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Cotton Yield Forecasting for the Southeastern United States

Permanent Link: http://ufdc.ufl.edu/UFE0041500/00001

Material Information

Title: Cotton Yield Forecasting for the Southeastern United States
Physical Description: 1 online resource (146 p.)
Language: english
Creator: Pathak, Tapan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: climate, cotton, cropgro, forecast, glue, indices, sensitivity, simulation, southeast, uncertainty, yield
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: Cotton is the most important fiber crops in the United States, accounting for approximately 20% of the total production in the world and more than $25 billion in products and services annually. The Southeastern United States holds a major share of total cotton production of the country. While evidence clearly shows an increase in cotton planted over the time, climate variability is a major concern that could adversely affect its production in the southeastern United States. An effective way to reduce agricultural vulnerability to climate variability is through the implementation of adaptation strategies such as crop yield forecasts to mitigate negative consequences or take advantage of favorable conditions. The use of climate forecasts and climate indices to forecast cotton yield using the CROPGRO-Cotton model and principal component regression model, respectively, were assessed in this study. Using the crop model, inseason updating of the cotton yield forecast with real weather data along with the climatology significantly improved the accuracy of the forecast. With principal component regression models, cotton yield forecasts with significant skills were obtained with a lead time of approximately two months before cotton planting. Results indicated good potential for forecasting cotton yield for the southeastern United States.
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 Tapan Pathak.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Jones, James W.
Local: Co-adviser: Fraisse, Clyde W.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041500:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041500/00001

Material Information

Title: Cotton Yield Forecasting for the Southeastern United States
Physical Description: 1 online resource (146 p.)
Language: english
Creator: Pathak, Tapan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: climate, cotton, cropgro, forecast, glue, indices, sensitivity, simulation, southeast, uncertainty, yield
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: Cotton is the most important fiber crops in the United States, accounting for approximately 20% of the total production in the world and more than $25 billion in products and services annually. The Southeastern United States holds a major share of total cotton production of the country. While evidence clearly shows an increase in cotton planted over the time, climate variability is a major concern that could adversely affect its production in the southeastern United States. An effective way to reduce agricultural vulnerability to climate variability is through the implementation of adaptation strategies such as crop yield forecasts to mitigate negative consequences or take advantage of favorable conditions. The use of climate forecasts and climate indices to forecast cotton yield using the CROPGRO-Cotton model and principal component regression model, respectively, were assessed in this study. Using the crop model, inseason updating of the cotton yield forecast with real weather data along with the climatology significantly improved the accuracy of the forecast. With principal component regression models, cotton yield forecasts with significant skills were obtained with a lead time of approximately two months before cotton planting. Results indicated good potential for forecasting cotton yield for the southeastern United States.
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 Tapan Pathak.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Jones, James W.
Local: Co-adviser: Fraisse, Clyde W.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041500:00001


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COTTON YIELD FORECASTING FOR THE SOUTHEASTERN UNITED STATES


By

TAPAN BHARATKUMAR PATHAK















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

2010



























2010 Tapan Pathak
















To, my loving wife, my parents, and my family









ACKNOWLEDGMENTS

My PhD dissertation was one of the most important life changing journeys of my

life. I have seen good times as well as hard times throughout my PhD student life. I

enjoyed the good times and tried to learn and improve from the experiences of hard

time. PhD degree was like a dream for me and this dream would not have been

possible without constant high quality guidance and support from my major advisor Dr.

James W. Jones. He is one of the best advisors and I was fortunate to have him as my

PhD supervisor. He always encouraged me to explore innovative ideas but at the same

time made sure that those ideas are executed in a systematic scientific manner. I have

seen so much professional improvement in myself in last 5 years, which was solely due

to his valuable guidance. There is so much to say about Dr. Jones and it is hard to

narrate on a single page, but I must say that I will have my deepest respect for him

throughout my career and will always try to follow his advice for my own professional

development.

I would also like to express my deepest respect and gratitude towards my PhD

co-advisor Dr. Clyde W. Fraisse. He was always helpful in providing me with new

research ideas. His enthusiasm over implementing them always motivated me. I have a

lot to learn from him and this dissertation would not have been possible without his

support. I would like to thank my committee members, Dr. David Wright, Dr. James

Heaney, and Dr. Gregory Kiker for their valuable guidance and recommendations. I am

also thankful to Dr. Kenneth Boote for allowing me use his lab instruments for my

research and also for his valuable advice. I would also like to extend my

acknowledgement to Dr. Hoogenboom and Dr. Jasmeet Judge for providing me with

experimental data to run my analyses. I am greatly thankful to all my friends at McNair









Bostick Simulation Laboratory (MBSL) for keeping cheerful yet non-disturbing work

environment. I really enjoyed working with them. I enjoyed the company of "super

friend" Dr. McNair Bostick, I will always miss him.

I would like to thank all my family members for their constant support and

motivation throughout my PhD. I wish I could list out and thank all of them individually,

but I am afraid that it will take up many more pages. I would like thank my mom and dad

for their blessings, inspiration, and unconditional care. No words are enough to show

my gratitude towards them. Finally, I have an opportunity to thank the most beautiful,

loving, caring woman of my life, Rucha for her countless sacrifices and constant support

throughout my PhD. She has seen all the ups and downs with me and I could not have

done my PhD without her company. At the end, I would like to acknowledge our little

lucky charm, who is soon to arrive in this world.









TABLE OF CONTENTS

page

ACKNOW LEDG M ENTS ............................. ........ ............. ............... 4

L IS T O F T A B L E S .......... .............. ................. .......... .... ................................ 9

LIST O F FIG URES........................................... ............... 12

ABSTRACT ........................ ............................................. 14

1 INTRODUCTION .............................. ............. .................. 15

2 Use of Global Sensitivity Analysis for CROPGRO-Cotton Model Development...... 19

Introduction ................... .. ......... ................ 19
Materials and Methods...... .................................... 23
Overview of CSM-CROPGRO Cotton Model.................. .............. 23
Site and Experiment Description ............................ ........ 24
Sensitivity A nalysis.............................. ............... 25
Local sensitivity............................. ............... 26
Global sensitivity ............... .... ......... ............... 26
Results and Discussion.......................................... ............... 30
Local Sensitivity Analysis ....... .. ........................................................ ...... 30
Global Sensitivity Analysis.............................. .................... 30
C o n c lu s io n s .............. ..... ............ ................. ........................................... 3 3

