, the prior distribution was representative of a higher LAI but the data corresponded to a much lower LAI. This mismatch of scale between the data and the prior distribution could be proved by

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133 showing that Maxi mum Likelihood Estimators (MLE) of MaxLAI for the three maturity groups would lay in different regions of the broader distribution of MaxLAI It may be better in this situation to use a non informative distribution or a normal distribution with expected va lue s representative of the respective maturity groups (Iizumi et al., 2009) Some authors suggested the use of the Gelman statistic (Gelman and Rubin, 1992) that compar es the within and between run variations calculated from multiple runs with different starting values to determine the convergence of the MH algorithm (Marshall et al., 2004) We constructed chains with different starting values and found that they were insensitive to the initial conditions, which was consistent with findings from previous studies (Hassan et al., 2009) This behavior is representative of rapidly mixing chains that tend to return to their stationary distribution independently of a reasonably selected starting point. Our results showed that the prior and the proposal distributions had the greatest influence on the behavior of the MH chain. The reduction in uncertainties in the posteriors in the detailed case calibration was not only attributed to the lower parameter t o data ratio but also to the variety of data types involved in the algorithm. By data type we mean a specific aspect of growth, development and yield collected in an experiment. The limited case calibration used two data types ( end of season biomass and gr ain yield) while the detailed case was based on three data types ( in season biomass, grain yield and LAI). Combining with the number of data points in each data type gives 2 data values (limited case ) compared to 21 data values (detailed case ) assuming 10 in season biomass and LAI measurements. In addition, the number of parameters that entered the MH algorithm in the detailed calibration was considerably reduced through a stepwise approach that allowed

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134 isolation and separate estimation of some parameters e ntirely characterized by specific data types (Figure 3 1). It can be inferred that higher accurac ies in the detailed case calibration were due to this stepwise approach, the higher number of data types and a lower ratio of parameters estimated to data poin ts used. Findings from this study confirmed the importance of using several error measures in the evaluation of a model as suggested by other authors (Wallach, 2006) Using multiple error statistics also aids in recovering different aspects of the differences between observations and measurements (Kobayashi and Salam, 2000) For example, a high correlation coefficient and WI does not necessarily imply accurate predictions by the model. A high correlation coefficient suggests that a strong linear association between simulations and measurements was found. A high WI indicates that the model r epresents the measurements more accurately than the mean of measurements. In Table 3 11 high values of the correlation coefficient and the WI were associated with high RMSE and negative bias (peanut medium maturity group, rainfed). This combination of ski llful and poor error signals showed that although the model under predicted the observations with a large bias, the pattern of biomass evolution in the simulations matched closely that of the measurements (Figure 3 14A). Conclusions D etailed and simple ap proach es to parameter estimation, both based on the M etropolis H astings algorithm, were used to develop parameter sets for three maturity groups of maize, peanut and cotton for the SALUS crop model Independent testing of the model and comparison with DSSA T models w ere performed to assess the validity of the estimated parameters. The MCMC approach used provided a sound framework for analyzing not only the mean estimates of the parameters but also contributed to

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135 understanding uncertainties associated with th e estimates and how they might affect model predictions. The detailed case demonstrated strong advantages over the limited case It resulted in MaxLAI and MaxRUE distributions that were mostly Gaussian. The variances of these distributions were smaller. The separation between different maturity classes was distinct. However, the detailed case required using in season growth data, which is not always collected or a vailable. The limited case was implemented based on measured season length and final growth data. For maize, differences between the means and standard deviations of parameters using the detailed and the limited cases were small except for MaxLAI that exhi bited a standard deviation 2.3 times higher in the limited case For peanut, the limited case failed to distinguish the three maturity groups based on MaxLAI and MaxRUE These two critical parameters had higher values (for the medium and long maturity grou ps) and a MaxLAI standard deviation up to 3.6 times higher than that of the detailed case The RelLAIP1 was under estimated and the RelLAIP2 was over estimated in all maturity groups. For cotton, only MaxLAI RelLAIP1 SnParLAI and SnParRUE were smaller in the limited case All other parameters wer e consistent with the detailed case I ndependent testing results showed that maize growth simulations (based on both cases simulated with mixed success. Leaf area index was generally consistent with observations. Higher errors and under prediction of crop growth were generally associated with the limited approach. SALUS simulations of crop growth based on the detailed case were generall

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136 for maize, DSSAT models outperformed SALUS based on the limited case We note, not calibrated in this study. Compensation of model error s can affect parameters estimated from limited data (for example end of season data only) or data based on only one aspect of growth (for example yield) even if a Bayesian method like MCMC MH is used. Caution should be used when interpreting simulated in s eason crop growth based on parameters estimated with limited data. Results obtained in this study suggested that the SALUS model was sufficiently stable for simulating growth and yield for maize, peanut and cotton based on parameters obtained from the deta iled case calibration. It was not clear what the predictions of peanut biomass and LAI were. However, it was suggested that these under predictions might be related to the indeterminate nature of this crop. Applicat ions of the model for predicting peanut yield late in the season might result in higher bias than earlier in the season. In addition, d atasets used for testing the model came from a limited number of studies Further testing of the model using datasets fro m a wide range of environments (for example, state variety trials) will help establish the response of the model to different soils, climates, and crops. Ongoing improvements to the simple SALUS model include the simulation of the effect of water stress on harvest index.

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137 Table 3 1. List of SALUS crop parameters estimated Parameter Unit Definition HrvIndex Crop harvest index LAIMax m 2 m 2 Maximum expected Leaf Area Index RelLAIP1 Parameter for shape at point 1 on the potential LAI curve RelLAIP2 Parameter for shape at point 2 on the potential LAI curve RelTTSn Relative thermal time at beginning of senescence RelTTSn2 Relative thermal time beyond which the crop is no longer sensitive to water stress RLWR cm g 1 Root length to weight ratio RUEMax g MJ 1 Maximum expected Radiation Use Efficiency SnParLAI Parameter for shape of potential LAI curve after beginning of senescence SnParRUE Parameter for shape of potential RUE curve after beginning of senescence StresLAI Factor by which LAI senescence due to maximum water stress is increased between RelTTSn and RelTTSn2 StresRUE Factor by which RUE decline due to maximum water stress is accelerated after the beginning of leaf senescence TTMature o C Thermal time from planting to maturity Table 3 2. Potential growth and development characteristics of different maturity groups of maize used in estimating parameters for SALUS Growth aspect Statistic Short ( PIO 3382 ) Medium ( McCurdy 84aa ) Long ( PIOx304C, H610 ) Season length Mean 1660 1878 2099 ( o C season 1 ) St an d ard deviation 19 50 76 Maximum LAI Mean 3.28 4.72 5.49 (m 2 m 2 ) Standard deviation 0.27 0.21 0.15 Grain yield Mean 12074 16292 8064 (kg ha 1 ) Standard deviation 3442 3903 2437 Harvest index Mean 0.58 0.59 0.35 Standard deviation 0.04 0.06 0.06

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138 Table 3 3 Potential growth and development characteristics of different maturity groups of peanut used in estimating parameters for SALUS Growth aspect Statistic Short ( Chico ) Medium ( Florunner ) Long ( Southern Runner ) Season length Mean 1406 1757 1880 ( o C season 1 ) Standard deviation 40 51 65 Max imum LAI Mean 2.25 5.75 6.43 (m 2 m 2 ) Standard deviation 0.30 0.72 0.78 Grain yield Mean 2731 5532 5293 (kg ha 1 ) Standard deviation 563 795 689 Harvest index Mean 0.40 0.42 0.37 Standard deviation 0.03 0.02 0.02 Table 3 4 Potential growth and development characteristics of different maturity groups of cotton used in estimating parameters for SALUS Growth aspect Statistic Medium ( Deltapine 77 ) Medium ( Deltapine 55 ) Season length Mean 1905 1904 ( o C season 1 ) St andard deviation 14 14 Max imum LAI Mean 2.18 3.25 (m 2 m 2 ) St an d ard deviation 0.34 0.45 Grain yield Mean 4745 5052 (kg ha 1 ) St an d ard deviation 794 524 Harvest index Mean 0.50 0.42 St an d ard deviation 0.01 0.02 Table 3 5 Parameters with fixed values during model calibration Unit Maize Peanut Cotton EmgInt o C 34.715 37.25 37.25 EmgSlp o C cm 1 5.1 6.55 6.55 SeedWt g seed 1 0.309 0.655 0.309 TFreeze o C 0.00 0.00 0.00 TBase o C 8.5 11.5 12.5 TOpt o C 29.5 32.75 31 TTGerminate o C 18.5 25.5 27.5

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139 Table 3 6 Prior information on the parameter expressed in the form of ranges Parameter Unit Maize Peanut Cotton Min Max Min Max Min Max HrvIndex 0.25 0.63 0.27 0.58 0.30 0.55 MaxLAI m 2 m 2 0.40 7.84 1.91 8.11 1.22 6.50 RelLAIP1 0.017 0.089 0.010 0.045 0.003 0.025 RelLAIP2 0.819 0.995 0.720 0.950 0.600 0.970 RelTTSn 0.36 0.62 0.51 0.71 0.45 0.98 RelTTSn2 0.55 0.90 0.55 0.90 0.55 0.90 RLWR cm g 1 798 12000 6500 9500 6500 9600 MaxRUE g MJ 1 2.80 4.50 1.20 3.02 2.00 3.00 SnParLAI 0.22 0.50 0.05 0.14 0.01 0.11 SnParRUE 0.22 0.50 0.05 0.14 0.01 0.11 StresLAI 1.00 10.00 1.00 10.00 1.00 10.00 StresRUE 1.00 10.00 1.00 10.00 1.00 10.00 TTMature o C 925 2224 1473 1961 1718 2271 Min: Minimum, Max: Maximum

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140 Table 3 7 Description of datasets used in model calibration and testing Crop Description Short Medium Long Maize Calibration Location Florence SC Gainesville FL Waipio HI Cultivars PIO 3382 McCurdy 84aa PIO x 304C and H610 Year 1981 1982 1983 Reference (Bennett et al., 1986) (Singh, 1985; Ma et al., 2006) Validation Location Gainesville FL Cultivars McCurdy 84aa Year 1982 Reference (Bennett et al., 1986) Peanut Calibration Location Green Acres FL Gainesville FL Gainesville FL Cultivars Chico Florunner Southern runner Year 1989 1984 1990 Validation Location Marianna FL Marianna FL Cultivars Florunner Southern runner Year 1983 1983 Cotton Calibration Location Camilla GA Cultivars Deltapine 555 Year 2004 Reference (Guerra et al., 2007) Validation Location Maricopa AZ Cultivars Deltapine 77 Year 1989 Reference (Mauney et al., 1994)

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141 Table 3 8 M eans and standard deviations of the p osterior distributions of maize parameter s for two methods of parameter estimation Short Medium Long Limited Limited Detailed Limited Means HrvIndex 0.47 0.49 0.48 0.45 MaxLAI 5.33 5.14 4.75 5.17 MaxRUE 3.81 3.81 3.98 3.79 RelLAIP1 0.054 0.054 0.011 0.055 RelLAIP2 0.910 0.912 0.945 0.912 RelTTSn 0.50 0.50 0.55 0.51 RelTTSn2 0.73 0.73 0.72 0.72 RLWR 6945 7125 7461 6885 SnParLAI 0.357 0.356 0.312 0.355 SnParRUE 0.351 0.354 0.312 0.360 StresLAI 5.48 5.80 6.68 5.09 StresRUE 5.52 6.03 5.60 5.42 TTMature 1610 1753 1753 1967 Standard deviations HrvIndex 0.09 0.09 0.10 0.09 MaxLAI 1.50 1.56 0.67 1.59 MaxRUE 0.41 0.40 0.31 0.42 RelLAIP1 0.000 0.000 0 0.000 RelLAIP2 0.045 0.045 0 0.045 RelTTSn 0.07 0.06 0 0.06 RelTTSn2 0.09 0.09 0.09 0.09 RLWR 2770 2622 2635 2778 SnParLAI 0.071 0.071 0 0.071 SnParRUE 0.071 0.071 0 0.071 StresLAI 2.37 2.36 2.61 2.36 StresRUE 2.38 2.27 2.44 2.36 TTMature 0 0 0 0

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142 Table 3 9 M eans and standard deviations of the p osterior distributions of peanut parameter s for two methods of parameter estimation Short Medium Long Limited Detailed Limited Detailed Limited Detailed Means HrvIndex 0.41 0.39 0.42 0.38 0.42 0.40 MaxLAI 4.21 2.78 4.97 6.37 4.87 7.53 MaxRUE 1.53 1.74 2.10 2.25 1.89 2.39 RelLAIP1 0.027 0.039 0.027 0.045 0.027 0.067 RelLAIP2 0.828 0.698 0.837 0.782 0.831 0.723 RelTTSn 0.61 0.69 0.61 0.60 0.61 0.65 RelTTSn2 0.74 0.72 0.72 0.69 0.72 0.63 RLWR 7911 7978 8006 8025 7954 8174 SnParLAI 0.096 0.062 0.096 0.115 0.096 0.965 SnParRUE 0.099 0.062 0.095 0.115 0.096 0.965 StresLAI 5.62 5.70 5.46 4.40 5.50 5.04 StresRUE 5.95 5.76 5.27 5.05 5.68 5.93 TTMature 1521 1521 2057 2057 2368 2368 Standard deviations HrvIndex 0.08 0.07 0.08 0.07 0.08 0.08 MaxLAI 1.60 0.44 1.60 0.65 1.66 0.46 MaxRUE 0.24 0.24 0.38 0.22 0.36 0.22 RelLAIP1 0.000 0 0.000 0 0.000 0 RelLAIP2 0.063 0 0.063 0 0.063 0 RelTTSn 0.05 0 0.05 0 0.05 0 RelTTSn2 0.09 0.09 0.09 0.09 0.09 0.05 RLWR 824 853 796 812 797 811 SnParLAI 0.032 0 0.032 0 0.032 0 SnParRUE 0.032 0 0.032 0 0.032 0 StresLAI 2.44 2.48 2.37 2.30 2.38 2.56 StresRUE 2.41 2.45 2.35 2.35 2.38 2.36 TTMature 0 0 0 0 0 0

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143 Table 3 10 M eans and standard deviations of the p osterior distributions of cotton parameter s for two methods of parameter estimation Limited Detailed Mean St an d ard dev iation Mean St an d ard dev iation HrvIndex 0.41 0.06 0.40 0.06 MaxLAI 2.44 0.94 3.98 0.71 MaxRUE 2.38 0.25 2.40 0.24 RelLAIP1 0.014 0.000 0.074 0 RelLAIP2 0.765 0.095 0.797 0 RelTTSn 0.69 0.14 0.69 0 RelTTSn2 0.73 0.09 0.71 0.09 RLWR 8017 820 8066 843 SnParLAI 0.061 0.032 0.976 0 SnParRUE 0.063 0.032 0.976 0 StresLAI 5.51 2.35 5.20 2.33 StresRUE 5.41 2.33 5.54 2.35 TTMature 1930 0 1930 0 Table 3 11 Summary statistics used to measure the ability of the SALUS model to predict in season biomass during detailed parameter estimation Crop Cultivar Treatment RMSE NRMSE Willmott Correlation Bias Maize Medium Irrigated 780 0.07 1.00 1.00 137 Medium Rainfed 718 0.16 0.98 0.99 397 Peanut Short Irrigated 657 0.26 0.96 0.93 142 Medium Irrigated 901 0.14 0.99 0.98 22 Medium Rainfed 1867 0.28 0.94 0.96 1317 Long Irrigated 1123 0.15 0.99 0.97 221 Cotton Medium Irrigated 1589 0.24 0.95 0.98 971 Medium Rainfed 734 0.14 0.97 0.98 610

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144 Table 3 12 Summary statistics used to measure the ability of the SALUS model to predict in season LAI during detailed parameter estimation case Crop Cultivar Treatment RMSE NRMSE Willmott Correlation Bias Maize Medium Irrigated 0.13 0.04 1.00 1.00 0.05 Medium Rainfed 0.46 0.32 0.91 0.91 0.33 Peanut Short Irrigated 0.17 0.12 0.98 0.97 0.04 Medium Irrigated 0.40 0.11 0.99 0.98 0.10 Medium Rainfed 0.62 0.17 0.96 0.96 0.31 Long Irrigated 1.03 0.29 0.94 0.96 0.71 Cotton Medium Irrigated 0.15 0.07 0.99 0.99 0.07 Medium Rainfed 0.47 0.25 0.63 0.55 0.14 Table 3 1 3 Summary statistics used to measure the ability of the SALUS model to predict final biomass and final grain yield during limited parameter estimation case RMSE NRMSE Willmott Correlation Bias Final biomass Maize 2332 0.14 0.95 0.96 1364 Peanut 1100 0.12 0.97 0.93 78 Cotton 2131 0.25 0.65 1.00 1173 Final grain yield Maize 771 0.10 0.98 1.00 300 Peanut 270 0.07 0.99 0.98 114 Cotton 504 0.14 0.93 1.00 435

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145 Table 3 1 4 Summary statistics used to measure the ability of the SALUS model to predict in season biomass, in season LAI, final biomass and grain yield during independent testing Crop Cultivar RMSE NRMSE Willmott Correlation Bias In season biomass Maize Medium 868 0.11 1.00 0.99 424 Peanut Medium 1543 0.24 0.97 0.97 1109 Long 567 0.10 1.00 1.00 286 Cotton Medium 839 0.19 0.99 0.97 228 In season LAI Maize Medium 0.42 0.19 0.97 0.98 0.31 Peanut Medium 0.51 0.16 0.98 0.97 0.30 Long 0.98 0.26 0.95 0.97 0.66 Cotton Medium 1.22 0.63 0.62 0.45 0.86 Final biomass All crops 2185 0.14 0.90 1.00 1781 Grain yield All crops 1727 0.28 0.89 1.00 167

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146 Figure 3 1. Diagram of the limited and detailed case parameter estimation procedures

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147 Figure 3-2. Diagnostic plots and distribut ion of maize medium maturity groups maximum LAI and maximum RUE calibrated using the detailed dataset 01 02 03 04 0 0.00.20.40.60.81.0 LagAutocorrelation of maximum LAI A 01 02 03 04 0 0.00.20.40.60.81.0 LagAutocorrelation of maximum RUE B 34567 IterationMaximum LAI ( m2 m2) 0250500750100049250495004975050000 C 3.03.54.04.5 IterationMaximum RUE (g MJ 1) 0250500750100049250495004975050000 D 01000020000300004000050000 2345678 Number of model executionsMean Maximum LAI ( m2 m2)E 01000020000300004000050000 3.03.54.04.5 Number of model executionsMean Maximum RUE (g MJ1)FMaximum LAI ( m2 m2)Density 12345678 0.00.20.40.6 GMaximum RUE (g MJ 1)Density 3.0 3.5 4.0 4.5 0.00.20.40.60.81.01.2 H