3 Uncertainty Analysis and Parameter Estimation of CROPGRO Cotton Model .... 45

Introduction ................... ........ ............... 45
Materials and Methods...... .................. ............... ......... 48
Description of Field Sites and Measured Datasets ............... .............. 48
The CROPGRO-Cotton Model ......... ........................... 49
Uncertainty Analysis and Parameter Estimation Procedures ....................... 50
Parameter selection and prior distributions .................... ................ 50
Likelihood function ............... ..... ......... ..... ......... 52
Posterior distribution .............................................. 53
Uncertainty bounds for model predictions ...... ......... .... ................ 54
Statistical methods for model testing ........ ............... ............... 55
Results and Discussion........................................... 56
Simulations Using Unmodified Parameters ....... ........ ..... .................. 56
Parameter Estimates and Uncertainties ................ ........... 57
Comparison with prior distribution .................................. .. ............... ..... 57
Comparison with DSSAT default values ...... ......... .... ................. 58
Model predictions based on estimated parameters.............................. 59
Model output uncertainties ............................ ........... 60
C o n c lu s io n .............. ................. ............................................... ............... 6 1









4 In-Season Updates of Cotton yield forecasts using cropgro-cotton model........... 74

Introduction .................... ............. ............... 74
Material and Methods ........................ ................... 77
Outline of the Forecasting Method ............................ .............. 77
M odel Description and Input Data ....................................... ......................... 77
Comparison between Before-Season and In-Season Cotton Yield Forecasts
Based on C lim atology ........................... ... ................... ........................... 78
Comparison of Cotton Yield Forecasts Based on ENSO Indices ..................... 79
Comparison Between Climatology Based and ENSO Tailored Cotton Yield
Forecast ............... ......... .................. 80
R esu lts a nd D iscussio n................ ................. ... ............... ......... ............. 80
Comparison between Before-Season and In-Season Cotton Yield Forecasts
based on C lim atology........................ .......... ............ ........ ........... ..... 80
Comparison of Cotton Yield Forecasts based on ENSO Indices................... 81
El-Niio phase ................ ......... ........ ........ 81
La-Niia phase.................................. ............... 82
N neutral phase .............................................................. 82
Comparison Between Climatology Based and ENSO Tailored Cotton Yield
Forecast ............... ......... .................. 83
C o n c lu s io n s .............. ..... ............ ................. ........................................... 8 3

5 Cotton Yield forecasting for the Southeastern USa using climate indices............ 101

Intro d u ctio n .............. ................. ............................................. ............... 10 1
Materials and Methods................ ......... ...... ......... 103
Historic Cotton Yield Data ...... ............................... .................... 103
Climate Data............................................. 104
Atmospheric and Oceanic Climate Indices...... ........ .... ................. 104
Oceanic niio index (ONI)................................. ............... 105
Tropical north Atlantic (TNA) index ......... .... ................ ........... 105
Atlantic meridional mode (AMM) index ................ ............. ............... 106
North oscillation index (NO I) ........... ... .......... .......................... ............ 106
N orth pacific (N P ) pattern................................................ .... ............. 106
Tropical north hemisphere (TNH) index....... ................................. 107
Quasi-biennial oscillation (QBO) index .............. ............ 107
C orrelation A analysis .............................. ... .... .. ......................... 107
Correlations of Climate Indices with Temperature and Precipitation ............. 108
Correlations of Climate Indices with Cotton Yield ............... ................ 108
Principal Component Regression ...................... .. ......... .. ............. 109
Leave One Out Cross Validation .............. ............. ........ ............... 110
Categorical Yield Forecast Contingency Table............... .......................... 110
Results and Discussion....................................... 111
Historic Cotton Yield Data ...................... ...... .......... ............ 111
Correlation Analysis .... .................. ...... ... .. ......... .. 112
Correlations of climate indices with temperature and rainfall ............... 112
Correlation of climate indices with cotton yield...................................... 113


7









Principal Com ponent Regression .............. ............... .............................. 114
Leave O ne O ut Cross Validation ....................................... ......................... 115
Categorical Yield Forecast Contingency Table......................................... 117
C o n c lu s io n s .............. ..... ............ ............................... ........................................ 1 1 8

6 CONCLUSIONS AND FUTURE WORK .................................. ....................... 133

LIST OF REFERENCES ....... .................. ......... ......... 136

BIOGRAPHICAL SKETCH .............. ............ ... ......................... 146









































8









LIST OF TABLES


Table page

2-1. List of cultivar parameters in CSM-CROPGRO-Cotton Model.......................... 37

2-2. Local sensitivity indices with respect to selected model parameters for dry
m matter yield .............. ...... .................. .. ............... 38

2-3. Local sensitivity indices with respect to selected model parameters for season
le n g th .................. ................................. ....... ...... ...... 3 9

2-4. Model parameters and their range of uncertainty selected for the global
sensitivity analysis .......... ............ ......... ................ ............... 40

2-5. Global sensitivity indices for dry matter yield including main effects and
interactions .............. ...... ......... ........ .... ........ ..... ......... 41

2-6. Global sensitivity indices for season length including main effects and
interactions .............. ...... ......... ........ .... ........ ..... ......... 42

2-7. Model parameter rankings based on local and global sensitivity indices for dry
m matter yield .............. ...... .................. .. ............... 43

2-8. Model parameter rankings based on local and global sensitivity indices for
season length ............. ..... .. .... ... ............... ............... ........... 44

3-1. Information about the experimental sites, planting date, type of soils, and
weather characteristics .............................................................. 67

3-2. The CROPGRO-Cotton parameters and uncertainty ranges used for GLUE
prior distributions ......... ............ ......... ............ ............... .......... 68

3-3. The CROPGRO-Cotton average model predictions using DSSAT default
parameters in comparison with corresponding measured data ....................... 69

3-4. Parameter uncertainties and fundamental statistics of prior and posterior
d istributio ns ....... ..... ............ ........... ......... .............................. 70

3-5. The CROPGRO-Cotton average model predictions using estimated parameters
in comparison with corresponding measured data .................................... 71

3-6. Comparison of RMSE, and d-statistics of simulated LAI, and biomass
components for four sites based on DSSAT default model parameters and
GLUE estimated parameters .............. ................ ............... ... .... ........ 72

3-7. Comparison of output uncertainties in model outputs of LAI and above ground
biomass components for prior and posterior distribution ............... ............... 73









4-1. Measures of model deviations for seed cotton yield (Quincy, FL) before season
using no forecast except climatology ........... ........................ ...... ............ 86

4-2. Measures of model deviations for seed cotton yield (Quincy, FL) in-season
(July 1) using no forecast except climatology ...................... ........................ 87

4-3. Measures of model deviations for seed cotton yield (Quincy, FL) in-season
(August 1) using no forecast except climatology ............... ............. .......... 88

4-4. Statistical comparison of cotton yield forecasts obtained before-season with in-
season updated cotton yield forecasts.. .............. ................. ..... ......... 89

4-5. Measures of model deviations for seed cotton yield (Quincy, FL) using El Niio
forecast based on JMA index ........... ........ .. ......................... ............... 90

4-6. Measures of model deviations for seed cotton yield (Quincy, FL) using El Niio
forecast based on MEI index ..................... ................ ...... ......... 91

4-7. Measures of model deviations for seed cotton yield (Quincy, FL) using El Niio
forecast based on ONI index ..................... ................ ...... ......... 92

4-8. Measures of model deviations for seed cotton yield (Quincy, FL) using La Nina
forecast based on JMA index ........... ........ .. ......................... ............... 93

4-9. Measures of model deviations for seed cotton yield (Quincy, FL) using La Nina
forecast based on MEI index ..................... ................ ...... ......... 94

4-10. Measures of model deviations for seed cotton yield (Quincy, FL) using La
N iia forecast based on O N I index ................................................ ... .................. 95

4-11. Measures of model deviations for seed cotton yield (Quincy, FL) using Neutral
forecast based on JMA index ........... ........ .. ......................... ............... 96

4-12. Measures of model deviations for seed cotton yield (Quincy, FL) using Neutral
forecast based on MEI index ..................... ................ ...... ......... 97

4-13. Measures of model deviations for seed cotton yield (Quincy, FL) using Neutral
forecast based on ONI index ..................... ................ ...... ......... 98

4-14. Statistical comparison of cotton yield forecasts tailored to ENSO forecasts by
three indices. ........... .... .......... ................................. ........... 99

4-15. Statistical comparison of cotton yield forecasts using only climatology forecast
with ENSO tailored cotton yield forecasts using MEI.......... .. ............... 100

5-1. A 2x2 contingency table for categorical cotton yields................................. 128

5-2. Pearson's correlations and MSE for cross validated cotton yields for the
counties in G eorgia and Alabam a............... ................. ......... ....... .............. 129









5-3. Significant principal components (PCs) of principal component regression
models for cotton producing counties of Georgia and Alabama .................. 130

5-4. Loadings of principal components (PCs) of climate indices ...... ....................... 131

5-5. Skills of categorical cross validated cotton yield forecasts for counties of
Georgia and Alabam a ................................................................................ 132









LIST OF FIGURES


Figure page

2-1. Local Sensitivity indices for irrigated and rainfed conditions for 2000 (top) and
2003 (bottom ). ............................................................................. ..................... 35

2-2. Global Sensitivity indices for irrigated and rainfed conditions for the year 2000
(top) and 2003 (bottom ) ............................................................................. 36

3-1. Scatter plot of simulated vs. measured values for A) leaf area index, B) leaf
weight, C) boll weight, D) stem weight for all four experiments.. ................... 62

3-2. Simulated and observed values for A) leaf area index, B) leaf weight (kg/ha),
C) boll weight (kg/ha), and D) stem weight (kg/ha) for experiments 1-4 using
unmodified cultivar parameter values. ........................ .................. 63

3-3. Posterior probability distributions of model parameters.................. ........... 64

3-4. Scatter plot of simulated vs. measured values for A) leaf area index, B) leaf
weight, C) boll weight, D) stem weight for all four experiments.. ................... 65

3-5. Simulated and observed values for A) leaf area index, B) leaf weight, C) boll
weight, and D) stem weight for four experiments using estimated cultivar
param eter va lues ............. ........................................................... .......... 66

4-1. Distribution of forecasted cotton yields for the 1980 cotton season at Quincy,
Florida simulated using 1951-2005 historical weather data.............................. 85

5-1. Correlations of climate indices with temperature during the cotton growing
se a so n ......... ... ......... .... ............................ ............. .............. 12 0

5-2 Correlations of climate indices with rainfall during the cotton growing season..... 121

5-3. Correlations climate indices with cotton yield ........................... ..................... 122

5-4. Correlations of historic cotton residuals with cross validated cotton yield
residuals using the principal component regression of January and February
clim ate indices........................ .......... .................. ......... ...... ......... 123

5-5. Time series comparison between observed and cross validated cotton yield
residuals for four counties of Alabama and Georgia that showed the
maximum (A and B) and minimum correlations (C and D).............................. 124

5-6. Histogram of residual errors across the entire cross validated county cotton
yields. .................... .. .............. ......... ...... .. ............... 125









5-7. Probability of detecting county level cotton yields using cross validated cotton
forecasts for two categories........ ... ... .... .......................... ............... 126

5-8. Percent correct cross validated cotton yield forecasts based on principal
components regression model of climate indices and contingency table. ........ 127









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

COTTON YIELD FORECASTING FOR THE SOUTHEASTERN UNITED STATES
By

Tapan Bharatkumar Pathak

August 2010

Chair: James W. Jones
Cochair: Clyde W. Fraisse
Major: Agricultural and Biological Engineering

Cotton is the most important fiber crops in the United States, accounting for

approximately 20% of the total production in the world and more than $25 billion in

products and services annually. The Southeastern United States holds a major share of

total cotton production of the country. While evidence clearly shows an increase in

cotton planted over the time, climate variability is a major concern that could adversely

affect its production in the southeastern United States. An effective way to reduce

agricultural vulnerability to climate variability is through the implementation of adaptation

strategies such as crop yield forecasts to mitigate negative consequences or take

advantage of favorable conditions. The use of climate forecasts and climate indices to

forecast cotton yield using the CROPGRO-Cotton model and principal component

regression model, respectively, were assessed in this study. Using the crop model, in-

season updating of the cotton yield forecast with real weather data along with the

climatology significantly improved the accuracy of the forecast. With principal

component regression models, cotton yield forecasts with significant skills were

obtained with a lead time of approximately two months before cotton planting. Results

indicated good potential for forecasting cotton yield for the southeastern United States.









CHAPTER 1
INTRODUCTION

Cotton is the single most important fiber crop in the world, accounting for more

than 35% of the total fiber production. In terms of the world rankings, the United States

is ranked second in cotton production, accounting for 19.9% of total world production

(USDA ERS, 2009). The United States cotton industry is one of the major economic

drivers of the country accounting for more than $25 billion in products and services

annually. The Southeastern United States holds a major share of total cotton production

in the United States; approximately, one fourth of total produced comes from this region.

For instance, Georgia is ranked second to Texas in total cotton produced in the United

States. In recent years, there has been an increased need for fiber supply, which has

triggered increased cotton production in this region. Increases in acreage planted to

cotton in Georgia and Alabama were approximately 26% and 41% in the last decade,

respectively (NASS, 2007).

Although cotton is considered as a drought tolerant crop, climate variability may

adversely impact cotton production. Especially, cotton produced under rain fed

conditions could be severely affected by a variable climate. El Niio Southern Oscillation

(ENSO) is a dominant phenomenon of climate variability in this region and other

locations worldwide. The ENSO phenomenon is governed by the shift in sea surface

temperature (SST) in the Pacific, which affects inter annual climate variability across

most parts of the world including the southeastern United States (Hansen et al., 1998;

Jones et al., 2003; Ropelewski and Halpert 1986, Kiladis and Diaz 1989; Mo and

Schemm 2008; Mennis 2001). Hansen et al. (1998) showed that ENSO phase

significantly influenced six major crops, including cotton, in the southeastern United









States. Their results showed that cotton area harvested in Alabama, Georgia, Florida,

and South Carolina were significantly influenced by ENSO.