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148 Figure 3-3. Diagnostic plots and distribut ion of peanut medium maturity groups maximum LAI and maximum RUE calibrated using the detailed dataset 01 02 03 04 0 0.00.20.40.60.81.0 LagAutocorrelation of maximum LAI A 01 02 03 04 0 0.00.20.40.60.81.0 LagAutocorrelation of maximum RUE B 5678 IterationMaximum LAI ( m2 m2) 0250500750100049250495004975050000 C 1.62.02.42.8 IterationMaximum RUE (g MJ 1) 0250500750100049250495004975050000 D 01000020000300004000050000 45678 Number of model executionsMean Maximum LAI ( m2 m2)E 01000020000300004000050000 1.52.02.53.0 Number of model executionsMean Maximum RUE (g MJ1)FMaximum LAI ( m2 m2)Density 345678 0.00.10.20.30.40.50.6 GMaximum RUE (g MJ 1)Density 1.5 2.0 2.5 3.0 0.00.51.01.5 H

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149 Figure 3-4. Diagnostic plots and distribut ion of cotton medium maturity groups maximum LAI and maximum RUE calibrated using the detailed dataset 01 02 03 04 0 0.00.20.40.60.81.0 LagAutocorrelation of maximum LAI A 01 02 03 04 0 0.00.20.40.60.81.0 LagAutocorrelation of maximum RUE B 23456 IterationMaximum LAI ( m2 m2) 0250500750100049250495004975050000 C 2.02.22.42.62.83.0 IterationMaximum RUE (g MJ 1) 0250500750100049250495004975050000 D 01000020000300004000050000 23456 Number of model executionsMean Maximum LAI ( m2 m2)E 01000020000300004000050000 2.02.22.42.62.83.0 Number of model executionsMean Maximum RUE (g MJ1)FMaximum LAI ( m2 m2)Density 123456 0.00.10.20.30.40.5 GMaximum RUE (g MJ 1)Density 2.02.22.42.62.83.0 0.00.51.01.5 H

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150 Figure 3-5. Posterior distribution of maximu m LAI for three maize maturity groups under A) limited and B) detailed dataset calibration, shown with their means Figure 3-6. Posterior distri bution of maximum RUE for th ree maize maturity groups under A) limited and B) deta iled dataset calibration, shown with their means 2468 0.00.20.40.6 Maximum LAI ( m2 m 2)Gaussian kernel density Limited dataset Short Medium LongA 2468 0.00.20.40.6 Maximum LAI ( m2 m 2)Gaussian kernel density B 3.03.54.04.5 0.00.20.40.60.81.01.2 Maximum RUE (g MJ 1)Gaussian kernel density Limited dataset Short Medium LongA 3.03.54.04.5 0.00.20.40.60.81.01.2 Maximum RUE (g MJ 1)Gaussian kernel density B

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151 Figure 3-7. Posterior distribution of ma ximum LAI for three peanut maturity groups under A) limited and B) deta iled dataset calibration, shown with their means Figure 3-8. Posterior distribution of ma ximum RUE for three peanut maturity groups under A) limited and B) deta iled dataset calibration, shown with their means 2345678 0.00.20.40.60.81.0 Maximum LAI ( m2 m 2)Gaussian kernel density Limited dataset Short Medium LongA 2345678 0.00.20.40.60.81.0 Maximum LAI ( m2 m 2)Gaussian kernel density Detailed dataset Short Medium LongB 1.52.02.53.0 0.00.51.01.52.0 Maximum RUE (g MJ 1)Gaussian kernel density Limited dataset Short Medium LongA 1.52.02.53.0 0.00.51.01.52.0 Maximum RUE (g MJ 1)Gaussian kernel density B

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152 Figure 3-9. Posterior distri bution of A) maximum LAI and B) maximum RUE using the limited and detailed da tasets for cotton Figure 3-10. Calibration: comparison of observed and simulated biomass and grain yield based on mean parameter values from the detailed (A and C) and limited (B and D) case distributions 23456 0.00.10.20.30.40.5 Maximum LAI ( m2 m 2)Gaussian kernel density A 2.02.22.42.62.83.0 0.00.51.01.5 Maximum RUE (g MJ 1)Gaussian kernel density Limited dataset Detailed datasetB 05000100001500020000 0500015000 Observed biomass (kg ha 1)Predicted biomass (kg ha 1) Maize Peanut CottonA 05000100001500020000 0500015000 Observed biomass (kg ha 1)Predicted biomass (kg ha 1) Maize Peanut CottonB 0200040006000800012000 02000600010000 Observed grain yield (kg ha 1)Predicted grain yield (kg ha 1) Maize Peanut CottonC 0200040006000800012000 02000600010000 Observed grain yield (kg ha 1)Predicted grain yield (kg ha 1) Maize Peanut CottonD

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153 Figure 3-11. Calibration: maize medium irri gated biomass and LAI simulated by DSSAT and SALUS based on the detailed (A and C) and limited cases (B and D) Figure 3-12. Calibration: maize medium ra infed biomass and LAI simulated by DSSAT and SALUS based on the detailed (A and C) and limited (B and D) cases 020406080100120 0500015000 Days after plantingMaize biomass (kg ha 1) Observed SALUS DSSATA 020406080100120 0500015000 Days after plantingMaize biomass (kg ha 1) Observed SALUS DSSATB 020406080100120 012345 Days after plantingMaize LAI (m2 m 2) C 020406080100120 012345 Days after plantingMaize LAI (m2 m 2) D 020406080100120 02000600010000 Days after plantingMaize biomass (kg ha 1) Observed SALUS DSSATA 020406080100120 02000600010000 Days after plantingMaize biomass (kg ha 1) Observed SALUS DSSATB 020406080100120 0.01.02.03.0 Days after plantingMaize LAI (m2 m 2) C 020406080100120 0.01.02.03.0 Days after plantingMaize LAI (m2 m 2) D

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154 Figure 3-13. Calibration: peanut medium i rrigated biomass and LAI simulated by DSSAT and SALUS based on the detail ed (A and C) and limited (B and D) cases Figure 3-14. Calibration: peanut medium rainfed biomass and LAI simulated by DSSAT and SALUS based on the detailed (A and C) and limited (B and D) cases 020406080100120140 04000800012000 Days after plantingPeanut biomass (kg ha 1) Observed SALUS DSSATA 020406080100120140 04000800012000 Days after plantingPeanut biomass (kg ha 1) Observed SALUS DSSATB 020406080100120140 0123456 Days after plantingPeanut LAI (m2 m 2) C 020406080100120140 0123456 Days after plantingPeanut LAI (m2 m 2) D 020406080100120140 04000800012000 Days after plantingPeanut biomass (kg ha 1) Observed SALUS DSSATA 020406080100120140 04000800012000 Days after plantingPeanut biomass (kg ha 1) Observed SALUS DSSATB 020406080100120140 0123456 Days after plantingPeanut LAI (m2 m 2) C 020406080100120140 0123456 Days after plantingPeanut LAI (m2 m 2) D

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155 Figure 3-15. Calibration: cotton medium i rrigated biomass and LAI as simulated by DSSAT and SALUS based on the detail ed (A and C) and limited (B and D) cases Figure 3-16. Calibration: cotton medium ra infed biomass and LAI as simulated by DSSAT and SALUS based on the detail ed (A and C) and limited (B and D) cases 0 50 100150 04000800012000 Days after plantingCotton biomass (kg ha 1) Observed SALUS DSSATA 0 50 100150 04000800012000 Days after plantingCotton biomass (kg ha 1) Observed SALUS DSSATB 0 50 100150 0.01.02.03.0 Days after plantingCotton LAI (m2 m 2) C 0 50 100150 0.01.02.03.0 Days after plantingCotton LAI (m2 m 2) D 0 50 100150 02000400060008000 Days after plantingCotton biomass (kg ha 1) Observed SALUS DSSATA 0 50 100150 02000400060008000 Days after plantingCotton biomass (kg ha 1) Observed SALUS DSSATB 0 50 100150 0.01.02.03.0 Days after plantingCotton LAI (m2 m 2) C 0 50 100150 0.01.02.03.0 Days after plantingCotton LAI (m2 m 2) D

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156 Figure 3-17. Calibration: distribution of peanut medium maturity groups in-season biomass (A and B) and LAI (C and D) for the irrigated (A and C) and rainfed (B and D) treatments, s hown with observed data Figure 3-18. Validation: observed and simulated biomass and grain yield using mean parameter values from the detailed (A and C) and limited (B and D) cases for all treatments used in the independent testing 5000100001500020000 667380101108115122129143 Days after plantingPeanut biomass (kg ha 1) Observed SimulatedA 5000100001500020000 6673808794101108115122129136143 Days after plantingPeanut biomass (kg ha 1) Observed SimulatedB 234567 667380101108115122129143 Days after plantingPeanut LAI (m2 m 2)C 234567 6673808794101108115122129136143 Days after plantingPeanut LAI (m2 m 2)D 050001000015000 050001000015000 Observed biomass (kg ha 1)Predicted biomass (kg ha 1) Maize Peanut CottonA 05000100001500020000 0500015000 Observed biomass (kg ha 1)Predicted biomass (kg ha 1) Maize Peanut CottonB 0200040006000800012000 02000600010000 Observed grain yield (kg ha 1)Predicted grain yield (kg ha 1) Maize Peanut CottonC 0200040006000800012000 02000600010000 Observed grain yield (kg ha 1)Predicted grain yield (kg ha 1) Maize Peanut CottonD

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157 Figure 3-19. Validation: i ndependent testing of maize medium maturity groups with parameters from the detail ed (A and C) and limited (B and D) cases, using the vegetative stress treatment from the Gainesville 1982 experiment Figure 3-20. Validation: i ndependent testing of peanut medi um maturity groups with parameters from the detail ed (A and C) and limited (B and D) cases, using the Marianna 1983 experiment 020406080100120 050001000020000 Days after plantingMaize biomass (kg ha 1) Observed SALUS DSSATA 020406080100120 050001000020000 Days after plantingMaize biomass (kg ha 1) Observed SALUS DSSATB 020406080100120 01234 Days after plantingMaize LAI (m2 m 2) C 020406080100120 01234 Days after plantingMaize LAI (m2 m 2) D 0 50 100150 04000800012000 Days after plantingPeanut biomass (kg ha 1) Observed SALUS DSSATA 0 50 100150 04000800012000 Days after plantingPeanut biomass (kg ha 1) Observed SALUS DSSATB 0 50 100150 012345 Days after plantingPeanut LAI (m2 m 2) C 0 50 100150 012345 Days after plantingPeanut LAI (m2 m 2) D

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158 Figure 3-21. Validation: i ndependent testing of peanut l ong maturity groups with parameters from the detail ed (A and C) and limited (B and D) cases, using the Marianna 1983 experiment Figure 3-22. Validation: i ndependent testing of cotton m edium maturity groups with parameters from the detail ed (A and C) and limited (B and D) cases, using the Arizona control CO2, 1989 experiment 050100150 04000800012000 Days after plantingPeanut biomass (kg ha 1) Observed SALUS DSSATA 050100150 04000800012000 Days after plantingPeanut biomass (kg ha 1) Observed SALUS DSSATB 050100150 0123456 Days after plantingPeanut LAI (m2 m 2) C 050100150 0123456 Days after plantingPeanut LAI (m2 m 2) D 0 50100150 02000600010000 Days after plantingCotton biomass (kg ha 1) Observed SALUS DSSATA 0 50100150 02000600010000 Days after plantingCotton biomass (kg ha 1) Observed SALUS DSSATB 0 50100150 0.01.02.03.0 Days after plantingCotton LAI (m2 m 2) C 0 50100150 0.01.02.03.0 Days after plantingCotton LAI (m2 m 2) D

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159 CHAPTER 4 SPATIAL AND TEMPORAL VARIABILITY OF RAINF ALL IN SOUTHWEST GEO RGIA Introduction Precipitation ranks among the most variable components in the climate system. It is also the most recurrent meteorological variable in variability studies (Hubbard, 1994; Willmott et al., 1996) Numerous studies have shown that precipitation var ies both in space and time at regional (Baigorria et al., 2007) state (Boone et al., 2012) and watershed level s (Bosch et al., 1999) The strong spatial and seasonal trends demonstrated in these studies suggest that observed variability at regional level would not be preserved at smaller scales where water use and management decisions are taken or implemented. For example, the assumpti on of spatial homogeneity of precipitation used in some modeling applications is not valid (Goodrich et al., 1995) Due to its inherent variability, pre cipitation constitutes one of the most difficult atmospheric variables to predict or generate (Guenni and Hutchinson, 1998; Baigorria and Jones, 2010) Ward and Robinson ( 2000) observed that while the pattern of preci pitation has deterministic characteris tics, its timing and magnitude are essentially stochastic, which makes its variability large and prediction challenging. If regional variability is not valid at local scale s then an understanding of smaller scale varia bility is required. In addition to scientific understanding, quantification of precipitation variability produces vital information for a range of management and modeling applications. Moreover, stud ies of precipitation variability inform on underlying pro cesses governing the formation of precipitation in a given region A s an important component of the water cycle, land cover and land use exert a significant influence on the occurrence and distribution of precipitation and more

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160 generally affect local and regional climate (Pielke and Avissar, 1990) The physical basis for this relationship is that since t he dominant components of net radiative energy at the land surface are latent and sensible heat the presence of vegetative cover and moisture sources favors evapotranspiration therefore increas es latent heat exchange. More latent heat creates a higher potential for moist convection and increase s convective available potential energy which in turn promotes precipitation (Pielke, 2001) O bservational and modeling studies have demonstrated that the rel ative proportions of latent and sensible heat significantly affect the timing and intensity of cloud formation over an area Results from a range of these studies are summarized in the review by Pielke ( 2001) For example, Barnston and Schickedanz ( 1984) found that over the southern Great Plains, irrigation resulted in a decrease of the daily maximum temperature by 2 o C in dry, hot conditions and an increase in precipitation when synoptic conditions allowed an uplift of the additional moisture produced by irrigation. Other studies suggested that severe thunderstorms were more likely over irrigated areas than over a prairie (Pielke and Avissar, 1990) Ava ilability of precipitation data at the appropriate spatial resolution largely dictates the degree to which the variability information is accounted for in management decisions or incorporated in modeling studies. Although networks of weather stations are o ften available at state and watershed levels in many regions in the U.S. (Bosch et al., 2007) systematic rainfall measurement at a spatial resolution higher than th e county level is not widespread. The relevance of dense precipitation measuring networks was emphasized in a host of studies (McConkey et al., 1990; Willmott et al., 1996; Bosch et al., 1999; Changnon, 2002; van de Beek et al., 2 011) In particular, Willmott et al. ( 1996)

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161 found using 457 weather stations in the U.S. that most of the spatio temporal v ariability in long term averages o f precipitation was spatial. The authors concluded that this patial variability was insufficiently captured the networks of weather stations studied. While the importance of precipitation variability is widely recognized, the scale at which this variabilit y becomes critical strongly depends on the study considered. In Canada, McConkey et al. ( 1990) found that spatial variability was considerably larger for small storms (less than 7.5 mm). In extreme cases, rainfall differences at sites only 800 m apart were 12.5 mm or more per storm day (McConkey et al., 1990) In Denmark, rain gauges located in a single radar pixel of dimensions 500 m by 500 m exhibited up to 100% variability (Jensen and Pedersen, 2005) Other studies in mountainous areas found strong correlations (hence less variability) at sep aration distances less than 4 km (Buytaert et al., 2006) In all these studie s the critical threshold distance where rainfall variability was found depended upon the smallest spacing between rain gauges. In Oklahoma, Goodrich et al. ( 1995) found that an average gradient of 1.2 mm per 100 m per storm was present in the variability of rainfall in a small catchment of 4.4 ha. In an analysis of five dense rain gauge networks, Krajewski and Ciach ( 2003) concluded that sites situated in or near the Tropics such as Florida and Brazil presented the lowest rainfall correlation values while locations further north such as Oklahoma and Iowa had longer correlation r anges. In the U.S. High Plains, Hubbard ( 1994) estimated that to explain 90% of variability in precipitation between sites, spacing between rain gauges needed to be smaller than 5 km. Among the meteorological variables studied (precipitation, air temperature, relative humidity, solar radiation, evapotranspiration, wind, soil temperature), precipitation was the most variable in space and time. These

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162 results show that precipitation spatial variability is influenced by climate regimes, relief and the time scale considered. In partic ular, it has been shown that precipitation climatologies are strongly affected by the density of weather locations considered. Willmott et al. (1994) demonstrated th at precipitation averages for different continents could be estimated more accurately if a larger numb er of weather locations were used and important precipitation gradients were captured The present study was designed to provide a quantitative understanding of the spatial and temporal variability of rainfall from farm ( less than 10 km) to county (60 km) levels in a way that contributes to aggregation and disaggregation of rainfall and the implications of these scale changes on crop predictions in the southeast ern U S. The southwestern part of Georgia has been traditionally an influential contributor to row crop production in the state and the southeast ern U S (USDA, 2011) It was anticipated that this region (hereafter referred to as study area) would experience precipitation variability found in other studies for the southeast ern U.S. However, smaller scale precipitation heterogeneity has not been systematically quantified in the area. Therefore, the magnitude of this variability remained unknown. Essentially all precipitation received in the area is in the form of rainfall which is mainly driven by frontal and convective processes. During the winter season, stratiform precipitat ion controlled by synoptic scale disturbance dominates as air masses from Canada, the Gulf of Mexico and the Atlantic Ocean create frontal activities in the region. During the warm summer seasons, the Tropical Gulf and the Tropical Atlantic air masses are still of great importance (Sorman, 1975) and their movement is enhanced by local convection uplift mechanisms. This is facilitated by the culminat ion of latent heat inherent to summer

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163 afternoons and result in intense and short duration thunderstorms (Bosch et al., 1999) Being located in the mid latitudes, the region occasionally receives significant amount of prec ipitation due to tropical cyclones. Earlier studies conducted in a neighboring watershed indicated that rainfall characteristics and correlation patterns were largely dependent upon the season with winter and summer exhibiting the highest contrast in virtu ally all aspects (Sorman, 1975; Bosch et al., 1999) This paper concentrates only o n the spatial and temporal rainfall variability component of our research. Specific objectives were to: 1. Describe the characteristics of storms occurring in the study area; 2. Quantify correlations of daily rainfall events and amounts among rain gauges ; 3. Descr ibe spatial and temporal changes in correlations among rain gauges ; 4. Model the spatial correlation structure to interpolate rainfall and compare results with the Inverse Distance Weighting approach. Materials and Methods Study Area The study area lies in so uthwest Georgia and covers three counties, Dougherty, Baker and Mitchell. This area is essentially covered by the Lower Flint watershed. Current land use is predominantly farming based with maize, peanut and cotton as the most common row crops planted in v arious rotation patterns. Variability of total rainfall (from June 2010 to May 2011) indicated that Dougherty County (that had the largest number of plantations) showed a tendency to receive more rainfall than Baker and Mitchell (Fig ure 4 1). A total of 46 tipping bucket rain gauges were installed between August 2009 and April 2010 on 30 farms (Fig ure 4 1) over a total area of 3100 km 2 Locations for these