Jones et al. (2003) stated that the main reason that the climate variability is often

so devastating to agriculture is that we do not know what to expect in the next growing

season. Effective application of climate forecast and climate indices may provide an

opportunity to tailor agricultural decisions for higher economic returns to growers. There

have been many studies that evaluated the potential benefits of using climate forecasts

on decision making processes in agriculture as a way to adapt to climate variability

(Hansen et al., 2005; Podesta et al., 2002; Jones et al., 2003; Hansen et al., 1998).

An effective way to reduce agricultural vulnerability to climate variability is through

an effective use of climate forecasts. One potential adaptation tool is yield forecasting

based on climate information. Crop yield forecasts could be used by farmers to mitigate

negative consequences of unfavorable climate, or benefit from anticipated favorable

climate conditions (Baigorra et al., 2010). If growers know the expected cotton yield for

the coming season, they may be able to decide on alternative management strategies

to reduce the production risks (Jones et al., 2000; Hansen, 2005; Vedwan et al., 2005;

Jagtap et al., 2002). Crane et al. (2010) conducted a research study to explore the

potentials and constraints for farmers' application of climate forecasts. Their research

documented farmers' perspectives of adjusting their decisions using climate forecasts to

help them adapt to climate variability. Some of the documented long term decisions

were crop type, buying appropriate crop insurance, and areas to plant. Pre-season crop

yield forecasts would help growers in making the above mentioned decisions. For

example, growers could purchase higher crop insurance coverage, plant different crop,









plant less etc. in order to compensate for an adverse effect of climate variability on their

cotton yields.

Crop models have shown potential for use in forecasting crop yield if climate data

are provided to the model is in terms of a forecast. The main advantage of a crop model

is that it can produce a range of possible climate forecasts using uncertain climate

forecasts. Before the start of crop growing season, weather is entirely uncertain, this

translates into uncertainties in crop yield. If the model is updated during a season with

observed weather data, some of the weather uncertainties are eliminated. Although

weather uncertainties at the later stages of crop growth still impact the final crop yield, it

may be possible to improve the accuracy of crop yield prediction by in-season updating

the model with real weather data.

A model to simulate cotton growth and development has recently been developed

for the Decision Support System for Agrotechnology Transfer (DSSAT) called

CROPGRO-Cotton model (Jones et al., 1998; Hoogenboom et al., 2004). Since the

CROPGRO-Cotton model is relatively new, it is important to calibrate and evaluate the

model for t field conditions before it can be used for forecasting cotton yield. Hence,

determining and understanding how sensitive the simulations of certain model

processes are with respect to model parameters and estimating them is useful for

model improvements.

While growth and development of crops are known to be influenced by weather

during the growing season, it is a common practice to predict crop yield based on

weather variables (Sakamoto, 1979; Idso et al., 1979; Walker, 1989; Alexandrove and

Hoogenboom, 2001). However, crop yield predictions based on observed weather









cannot be made available before the planting season (Kumar, 2000). Attempts to obtain

long-term forecasts using alternatives to weather variables such as climate indices that

exhibit teleconnections with weather are limited. Large scale teleconnection indices

greatly influence the climate and agriculture in the southeastern United States (Stenseth

et al., 2003; Enfield, 1996; Bell and Jenowiak, 1994; Martinez et al., 2009). Using those

large scale climate indices as an early indicator to cotton yield could provide valuable

information to the growers in the Southeastern United States.

The overall research question addressed in this dissertation is "Do the use of

climate forecasts and climate indices by crop model and empirical models provide

potential in forecasting cotton yield for the southeastern United States?" Specific

objectives include:

Objective 1: To conduct a global sensitivity analysis of the CROPGRO-Cotton model

Objective 2: To estimate model parameters and conduct an uncertainty analysis of the
CROPGRO-Cotton model

Objective 3: To evaluate the use of in-season updates of cotton yield forecasts using
the climate forecasts

Objective 4: To evaluate the use of climate indices for cotton yield forecasting in the
Southeastern United States









CHAPTER 2
USE OF GLOBAL SENSITIVITY ANALYSIS FOR CROPGRO-COTTON MODEL
DEVELOPMENT

Introduction

The need for information in agriculture is increasing due to market and economic

pressures combined with the need for better management of our natural resources.

Crop models, widely used as research and teaching tools, are now becoming important

tools for agricultural decision makers, as the need for information in agriculture

increases. Crop models range in complexity from simple ones with a few state variables

to complex ones having large numbers of model parameters and state variables. The

Decision Support System for Agrotechnology Transfer (DSSAT) (Jones et al., 1998;

Hoogenboom et al. 2004) contains complex dynamic models that simulate crop growth

and yield as a function of soil and weather conditions and crop management regimes.

DSSAT can also be used to help researchers, extension agents, growers, and other

decision-makers to analyze complex alternate decisions (Tsuji et al., 1998).

Cotton (Gossypium hirsutum L.) is the single most important textile fiber in the

world, accounting for over 40 percent of total world fiber production. While some 80

countries from around the globe produce cotton, the United States, China, and India

together provide over half the world's cotton. The United States, while ranking second to

China in production, is the leading exporter, accounting for over one-third of global trade

in raw cotton (MacDonald, 2000). Due to the importance of cotton in the world in

general, and in the southeastern USA in particular, a model to simulate cotton growth

and development is currently being developed by the DSSAT crop modeling group. The

Cropping System Model (CSM, Jones et al., 2003) contains models of 21 crops based

on the CROPGRO, CERES and other models. The new cotton model has been









developed using the CSM-CROPGRO crop template that allows its integration with

other modules of the cropping system (Messina et al., 2004). The CROPGRO

development team has used this approach in creating models for different species,

including brachiaria grass (Giraldo et al., 1998), tomato (Scholberg et al., 1997), and

velvet bean (Hartkamp et al., 2002, Boote et al., 2002). CROPGRO was originally

developed as a process-oriented model for grain legumes, based on the SOYGRO,

PNUTGRO, and BEANGRO models that consider crop carbon, water, and nitrogen

balances (Boote et al., 1998). Its ability to represent different crops is attained through

input files that define species traits and cultivar attributes (Boote et al., 2002). Outputs

from CROPGRO models depend on a large number of model parameters associated

with the species traits and cultivar attributes.

Determining and understanding how sensitive the simulations of certain model

processes are with respect to model parameters is useful for guiding model developers.

The effects of particular model parameter on a given output can be determined by

measuring the relative influence of the model parameter on model output. Sensitivity

analysis is useful for identifying the most and the least important model parameters to

the given model output so that it can contribute to the simplification of a model (Saltelli

et al., 2000). There are a number of methods and techniques available for performing

sensitivity analysis (Saltelli et al., 2004), local and global sensitivity analyses are the

most commonly used methods.

Ruget et al. (2002) performed a local sensitivity analysis on the STICS crop

simulation model (Brisson et al., 1998) to determine how sensitive the simulation of

processes in each module was to the model parameters. Leaf area index was sensitive









to all the model parameters of the leaf area index module (crop density, rate of LAI

growth, and density effect on tillering), the cumulated root length was sensitivity to two

of the model parameters of the root module (rooting depth for half water absorption, and

rate of root deepening), whereas mineralization was most sensitive to humification

depth. Xie et al. (2003) conducted local sensitivity analysis of the ALMANAC model

(Kiniry et al., 1992) to input variables such as solar radiation, rainfall, soil depth, soil

plant available water, and runoff curve number and the impact on grain yield of sorghum

and maize. They found that runoff curve number change had the greatest impact on

simulated yield.

Global sensitivity analysis differs from local methods by accounting for the

variance of the model output associated with model parameters over their entire range

of uncertainty. Homma and Saltelli (1996) explored methods of global sensitivity

analysis of nonlinear models to calculate the fractional contribution of model parameters

to the variance of model predictions. Makowski et al. (2004) used global sensitivity

analysis to determine the contribution of generic model parameters to the variance of

crop model predictions. A sensitivity analysis was performed for three output variables

of the AZODYN wheat model (Jeuffroy and Recous, 1999) that included grain yield,

grain protein content, and the nitrogen nutrition index. Out of thirteen different model

parameters, five were found to have the most influence on grain yield and grain protein

content. The only model parameter that affected the nitrogen nutrition index was the

ratio of leaf area index to critical nitrogen concentration. This study concluded that

model parameters with the least influence on important simulated processes may not

need to be accurately estimated.









A sensitivity analysis allows modelers to rank model parameters in order of their

influence on model output. Based on the rankings it can be used to identify model

parameters that need a high accuracy in their estimates. Sensitivity analysis can also be

used to check whether the behavior of the model output is as expected with respect to

change in the input.

For the CSM crop models, it is practically impossible to measure or estimate all

the model parameters with a high level of accuracy. The CSM-CROPGRO-Cotton

model under development was initially parameterized using data from the literature

(Messina et al., 2004) and evaluated for different environmental conditions using those

parameters. Thus, there was uncertainty in the values of model parameters and how

they may affect the output.

This study was conducted for two purposes. The first objective was to determine

whether the global sensitivity analysis method would provide information on model

performance that differs from the simpler local sensitivity method. This type of sensitivity

analysis had not been used in the past with the CSM model. The central hypothesis in

this case was that global sensitivity analysis will lead to improved understanding of the

importance of model parameters since it accounts for the variance of model output

associated with the variance of model parameters over the range on uncertainty in each

parameter. The second objective was to determine how sensitive the prototype cotton

model predictions are to an important subset of its crop growth and development

parameters. Although the prototype model was based on an existing crop model it was

not clear how these model parameters would affect the most critical outputs, such as

yield and season length. We also did not know how these effects would differ between









rainfed and irrigated conditions. We hypothesized that the sensitivity of yield and

season length to changes in model parameters does not vary with weather and

irrigation. Results from this study were needed to guide further model parameter

estimation efforts for improving the cotton model.

Materials and Methods

Overview of CSM-CROPGRO Cotton Model

The cotton model is based on the modular code of the CSM-CROPGRO model

(Jones et al., 2003). This model simulates crop growth and development independent of

location, season, and crop management system. Its flexible physiological framework

provides a convenient template to implement a cotton model that can be immediately

integrated with other crop models (Messina et al., 2004). CSM-CROPGRO is composed

of several modules that make up a land unit in a cropping system. The primary modules

are crop, soil, weather, soil-plant-atmosphere, and management. The soil module

integrates information from four sub modules: soil water, soil temperature, soil carbon,

and nitrogen dynamics. The soil is represented by a one-dimensional profile, consisting

of a number of vertical soil layers. The main function of the weather module is to read or

generate daily weather data required by the model, including minimum and maximum

air temperatures, solar radiation, and precipitation. The soil-plant-atmosphere module

computes daily soil evaporation and plant transpiration while the management module

determines when field operations are performed by calling sub modules related to

planting, harvesting, inorganic fertilization, irrigation, and application of crop residues or

organic materials. The Crop module can predict the growth and development of a

number of different crops, each crop has its own model parameter files. These modules

describe the time changes that occur in a land unit due to management and weather.









The CSM-CROPGRO model has three sets of parameters that account for

differences in development, growth, and yield between species, ecotypes, and cultivars

(Boote et al., 2003). Cultivar parameters are specific to a particular variety, Ecotype

parameters are for a group of cultivars, and Species parameters are common to all

cultivars. Mainly the model cultivar parameters (Table 2-1) are vital to consider for

sensitivity analysis.

Site and Experiment Description

Sensitivity analyses were conducted for two cropping seasons, 2003 for which we

had observed data collected in an experiment conducted at the C.M. Stripling Irrigation

Research Park (SIRP), Camilla, GA (31011 N, 84012W), and 2000 which was a dry year

to compare the results from irrigated and rainfed conditions. Daily weather data

consisting of maximum and minimum temperature, solar radiation, precipitation, and

wind speed were obtained from a local weather station at SIRP. Maximum temperatures

varied from 24 to 330C; the minimum temperatures varied from 10 to 220C; and the

average temperatures varied from 18 to 270C. The extremes for minimum temperatures

occurred at the end of the growing season. Long term average precipitation (1939 to

2003) for June and July were 131.1 mm and 150.9 mm, respectively. During the 2000

cropping season the total precipitation for June and July were 63.2 mm and 102.4 mm,

respectively. In 2003, June and July precipitation totaled 139.9 mm and 203.6 mm,

respectively. Unlike 2003, no field experiment was conducted during 2000. The main

reason of performing the sensitivity analysis for this year was to include a dry cropping

season. Comparison of dry and wet years would allow us to evaluate the hypothesis

that the importance of model parameters do not vary with irrigated and rainfed

conditions.









A 34 ha field was planted with a late maturing cotton variety, DP 555, using a

conventional tillage system. The field was sown during the first week of May with a plant

population of approximately 110,000 plants per hectare. The soil type at the study site

was classified as an Orangeburg loamy sand (Fine-loamy, siliceous, thermic Typic

Paleudults) (Source Mitchell County SCS Map, Soil Conservations Service). The

experiment had two treatments; one was rainfed and the other was irrigated. All other

inputs were the same for both treatments.

Sensitivity Analysis

The principle of sensitivity analysis is firstly to generate output variability

associated with the variability of input, and secondly to assign the simulated output

variability to the model parameters that affect it the most (Ruget et al., 2002). The most

crucial step in sensitivity analysis is the selection of the model parameters and their

uncertainty ranges. Including a large number of model parameters for global sensitivity

analysis would result in an unrealistically high number of simulation runs and impractical

computational load (Thorsen et al., 2001).