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164 rain gauges were identified through on farm visits and consultation with farmers and county extension s with the top of the gauge raised to approximately 61 cm above the ground. Although the locations of the gauges could not be determined prior to the beginning of the study, the distribution of th e pairwise separation distances approached a normal shape with a mean of 25 km and a standard deviation of 12 km (Fig ure 4 2). A deliberate effort was made to include a wide range of distances (1 to 62 km) to cover different scales of observed rainfall var iability reported in the literature and verify if measurable variability exists at farm level. In addition to these rain gauges, the University of Georgia operates 4 weather stations in the area as part of the Georgia Automated Environmental Monitoring Network (GAEMN). The analyses conducted in this paper required 5 min rainfall data, hence only rainfall data from the 46 rain gauges were used. Tipping Bucket Rain Gaug e The rainfall data analyzed in this paper were collected using tipping bucket rain gauges. A typical HOBO rain gauge is a relatively simple device that is equipped with a funnel to collect and direct the rainfall as a narrow stream into the tipping bucket a magnet switch and a small data logger. Rainfall travels down through the funnel and fills the upper side of the bucket that tips under the weight of the water, releasing the magnet and raising the other side of the bucket. This rainfall event is record ed by the data logger. The rainfall amount corresponding to a tip of the bucket equals 0.254 mm (0.01 inches). The rainfall amount collected during a specified period is simply the number of tips registered during that period multiplied by 0.254 mm. Prior to installation, the rain gauges were calibrated to ensure that they provide an accurate number of tips for a given volume of water with a tolerance of +/ 2 tips. It has been documented that

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165 during intense thunderstorms the tipping bucket mechanism tends to underestimate the actual amount of rainfall as part of the rain falling between two successive tips fails to get captured by the bucket (La Barbera et al., 2002) Molini et al. ( 2005) estimated that the resulting bias was about 10 15% for high intensity rainfall in excess of 200 mm h 1 The rainfall data was not adjusted for high intensi ty events because 90% of storms in the area had an intensity of 50 mm h 1 or less. The highest intensity recorded was 120 mm h 1 which was a rare event. The Rainfall Data The original rainfall data w ere collected at a temporal resolution of 5 min and spanned the period May 2010 to August 2011. Depending on the analysis performed the data w ere temporally aggregated to obtain hourly, daily or seasonal rainfall. Because the characteristics of rainfall varie d with season, analyses were conducted for each of the four seasons separately, winter (December January February), spring (March April May), summer (June July August) and fall (September October November). This seasonal grouping was motivated by observed temporal patterns in storm properties and rainfall correlations near the study area (Bosch et al., 1999) in the southeast U.S. (Baigorria et al., 2007) and in other regions in the U.S. (Lyons, 1990) Long term record of the Palmer Drought Seve rity Index (PDSI, Heim Jr, 2002) obtained from the National Climatic Data Center (NCD C, 2012) confirmed that over the study area, 2010 was a wet year in all seasons while 2011 was dry in winter and spring with a tendency to be extremely dry in the summer and fall (Fig ure 4 3). Analysis of the Spatial Variability of Storms This analysis was conducted on the 5 min rainfall data and consisted of isolating and characterizing individual storms that were observed in each season. The analysis

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166 was performed at both regional and local level s to extract information about storm characteristics at e ach site and examine how regional patterns in storm attributes evolve over time. The core of this analysis was the definition of storm events that were subsequently identified throughout the time series. In the regional storm analysis, storm events were defined regionally. The beginning of an event was marked by the observation of positive rainfall depth, that i s a value greater or equal to 0.254 mm (Diem, 2011) at any of the 46 sites. The storm event was ended when all of the 46 sites stopped receiving a positive rainfall. During a particular event, rainfall may start and end at specific rain gauges but a storm considered as regional would end only when all rain gauges stop recording rainfall. This implied that different sites cou ld have different beginning and end times as well as different storm durations. A typical storm event may contain brief dry periods embedded in it, during which cloud movements continue followed by an increase or decrease in rainfall intensity. A minimum d uration between two storm events to consider them separate was defined to account for this type of behavior. If this duration was set to a low value, many storms would be identified and some storms would be split into several sub storms. On the contrary, a high value would result in few long duration storms because some storms would be merged together. A calibration of this parameter was performed (by running the analysis using different values) to obtain a value of 1 hour. Other authors have used larger du rations for example 6 hours (Huff and Shipp, 1969; Changnon, 2002) but this duration was calibrated to confine most precipitation events within a 24 hour period to enable comparison with daily rainfall (Huff and Shipp, 1969) T he 1 hour dry duration was supported by the need to capture shor t duration

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167 thunderstorms in a region where mean summer rainfall duration was found to be one hour or less (Sorman, 1975; Bosch et al., 1999) Other criteria defined to tailor the a lgorithm for our context a re summarized in Table 4 1. The characteristics of the storms (e.g. duration, intensity, total rainfall depth) were computed for each event. Global storm duration was computed as the time difference between the end and the beginning of the event. Within each storm, specific durations to each location were also calculated and averaged to obtain aggregated storm durations. Similarly, stor m rainfall intensity was computed at each location as the ratio of storm rainfall depth to location specific storm duration. Aggregated versions of these storm attributes were derived as basic storm characterization. In addition to the basic statistics, a large storm characterization was also conducted to examine the variability of storms that produce significant amount of rainfall. A large storm was defined as one that produced at least 25.4 mm of rainfall depth at one or more locations covered by the even t. While the regional storm analysis emphasized the regional aspect of the rainfall process, the local analysis concentrated on rainfall variability at specific locations. Basic storm characterization was performed at each location individually. This analy sis sought to reveal if there was any extreme behavior in the storm properties that was absorbed in the regional analysis. To demonstrate qualitatively possible association between mid tropospheric troughing and large scale rainfall events, 500 mb geopoten tial height maps were obtained from the NCEP/NCAR reanalysis data (Kalnay et al., 1996) Analysis of the Spatial Variability of Rainfall Correlations The correlation analysis was carried out using hourly and daily rainfall amounts and daily events to reveal any influence exerted by the time scale of the data. Hourly

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168 correlations were expected to highlight differences in within day and within storm variations across locations while correlations based on daily rainfall amount s and event s would emphasize similarities that are releva nt to process models using rainfall on a daily time step. Spearman rank correlations were computed for each pair of locations after eliminating dry days and dry hours at both locations to avoid overestimating the correlation value. The effect of omnidirect ional distance was investigated by studying the relationship between correlation and distance separating pairs of gauges. The effect of direction was examined by verifying if there w as any influence of the angles associat ed with the pairs of locations on t heir correlation values. The direction considered here was in the sense of bearing i.e. the direction of travel from one point to the other. North was established as 0 o east was 90 o with the angle increasing clockwise. The direction of travel did not depe nd on the departing point meaning that angles along the same axes were equivalent (angle ). The profile of correlation decay from a given location was depicted by mapping the correlation between that location and the remaining others. Analysis o f Spatial Dependence for Rainfall Interpolation In the analysis of spatial dependence, our interest was to generalize the correlation analysis into a formal model that could be used for interpolating rainfall. The interpolation method that meets this requi rement is known as kriging which has several variants depending on the implementation (Goovaerts, 1997) As a geostatistical method, kri ging requires that rainfall amount recorded at a location be regarded as a random variable with a probability density function. The set of random variables

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169 where is the total number of locations where rainfall data were measured, define a random function or process. Following this framework, the procedure of kriging interpolation can be summarized in three steps. First, the sample semivariogram (or simply variogram) was estimated. The spatial variation in the random proc ess was described by the variogram that summarizes the degree of similarity among pairs of random variables as measured by the semivariance. The estimator of the semivariance based on the sample data was (Webster and Olivier, 2007) : ( 4 1 ) where and represent the values of rainfall amounts measured at a pair of locations separated by the distance ; is the number of pairs of data points corresponding to the lag The semivariance was computed based on daily rainfall data at each location using the original definition of semivariance (Webster and Olivier, 2007) : ( 4 2 ) This definition indicates that the semivariance is equivalent to the average variance at both locations minus their covariance. The relationship between the sample semivariance and separation distance was depicted by the sample variogram that was anisotropic, i.e. no directional effect was taken into account. A critical assumption in geostatistical modeling is that of stationarity of the random process. In our context, it is sufficient to interpret stationa rity as

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170 constancy of the mean rainfall amount (daily or seasonal) over the study area and dependence of the semivariance on separation distance only. The constancy of the mean implies that the variability observed in individual observations can be attribut ed to random fluctuations of rainfall and not to an underlying driving force. If such an underlying factor exists its influence must be eliminated via trend removal. Polynomial functions of the spatial coordinates (longitude and latitude) from degree one t o three were fitted to determine if they would explain any significant amount of variability in daily or total seasonal rainfall. Degree two polynomials were retained and used to remove trends prior to computing the sample variograms because there was no a dditional improvement in the amount of variability explained at the third degree. Kriging performed without trend removal was termed ordinary kriging while universal kriging referred to kriging with a spatial drift. The second step of the analysis consist ed of generalizing the sample variogram into a variogram model. The sample variogram describes the covariance function at discrete lags but kriging predictions are often needed at any lags. The variogram model represents the covariance function with such s patial continuity. In this application, the spherical model was selected as it fitted appropriately the sample variogram and has been recognized as a robust model in other rainfall studies (We bster and Olivier, 2007; van de Beek et al., 2011) : ( 4 3 ) where the model parameters are the nugget or variability at zero lag; the sill or the maximum semivariance; the range or distance beyond which the process

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171 becomes decorrelated. The variogram model parameters were fitted using weighted least squares (Diggle and Ribeiro Jr, 2007) In the third and last step, the interpolated rainfall at a new location was obtained as a weighted linear combination of available samples. A kriging estimate is unbiased (the expected value of the error on the estimate equals zero) and its variance minimum: ( 4 4 ) where is the interpolated value at the new location is the weight associated with the measurement and is the number of samples (measurements) available for the estimation. A comparison was performed between kriging and the inverse distance weighting (IDW) interpolation method to elucidate accu racy gains resulting from accounting for spatial correlation in the interpolation procedure. Some studies that compared different interpolations methods reported that in low density sampling situations, IDW outperformed kriging (Nalder and Wein, 1998) Inverse Distance Weighting is unbiased as well and as a weighted linear combinatio n method, it also makes use of E quation 4 4. The key difference between IDW and ordinary kriging however, is that in IDW the weights are exclusively based on distance which d enies this approach any account for spatial correlation in the data. Mathematically this translates to ( 4 5 ) where is the number of data points available for the estimation at location and is the Euclidian distance between the estimation location and the sample location.

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172 For each of the three approaches (ordinary kriging, universal kriging and IDW), daily rainfall at each point was interpolated based on the remaining data points (lea ve one out predictions). Results and Discussion Spatial and Temporal Variability of Storms Total seasonal rainfall (TSR) at a location varied from 60 mm (in Fall 2010) to 494 mm (in summer 2011). Summer rainfall exhibited the highest spatial variability wi th a standard deviation of 65 mm (in 2010) and 66 mm (in 2011). However, the study area received more rain in summer 2010 (mean of 355 mm over the whole study area) than in summer 2011 (mean of 261 mm). Fall 2010, winter 2011 and spring 2011 showed similar TSR variance (standard deviations of 24, 23 and 29 mm respectively) but winter 2011 was the second largest rain producer following the two summers (means of 138, 235 and 162 mm respectively). Temporally aggregated rainfall as TSR did not inform on the cha racteristics of specific storms that produced the rainfall The study of these storms provided further ins ight into the mechanics behind the variability in TSR. All regional storm events A total of 137 storms meeting the criteria defined in Table 4 1 were identified during the period spanning June 2010 to August 2011. More than 40% of the storms (exactly 56 storms) occurred in summer 2011 alone while 22% (30 storms) occurred in summer 2010 (Fig ure 4 4); however, 2010 storms produced higher rainfall amounts. Winter 2011 produced 20 storms (15% of all storms) while fall 2010 and spring 2011 had nearly the same number of storms (15 and 16 storms respectively, representing 11 and 12% of all storms). Sp ecific characteristics of these storms were highly variable and their combination can be regarded as a defining factor of these seasons.

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173 There was a large difference in average rainfall duration across seasons. Summer storms had an average duration of 2.79 hours in 2010 and 1.6 hours in 2011 (Tab le 4 2). There was a large variability in the duration of summer regional storms with coefficients of variability (CV) exceeding 200%. In contrast to the relatively short duration and highly variable storms observed in summer, the average winter storm lasted 9.33 hours with comparatively little variation around this mean (standard deviation of 5.43 hours). Between the two extremes represented by summer and winter, the variability among regional storm durations were s imilar for fall 2010 and spring 2011 but fall storms had a tendency to last longer. Spatially aggregated storm durations followed similar trends as the regional storm durations but the means were smaller and the CVs slightly larger for all seasons (Tab le 4 2). The mean global durations were larger, sometimes nearly twice as large (e.g. summer 2011, Tab le 4 2) because they included the earliest and latest tips at the first and last rain gauge to mark the beginning and end of the storms; thus they are to be interpreted as the longest storm durations within the conditions of the analysis. The spatially aggregated duration accommodated subtle variations in storm duration as it moves through specific locations. Based on the spatially aggregated statistics the av erage summer storm had a mean duration of 1.5 hours in 2010 and 0.93 hours in 2010 while for winter 2011, this mean was as high as 6 hours. Based on the Empirical Cumulative Distribution Functions (ECDF) estimated from the spatially aggregated storm durati ons, 80% of storms in summer had a duration of at most 47 min regardless of the year. This duration was approximately 9 hours in winter 2011, 7 hours in fall 2010 and 3.5 hours in spring 2011 (Fig ure 4 5A).

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174 The average storm size measured as its spatial c overage in percentage of the number of gauges present in the study area, was 20% in summer 2010 and 9% in summer 2011 (that is 9 locations in 2010 and 4 locations in 2011). This was in contrast to winter storms that covered most locations, 89% of the sites on average. Fall 2010 and spring 2011 storms covered about half of the locations on average. Although the mean number of locations covered by storms varied with season, there was at least one storm in each season that affected all 46 locations simultaneou sly. The smallest storm in each season was localized to a single site (Tab le 4 2). The variability in storm spatial coverage between these two extremes was strongly dependent on the season (Tab le 4 2). Similarly to global storm duration, the order of incre asing stability in storm spatial coverage was summer 2011, summer 2010, fall 2010 and spring 2011, and winter 2011. Aggregated rainfall amount per storm varied overall from 0.51 mm to 54 mm (Fig ure 4 5C). The average summer storm yielded 6 to 7 mm. Average rainfall depths were similar in fall and spring and closer to values obtained in winter 2011 (Tab le 4 2). Winter precipitations produced nearly twice as much rainfall as in summer with about half the variability observed in any other seasons (Tab le 4 2). Unlike rainfall amount, aggregated storm intensities were larger and less variable in summer than in winter. This means that summer rainfall was consistently more intense, with an approximate average rate of 10 mm h 1 which was more than 3 times the avera ge intensity in winter (Tab le 4 2). With regard to storm intensity, summer ECDFs completely dominated winter ECDFs, and almost all of fall and spring ECDFs, over the whole range of intensity values (Fig ure 4 5D).

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175 It was found that although summer precipita tion exhibited distinct properties, i t w as characterized by a certain likelihood of occurrence of extreme events. For example summer storms were generally short, nonetheless, the longest continuous regional precipitation lasted between 3.5 and 33.75 hours depending on the gauge location (24.7 hours on average) and started on June 5, 2010 at 13.30 h (summer 2010). Likewise, rainfall amount per storm was regularly lower in summer; however, the heaviest precipitation of the period covered by the analysis was registered on July 15, 2011 at 17.30 h (summer 2011) and produced between 2.3 and 107 mm depending on the location (average of 54 mm). Not surprisingly, the most intense storm started on August 21, 2010 at 15.30 h had a maximum duration of 65 mns, and cov ered only 8 locations with intensities ranging from 9 to 54 mm hr 1 (average 30 mm hr 1 ). Some of these events that had a large spatial extent like the long duration June 5 storm were controlled by mid tropospheric troughing (Fig ure 4 6). As expected given its synoptic scale the little variation (CV of 15%). This result provided evidence for the existence of mesoscale to synoptic influence on summer precipitatio n in the study area. It was verified that the largest events in each season (in terms of rainfall amount and spatial coverage) had some relationship with 500 mb geopotential heights as well (Fig ure 4 6).The relationship between mid tropospheric troughing a nd summer precipitation was discussed by Diem ( 2006, 2011) for Georgia and the southeast U S and Tymvios et al. ( 2010) in other parts of the world. Large regional storm events Large storms occurred in summer and winter more frequently than in fall and spring at a rate of 3 storms per season (spring 2011) to 7 storms per season (winter

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176 2011). These storms had a considerably longer duration in summer (about 5 hours on average), which reduced the discrepancy between the five seasons (Tab le 4 3). D ifferences between large events decreased regardless of the characteristic considered because the main con tributors to the variation (small events) were eliminated. All large winter storms covered 100% of the study area. The smallest spatial coverage observed was 56% (i.e. 26 locations o f 46 ) in summer 2011 (Tab le 4 3). These large storms appeared to be more intense as well and their average rainfall amount was approximately 20 mm, which was similar for all seasons except for spring 2011 (Tab le 4 3). Dry d uration between regional storms Considering all storms identified, the dry periods between events ranged in duration from the 1 hour minimum to 27 days with variability within this range exceeding 100% (Table 4 2). As expected large rainfall events occurred less frequently and were disrupted every 3 hours to 40 days (Tab le 4 3). Fall and spring showed the lon gest periods without rainfall (13 15 days on average). The maximum dry duration that encompassed 80% of all dry periods was 4 days in summer 2010, 6 days in winter 2011, 8.5 days in fall 2010 and spring 2011, and 2.7 days in summer 2011 (Fig ure 4 5B). The dry durations correspond to the minimum drought periods possible between storms when all locations were simultaneously dry. Specific sites might demonstrate longer dry periods. These dry durations were constrained to a minimum of 1 hour (Tab le 4 1) to cap ture small storms that emerge especially in the summer. In a neighboring watershed, Sorman ( 1975) f ound that the average duration of summer rainfall cells was 53 min, which was later confirmed by Bosch et al. ( 1999) In the present study, mean