Local sensitivity analysis was performed on the entire set of cultivar model

parameters listed in Table 2-1 and also on one of the species parameters, light

extinction coefficient (KCAN). Messina et al. (2004) recommended that KCAN should be

considered as a cultivar or ecotype parameter because initial estimates of KCAN from

literature data showed variations between and within seasons, with planting dates, and

between cultivars (Rosenthal and Gerik, 1991; Milroy et al., 2001; Milroy and Bange,

2003; Bange and Milroy, 2004). The main reason for including KCAN in the sensitivity

analysis was to help answer the question whether KCAN was sufficiently important

parameter to warrant its inclusion as an ecotype parameter. Results from this local









sensitivity analysis were used to select model parameters for the global sensitivity

analysis.

Local sensitivity

Local sensitivity is often used to provide a normalized measure for comparing

sensitivity of a model to several parameters. In order to measure relative sensitivity of

an output relative to a particular model parameter, only that parameter is changed in the

vicinity of a base value; all other parameters are fixed to their base values. Local

sensitivity was calculated for model responses using the base and + and 5% changes

in the base value. Sensitivity indices were obtained by computing the change in the

output relative to changes in parameters. Relative sensitivities for dry matter yield and

season length were defined as follows:

(Y / 0) =(Y/Y)/(O0/ ) (2-1)

o, (M / ) = (MIM) /(0/O0) (2-2)

Where Y is simulated dry matter yield and M is simulated length of the growing

season obtained for each level of an individual model parameter (8) while keeping all

other model parameters at their base values. (8Y/Y)and (OM/M) represent fraction

changes in simulated outputs for dry matter and season length relative to the fraction

changes in inputs(a8/8), respectively. U,(Y/O) and o,(M/O) represent local

sensitivities for the dry matter and season length, respectively.

Global sensitivity

Measuring model sensitivity for each model parameter 9 separately with all other

model parameters fixed at their single base values prevents the detection and









quantification of interactions. A key aspect of most global sensitivity methods is the

ability to take these interactions into account.

Factorial design is a method of global sensitivity analysis that allows for

simultaneous evaluation of the influence of many model parameters. It follows the

classical theory of experimental design where nature is replaced by the simulated crop

model (Box and Draper, 1987). In this study, selection of model parameters for global

sensitivity analysis was based on results from the local sensitivity analysis. A

simplification of the deterministic model can be used to represent the two output state

variables, dry matter yield (Y) and season length (M), as a function of model

parameters:

Y = f(O) and M = f(O) (2-3)

Where e = model parameters

Complete factorial design uses all possible combinations of chosen factors and

levels. For example, eight model parameters and three levels would create 38

combinations. For such a factorial experiment, the analysis can be expressed by

decomposing the function Y= f(8) and M = f(Q) into main effects and interactions:

Yabcdefgh = [I + OXa + Pb +... + rabcdefgh (2-4)

Mabcdefgh = [l + O(a + Pb +... + rabcdefgh (2-5)

Yabcdefgh = f (a,b,c,d,e,f,g,h) and Mabcdefgh = f(a,b,c,d,e,f,g,h) denote the model

responses of dry matter yield and growing season length, respectively, when 61= a, e2 =

b, e3 = c, 84 = d, e5 = e, e6 = f, 87 = g and e8 = h; p is the overall mean of the model

responses; Oaa, Pb, ..., Sh represent the main effects of model parameters 61, 62... e8









when 61= a, 02 = b, ...08 = h; qab is the interaction between a and b, qgh is the interaction

between g and h, and so on.

The overall response variability can be separated into factorial terms as follows:


(Yicdefgh -)2 =bja2 +MS82 + b2 +....+ (2-6)
abcdefgh a b ab

Where (Ybcdefgh 2 or total sum of squares (SST), represents the total
abcdefgh

variability in the model responses, m a, is the sum of squares (SS1) associated with
a

the main effect of m levels of model parameters e1, and so on. The NCSS (Hintze,

2004) statistical software was used for calculating the sum of squares of the main

effects for the complete factorial design.

For the sensitivity analysis of a deterministic model, the main interest lies in

comparing the contributions of the factorial terms to the total variability. The main effect

sensitivity (Si=1 to 8) indicates the relative importance of individual model parameter

uncertainty and can be calculated by dividing the corresponding main effect sum of

squares by the total sum of squares (Equation 7).


SSS (2-7)
SS,

Interaction sensitivity indices are measures of the interactive influences of the

model parameters on the output variance and were calculated by dividing the interaction

sum of squares of the model parameters by the total sum of squares.

Global sensitivity indices indicate the overall impact of model parameters on the

output variance when model parameters vary over their entire range of uncertainty.









Global sensitivity indices for selected model parameters were calculated by following

equation (Equation 8).

ss, +ss,,
Sgloba(,) SS (2-8)
SST

Where, Sgloba,,i indicates global sensitivity index, SS, is the main effect sum of

squares, SS,, is interaction sum of squares, and SST is total sum of squares, for

parameters i = 1 to 8.

Global sensitivity analysis apportions the output variability to the variability in

model parameters covering their entire range space, and hence it was important to

decide the range of selected model parameters. The ranges of model parameters

should be chosen such that they represent the expected extreme values of those

parameters. The ranges of some of the model parameters SLAVR, KCAN, and XFRT

were obtained from the literature (Bange and Milroy, 2000; Milroy et al., 2001; Milroy

and Bange, 2003; Reddy et al., 1993; Reddy et al., 1992; Reddy et al., 1991; Messina

et al., 2004).

Published data by Wright and Sprenkel (2006) on the ranges of different growth

stages were used to determine the ranges of the model parameters that deal with crop

growth duration. Information on certain crop growth stages was not available in the

published literature so in order to make maximum use of available dataset it was

assumed that the ratio of parameters on crop growth stages for the cotton model were

same as the ratio of those parameters for the soybean model. Data for soybean

parameters were obtained from Boote et al. (2003). In the case of SFDUR and PODUR,

no information on ranges was available. Instead of using an arbitrary range, the









percentage variance from the mean value for soybean parameters was applied to the

base cotton model parameters.

Results and Discussion

Local Sensitivity Analysis

Model parameters that were selected for global sensitivity analysis based on the

initial local sensitivity analysis are shown in Tables 2-2 and 2-3. Sensitivity indices of the

other parameters were either zero or very small. For both treatments and years, KCAN

was the parameter that most affected the dry matter yield. For the 2000 rainfed

condition, magnitudes and orders of local sensitivity indices were different from 2000

irrigated condition and 2003 irrigated and rainfed conditions (Table 2-2, Figure 2-1). As

an example, dry matter yield was more sensitive to XFRT than EM-FL for 2000 rainfed

condition whereas it was vice versa for all other cases. One reason for such differences

could be because the model is non-linear in its responses and local sensitivity analysis

does not consider the range of uncertainty.

Only three model parameters, EM-FL, FL-SD and SD-PM, affected the response

of season length. The time between first seed and maturity (SD-PM) was the model

parameter that influenced season length the most (Table 2-3).

Global Sensitivity Analysis

Based on the local sensitivity analysis results of all the cultivar model parameters

and one species model parameter, eight parameters were selected for global sensitivity

analysis (Table 2-4). Table 2-5 and 2-6 shows the calculated global sensitivity indices

for dry matter yield and season length taking into account all main effects and

interactions related to corresponding model parameter. The first ten interaction terms in

order of their magnitudes of sensitivity indices are listed in Table 2-5.









Unlike local sensitivity indices, global sensitivity indices were consistent in terms of

order of sensitivity across rainfed and irrigated conditions and years. For a given

management condition and year, SLAVR had the highest sensitivity index followed by

KCAN. Two model parameters, PODUR and SFDUR, showed the least influence on dry

matter yield across both treatments and years. For lower specific leaf areas, thicker and

smaller leaves would reduce light capture and net photosynthesis. On the other hand for

higher specific leaf areas, leaves are thinner and larger resulting in increased light

capture and hence increased net photosynthesis. Thus changing SLAVR would

indirectly affect canopy net photosynthesis which eventually affects growth and yield.

KCAN was the second most important parameter for dry matter yield. The light

extinction coefficient, KCAN, is used to compute light interception depending on leaf

area index. The highest interaction effect was obtained between KCAN and SLAVR.

The model parameter XFRT was the third most important model parameter for crop

yield. Parameter values of SLAVR and KCAN mainly control leaf expansion and light

capture and hence control daily assimilates. XFRT regulates the partitioning of daily

assimilates that goes to seed. XFRT being the third most important parameter, its

interaction with SLAVR and KCAN being the second and third most important

interactions was logical.

For 2000, irrigated and rainfed conditions provided similar sensitivity indices

(Figure 2-2). There were small differences in the values due to irrigation and year;

however the order of importance of model parameters was consistent. Year 2003 was a

wet year and hence even with the rainfed conditions, the indices were consistent in









terms of values and order. Overall, global sensitivity indices did not show variations in

order of importance with different treatments.

Season length was sensitive to only three model parameters, EM-FL, FL-SD, and

SD-PM. Season length is mostly determined by parameters that control the duration of

different crop growth stages. In our study three duration model parameters were

selected that covered the whole crop season length. SD-PM was the most important

model parameter, partly due to greater uncertainty in this parameter, affecting season

length, followed by FL-SD, and EM-FL respectively (Table 2-6).

Comparison of Local and Global Sensitivity Analysis Results

For comparing local and global sensitivity analysis results, only rankings were

taken into consideration. The reason for that was because local sensitivity index is the

ratio of percentage change in the output response to the percentage change in the

model parameter, whereas the global sensitivity index is the measure of percentage

contribution of an individual model parameter to overall output variance.

Based on local sensitivity results, KCAN was the most important model parameter

for cotton dry matter yield followed by SLAVR, which was opposite to global sensitivity

results. The main reason for these differences was because local sensitivity analysis

focuses on local impact of the model parameter on the model response where model

parameters varied in small intervals around the base value of the model parameter. For

nonlinear models, finding the most important model parameter with such sparse domain

coverage may be misleading. On the other hand, global sensitivity analysis takes into

account the main effects and interactions between parameters over their entire

uncertainty ranges.









For this study, irrigated and rainfed conditions for dry and wet years were used to

compare local sensitivity and global sensitivity analyses results. The model parameter

rankings did not change with years and treatments for global sensitivity analysis,

whereas they varied among the years and treatments for local sensitivity analysis. Both

methods provided similar results for two variables (PODUR and SFDUR) showing that

model sensitivity over the range of parameter uncertainty was small. Such information

can be useful to focus additional research and possibly to simplify the model by

reducing the number of model parameters that one has to estimate.

Season length response was sensitive to only three model parameters, EM-FL,

FL-SD, and SD-PM. Out of these three SD-PM was the most important model

parameter followed by FL-SD, and EM-FL, respectively. These rankings were the same

for both sensitivity analysis methods. The reason for season length response being

sensitive to only three model parameters was because those model parameters were

the crop growth duration model parameters selected for this analysis.

Conclusions

This study evaluated how sensitive the cotton model predictions were to a

selected set of model parameters. Local and global sensitivity analyses were used to

determine dry matter yield and season length sensitivity to model parameters under

irrigated and rainfed conditions for two cropping seasons. Results demonstrated that, in

accordance with our first hypothesis, global sensitivity analysis improved our

understanding of how sensitive the prototype cotton model was to the selected set of

parameters over the ranges of parameter uncertainties. In addition to accounting for the

variance of model output associated with the variance of model parameters over the

entire range on uncertainty, it had an advantage of considering the interactions among









model parameters. The most influencing model parameter on dry matter yield was the

specific leaf area (SLAVR). Local sensitivity analysis indicated that the extinction

coefficient (KCAN) was the most influencing model parameter.

The global sensitivity analysis results also demonstrated that, consistent with our

second hypothesis, sensitivity of dry matter yield and season length to the selected set

of model parameters did not vary between irrigated and rainfed conditions or with years.

However, that was not true for local sensitivity analysis. Results from this study

indicated that more research is needed to reduce the range of uncertainties of both

KCAN and SLAVR. Experiments have shown variations in KCAN values for different

cultivars and hence it was suggested that it should be included in ecotype set of model

parameters rather than in species file. That suggestion was supported from the results

of this study. The parameters selected for this study were associated with crop growth

and development. Additional studies are needed to assess model sensitivity to soil

water and nitrogen parameters which were held constant for this study.

Global sensitivity analysis can be a valuable tool for application with large, highly

non-linear models, such as the DSSAT-CSM models. However, the use of a complete

factorial design and analysis of variance can result in a large number of simulation runs

when there are many model parameters. The choice of model parameters to be

evaluated should be considered with care, taking into account available resources.














































* Irrigated
O Rain fed


KCAN EM-FL FL-SD SD-PM SLAVR XFRT
(01) (02) (03) (04) (05) (06)

Parameters


SFDUR PODUR
(07) (08)


Figure 2-1. Local Sensitivity indices for seed cotton yield for irrigated and rainfed
conditions for 2000 (top) and 2003 (bottom).


U Irrigated
3.5 O Rain fed


3


2.5


S2


1.5





0.5



KCAN EM-FL FL-SD SD-PM SLAVR XFRT SFDUR PODUR
(01) (02) (03) (04) (05) (06) (07) (08)
Parameters


3.5


3


2.5
-a

-h 2


1.5


S1


0.5


0













* Irrigated
o Rain fed


0.6000


0.5000


0.4000
-


. 0.3000
-


S0.2000
5

0.1000


0.0000


SD-PM SLAVR
(04) (05)
Parameters


XFRT
(06)


SFDUR PODUR
(07) (08)


U Irrigated
0.6000 Rain fed


0.5000


I 0.4000


0.3000


0.2000
5

0.1000


0.0000 ~
KCAN EM-FL FL-SD SD-PM SLAVR XFRT SFDUR PODUR
(01) (02) (03) (04) (05) (06) (07) (08)
Parameters


Figure 2-2. Global Sensitivity indices for seed cotton yield for irrigated and rainfed
conditions for the year 2000 (top) and 2003 (bottom).