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177 rainfall duration was less than an hour in summer 2011 and more than an hour in summer 2010 (Tab le 4 2). Specification of a longer minimum dry duration would have resulted in longer summer events and an inability to capture short duration summer thunderstorms. Local storm analysis If st orm events were identified at each location separately, it would be possible to establish ECDFs describing the probability of occurrence of an event anywhere in the study area. This feature was depicted on Figure 4 7 for each season and storm attribute. Th e most striking observation was that although the relationships between the seasons seemed to be conserved to a certain degree, the variability across seasons became smaller and almost disappeared in rainfall amount (Fig ure 4 7C). Another aspect of the loc al analysis was the range of rainfall intensity and amount that can be produced on a single storm. Rainfall amounts as high as 100 mm per storm and intensities up to 120 mm hr 1 were obtained although these were rare events (Fig ure 4 7C D). The number of events recorded at a single location was higher than in the regional analysis in some seasons because the local analysis did not consider the evolution of the storm at neighboring gauges and was more likely to split large storms. Large rainfall events were particularly sparse in 2011 as some locations never experienced storms with rainfall amount of at least 25.4 mm (Tab le 4 4). In general these rainfall events appeared to be the result of afternoon thunderstorms in summer (Fig ure 4 8E). In winter and spri ng, the highest peak in precipitation onset time was between 05.00 h and 10.00 h and these events could end at any time of the day (Fig ure 4 8E F). On average, all summer and fall storms occurred in the afternoon and before 17.00 while all spring and nearl y all winter storms occurred in the morning and after

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178 07.00 (Tab le 4 4). Timing of maximum precipitation followed a pattern of mid to late afternoon (MLA) in the summer and late evening early morning (LE EM) in the winter (Figure 4 8E). The MLA diurnal pa ttern has been reported to be characteristic of precipitation occurring over land (Yang and Smith, 2006) or in coastal areas of the southeastern United States (Wallace, 1975) Diurnal variations in summer precipitations may be mostly associated with a higher degree of convective activity during this season. The diurnal cycle in sen sible heat exchange between the ground and the lower atmosphere creates conditions favorable for convective activity in summer afternoons (Wallace, 1975) A general explanation for the LE EM pattern observed in winter is the reduction in convective activity during this season coupled with the increase in st r atiform precipitation. A more condensed view of the characteristics of local storms was obtained by calculating their means by location and by season and estimating kernel densities from these means (Fig ure 4 8A D). The results were concordant with findings in the regional analysis. These distributions appeared to be symmetric and their shape, location and dispersion were strongly influenced by the season of interest. For summer that had data spanning two years, the shape and dispersion of the distri bution seemed to be preserved; only the location of distribution changed with the year. A major connection between the regional and the local analysis was that the means of spatial aggregates (Tab le 4 2) tended to coincide with the highest peaks of the dis tributions of means obtained from the local analysis for summer rainfall (Fig ure 4 8). In winter, the maximums. In other words, precipitation durations in the local analysis were too short in

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179 the winter, which was due to a too small minimum dry duration value used to separate the events. This behavior suggested that winter rainfall events were frequently interrupted by dry spells lasting more than an hour at specific sites wi thout affecting the large scale evolution of the storm. The lack of such disparity in summer confirmed the short duration of its rainfall events. Summer storm duration results obtained in the present study were concordant with findings reported in Bosch et al. ( 1999) and Sorman ( 1975) when considering the mean of spatially aggregated durations (Tab le 4 2). The means of the distribution of summer storm duration estimated from the local analysis were also in agreement with these findings. However, there was little variation in mean preci pitation duration across seasons in the results by Bosch et al. ( 1999) who reported a mean duration of 1.8 hours for winter and 1.1 hours for summer. The relationship between st orm durations across seasons was similar to findings by Changnon ( 2002) in Illinois. For example, mean winter rainfall duration was about 4.1 times as large as mean summer rainfall duration (Tab le 4 2), which was c omparable to a ratio of 4.5 in s outhern Illinois. However, in g eneral, variability within storm characteristics would greatly depend on the definition of a storm and the parameters used to identify it. A limitation of the present study is the number of years involved in the identification of storms. Although, the resu lts clearly indicated crisp differences between seasons, inter annual fluctuations would be ineluctable and specific values of the seasonal characteristics (such as rainfall duration) may be representative of the year or the type of year considered in the analysis. Correlations of Daily and Hourly Rainfall Amount s and Event s In all seasons, correlations of rainfall amount and event decreased with increasing separation distance (Fig ure s 4 9 and 4 10). The steepest descent was observed in

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180 summer where the sh ape of the correlation cloud was consistent and independent of the year. In winter, higher correlations extended over longer distances and were more resistant to the prompt decline observed in summer. Fall and spring appeared to exhibit a mix of characteri stics from summer and winter and could be uncritically regarded as transitional periods. Summer rainfall amount correlations ranged from 0.30 to 0.82 (in 2011) and 0.28 to 1.00 (in 2010). In winter the lowest correlation value was 0.54. The mean distance corresponding to a mean correlation of 0.90 was less than 3.3 km in summer and approximately 18 km in winter (Tab le 4 5). This result was illustrated more sharply in Figure 4 11 that depicted the change in correlation of rainfall amount between a particul ar site and the remaining locations. These results were concordant with findings reported by Huff and Shipp ( 1969) in Illinois (USA). Near the study area in Georgia, Bosch et al. ( 1999) estimated (based on a correlation model) that the distance corresponding to a correlation coefficient of 0.9 was 1.9 km in the summer and 9.2 km in the winter However, unlike these studies, the correlation value was not affected by the angle of orientation of location pairs. Based on the classification by Huff and Shipp ( 1969) winter correlation variation with distance was representative of precipitation induced by low pressure center passages and fronts while summer c orrelation demonstrated characteristics of air mass storms. The profile of the average relationship as portrayed in Figures 4 9 and 4 10 by the mean correlation versus mean distance showed that over the entire range of pairwise distances studied (1.8 to 6 2 km), the estimated curves dominated each other in the order winter 2011 > fall 2010 and spring 2011 > summer 2010 and summer 2011. The variability among seasons was s maller for rainfall events (Figure 4 10) with mean

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181 correlations ranging from 0.36 (in su mmer 2011) to 0.87 (in winter 2011) at the largest average separation distance. For rainfall amount, this range extended from 0.07 to 0.76 in the same respective seasons. This feature was even more explicit with the average change in correlation variance with distance: the mean standard deviation ranged from 0.03 (in winter 2011) to 0.22 (in summer 2010) for rainfall amount and, 0.04 to 0.12 (in the same respective seasons) for rainfall event at the smallest mean distance of 3.31 km (Tables 4 5 and 4 6). T his pattern in the magnitude of correlation variability was predictable due to the binary nature of the event data, which recognized only the occurrence of a rainfall event without accounting for amount differences. Correlation variance of rainfall amount increased slightly with distance in winter 2011 but a discernible pattern could not be established in other seasons although in summer there was a slight tendency to decline (Tab le 4 5). For rainfall event, the variability in mean correlation variance with distance was even less perceptible (Tab le 4 6). The general correlation pattern described for daily rainfall was valid for hourly rainfall as well. However, the specific correlation values had a tendency to be lower probably because hourly rainfall incor porated within storm variability. For two sites, within storm variability implied that their correlation coefficient would depend upon whether they both had effectively received rainfall every single hour that the event continued. This is even more critica l for winter precipitation that generally lasted more than one hour. For the same reason, winter correlation variances were higher for hourly data than for daily data. In other seasons, hourly rainfall yielded higher correlation variances than daily rainfa ll at distances smaller than 13 km; this trend was reversed beyond 13 km. Other authors reported increasing correlation variance with distance in

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182 different climates (Sumner, 1983; Baigorria et al., 2007) Normally, this would mean that a few lo cations far apart were still highly correlated, which could be the reflection of local influences (for example topography) on the winter rainfall, or regional influences (for example air mass) on the summer rainfall. These local or regional factors would n ot completely alter the quasi permanent correlation trends in the two contrasting seasons. Pronounced and steady increase in correlation variance with distance was not observed in the present study most likely because of the relatively smaller extent of th e study area (maximum distance of 62 km) and the lack of repetition of seasons. Modeling the Spatial Dependence for Rainfall Interpolation The shape of the variogram models depended upon the season and whether the spatial trends were removed prior to fitting them (Fig ure 4 12). Prior to trend removal (Fig ure 4 10A) the semivariance increased rapidly over a short distance to reach its maximum value in summer. In the other seasons, the rise in the semivariance was gradual and particularly more sustained in the winter. After trend removal (Fig ure 4 12B) the rate of increase in the semivariance became less strongly dependent upon the season suggesting that the increase in semivariance observed initially could not be attributable to distance alone. Between 4 and 8 km, the semivariance increased at a rate of 8 mm 2 km 1 in summer 2010, 6 mm 2 km 1 in summer 2011 and only 0.66 mm 2 km 1 in winter 2011 before trend removal. When the trends were removed, these rates dropped to 3.4, 2.3 and 0.37 mm 2 km 1 respectively These shape differences were directly dictated by the values of the model parameters. The nugget was the only model parameter that was not influenced by the season or trend removal. In this study, the nugget effect was non existent indicating that there was no or little variation in daily rainfall measured at the closest locations. In other

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183 words, sampling error was negligible in this experiment. In high contrast to the nugget, the range and sill were clearly responsive to seasons and trends. Between seas ons, the maximum distance at which daily rainfall was no longer correlated (range) varied from 12 km (in summer 2011) to 47 km (in winter 2011). At these distances, the spatial processes reached their maximum variances of 69 and 21 mm 2 respectively (sill). The reduction in these variances due to accounting for longitude and latitude effects was 62% in summer 2011 and 81% in winter 2011. The new correlation lengths were respectively 9 and 12 km respectively. It was evident from this anal ysis that winter rainfall was essentially stable and dominated by large scale driving forces while summer rainfall was more localized and variable as established in the correlation analysis and other studies (Baigorria et al., 2007; van de Beek et al., 2011) An interesting feature of our analysis was that while trend removal resulted in a reduction of the influence of the seasons on the range, the same statement was not true for the sill. The seasonal differences in the sill appeared to be rather exacerbated with the trend removal (Tab le 4 7) and this was a reflection of differences in the nature and scale of variability in rainfall across the seasons. Differences in the variogram model parameters affected the predictability of total seasonal rainfall in various ways. Winter and spring 2011 rainfall was mor e predictable because these two seasons combined high range (of correlation) and low sill (variance). The higher predictability of winter and spring rainfall was evident from the narrow scatter of the 1:1 relationship shown in Figure 4 13. All interpolatio n approaches included, Root Mean Square Errors (RMSE) of rainfall for these two seasons ranged from 17 (winter) to 22 mm (spring) per season ; in comparison, corresponding mean s of total seasonal

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184 rainfall were 236 and 168 mm for these seasons. Correlation b etween observed and predicted rainfall for these same seasons ranged from 0.70 (winter, IDW) to 0.77 (spring, universal kriging, Tab le 4 7). Summer and fall rainfall were the least predictable as these seasons resulted in the largest errors and the smalles t values of correlation between measured and interpolated rainfall (Tab le 4 7). Prediction differences due to interpolation methods or accounting for spatial trends in kriging were hardly noticeable (Fig ure 4 14). These results remained essentially unchang ed when total seasonal rainfall was interpolated directly using the variograms based on daily data (results not shown) suggesting that variogram characteristics of spatial variation in rainfall were similar at daily and seasonal scales. These results wer e comparable to findings by Nalder and Wein ( 1998) who reported mixed results from the comparison of different interpolation methods, with IDW outperforming kriging when sampling density was low. Other stud ies reported improved kriging predictions when the spatial trend was removed using meaningful explanatory factors such as slope, aspect and topography (Buytaert et al., 2006) It has been established that in general, simple interpolation methods like IDW will perform as well as advanced methods if sufficient data are available (Willmott et al., 1996; Bolstad, 2008) Bivand et al. ( 2008) suggested that ordinary kriging would tend to produce results similar to IDW if the variogram used had no nugget effect. Ho wever, despite the lack of nugget effect in the present study we could not associate the similarity between IDW and kriging to this absence of microscale variability as we explored the use of different values of the nugget with no significant impact on th e results. The range was the only variogram model parameter that was found to influence the kriging predictions

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185 and this was more critical for ordinary than it was for universal kriging. The sensitivity of ordinary kriging predictions to the range was just ifiable because the range practically determines the number of sampled locations to participate in an estimation as well as the magnitude of their weights by influencing their statistical distance to the estimation point (Isaaks and Srivastava, 1989) The similarity between ordinary kriging and IDW was attribut ed to little differences between statistical distance (based on correlations) and geographical distance, which seemed to be an inherent property of spatial variation of rainfall (Grimes and Pardo Iguzquiza, 2010) The similarity between kriging and IDW rainfall estimates did not necessarily mean that the two approaches were equivalent in all respects. It was found that kriging demonstrated desirable values of properties such as unbiasness and overdispersion. Althoug h IDW and ordinary kriging were unbiased, IDW was more likely to result in larger bias after predictions. For most seasons, ordinary kriging predictions resulted in a bias equal or close to zero. Furthermore, both IDW and kriging produced predictions that had a variance lower than the variance of the measurements (overdispersion), meaning that a portion of the measured variance could not be explained by the prediction model. This smoothing side effect was known to affect kriging (Webster and Olivier, 2007) but in the present study, it affected IDW even more. The ratio between obser ved and predicted variance ranged from 1.1 to 1.5 in both kriging combined and 1.7 to 2.7 in IDW. Conclusion s s in southwest Georgia provided the opportunity to investigate storm ch aracteristics and spatio temporal rainfall relations at scales ranging from 1 to 60 km. Summer and winter

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186 portrayed the highest contrast in terms of storm characteristics. Most summer storms were more frequent, had an approximate duration of one hour or le ss and were characterized by moderate rainfall amount s and high rainfall intensit ies Winter rainfall events had longer durations and always covered a large portion of the study area. Due to the scale and duration of winter rainfall events they produced h igher rainfall amount s per storm but their overall rainfall intensities were the lowest of all seasons. Fall and spring tended to exhibit a mix of characteristics from the two contrasting seasons and could be regarded as transition seasons. They could also be distinguished by longer rainfall interruptions. Statistical distribution s of mean storm characteristics and empirical cumulative distribution functions were estimated from the data to reveal the trends and ranges provided by the analysis. It was demons trated that although summer rainfall tended to be convective in nature, it was also affected by large scale synoptic controls. Correlation s of daily and hourly rainfall amount s between pairs of locations were inversely related to their separation distance s. Summer correlations decreased faster than any other seasons. The w inter correlation curve was entirely superior to those of the other seasons over the whole range of distance investigated. Spring and fall correlation curves were similar and located betw een the two extremes. The spatial variation of the correlation between a given location and the remaining sites was consistent with the correlation distance relationship and closely related to the scale of precipitation processes affecting the different se asons. Rainfall occurrence at a location in summer seemed to be independent of other locations while in the winter rainfall tended to occur or not to occur over the whole study area simultaneously In summer, a correlation of 0.90 was only possible in the immediate neighborhood of the location

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187 considered (less than 3.3 km) while in winter, this distance extended to approximately 18 km. A consistent relationship between the variance of correlation and separation distance could not be established. Correlation of daily and hourly rainfall events exhibited the same characteristics as their rainfall amount analogues. The orientation of When the correlation distance relatio nship was generalized into a variogram model, similar results were obtained. For the contrasting seasons (summer and winter) the distance at which daily rainfall was no longer correlated (range) was respectively 12 and 47 km, assuming there were trends dri ving this relationship. When these trends were removed the two ranges became smaller and closer to each other, respectively 9 and 12 km. Winter, spring and fall rainfall (lower variance) was more predictable than summer rainfall (higher variance). Differen ces between kriging and IDW interpolation approaches were negligible except in summer where IDW resulted in lower errors This study has contributed high temporal and spatial resolution rainfall data that are needed to fill the gap between current state le vel weather networks and an understanding of the variability of rainfall at a lower scale. It also supplied detailed storm information that was nonexistent in the study area therefore providing a basis for future investigations. For example, knowledge of the distribution of dry period s is important for drought monitoring and modeling of crop growth in rainfed or irrigated systems. Although similar to results from other studies, findings related to storm variability and rainfall correlation provided specifi c characteristics that were more representative of the r patterns. However, the data were limited in time. This limitation may

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188 have more influence on distributions and specific statistics estimated but should have little effect on characteri stics and patterns of the seasons. Findings from this study demonstrated that winter rainfall was more correlated at a mean distance of 54 km between locations than summer rainfall was at a mean distance of 3 km Given the large scale of precipitation proc esses in the winter, we do not expect significant differences in winter rainfall among locations separated by 60 km or less in the study area. Furthermore, characteristics of winter rainfall found in this study may be similar in areas located at 60 to 90 km from our study area. It is difficult to generalize summer results due to the local nature of convective processes that dominate rainfall variability in this season. Some rainfall amount differences were observed even between locations only 1 km apart. However, our study did not contain a sufficient number of locations at short distances to reliably estimate high frequency rainfall variability. In particular, a small number of rain gauges were located near the county b oundaries. Therefore, caution should be used when extrapolating summer results to these areas. Since most of the growing season in the study area occurs during the summer, we anticipate that the high rainfall variability observed in this season will transl ate into large uncertainties in crop yield.

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189 Table 4 1. Parameters for performing and tuning the analysis of spatio temporal variability of storms Parameter ID Parameter definition Value Unit RAINRES Minimum rainfall depth detected by data logger 0.254 mm RAINSUM Minimum total rainfall depth during an event to consider a location rainy 0.254 mm DRYDUR Minimum duration of dry spell that must separate two rainfall events for them to be considered separate 60 min RAINDUR Minimum duration of a storm event for the storm to be considered in this analysis 1 min RAINLAR Amount of rainfall at a location for the event to be considered a large one 25.4 mm

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190 Table 4 2. Characteristics of all storms identified during the period analyzed Season Summer Fall Winter Spring Summer Year 2010 2010 2011 2011 2011 Number of storms 30 15 20 16 56 Global storm duration (hour) Mean 2.79 5.67 9.33 3.61 1.60 SD 6.45 6.79 5.43 3.95 3.93 CV (%) 231 120 58 109 245 Aggregated storm duration (hour) Mean 1.48 3.67 6.04 2.07 0.93 SD 4.46 4.75 4.76 2.44 2.59 CV (%) 302 130 79 118 279 Number of locations covered Mean 9 22 41 23 4 SD 14 22 14 23 10 Min 1 1 1 1 1 Max 46 46 46 46 46 Aggregated rainfall amount (mm storm 1 ) Mean 6.91 10.06 11.09 9.05 6.06 SD 8.98 13.55 8.58 12.02 8.11 Min 0.51 0.51 0.51 0.51 0.51 Max 42.54 49.49 27.50 38.63 53.67 CV (%) 130 135 77 133 134 Aggregated rainfall intensity (mm h 1 storm 1 ) Mean 10.36 6.01 3.20 7.26 10.50 SD 6.59 5.18 2.92 4.93 6.86 Min 1.94 0.63 0.29 1.59 2.03 Max 30.24 18.29 10.86 17.85 42.06 CV (%) 64 86 91 68 65 Minimum duration between storms (day) Mean 2.85 6.02 3.57 5.95 1.56 SD 3.58 7.12 4.28 5.42 1.54 Min 0.06 0.16 0.05 0.04 0.05 Max 14.01 27.13 14.96 19.45 6.59 CV (%) 126 118 120 91 99

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191 Table 4 3. Characteristics of large storms identified during the period analyzed Season Summer Fall Winter Spring Summer Year 2010 2010 2011 2011 2011 Number of storms 7 5 7 3 6 Number of regional storms* 3 7 18 8 3 Global storm duration (hour) Mean 9.37 10.78 11.86 8.58 9.15 SD 11.57 5.66 4.22 3.72 9.45 CV (%) 123 53 36 43 103 Aggregated storm duration (hour) Mean 5.07 6.81 7.84 5.85 4.91 SD 8.74 4.88 4.77 2.45 7.16 CV (%) 172 72 61 42 146 Number of locations covered Mean 29 39 46 46 26 SD 17 13 0 1 22 Min 8 15 46 45 5 Max 46 46 46 46 46 Aggregated rainfall amount (mm storm 1 ) Mean 19.65 24.02 21.00 31.88 19.01 SD 11.07 16.11 3.32 8.68 17.14 Min 8.45 10.25 16.81 22.09 9.24 Max 42.54 49.49 27.50 38.63 53.67 CV (%) 56 67 16 27 90 Aggregated rainfall intensity (mm hr 1 storm 1 ) Mean 13.58 4.43 4.17 5.86 11.46 SD 10.31 1.77 3.23 1.18 8.92 Min 1.94 2.55 1.11 5.09 2.87 Max 30.24 7.34 10.86 7.21 21.89 CV (%) 76 40 77 20 78 Minimum duration between storms (days) Mean 14 15 9 13 10 SD 15 13 9 10 12 Min 1 1 0.12 5 1 Max 40 31 20 20 28 CV (%) 112 85 105 82 122 *Regional storm: storm covering at least 90% of all locations

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192 Table 4 4. Number of storms and r anges of location specific means of all storms identified in the local analysis Season Summer Fall Winter Spring Summer Year 2010 2010 2011 2011 2011 Number of location specific storms (number of storms per location) Min 17 8 20 15 16 Max 55 22 39 31 55 Number of location specific large storms (number of storms per location) Min 1 1 0 1 0 Max 8 3 3 4 5 Mean duration of storms at a location (hour) Min 0.70 1.54 1.22 1.19 0.73 Max 2.36 2.92 2.81 1.94 2.34 Mean rainfall per storm at a location (mm storm 1 ) Min 6.90 6.07 5.23 5.84 4.10 Max 12.59 12.28 8.56 13.31 13.35 Mean storm intensity at a location (mm hr 1 storm 1 ) Min 9.11 2.16 2.78 4.62 2.52 Max 20.00 8.21 6.33 14.64 16.23 Mean dry duration between storms at a location (day) Min 1.53 3.43 2.28 3.00 1.63 Max 5.40 7.15 4.49 6.20 3.76 Mean storm onset time (24 hour format) at a location Earliest 15 13 9 7 14 Latest 17 17 13 11 17

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193 Table 4 5. Spearman correlation of daily rainfall amount and gauge separation distances Distance (km) Number Statistic Summer Fall Winter Spring Summer Interval Mean of Points 2010 2010 2011 2011 2011 0 5 3.31 23 Mean 0.68 0.85 0.97 0.84 0.61 Std 0.22 0.15 0.03 0.13 0.17 5 10 7.97 84 Mean 0.48 0.82 0.95 0.73 0.38 Std 0.14 0.17 0.04 0.12 0.13 10 15 12.66 121 Mean 0.34 0.74 0.93 0.66 0.27 Std 0.12 0.22 0.04 0.13 0.13 15 20 17.72 159 Mean 0.24 0.70 0.91 0.61 0.20 Std 0.12 0.20 0.04 0.16 0.13 20 30 24.83 296 Mean 0.16 0.67 0.87 0.55 0.11 Std 0.12 0.21 0.06 0.15 0.13 30 40 34.50 224 Mean 0.07 0.62 0.82 0.53 0.03 Std 0.11 0.18 0.08 0.13 0.12 40 50 44.32 104 Mean 0.04 0.52 0.79 0.51 0.02 Std 0.14 0.21 0.09 0.16 0.12 50 62 53.76 24 Mean 0.06 0.58 0.76 0.47 0.07 Std 0.11 0.15 0.11 0.13 0.09 *Std: standard deviation Table 4 6. Spearman correlation of daily rainfall event and gauge separation distances Distance (km) Number Statistic Summer Fall Winter Spring Summer Interval Mean of Points 2010 2010 2011 2011 2011 0 5 3.31 23 Mean 0.72 0.87 0.93 0.90 0.71 Std 0.12 0.06 0.04 0.05 0.09 5 10 7.97 84 Mean 0.65 0.85 0.92 0.86 0.60 Std 0.08 0.10 0.04 0.06 0.11 10 15 12.66 121 Mean 0.58 0.82 0.92 0.82 0.54 Std 0.08 0.10 0.04 0.07 0.09 15 20 17.72 159 Mean 0.54 0.81 0.90 0.81 0.51 Std 0.08 0.10 0.04 0.09 0.10 20 30 24.83 296 Mean 0.50 0.81 0.89 0.79 0.46 Std 0.08 0.11 0.04 0.08 0.10 30 40 34.50 224 Mean 0.46 0.81 0.89 0.77 0.43 Std 0.09 0.10 0.04 0.08 0.10 40 50 44.32 104 Mean 0.45 0.77 0.88 0.74 0.40 Std 0.09 0.12 0.04 0.10 0.11 50 62 53.76 24 Mean 0.44 0.80 0.87 0.74 0.36 Std 0.08 0.09 0.06 0.08 0.11 *Standard deviation

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194 Table 4 7. Geostatistical model parameters (range and partial sill) and evaluation statistics comparing observed and predicted rainfall from IDW and kriging with and without trend removal Parameter Trend Summer Fall Winter Spring Summer 2010 2010 2011 2011 2011 Range (km) Not removed 15 34 47 27 12 Removed 9 8 12 11 9 Partial sill (mm 2 ) Not removed 95 44 21 31 69 Removed 38 7 4 8 26 Correlation between observed and predicted Kriging, Not removed 0.42 0.42 0.72 0.73 0.48 Kriging, Removed 0.34 0.25 0.71 0.77 0.37 IDW 0.47 0.32 0.70 0.72 0.50 Root Mean Squared Error (mm) Kriging, Not removed 62 22 17 20 58 Kriging, Removed 71 27 18 19 67 IDW 57 22 17 22 56

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195 Figure 4 1. Study area with locations where rainfall was collected and interpolated total rainfall from June 2010 to May 2011 (12 months)

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196 Figure 4 2. Distribution of pairwise distances between rain gauges with estimated kernel density

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197 A B C D Figure 4-3. Long-term variability of the Palmer Drought Severi ty Index (PDSI) over the study area in winter, spring, summer and fall 190019201940196019802000 -5 0 5 YearPalmer Dought Severity Index Extremely dry Extremely moist2011January 190019201940196019802000 -5 0 5 YearPalmer Dought Severity Index Extremely dry Extremely moist2011April 190019201940196019802000 -5 0 5 YearPalmer Dought Severity Index Extremely dry Extremely moist2011July 190019201940196019802000 -5 0 5 YearPalmer Dought Severity Index Extremely dry Extremely moist2011October

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198 B Figure 4-4. Number of storms by month Jun 2010 Jul 2010 Aug 2010 Sep 2010 Oct 2010 Nov 2010 Dec 2010 Jan 2011 Feb 2011 Mar 2011 Apr 2011 May 2011 Jun 2011 Jul 2011 Aug 2011Number of storms 0 5 10 15 20 Large storms All storms

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199 A B C D Figure 4-5. Empirical cumulative distribution functions of various characteristics of the regional storm analysis 0510152025 0.00.20.40.60.81.0 Aggregated storm duration (hour)Probability Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011 0510152025 0.00.20.40.60.81.0 Minimum duration between storm events (day)Probability Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011 01020304050 0.00.20.40.60.81.0 Aggregated storm rainfall (mm storm 1)Probability Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011 010203040 0.00.20.40.60.81.0 Aggregated storm intensity (mm hour 1 storm 1)Probability Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011

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200 A B C D Figure 4-6. Profiles of 500 mb daily com posite mean geopotential heights for rainfall events that produced in each season the largest rainfall amount at one or more locations and covered the entire study area. A. su mmer 2010, B. fall 2010, C. winter 2011 and D. spring 2011. T he arrow in A marks the state of Georgia where the study area is located. Image provided by the NOAA/ESRL Physical Sciences Division, Boulder Colorado from their web site at http://www.esrl.noaa.gov/psd/data/composites/day/ accessed January 5, 2012

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201 A B C D Figure 4-7. Empirical cumulative distribution functions of various characteristics of the local storm analysis 05101520 0.00.20.40.60.81.0 Storm duration at any location (hour)Probability Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011 0102030 0.00.20.40.60.81.0 Duration between location-specific storms (day)Probability Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011 020406080100 0.00.20.40.60.81.0 Storm rainfall at any location (mm storm 1)Probability Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011 020406080100120 0.00.20.40.60.81.0 Storm intensity at any location (mm hour 1 storm 1)Probability Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011

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202 A B C D E F Figure 4-8. Kernel density estimates of location mean storm characteristics and storm beginning and end times at any location 1.01.52.02.53.0 0.00.51.01.52.02.53.0 Mean storm duration at a location (hour)Density Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011 234567 0.00.51.01.5 Mean duration between storms at a location (day)Density Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011 4681012 0.00.20.40.6 Mean rainfall at a location (mm storm 1)Density Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011 5101520 0.00.10.20.30.40.50.6 Location mean storm intensity (mm hour 1 storm 1)Density Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011 05101520 0.000.020.040.060.080.100.12 Storm onset time (24-hour format)Density Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011 05101520 0.000.020.040.060.080.100.12 Storm end time (24-hour format)Density Summer 2010 Fall 2010 Winter 2011 Spring 2011 Summer 2011

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203 Figure 4 9. Relationship between correlation of daily rainfall amount and separation distance Figure 4 10. Relationship between correlat ion of daily rainfall event and separation distance

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204 Figure 4 11. Spatial variability of daily rainfall amount correlation between location in red and the remaining sites

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205 A B Figure 4 12. Sample variograms of daily rainfall (A) without and (B) with trend removal and corresponding fitted spherical variogram models

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206 A B C Figure 4 13. Comparison of the performance of ordinary kriging (A), universal kriging (B) and IDW interpolation of daily rainfall aggregated to seasonal level

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207 Figure 4 1 4. Comparison of ordinary kriging (OKriging), universal kriging (UKriging) and IDW map of interpolated total rainfall for summer 2010 and winter 2011

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208 CHAPTER 5 UNCERTAINTIES IN CRO P MODEL PREDICTIONS RESULTING FROM RAINF ALL VARIABILITY AT DIFFE RENT AGGREGATION SCA LES Introduction Crop production strongly depends on weather conditions because physiological processes that determine the potential development and growth of plants are controlled by weather. Further, actual crop yi eld levels attained in any environment are largely dictated by weather conditions both in rainfed and irrigation production systems (Royce et al., 2011) Studies have reported that in some cases, weather variability contributed up to 80% of the variability in agricultural production (Hoogenboom, 2000) Therefore, accurate simulation of crop yield variability require that crop models adequately account for the spatial and temporal variability in weather conditions (Hansen and Jones 2000) Crop models are generally designed to operate at field scales where the primary inputs driving model predictions, weather, soil and management are relatively homogeneous within the simulation unit. Uncertainties in simulating crop performance c an arise from model parameters and inputs. Much attention has been devoted in the literature to characterizing and quantifying parameter uncertainty and its effect on model predictions in location specific studies where spatial homogeneity of inputs may be reasonably assumed (Monod et al., 2006; Pathak et al., 2007; Confalonieri et al., 2010a) However, when using crop models over larger areas for simulating yield variability and aggregation strategies, uncertaint ies due to spatial heterogeneity of weather, soil and management become important (Therond et al., 2011) Some of these model inputs such as soil have a spatial distribution that is almost fractal in nature and uncertainties in crop model predictions arise partly from the inability to completely characterize this variability. Approaches to representing spatial uncertainty in inputs

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209 include geographic or probabilistic characterization (Hansen and Jones, 2000) For field scale c rop models additional sources of uncertainty, when dealing with scale changes, include emerging processes such as fluxes of water and nutrients between fields (Faivre et al., 2004) This paper concentrates on input uncertainty when applying crop models at a range of scale s from farm ( about 1 km) to region (60 km). P articular attention is devoted to the effect s of rainfall variability on model predictions at these scales We emphasize rainfall because of its importance for biological systems, in particular agricultural systems. Furthermore, rainfall is the most variable of the weather variables used by crop models and it represents the most recurrent meteorological variable in variability studies (Hubbard, 1994; Willmott et al., 1996) Space time variability of rainfall has a major influence on crop production as the amount of soil mois ture available for rainfed crop growth is directly related to rainfall. Crops respond to daily variation s in water through the regulation of their stomates. More sustained water deficit can result in loss of green leaf area, inhibition of photosynthesis an d in flowering cereals, reduction of the anthesis to silking interval. Management decisions such as irrigation, cultivar selection, planting and fertilization can be dictated by the distribution of rainfall. Predictive tools in agricultural assessment suc h as crop models account for rainfall as the variable that determines water availability and uptake by plants and therefore plant growth (Jones et al., 2003) Variability in water limited production can only be modeled if an accurate r epresentation of the spatial and temporal variability of rainfall is realized. Availability of weather data at the appropriate spatial resolution largely dictates the degree to which spatial and temporal variability of rainfall is incorporated in modeling studies. While networks of weather stations are

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210 available at state and watershed levels in many regions in the U.S. (Bosch et al., 2007) long term rainfall measurem ent s at a spatial resolution finer than the county level is not widespread. This creates a gap between the scale at which rainfall data are usually available and the scale at which modeling studies are conducted. Researchers have dealt with this disparity of scale by assuming that rainfall would be relatively uniform within their study region and using data from the nearest weather station (Goodrich et al., 1995) This practice implicitly attaches some level of uncertainty to the observed rainfall that is propagated through the crop model. A number of studies have evaluated uncertainties in model predictions caused by rainfall variability or an incomplete knowledge of this variability. Using the CERES Maize crop model, ( 2002) found differences in simulated crop yield attribu table to spatial rainfall variability of 15.8%. Based on the magnitude of rainfall spatial variability observed in their studies, they suggested that on site precipitation data would be necessary for accurate crop yield modeling. In a hydrology and water q uality model, Chaubey et al. ( 1999) found that uncertainties due to the spatial variability of rainfall resulted in even l arger uncertainties in modeled runoff and sediment outputs. In a study using the Soil and Water Assessment Tool (SWAT), Cho et al. ( 2009) found that decreasing the density of rain gauges that capture the rainfall spatial variability resulted in an exponential increase in model output uncertainty. Spatial variability of rainfall in the southeast U S can be reasonably simplified as characterized by widespread correlations in winter and spring, and rapidly decaying correlations in the summer (Baigorria et al., 2007) These characteristics extend to local scales (Bosch et al., 1999) Further insights into the spatial variability of rainfall in the

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211 region was obtained through a network of 46 rain gauges installed in 2009 and 2010 in t hree counties in southwest Georgia (Dougherty, Baker and Mitchell, Fig ure 5 1). A detailed analysis of storm characteristics and correlations of rainfall amounts and events was conducted in Chapter 4. The study area is a major contributor to row crop produ ction in Georgia and in the southeast U S (USDA, 2011) with 36%, 30% and 9% of Mitchell, Baker and Dougherty counties respectively classified as cultivated areas (USDA, 2001) Forests covered a significant proportion of the area as well (34%, 35% and 38% respectively) while developed areas were the least im portant (6%, 4% and 18% respectively, Fig ure 5 1). E ffects of uncertainties in rainfall and other environmental factors on crop yield at the range of scales covered by the network of 46 rain gauges have not been investigated in the region. A number of ques tions arose as deliberate efforts were being implemented to quantify these uncertainties : 1. How much variability in aggregated crop predictions is attributable to rainfall spatial variability? 2. What are uncertainties in model predictions associated with inco mplete sampling of the spatial variability of rainfall in the study area? 3. Is the effect of spatial variability of rainfall on crop predictions affected by long term seasonal rainfall variability? To answer these questions this paper examined the following objectives: 1. Quantify the variability in maize yield and season length due to spatial variability of rainfall, soil, cultivar and planting date; 2. Assess the effect of density of weather locations on simulated maize yield and season length aggregated at diff erent scales across soil, cultivar and planting date spatial heterogeneity; 3. Investigate the coupled effect of long term seasonal and spatial rainfall variability on maize yield and season length aggregated at different scales across soil, cultivar and plan ting date spatial variation.

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212 Materials and Methods The study area was located in southwest Georgia and consisted of three counties, Dougherty, Baker and Mitchell. This area exhibited spatial variation in rainfall (Fig ures 5 1 and 5 2) and soil, as well as variation s in management generally found in any agricultural region. This spatial variability in the crop environment (weather, soil, cultivar and planting date) produced variability in maize yield as shown in Fig ure 5 3. Characterization of Spatial Heter ogeneity Spatial variation in model inputs was characterized for weather, soil, cultivar and planting date. Variability in weather was sampled as 50 weather locations that consisted of 4 weather stations from the Georgia Automated Environment Monitoring Network ies (Fig ure 5 1). Spacing between the rain gauges ranged from 1 km to 60 km. The locations of the weather stations and rain gauges represented the spatial points where crop yield was simulated. The length of weather record was limited for the rain gauges which covere d only the period April 21, 2010 to December 31, 2011. Furthermore, the rain gauges measured only rainfall while crop model simulations required daily inputs of minimum and maximum temperatures as well as solar radiation. Therefore, temperature data from t he 4 GAEMN weather stations and 7 other neighboring GAEMN stations (Figure 5 1) were used to interpolate minimum and maximum temperatures to the rain gauge locations. Solar radiation was not measured by the GAEMN stations and was consequently estimated for all 50 weather locations using an improved Bristow Campbell method (Thornton and Running, 1999) Significant precipitation variations were observed in the study area. In summer 2010, some locations registered about 500 mm o f rainfall while other sites received only 200 mm (Table 5 1). Summer rainfall was

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213 particularly variable in 2011 with a coefficient of variation of 25%. Daily rainfall was even more spatially variable than total seasonal rainfall. Since a large part of the growing season in the study area occurs during the summer, variability in crop yield w as more likely to be correlated with variability in summer rainfall. Variability in soil was characterized by identifying 6 soil profiles from 6 major soil series found in the study area based on the STATSGO database (NRCS, 2010) detailed soil survey data and online soil characterization information from the United States Department of Agriculture (USDA, Table 5 2). These soils covered a significant area of the three counties and represented a wide range of soil properties found in the study area. Maize cultivar variability was represented by parameters calibrated in a previous study and included a short, medium and long duration maturity group (Tables 5 3 and 5 4). Planting date variation was charac terized by sampling weekly dates within a window defined based on maize usual planting dates in Georgia (USDA, 1997) This window was March 1 st to May 5 th which corresponded to 10 planting dates for years with complete weather data. Only 3 planting dates were used in 2010 because the observed rainfall data started on April 21, 2010. Overview of the Simple SALUS Crop Model All crop pred ictions were produced using the simple SALUS (System Approach to Land Use Sustainability ) crop model (Basso et al., 2006) within DSSAT (Decision Support System for Agrotechnolog y Transfer) based on crop parameters defined in Table 5 4. This model was selected due to its simplicity in reasonably simulating crops and grasses using a significantly smaller number of parameters when compared to more detailed crop models (Chapters 2 an d 3) Interest in simulation crop performance over large areas has generated attention to simpler and generic crop models (Faivre et

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214 al., 2004; Bondeau et al., 2007; Osborne et al., 2007; Adam et al., 2011) The benefits of these simple models could be highlighted as estimating more accurately seasonal variation in leaf area index (LAI), representing crop processes with a smaller number of parameters and therefore not requiring intensive parameterization, and allowing parameterization for crop or grasses not initially modeled. The sensitivit ies of the model outputs to uncertainties in crop parameters for different environments (representing variation in soil and weather), crops and production levels w ere evaluated in a previous study (Chapter 2) The model was also calibrated for maize for the three maturity groups simulated in the present study as well as for peanut and cotton (Chapter 3) The SALUS model integrate s information on daily weather (solar radiation, maximum and minimum temperatures and rainfall), soil properties, potential crop characteristics and management to simulat e plant growth and yield Total plant growth duration i s described in terms of thermal time and progress towards maturity i s modeled as a cumulative fraction of t his duration. Potential LAI i s simulated directly based on an empirical sigmoid curve that i s characterized by plant specific parameters. Potential rate of plant biomass growth i s computed as the product of intercepted photosynthetically active radiation and a plant specific maximum radiation use efficiency (RUE). Biomass partitioning between roots and aerial plant parts use s an exponential decrease function based on work by Swinnen et al. ( 199 4) Crop yield i s derived as a fraction of biomass corresponding to a crop specific harvest index. Sim ulation of soil water balance i s critical to accurately represent the effect s of precipitation on simulated crop yield s. These effects are summarized in the model through the computation of water stress experienced by the crop on a daily basis A

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215 brief description of the soil water balance used by DSSAT crop models is provided here. Water inputs in the form of precipitation and irrigation a re used to simulate plant transpiration, soil evaporation, runoff, drainage and water flow to adjacent layers. These processes were used to determine crop water uptake and stress. The evaluation of these processes use s daily weather data, meaning that within day varia tions or rainfall intensities a re not considered. Soil properties de fine how soil i s affected by the water balance processes. Depending on its properties, the soil may be more resistant to drought or possess a higher capacity to hold water by capill arity. Precipitation i s initially partitioned between runoff and infiltrati on. Drainage determine s water movement through the different layers of the soi l profile. Evapotranspiration i s calculated based on a modified Priestley Taylor approach which use s daily temperatures and solar radiation, initial soil albedo and LAI calculat ed by the crop model. Root water uptake use s root length density information provided by the SALUS crop model based on simula ted root growth. Water stress i s estimated as the ratio of potential root water uptake to potential plant transpiration with values between 0 and 1, to reflect the effect s of partial stomata closure when water deficit occur s A detailed description of the DSSAT soil water balance can be found in Ritchie ( 1998) In SAL US, the computed water stress i s used to reduce LAI and biomass growth rates and to accelerate senescence Global Sensitivity Analysis A global sensitivity analysis was carried out to quantify the contribut ions of spatially heterogeneous model inputs and their interactions to the overall variability in crop predictions. A factorial design was used, meaning that the crop model was executed for each unique combination of 50 sets of weather data (one from each rain

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216 gauge and weather station site) 6 soils, 3 cultivars and planting dates (3 in 2010 and 10 in 2011). The limited number of planting dates used in 2010 was due to the weather data starting on April 21, 2010. The total number of combinations was 2 700 i n 2010 and 9 000 in 2011. The simulations were conducted at water limited level with initial soil water set to drained upper limit. Plant population at planting was 6.0 plants ha 1 (Kiniry et al., 1992) The variabi lity in model predictions was decomposed into different sources of variation based on the statistical theory of linear models (similarly to the analysis of variance Monod et al., 2006 ). Considering the four input factors we can write simulated crop yield as where and represent respectively weather, soil, cultivar and planting date, in any given combination. We recall that there were 50 possible values for 6 values for 3 values for and 3 (2010) or 10 (2011) possible values for and respectively. The simulated crop yield (or any other model outputs) can be statistically modeled as ( 5 1 ) where is the simulated crop yield for all combinations of weather, soil, cultivar and planting date; represents the grand mean of crop yield, represent the main effects of weather, soil, cultivar and planting date respect ively; represents the interaction between weather and soil, and so on; represents the interaction between weather, soil and cultivar, and so on; represents the interaction between weather, soil, cultivar and planting date. Since we are dealing wit h a deterministic model there i s no error term in E quation 5 1, which implie s t hat a formal statistical test i s not possible. The total sum of squares

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217 associated with the simulated crop yield can be decomposed into factorial terms as follows: ( 5 2 ) where represents the total crop yield variability in terms of sum of squares; represents the sum of squares associated with the main effect of weather; is the sum of squares associated with the main effect of soil, and so on. Based on the variance decomposition in E quation 5 2 various sensitivity indic es relating variability in the input factors to variability in simulated crop yield were calculated as follows: 1. Main effect sensitivity index where ; is the sum of squares associated with the main effect of ; is the total sum of squares of crop yield; 2. Interaction sensitivity index where is the sum of squares associated with the interaction between factors and ; 3. Total sensitivity index where is the sum of squares associated with interactions involving factor These sensitivity indices represent the proportions of the varianc e in simulated crop predictions explained by the factor (e.g. weather) and/or interactions of interest. Effect of Weather Network Density This analysis investigated the effect s of increasing the density of weather locations between 1 and a maximum of 50, on the distribution of aggregate crop predictions. It was expected that a better sampling of the spatial variabi lity of rainfall (through the use of a higher number of weather locations) would result in a more precise simulation of

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218 crop yield and season length aggregates as observed for rainfall climatology means by Willmott et al. ( 1994) Each weather location was regarded as being characterized by its weather data and 54 (in 2010) and 180 (in 2011) combinations of soils, cultivars and planting dates. This configuration of the spatial heterogeneity implie s that rainfall was sampled in physical geographic space where variability in soil, cultivar and planting date occurred. Variability in crop predictions at the same weather location was therefore due to variability in soil, cul tivar and planting date. Illustrating for crop yield, t he aggregate over the study area characterized by weather locations and combinations of soil, cultivar and planting date was obtained by first aggregating over the weather locations to produ ce the average crop yield variability due to soil, cultivar and planting date. Next, this crop yield was aggregated over the combinations of soil, cultivar and planting date to produce the grand aggregate over the area, assuming equal weights for th e combinations of factor s (soil, cultivar, and planting date) and for the weather locations. ( 5 3 ) The quantity is the mean crop prediction ( aggregate ) when locations a re considered to characterize the spatial variability of weather over the study area. The number of weather locations can vary from 1 to the maximum number of weather locations. Each number of weather locations can be configured for a certain number of possibilities corresponding to the combinations of selected from Each combination produce s a crop yield aggregate and the ensemble aggregates (where is the total number of uniqu e combinations of weather locations taken from ), define the distribution of aggregates for a given This distribution was approximated

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219 by randomly drawing 10,000 combinations from and evaluating the model using these combinations. For a given variability among the 10,000 aggregates is a measure of uncertainty in crop yield (or season length) induced by spatial weather variability (mostly rainfall). Key moments such as expected value and variance were calculated to characterize the distribution of aggregate prediction s and assess uncertainties associated with them. A critical assumption in the network density analysis is that the full density of 50 weather locations represents variability of weather (mostly rainfall) ove r an area of 3100 km 2 Effect of Long term Rainfall Variability The relationship between the distribution of crop prediction aggregates and the density of weather networks may be affected by the year considered. To examine the effect s of long term seasonal rainfall variability on the relationship between network density and crop prediction aggregates, 30 years of synthetic weather data (rainfall and temperatures) were generated using the GiST geospatial temporal weather generator (Baigorria and Jones, 2010) GiST is a multi site generator of rainfall, temperatures and solar radiatio n and was selected because it i s one of the few parametric weather generators that take into account the spatial and temporal correlation str ucture of the weather variable generated. The generation of rainfall assumed that the serial autocovariance and the spatial correlation pattern over the study area did not change during the period considered (stationarity). For each location, GiST produced rainfall events based on a two state orthogonal Markov chain for discrete distributions, taking into account the rainfall state at the same location on the previous day and the rainfall states at two other most correlated locations (Baigorria and Jones, 2010) Rainfall

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220 amounts were generated by GiST on days when rainfall event occurred, using the observed distributions and spatial correlation pattern of rainfall computed in Chapter 4 GiST computes correlations betwee n pairs of locations on a monthly basis using daily observed data, which requires a certain number of days with rainfall events. Because only 2 ye ars of observed rainfall data were available (2010 and 2011) there were months with limited number of rainfall events, which prevented the software from computing the correlations. To produce more observations, it was assumed that the observed 2 year weather data were repeated 3 times. This implied that the spatial variability in observed weather was repeated ever y other year over a 6 year period. It can be demonstrated that this treatment of the observed data did not alter (or did not alter significantly) the statistics needed by the weather generator due to the following: 1. The probabilities of rainfall event (or n o rainfall event) at a location given a rainfall event (or no rainfall event) at other locations were not affected because GiST calculates these probabilities based on relative frequencies of rainy days; 2. The co vari ances calculated based on the original, no n replicated data were slightly larger than those calculated based on the replicated data by a factor of with and where is the number of observations in the original, non replicated data and is the number of replications (here =3) The number of observations in the replicated data is ; 3. Since a correlation is the ratio of a covariance and the product of two standard deviations, the factor indicated in ( 2 ) canceled out when correlations were computed in GiST Therefore, the correlations among the locations were not affected by the replication of the data. This was a critical requirement since we would like the weather generator to produce synthetic data that reproduced the observed correl ations faithfully. Distributions of crop prediction aggregates were produced for each year generated for selected weather network config urations as described earlier (E quation 5 3). It was anticipated that long term seasonal to annual weather variability w ould modify these

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221 distributions such that in some years the aggregate prediction s could be estimated more precisely. Results and Discussion Global Sensitivity Analysis Variability in simulated crop yield and season length Overall simulated grain yield variations among locations due to spatial heterogeneity of soil, cultivar, planting date and observed weather, ranged from 415 to 7387 kg ha 1 in 2010. Crop yield levels were relatively lower in 2011 (Fig ure 5 3), ranging from 90 to 5600 kg ha 1 suggestin g that lower rainfall amount in this year resulted in higher crop water stress. Overall season length variations w ere wider in 2011 as a larger number of planting dates were used compared to 2010. Crop duration ranged from 97 to 147 days in 2011 while this range was 93 to 121 days in 2010. The individual distributions of model predictions were strongly location dependent (Fig 5 4). Since the variations in soil, cultivar and planting date were assumed to be identical at each location, these distribution dif ferences represent interaction s among soil, management and weather, especially rainfall. The mean s of these distributions in 2010 ranged from 1019 to 4952 kg ha 1 for grain yield and 104 to 108 days for season length. As the location specific distributions were more similar in 2011, their means varied in a smaller range, from 751 to 2887 kg ha 1 for grain yield and 118 to 121 days for season length. Variability in season length was not necessarily correlated with variability in grain yield suggesting that water availability and not crop growth duration was the main driver of crop yield variations Standard deviations of grain yield distributions ranged from 343 to 1070 kg ha 1 in 2010 and 366 to 816 kg ha 1 in 2011. Since water stress does not influence crop duration in the current version of SALUS and

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222 there was little temperature variation from o ne location to another, the distributions of season length were similar and exhibited stable properties. The coefficient of variation for the distributions of season length was approximately 8% in 2010 and 10% in 2011. For crop yield these coefficients of variation varied among locations, rang ing from 15% to 34% in 2010 and 21% to 50% in 2011. In general our results indicated a strong effect of weather on the spatial variability of crop yield and season length (to a smaller extent) as reported in other mo deling studies These effects appeared to be mediated by other key environmental factors, in particular management and soil (Riha et al., 1996) Quantification of the specific effects of weather and other factors on variability in yield and season length required the partitioning of the total crop model prediction variance into individual components. Partitioning of model prediction variance Partitioning of the t otal variability in simulated crop yield, biomass and season length indicated that the importance of the four sources of variability (weather, soil, cultivar and planting date) essentially depended upon the crop prediction and the year considered. The main effects of the four factors together accounted for approximately 90% and 77% of the total variability in crop yield respectively in 2010 and 2011 (Table 5 5 and Fig ure 5 5). Second order interactions were responsible for 8.4% of crop yield variability i n 2010. In 2011, second order interactions had a higher influence on yield, accounting for 19.5% of the total crop yield variability. Differences between the two years were remarkable when only the main effects were considered. In both years, a large propo rtion of the variability in crop yield could be attributable to main effects and

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223 second order interactions only. These two sources of variation explained, respectively in 2010 and 2011, 98.2% and 96.2% of the total crop yield variability. The largest contr ibutor to the variability in simulated crop yield in both years was weather, which accounted for 53% and 33% of the variability in crop yield (in 2010 and 2011), not including interactions with other factors. We emphasize that variability in rainfall was h igh in the study area (Figure 5 2). Soil was the second most influential factor in 2010 (18% of the crop yield variability) but not in 2011 where planting date explained 23.5% of the crop yield variance. In both years, the most important interaction s invol ved weather. In 2010, interaction between weather and soil had the highest interaction sensitivity index while in 2011, interaction s between weather and planting date was the most influential of all interactions (Table 5 5). These results suggested that cr op yield variability in 2010 was essentially dominated by the main effects of weather and soil. In 2011, variability in crop yield was partitioned into moderate contributions from main effects and interactions. These patterns may be the result of the small er number of planting dates in 2010 (3 dates) compared to 2011 (10 dates), which prevented the isolation of the pure effect of year. This statement was confirmed by the larger value of the total sensitivity index (TSI) of planting in 2011 compared to 2010 (Table 5 6 and Fig ure 5 5). However, regardless of the year and number of planting dates, weather was ranked as the most influential factor of crop yield variability based on TSI. The order of importance of the other factors was soil, planting and cultivar in 2010 and planting, cultivar and soil in 2011. We restate that although rainfall variability in both years was high, 2011 was drier than 2010. For example, summer rainfall averaged over the study area 353 mm in 2010 compared to

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224 170 mm in 2011. Nearly al l the variability in season length was due to cultivar and planting date, in almost equal proportions in 2011 and in a dominant proportion for cultivar in 2010 (Table 5 5). This result was expected as the cultivars used were characterized by different crop growth durations. Similar controls of season length by crop duration parameters were reported for other crop models (Pathak et al., 2007) Ranking of factors for season length did not depend upon the year and could be summarized as cultivar and planting date by order of importance (Table 5 6). The simulated variability in crop yield observed in the area was present primarily because water stress was modeled. Variability in potential production would be limited in the study area because spatial differences in solar radiation and temperatures were small. In addition, studies have shown that in a given area temporal precipitation variability may be more influential than temp erature variability on crop yield (Riha et al., 1996) Therefore, timing of planting was critical because if synchronized with a period of adequate and well distributed rainfall, soil moisture recharge and consequently availability of water for plant uptake would be continually adequate Soil is the support for plant growth and its ability to store water between the wilting point and the field capacity drives the availability of soil water. The cultivars used differed not only in their potential yield but also in their growth duration. In this respect, the ti ming of their key development stages determined how a period of critical plant water demand would be concurrent with sufficient or limited water availability. As observed in the present study, the effect of rainfall was mediated by other factors such as so il properties (Riha et al., 1996) cultivar and planting date. Uncertainties in crop yield in rainfed conditions have been reported to be even more important than uncertainties in crop parameters

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225 (Aggarwal, 1995) We remark that the notable influence of weather was not an ar tifact of a more detailed sampling of spatial rainfall variability relative to other factors. It was confirmed that using a smaller number of weather locations produced similar results as using all 50. Previous studies have demonstrated that variability of rainfall in the southeast U.S. and in the study area was characterized by a rapid correlation decay over short distances, especially in the summer (Bosch et al., 1999; Baigorria et al., 2007) Therefore the large number of rainfall locations used was necessary to obtain a representative characterization of the spatial variability of rainfall. In general, season length variability wa s essentially due to cultivar differences (in 2010) and cultivar and planting date variability (in 2011). The largest proportion of crop yield variation was due to weather. Network Density Analysis Incomplete sampling of the rainfall spatial variability c an underestimate its effect on crop yield and lead to poor predictions of aggregate yields Nearest neighbor weather stations used in modeling studies may not be representative of the area for which they are used (Goodrich et al., 1995; Hoogenboom, 2000) For example, et al. ( 2002) concluded that the misuse of representative we ather stations to model yield could result in differences in simulated yield of 15.8%. We established, by characterizing the spatial variability of key model inputs, that weather variability (mostly rainfall) and all interactions involving weather could co ntribute 47% (in 2011) and 60% (in 2010) of the total variability in crop yield. How would an incomplete characterization of the spatial variability of rainfall impact aggregated crop yield over an area? Increasing the number of weather locations between a minimum of 1 and a maximum of 50 dramatically decreased the variance of the distribution of crop yield and

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226 season length aggregates over the study area (Fig ure 5 6). The profile s of the relationship between the distributions of aggregate d crop predictions and the density of weather locations were similar regardless of the year and the crop prediction considered. This result critically showed that the number of locations in a weather network had a strong influence on simulated aggregate yield. Uncertainties in aggregate crop yield and season length associated with incomplete sampling of the spatial variability of rainfall appeared to be larger in 2010 when rainfall had a stronger effect on the variability of crop predictions. In 2010, the standard deviations of simulated yield decreased from 769 kg ha 1 using 1 weather location to 16 kg ha 1 using 49 weather locations. The corresponding range in 2011 was 415 to 8.5 kg ha 1 In either year, standard deviations and coefficients of variation of the distribution of season length aggregates hardly changed (Fig ure 5 7B). Despite differences in the distribution of aggregates between 2010 and 2011, their coefficient s of variation changed in similar pattern and magnitude (Fig ure 5 7). A striking feature of the distributions of crop prediction aggregates was the stability of the means of these distributions. For season length, these means were practically constant over the whole range of variation of the weather network density (Fig ure 5 6). For crop yield, these means varied in a narrow range, from 3725 to 3754 kg ha 1 in 2010 and from 1545 to 1560 kg ha 1 in 2011. These variations were not monotonic and could be essentially attributable to random fluctuations associated with the repeated random sampling of weath er locations for estimating the distributions. A consequence of this result was that the mean of the distributions of crop prediction aggregates could be estimated using any number of sites through repeated sampling from the maximum

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227 network density. The pr ofiles of the distributions were not affected by changes in planting date if the aggregates were constructed assuming only heterogeneity of weather (Fig ure 5 8). Only the means and variances were affected. Comparison of two planting dates one week apart sh owed little differences (Fig ure 5 8). The decrease in variability in the aggregate crop predictions as the weather network density increased was not due to a reduction in the number of possible combinations of weather locations from which the resampling w as performed. The number of possible combinations of weather locations actually varied as a Gaussian like curve as the weather network density increased (Figure not shown). The number of possible combinations (i.e. ) was highest at = 25 weather lo cations. This means that the higher variability in aggregate crop predictions at lower network densities was associated with an inaccurate characterization of the true weather variability at those densities. Other studies that have evaluated uncertainties in model predictions resulting from incomplete sampling of rainfall have concluded that rainfall uncertainty was amplified when propagated to model outputs (Chaubey et al., 1999; Cho et al., 2009) A procedure similar to the network density analysis used in this study was applied b y Willmott et al. ( 1991, 1994) in the estimation of rainfall climatology means in different parts of the world. The authors found that estimates of the climatology means were highly variable and biased at low densities of rain gauges. Overall, uncertainties in season length aggregates (as measured by the coefficient of variation of their distributions) due to sampling density o f rainfall was less than 1% and decreased with sampling density. Uncertainties in crop yield decreased from a

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228 maximum value of 27% at sampling density 1 and reached an inflexion point of approximately 4% around a sampling density of 20 locations (Fig ure 5 7). Long term Seasonal Effects Most locations experienced a crop failure during March plantings in the majority of the years simulated (Fig ure 5 9A). This effect was due to generated cold minimum temperatures in March. This problem resulted from random sampling in the tails of the normal distributions used to generate temperatures. Because GiST constructed a normal distribution based on the observed temperature data from all years, this problem would occur randomly in generated data whenever observed col der and warmer years were used as inputs to the weather generator (Fig ure 5 9B). It was found that these crop failures inflated the variances of the crop model predictions and skewed their distributions significantly. Therefore, crop predictions correspond ing to March planting dates were removed from the simulations before any further analyses. The patterns of year to year variability in crop predictions using generated weather data (Fig ure 5 9C and D) were closely related to the variability in crop predict ions seen with observed weather data (Figure 5 4) This result was a reflection of the little year to year variability in observed weather data used as inputs to the weather generator. Maximum yield achieved in any year was 6865 kg ha 1 which was close to the maximum yield of 7387 kg ha 1 simulated in 2010. The least productive generated year had a maximum yield of 4311 kg ha 1 which was about 1500 kg ha 1 lower than the maximum simulated yield in 2011. Coefficients of variation of the yearly distribution s varied between 34% and 47%, which were close to their analogues using observed weather data (30% in 2010 and 44% in 2011). The yearly distributions of season length varied in the same manner with a constant coefficient of variation of 8%.

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229 The spatial dis tributions of aggregated maize yield predictions are shown in Figure 5 10. Each distribution (box plot) represents one generated year, corresponding to spatial variability (across the 50 weather locations) of aggregate yield predictions (over soil, cultiva r and planting date variations ). Therefore, these distributions reflect the effect of variability among years in generated weather on the spatial variation of aggregated maize yield predictions. The standard deviations of these distributions fluctuated fr om year to year between a minimum of 580 kg ha 1 and a maximum of 860 kg ha 1 The most stable year had a coefficient of variation of 28% while the most variable year had a coefficient of variation of 42%. The variation in the standard deviations and the c oefficients of variation over years seemed to demonstrate an alternation between series of stable and variable distributions. Aggregated season length hardly varied spatially and temporally with essentially constant standard deviation and coefficient of va riation of 1 day and 1% respectively (Fig ure 5 10). The year to year variations in the means of the spatial distributions in Fig ure 5 10 are shown in Fig ure 5 11. Over the 30 year period, yearly simulated mean maize yield (over the study area) varied betwe en 1 707 kg ha 1 and 2511 kg ha 1 with a long term mean of 2077 kg ha 1 The standard deviation of this long term temporal variability was 138 kg ha 1 which corresponded to a coefficient of variation of 7% (aggregated yield using observed data was 3731 kg ha 1 in 2010 and 1549 kg ha 1 in 2011). Mean season length was stable across the years, ranging from 110 days to 113 days with a long term mean of 111 days, a standard deviation of 0.74 days and a coefficient of variation of 0.66% (aggregated season length s based on observed weather were 106 days in 2010 and 121 days in 2011). It could be inferred that in general, crop yield differences

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230 between the years were small while season length differences were practically inexistent. The effect of long term seasonal weather variability on the distribution of aggregated maize yield for selected weather network densities are portrayed in Fig ure 5 12. These distributions varied in a similar pattern that was independent of the network density. It was established earlier using observed weather data that when the density of the weather network increased, the variance of the crop prediction aggregates decreased exponentially; however, the expected value of the prediction aggregates remained essentially constant. This same pa ttern was reproduced using generated weather data in each year (Fig ure 5 12). For any density size in Fig ure 5 12 (1, 10, 20 or 30 locations), the long term mean, standard deviation and coefficient of variation across the years were respectively 2078 kg ha 1 140 kg ha 1 and 7% for grain yield. These values were essentially the same as the ones obtained using the full density size (2077 kg ha 1 138 kg ha 1 and 7%). Season length variability was hardly noticeable with a year to year coefficient of variation of about 1%. The density of weather network had a strong effect on the variance of the distribution of aggregate maize yield (based on generated data) as found earlier using observed data. The coefficients of variation of the distributions of aggregate ma ize yield (in Fig ure 5 12) decreased from 34% at a density of 1 location to 10% at a density of 10 location s to 6% at a density of 20 locations in one of the years generated. In another year this decrease was respectively, for the same densities, 41%, 12% and 7%. The largest differences in the coefficients of variation among the years were observed at density 1 location with values ranging from 28 to 41%. At network densities of 10, 20

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231 and 30 locations, the coefficients of variation were more stable across the years. For these densities, they varied respectively from 8% to 12%, 5% to 7% and 3% to 5%. Variation in season length was identical and negligible in all years (about 1% at a network density of 1). These results suggested that the rate of variance red uction with increasing network density between 1 and 10 depended upon the year (Fig ure 5.13A). Other studies that have investigated the effect of observed or synthetic long term weather variability on simulated location specific or spatially aggregated cr op yield reported inter annual variability of an order of magnitude higher than found in the present study. For example, ( 20 02) reported that year to year variability in simulated maize yield over a period of 31 years of observed weather using the CERES Maize model of DSSAT was 21.5%. Using 100 years of synthetic weather, Riha et al ( 1996) found that the coefficient of variation due to year to year simulated yield differences ranged from 11 % to 20% for the EPIC corn model and 25 % to 31% for another maize model under different soils and environments. Hansen and Jones ( 2000) reported that coefficient of variation of temporal variability of aggregate soybean yield was predicted more accurately when soil and management heterogeneities were incorporated in the simulations. Accoun ting for these heterogeneities also resulted in a decrease in the same coefficient of variation from 27% to 20%. ( 2002) a nd Hansen and Jones ( 2000) who incorporated more than one weather location in their studies emphasized the positive contribution of spatially variable weather to the accuracy of simulated crop yield. Conclusions Findings from this study indicated that spatial heterogeneity in weather, soil, cultivar and planting date affect crop predictions at varying degrees. In the wetter year

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232 (2010) spatial maize yield variability was primarily due to spatial varia tion s in weather and soil and their interactions. In the drier year (2011) whe n timing of water availability was more critical, planting date was a major contributor to crop yield variance in addition to weather. These differences between the two years wer e probably enhanced by the limited number of planting dates used in 2010. Regardless of the year considered, the most influential factors on crop yield (by order of decreasing importance) were weather, soil, planting and cultivar in 2010 and weather, plant ing, cultivar and soil in 2011. Season length variability was largely due to cultivar in 2010 and cultivar and planting date in 2011. Uncertaint ies in predicting aggregated crop yield, biomass and season length due to incomplete spatial sampling of weather (mostly rainfall) decreased as the number of weather locations used increased from 1 to 50. Expressed in terms of crop yield coefficient of variation, this uncertainty decreased exponentially from 27% to approximately 4 % at a sampling density of 20 locati ons. Uncertainty in season length was less than 1% over the whole range of weather network densities. The general form of the relationship between maize yield distribution and density of weather sites was not affected by long term seasonal weather variabil ity; however, the mean of the distributions (which was independent of the density size for practical purposes) was specific to the yield level attainable in a given year. In addition, the rate of maize yield variance reduction with increasing network densi ty of between 1 and 10 sites depended on the year. Year to year variability of aggregate crop predictions was characterized by a coefficient of variation of 7% for yield and 1% for season length. The GiST weather generator proved to produce a spatial seque nce of weather data that accounted for

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233 correlations between locations. However, generation of cold temperatures resulted in crop failures at early planting dates. The smaller year to year variability in maize yield found in the present study was attributab le to the limited number of years used to generate the weather data. Uncertainties in characterizing the crop environment may affect estimation of crop parameters and results of model sensitivit ies to these parameters. Quantification of these uncertainties may guide the interpretation of results from these analyses. This research demonstrated that there was a large uncertainty associated with the assumption of homogeneity of rainfall used to model crop yield at a point (using data from the nearest weather s tation) or at a larger scale (using data from one or a few representative weather stations). Over an area of 3072 km 2 covered by the study, 10 weather locations were required to decrease the coefficient of variation of crop yield to 10%. Our findings indic ated that this uncertainty is larger if year to year variability in weather is considered simultaneously with spatial variation. Given that the Georgia Automated Environmental Monitoring Network had only 4 weather stations in the same area, we anticipate t hat most studies will use a density of weather stations that is insufficient for eliminating uncertainties associated with crop predictions. These uncertainties should be recognized when interpreting results from such studies. In addition, geo spatial weat her generators can aid in evaluating the impact of uncertainties in crop predictions due to spatial weather variability if correlations from a denser network of weather stations is known.

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234 Table 5 1. Characteristics of observed total seasonal rainfall (mm) at gauge locations during 2010 and 2011 over the study area Season Summer Fall Winter Spring Summer Fall Year 2010 2010 2011 2011 2011 2011 Months Jun Jul Aug Sep Aug Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Aug Nov Minimum 203 60 151 108 83 101 Maximum 494 196 274 235 373 198 Mean 355 138 235 162 264 152 Standard deviation 65 24 23 29 67 21 Coefficient of variation 0.18 0.17 0.1 0.18 0.25 0.14 Table 5 2. Some properties of soil s used in characterizing spatial soil variations Series Texture DUL minus LL in upper layer (mm 3 mm 3 ) Classification C overage of Baker+Mitchell and Dougherty (%) Orangeburg Loamy sand 0.078 Fine loamy, siliceous, thermic Typic Paleudult 10.8 and 18.8 Faceville Loamy sand 0.092 Clayey, kaolinitic, thermic Typic Paleudult 1 and 0 Lucy Sand 0.063 Loamy, siliceous, thermic Arenic Paleudult 6.2 and 2.1 Tifton Sand 0.064 Fine loamy, siliceous, thermic Plinthic Kandiudult 13 and 3.7 Bonneau Loamy sand 0.083 Loamy, siliceous, subactive, thermic Arenic Paleudult 3.1 and 0 Osier Loamy sand 0.102 Siliceous, thermic Typic Psammaquents 3 and 0 Source: NRCS ( 2010) ; DUL: Drained upper limit; LL: lower limit

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235 Table 5 3. D efinition of SALUS crop parameters No. Parameter Definition 1 EmgInt Intercept of emergence thermal time calculation 2 EmgSlp Slope of emergence thermal time calculation 3 HrvIndex Crop harvest index 4 LAIMax Maximum expected Leaf Area Index 5 RelLAIP1 Parameter for shape at point 1 on the potential LAI curve 6 RelLAIP2 Parameter for shape at point 2 on the potential LAI curve 7 RelTTSn Relative thermal time at beginning of senescence 8 RelTTSn2 Relative thermal time beyond which the crop is no longer sensitive to water stress 9 RLWR Root length to weight ratio 10 RUEMax Maximum expected Radiation Use Efficiency 11 SeedWt Seed weight 12 SnParLAI Parameter for shape of potential LAI curve after beginning of senescence 13 SnParRUE Parameter for shape of potential RUE curve after beginning of senescence 14 StresLAI Factor by which LAI senescence due to water stress is increased between RelTTSn and RelTTSn2 15 StresRUE Factor by which RUE decline due to water stress is accelerated after the beginning of leaf senescence 16 TBaseDe v Base temperature for development 17 TFreeze Threshold temperature below which crop development and growth stop 18 TOptDev Optimum temperature for development 19 TTGerminate Thermal time from planting to germination 20 TTMature Thermal time from planting to maturity

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236 Table 5 4. Values of crop parameters of the three cultivars used to characterize spatial variations in maize cultivar No. Parameter Unit Short Medium Long 1 EmgInt o C 35 35 35 2 EmgSlp o C cm 1 5 5 5 3 HrvIndex 0.47 0.48 0.45 4 LAIMax m 2 m 2 5.33 4.75 5.17 5 RelLAIP1 0.054 0.011 0.055 6 RelLAIP2 0.910 0.945 0.912 7 RelTTSn 0.50 0.55 0.51 8 RelTTSn2 0.73 0.72 0.72 9 RLWR cm g 1 6945 7461 6885 10 RUEMax g MJ 1 3.81 3.98 3.79 11 SeedWt g seed 1 0.309 0.309 0.309 12 SnParLAI 0.357 0.312 0.355 13 SnParRUE 0.351 0.312 0.360 14 StresLAI 5.48 6.68 5.09 15 StresRUE 5.52 5.60 5.42 16 TBaseDev o C 8.5 8.5 8.5 17 TFreeze o C 0 0 0 18 TOptDev o C 29.5 29.5 29.5 19 TTGerminate o C 18.5 18.5 18.5 20 TTMature o C 1610 1753 1967

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237 Table 5 5. Main effect and interaction sensitivity indices representing the partitioning of biomass, grain yield and season length variance into different sources of variation Biomass Grain yield Season length 2010 Weather 0.523 0.529 0.009 Soil 0.178 0.180 0.000 Cultivar 0.101 0.090 0.943 Planting 0.097 0.099 0.046 Weather x Soil 0.027 0.027 0.000 Weather x Cultivar 0.015 0.015 0.000 Weather x Planting 0.023 0.024 0.000 Soil x Cultivar 0.001 0.001 0.000 Soil x Planting 0.010 0.010 0.000 Cultivar x Planting 0.007 0.007 0.001 Higher order interactions 0.017 0.018 0.000 2011 Weather 0.329 0.333 0.003 Soil 0.07 0.071 0.000 Cultivar 0.14 0.128 0.523 Planting 0.232 0.235 0.473 Weather x Soil 0.007 0.007 0.000 Weather x Cultivar 0.02 0.019 0.000 Weather x Planting 0.106 0.107 0.000 Soil x Cultivar 0.001 0.001 0.000 Soil x Planting 0.015 0.015 0.000 Cultivar x Planting 0.045 0.046 0.000 Higher order interactions 0.035 0.036 0.000 Table 5 6. Total sensitivity indices (main effect and interactions combined) and ranking of the sources of variability involved in the partitioning of biomass, grain yield and season length variance Biomass Grain yield Season length Total Indices Ranking Total Indices Ranking Total Indices Ranking 2010 Weather 0.588 1 0.595 1 0.009 3 Soil 0.216 2 0.218 2 0.000 4 Cultivar 0.124 4 0.113 4 0.944 1 Planting 0.137 3 0.140 3 0.047 2 2011 Weather 0.462 1 0.466 1 0.003 3 Soil 0.093 4 0.094 4 0.000 4 Cultivar 0.206 3 0.194 3 0.523 1 Planting 0.398 2 0.403 2 0.473 2

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238 Figure 5 1. Land use and annual rainfall variability in study area Weather stations inside and around the study area shown in blue in the state of Georgia inset map were used for interpolating temperatures.

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239 Figure 5 2. Spatial variability of observed summer rainfall (in mm) in 2010 and 2011. The points show the locations where rainfall data were collected Figure 5 3. Spatial variability of simulated maize grain yield (in kg ha 1 ) in 2010 and 2011. The points show the locations where rainfall data were collected Simulated y ield at each site was aggregated over soil, cultivar, and planting date variations; therefore, differences among locations were due to weather and its interactions with soil, cultivar, and planting date.

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240 A B C D Figure 5-4. Uncertainty in simulated maize yi eld (A and B) and season length (C and D) due to spatial variations of soil, cultivar, and planting date at each weather location. Each line in each subplot represents one weather location. Variability within each line (cum ulative distribution) is due to soil, cultivar, and planting date spatial variations. 0200040006000 0.00.20.40.60.81.0 Grain yield (kg ha 1)Cumulative probability 2010 0200040006000 0.00.20.40.60.81.0 Grain yield (kg ha 1)Cumulative probability 2011 100110120130140 0.00.20.40.60.81.0 Season length (days)Cumulative probability 2010 100110120130140 0.00.20.40.60.81.0 Season length (days)Cumulative probability 2011

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241 A B C D Figure 5-5. Main effect and interaction sens itivity indices for describing sources of variability in maize grain yield (A and B) and season length (C and D) for the years 2010 and 2011 weathersoilcultivarplanting Interaction Main effectGrain yield sensitivity index 0.00.20.40.60.81.02010 weathersoilcultivarplanting Interaction Main effectGrain yield sensitivity index 0.00.20.40.60.81.02011 weathersoilcultivarplanting Interaction Main effectSeason length sensitivity index 0.00.20.40.60.81.02010 weathersoilcultivarplanting Interaction Main effectSeason length sensitivity index 0.00.20.40.60.81.02011

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242 A B C D Figure 5-6. Effect of increasing the density of weather locations on the distribution on simulated aggregate maize yield (A and B) and season length (C and D) across soil, cultivar, and plant ing date spatial variations 1591419242934394449 100020003000400050006000Density of weather locationsGrain yield (kg ha 1) 2010 1591419242934394449 100020003000400050006000Density of weather locationsGrain yield (kg ha 1) 2011 1591419242934394449 105110115120125130135Density of weather locationsSeason length (days) 2010 1591419242934394449 105110115120125130135Density of weather locationsSeason length (days) 2011

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243 A B Figure 5-7. Variability in the coefficient of variation of the distribution of simulated aggregate maize yield and season length as a function of the density of weather locations 01020304050 0510152025 Density of weather locationsGrain yield coefficient of variation (%) 2010 2011 01020304050 0.00.20.40.6 Density of weather locationsSeason length coefficient of variation (%) 2010 2011

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244 A B C D Figure 5-8. Effect of increasing the density of weather locations on the distribution of simulated aggregate yield of a medium maturity maize cultivar grown on a loamy soil at two planting dates in 2010 and 2011. A) April 21, 2010; B) April 28, 2010; C) March 1, 2011; D) March 8, 2011. 1591419242934394449 100020003000400050006000Density of weather locationsGrain yield (kg ha 1) Day 111, 2010 1591419242934394449 100020003000400050006000Density of weather locationsGrain yield (kg ha 1) Day 118, 2010 1591419242934394449 100020003000400050006000Density of weather locationsGrain yield (kg ha 1) Day 60, 2011 1591419242934394449 100020003000400050006000Density of weather locationsGrain yield (kg ha 1) Day 67, 2011

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245 A B C D Figure 5-9. Variability in simulated aggregat e maize yield and season length by weather location for generated years 1 with and without the effect of cold temperatures. A) With cold temperatures effect; B) Comparison of the distributions of a colder and a warmer y ear with the distribution used by GiST for the generation of temperature (all years); C) Variability in simulated aggregate maize yield with the effect of cold temperatures removed; D) Variability in simulated aggregate maize s eason length with the effect of cold temperatures removed. 01000200030004000500060007000 0.00.20.40.60.81.0 Grain yield (kg ha 1)Cumulative probability Year 1 -100102030 0.000.020.040.060.080.10 Minimum temperature ( C)Density Colder year Warmer year All years 01000200030004000500060007000 0.00.20.40.60.81.0 Grain yield (kg ha 1)Cumulative probability Year 1 100110120130 0.00.20.40.60.81.0 Season length (days)Cumulative probability Year 1

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246 A B Figure 5-10. Influence of year on the spatial di stribution of simulated maize yield (A) and season length (B) aggregated across soil, cultivar and planting date variations A B Figure 5-11. Effect of long-term seasonal va riability of weather on simulated aggregate maize yield (A) and season length (B) across weather, soil, cultivar and planting variations 1357912151821242730 1000200030004000YearSpatial distribution of grain yield (kg ha 1) 1357912151821242730 108110112114YearSpatial distribution of season length (days) 051015202530 1800200022002400 YearAggregated grain yield (kg ha 1) 051015202530 110.0111.0112.0113. 0 YearAggregated season length (days)

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247 A B C D Figure 5-12. Influence of year on the distri bution of simulated aggregate maize yield for selected weather network densities. Each box plot represents a distribution of aggregate yield; each point in the box plot corresponds to aggregate yield using a specific combination of 1, 10, 20 or 30 sites. 1357912151821242730 1000200030004000YearAggregated grain yield (kg ha 1) Density = 1 location 1357912151821242730 1000200030004000YearAggregated grain yield (kg ha 1) Density = 10 locations 1357912151821242730 1000200030004000YearAggregated grain yield (kg ha 1) Density = 20 locations 1357912151821242730 1000200030004000YearAggregated grain yield (kg ha 1) Density = 30 locations

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248 A B Figure 5-13. Effect of weather network density on the coefficient of variation of the distributions of simulated aggregate ma ize yield (A) and season length (B) for 30 years of generated weather data. Each line in each subplot represents one year 10203040 Density sizeCoefficient of variation (%) 11 02 03 0 0.10.20.30.40.50.6 Density sizeCoefficient of variation (%) 11 02 03 0

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249 CHAPTER 6 SUMMARY AND CONCLUSI ONS Spatial heterogeneity of the crop environment causes spatial variability in crop yield. An incomplete account for this spatial heterogeneity generates uncertainties in simulating aggregate crop yield. In this dissertation, some of the important sources of uncertaint y were evaluated with an emphasis on spatial and temporal precipitation variability. The overall outcome of this study was that precipitation variability exerted the largest influence on crop predictions among the other sources tested (soil, cultivar, and planting date) Aggregate biomass, grain yield and season length were highly sensitive to spatial and long term seasonal precipitation variability. Uncertainties in maize yield were particularly importan t when less than 10 weather locations were used to produce aggregates over an area of approximately 3100 km 2 To arrive at these conclusions, the objectives of the study were assessed in full details and organized in four chapters. In C hapter 2 a global u ncertainty and sensitivity analysis was carried out on the SALUS crop model, after th is generic model was integ rated in DSSAT. In C hapter 3 crop parameters were estimated for three row crops of great importance to the study area, maize, peanut and cotton. In C hapter 4 high resolution spatial and temporal rainfall data collected in the study area were used to enhance our understanding of rainfall variab ility at a range of scales. In C hapter 5 the effect s of uncertainties resulting from this rainfall varia bility and other inputs on crop model predictions were evaluated. Main Results of Chapter 2: Integrating SALUS in DSSAT Successful integration of the simple SALUS crop model into DSSAT demonstrated the efficiency of the modular structure of DSSAT in accom modating new crop models

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250 that can benefit from its user friendly graphical user interface and its well tested soil, weather and management modules. The integration of SALUS in DSSAT involved the introduction of new crop parameters to improve predictions by the model. A quantitative analysis of the relationships between crop parameters and SALUS model outputs was conducted in the form of uncertainty and sensitivity analysis. This analysis showed the potential for using a more complex crop model for estimatin g uncertaint y ranges for different crop parameters in a simple generic model while accounting for the correlation s among the crop parameters Results from the uncertainty and sensitivity analysis indicated that uncertainties in model predictions and their sensitivit ies to crop parameters depended upon the model output of interest (biomass, grain yield or season length), the production level (potential or water limited), the crop (maize, peanut or cotton) and the location (warmer or colder climates) but not on the year under consideration. Biomass and grain yield were more variable than season length. Uncertainties were larger for biomass and grain yield at water limited production than potential production. This was not true for season length as the model d id not account directly for the effect s of water deficit on the duration of growth. At higher latitudes, cooler temperatures resulted in longer growth duration s and more variability in model ou tputs, hence higher uncertainty In general the model was not sensitive to parameters that predict the timing of germination and emergence. The relative importance of all other crop parameters reflected a relationship between the category of the parameter and the situation simulated. These categori es were LAI growth, temperature thresholds crop duration, biomass accumulation, grain yield and water uptake parameters All these categories of

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251 parameters affected crop biomass and grain yield but their ranking varied with the condition simulated (combi nation of crop, production level, location and model output). A logic diagram was developed to summarize these results. The five most frequently influential parameters were maximum LAI, maximum RUE, base temperature, optimum temperature and any of the para meters used to characterize the LAI curve. Main Results of Chapter 3: Estimating Crop Parameters for DSSAT SALUS Results from the parameter estimation study emphasized findings from other studies that the Metropolis Hastings algorithm using Markov Chain M onte Carlo simulations i s a reliable method for estimating crop model parameters. Model predictions using parameters estimated with in season measurements (detailed data) were in closer agreement with observed data when compared to parameters estimated wit h end of season data (limited data) only. The distributions of parameters estimated using end of season data were also associated with higher variances. Differences in standard deviations of up to a factor of 3.6 were found between use of limited and detai led datasets to estimate maximum LAI. These results suggested that the estimation of highly influential parameters should include in season measurements of growth characteristics Independent testing of the model using the means of the posterior parameter distributions showed that the simulations were generally congruent with the data. Root mean squared errors ranged from 567 kg ha 1 to 1543 kg ha 1 for in season biomass and 0.42 m 2 m 2 to 1.22 m 2 m 2 for in season LAI. These errors represented respectivel y 10% to 24% (for biomass) and 16% to 63% (for LAI) of the means of measurements. Willmott model efficiency indices for all maize and peanut maturity groups evaluated were consistently larger than 0.95 indicating excellent agreement

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252 between measurements a nd simulations. Comparison between DSSAT SALUS and more complex DSSAT models indicated that simple crop models represent promising alternatives to more complex models because simple models use fewer parameters and can be parameterized more easily to simula te a range of crops Main Results of Chapter 4: Rainfall Variability Results from C hapter 4 confirmed that spatial and temporal variability of rainfall is high in the s outheastern U.S. not only at scales of about 60 km but also at farm scale ( less than 10 km). Characterization of individual storms indicated that summer (June July August) and winter (December January February) exhibited the highest contrast in practically all respects. Summer storms were generally localized, more frequent and characterized b y moderate rainfall amount s higher rainfall intensit ies and short duration s Most winter storms covered at least 90% of the study area (3100 km 2 ) and were characterized by longer durations, higher rainfall amount s and lower rainfall intensit ies Mean stor m duration was 1.5 hours in summer 2010, 0.93 hours in summer 2011 and 6 hours in winter 2011. Fall (September October November) and spring (March April May) demonstrated a mix of characteristics from the two extremes and can be regarded as transition seas ons. These two seasons were characterized by longer rainfall interruptions. Correlation s of daily and hourly rainfall amount s decreased with increasing distance between pairs of locations. Summer correlations decreased faster with distance than winter corr elation s The distance s corresponding to a correlation of 0.90 were smaller than 3 .3 km in the summer and approximately 18 km in the winter. This means that daily or hourly rainfall amounts in the summer were only similar in the immediate neighborhood of a location, which was in contrast to winter rainfall. The

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253 correlations. Generalization of the correlation distance relationship into a variogram model resulted in a range of 12 km in the summer and 47 km in the winter. Main Results of Chapter 5: Uncertainties in Crop Model Predictions Resulting from Rainfall Variability Results from C hapter 5 showed that spatial weather variability (especially rainfall) is a major so urce of uncertainty in crop yield based on observed weather data from 2010 and 2011. Weather and its interactions with other factors accounted for 60% and 49% of the total simulated crop yield variability respectively in 2010 and 2011. Cultivar and its int eractions with other factors explained 94% and 52% of variability in crop duration respectively in 2010 and 2011. The ranking of these factors by order of decreasing influence on crop yield was weather, soil, planting date and cultivar in 2010. In 2011, th is order was weather, planting date, cultivar and soil because of a more thorough coverage of the planting date uncertainty range. Uncertainty in predicting aggregated crop yield, biomass and season length due to incomplete spatial sampling of weather (mo stly rainfall) decreased as the number of weather locations used increased from 1 to 50. Expressed in terms of maize yield coefficient of variation, this uncertainty decreased exponentially from 27% to approximately 4 % at a sampling density of 20 locations Uncertainty in season length was less than 1% over the whole range of weather network densities. Based on 30 years of generated weather data, it was concluded that the general form of the relationship between maize yield distribution and density of weath er network was not affected by long term seasonal weather variability; however, year to year weather

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254 variability appeared to be an additional source of uncertainty in aggregating crop yield when less than 10 weather locations were used. Results from this s tudy may be modified by management and environmental factors. The strong effects of rainfall on crop predictions may be attenuated in irrigated cropping systems. In mountainous areas, changes in temperature and solar radiation may be as or more dominant th an rainfall, resulting in higher crop yield variability due to weather. Final Conclusions Several changes to the SALUS model during integration in DSSAT ha ve produced an improved model that responds adequately to different soils, climates, and crops. Findings from the global uncertainty and sensitivity analysis combined with results from the parameter estimation and independent testing suggested that the DSSAT SALUS crop model was sufficiently stable for simulating maize, peanut and cotton performance. However, the model is still under development and it was suggested that further testing using data from diverse environments be conducted to establish the robustness of its response s State variety trials provide a vital source of data for carrying out sy stematic testing of the model. Testing using these trials will also assist with establishing the It is important to note that the model was not designed to simulate subtle variations among cultivars i n the same maturity groups that are not characterized with current crop parameters. Detailed simulation of specific cultivar traits will probably involve the addition of new crop parameters, which will eventually increase the complexity of the model. It ha s been estimated that the use of a constant harvest index is not adequate when a stress prevents the accumulation of dry matter during the reproductive phase of growth. In

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255 addition, the model account for the effect of carbon dioxide on dry matter accumulat ion in a simplistic way, that is using a multiplicative factor. Therefore, proposed model improvement s include the simulation of the effect of environmental stresses on harvest index and a more robust account for the effect s of carbon dioxide need ed for st udying climate change impacts. Future research using the D S SAT SALUS mode l may involve applications for understanding feedbacks between croplands and the atmosphere as an integral component of a land surface model. Based on the network of 50 rain gauges in our study area of approximately 3100 km 2 the high spatial rainfall variability led to the conclusion that locations 54 km apart are more similar in the winter than locations less than 3 km apart are in the summer. This means that the existing 4 Georgia A utomated Environmental Monitoring Network weather stations in the study area should be sufficient to capture most of the rainfall variability in the winter. Based on the large scale nature of winter rainfall processes, we expect similar winter rainfall pat terns at locations situated at about 60 to 90 km from our study area. In the summer, however, generalization is diffi cult due to high frequency variations. Our data showed some differences in rainfall amount even at the smallest gauge separation distance o f 1 km. However, it is important to note that only a small number of these short distances were present in our analysis. Moreover, most of the rain gauges were concentrated in the interior of the counties so caution should be used when extrapolating result s to the county boundaries or to neighboring counties. Coupled to the measured rainfall spatial variability, spatial heterogeneity in soil, cultivar and planting date influence crop predictions at all scales and stages of model development. Uncertainties in these highly variable model inputs may affect estimation

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256 of crop parameters and results of model sensitivit ies to these parameters. In particular, significant bias may be introduced in crop parameters calibrated for a large area where spatial rainfall v ariability is present but not accounted for Several studies applying crop models at a regional scale often rely on one or a limited number of stations to characterize the spatial variability in weather. Our findings strongly suggest that in such cases, ag gregate crop prediction s obtained may be highly uncertain as they only represent one sample from the distribution of possible values. However, we recognize the challenges associated with characterizing weather variability. Geo spatial weather generators li ke GiST may be useful in generating spatial distributions around one or a few weather stations if spatial correlations of weather variables are known. Future research on the spatial and temporal variability of rainfall in the study area should include a s tudy of the relationship between radar estimates of rainfall and the ground truth data. An understanding of this relationship should enhance the confidence attached to radar data in areas of the s outheast ern U S that demonstrate weather systems similar to the ones present in our study area. If well calibrated, these radar data can constitute a source of daily rainfall data for various applications.

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257 APPENDIX SOME CHARACTERISTICS OF THE WEATHER LOCATIONS Table A 1. Geographic coordinates of the weather locations, total summer rainfall and simulated maize yield aggregates in 2010 and 2011 (over soil, cultivar and planting date variations at each location) Site ID Longitude Latitude Total summer rainfall in 2010 (mm ) Total summer rainfall in 2011 (mm) Simulated maize yield in 2010 (kg ha 1 ) Simulated maize yield in 2011 (kg ha 1 ) AD1 84.2250 31.3248 287 108 4334 1437 BK1 84.4119 31.1038 297 223 1019 2108 BF1 84.1297 31.3704 394 137 4703 1515 CF1 84.2654 31.1705 362 175 4054 911 BP1 84.4068 31.3734 294 138 2873 1587 BP2 84.4323 31.3594 339 154 2685 1516 DB1 84.2020 31.2977 333 154 4319 1465 EB1 84.0709 31.2197 390 154 3497 1542 GG1 84.2878 31.0821 274 201 3198 1702 GA1 84.3068 31.5562 373 146 4469 1777 GF1 84.1488 31.2164 413 139 4685 1140 GF2 84.0741 31.2684 416 120 3991 751 HF1 84.5214 31.3387 357 124 3521 1094 HF2 84.6188 31.3272 246 124 2752 1030 JF1 84.0821 31.3233 322 147 4335 1041 JC1 84.4466 31.1924 295 197 3032 1312 JC2 84.4917 31.2710 225 145 1804 1011 KF1 84.1511 31.3180 355 144 4263 1717 LR1 84.3689 31.2298 381 181 4412 1580 LR2 84.4331 31.1718 309 197 2818 1516 LW1 84.3585 31.5060 457 155 4002 1901 NA1 84.5335 31.0959 302 227 3765 1988 NA3 84.5372 31.1692 422 214 4927 2887 NL1 84.2625 31.4949 442 191 4215 1520 NL2 84.2779 31.5037 455 197 4739 1730 NP1 84.1828 31.4470 304 142 3681 1145 NP2 84.1559 31.4456 304 155 3700 2000 NP3 84.1692 31.4789 378 167 4192 1483 OW1 84.3290 31.3313 338 133 3319 1158 OW2 84.3110 31.3463 343 138 4201 1143 OW3 84.2913 31.3714 348 147 3285 1840 PJ1 84.2737 31.2415 394 166 4587 1801 PM1 84.2749 31.2635 383 170 4610 1750 PB1 84.3284 31.4029 373 146 3400 1712 PB2 84.3072 31.4043 438 133 4183 1661

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258 Table A 1. Continued Site ID Longitude Latitude Total summer rainfall in 2010 (mm) Total summer rainfall in 2011 (mm) Simulated maize yield in 2010 (kg ha 1 ) Simulated maize yield in 2011 (kg ha 1 ) PB3 84.3783 31.3916 312 162 2815 2426 PK1 84.3847 31.5195 405 149 3464 1949 RS1 84.0549 31.1194 332 235 3446 1812 RS2 84.2479 31.1170 309 187 3299 1169 SF1 84.2408 31.1637 367 186 4335 1171 SI1 84.3005 31.2859 309 169 3396 2178 TP1 84.3321 31.4414 494 154 3377 1820 TP2 84.3186 31.4530 493 150 4486 1616 WG1 84.1216 31.2093 203 167 3164 936 WT1 84.0031 31.4170 423 156 4952 1055 WT2 84.0978 31.4492 355 160 4229 1588 UGAB 84.6308 31.3532 287 228 3195 971 UGAD 84.0519 31.5540 372 251 4076 1598 UGCM 84.2916 31.2801 330 266 3635 1878 UGNB 84.4779 31.2239 331 271 3099 1818

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259 Figure A 1. Locations of rain gauges and weather stations in the study area

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260 Figure A 2. Elevation and annual rainfall variability in the study area. Source of elevation data (USDA, 1999)

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276 BIOGRAPHICAL SKETCH Kofikuma Dzotsi was born in Lome, the capital of Togo (West Africa). He graduated from high school in 1996 and attended the School of Agronomy at the University of Lome. Towards the end of his training he participated in a workshop on systems approach, sim ulation and modeling organized by the International Center for Soil Fertility and Agricultural Development (IFDC), which was his first contact with systems analysis and its use in agronomic modeling. The interest he developed for this field of research led to his thesis work in collaboration with IFDC on Long term assessment of variety and sowing time strategies for maize using DSSAT After graduation in 2002, he worked for IFDC as research assistant then later as an agronomist developing Integrated Soil Fe rtility Management (ISFM) strategies for basil ( Ocimum basilicum L.). In 2005, he joined the McNair Bostick Simulation Laboratory in the Agricultural and Biological Engineering department, University of Florida to work on soil and plant phosphorus modeling for his Master of Science degree. This opportunity represented for him the beginning of a formal training in systems analysis and simulation modeling In January 2008, he started a Doctor of Philosophy degree in the same department His research involved assessing uncertainties in simulated crop yield resulting from rainfall spatial variability Kofikuma Dzotsi is married and has two children.