KCAN EM-FL FL-SD
(01) (02) (03)









List of cultivar parameters in CSM-CROPGRO-Cotton Model


Numbers Parameters
1 CSDL


PPSEN

EM-FL

FL-SH
FL-SD
SD-PM

FL-LF


LFMAX

SLAVR

SIZLF
XFRT
WTPSD
SFDUR

SDPDV
PODUR

KCAN*


Definitions
Critical Short Day Length below which reproductive development
progresses with no day length effect (for short day plants) (hour)
Slope of the relative response of development to photoperiod with
time
(positive for short day plants) (1/hour)
Time between plant emergence and flower appearance (R1)
(photothermal days)
Time between first flower and first boll (R3) (photothermal days)
Time between first flower and first seed (R5) (photothermal days)
Time between first seed (R5) and physiological maturity (R7)
(photothermal days)
Time between first flower (R1) and end of leaf expansion
(photothermal days)
Maximum leaf photosynthesis rate at 30 C, 350 ppm C02, and
high light
(mg C02/m2-s)
Specific leaf area of cultivar under standard growth conditions
(cm2/g)
Maximum size of full leaf (three leaflets) (cm2)
Maximum fraction of daily growth that is partitioned to seed + shell
Maximum weight per seed (g)
Seed filling duration for boll cohort at standard growth conditions
(photothermal days)
Average seed per boll under standard growing conditions (#/boll)
Time required for cultivar to reach final boll load under optimal
conditions (photothermal days)
Canopy light extinction coefficient (* species parameter)


Table 2-1.









Table 2-2. Local sensitivity indices with respect to selected model parameters for dry
matter yield
Parameter(s) Base Year 2000 Year 2003
E Value Irrigated Rainfed Irrigated Rainfed
KCAN (81) 0.72 3.11 2.65 3.32 3.32
EM-FL (e2) 27.87 1.45 0.83 1.76 1.76
FL-SD (e3) 11.65 0.43 0.44 0.34 0.34
SD-PM (e4) 27.68 0.62 0.69 0.79 0.79
SLAVR (85) 170.00 1.76 0.99 1.91 1.91
XFRT (e6) 0.72 0.40 0.84 0.37 0.37
SFDUR (e7) 35.00 0.21 0.19 0.03 0.03
PODUR (e8) 8.00 0.09 0.12 0.13 0.13









Table 2-3. Local sensitivity indices with respect to selected model parameters for
season length
Parameter(s) Base Year 2000 Year 2003
E Value Irrigated Rainfed Irrigated Rainfed
KCAN (81) 0.72 0.00 0.00 0.00 0.00
EM-FL (e2) 27.87 0.31 0.32 0.32 0.32
FL-SD (e3) 11.65 0.10 0.10 0.10 0.10
SD-PM (e4) 27.68 0.42 0.43 0.43 0.43
SLAVR (85) 170.00 0.00 0.00 0.00 0.00
XFRT (96) 0.72 0.00 0.00 0.00 0.00
SFDUR (e7) 35.00 0.00 0.00 0.00 0.00
PODUR (e8) 8.00 0.00 0.00 0.00 0.00









Table 2-4. Model parameters and their range of uncertainty selected for the global
sensitivity analysis
Parameter(s) Uncertainty Range Reference
E Minimum Base Maximum For Uncertainty Range
KCAN (81) 0.50 0.72 0.95 Rosenthal and Gerik,
1991;Milroy et al., 2001; Milroy
and Bange, 2003; Bange and
Milroy, 2004
EM-FL (92) 27.72 27.87 28.02 Wright and Sprenkel, 2006
FL-SD (e3) 9.03 11.65 14.27 Wright and Sprenkel, 2006;
Boote et al., 2003
SD-PM (e4) 21.46 27.68 33.91 Wright and Sprenkel, 2006;
Boote et al., 2003
SLAVR (85) 90.00 170.00 250.00 Reddy et al. 1993; Reddy et
al., 1992; Reddy et al., 1991
XFRT (e6) 0.50 0.72 0.95 Reddy et al. 1993; Reddy et
al., 1992; Reddy et al., 1991
SFDUR (e7) 31.12 35.00 38.88 Boote et al., 2003
PODUR (e8) 5.82 8.00 10.18 Boote et al., 2003









Table 2-5. Global sensitivity indices for dry matter yield including main effects and interactions
2000 Irrigated Sensitivity 2000 Rainfed 2003 Irrigated Sensitivity 2003 Rainfed Sensitivity
Parameter(s) Indices Sensitivity Indices Indices Indices
Main Effects Main Effects Main Effects Main Effects
& Global & Global & Global & Global
9 Interactions Indices Interactions Indices Interactions Indices Interactions Indices
KCAN (81) 0.3848 0.4802 0.4109 0.4976 0.3761 0.4832 0.3762 0.4832
EM-FL (e2) 0.0002 0.0022 0.0002 0.0022 0.0002 0.0023 0.0002 0.0023
FL-SD (e3) 0.0057 0.0122 0.0065 0.0131 0.0058 0.0132 0.0058 0.0132
SD-PM (e4) 0.0203 0.0359 0.0196 0.0325 0.0165 0.0311 0.0165 0.0310
SLAVR (e8) 0.4491 0.5451 0.4262 0.5132 0.4549 0.5631 0.4550 0.5631
XFRT (96) 0.0224 0.0479 0.0291 0.0532 0.0182 0.0400 0.0182 0.0400
SFDUR (e7) 0.0002 0.0009 0.0001 0.0010 0.0000 0.0011 0.0000 0.0011
PODUR (e8) 0.0004 0.0020 0.0007 0.0027 0.0010 0.0029 0.0010 0.0029
KCAN x SLAVR 0.0716 n/a 0.0651 n/a 0.0855 n/a 0.0855 n/a
KCAN xXFRT 0.0107 n/a 0.0100 n/a 0.0089 n/a 0.0089 n/a
SLAVR xXFRT 0.0096 n/a 0.0102 n/a 0.0082 n/a 0.0082 n/a
SD-PM x SLAVR 0.0065 n/a 0.0045 n/a 0.0059 n/a 0.0059 n/a
KCAN x SD-PM 0.0053 n/a 0.0046 n/a 0.0047 n/a 0.0047 n/a
KCAN x SD-PM x
XFRT 0.0038 n/a 0.0029 n/a 0.0034 n/a 0.0034 n/a
FL-SD x SLAVR 0.0018 n/a 0.0017 n/a 0.0020 n/a 0.0020 n/a
KCAN x FL-SD 0.0015 n/a 0.0016 n/a 0.0016 n/a 0.0016 n/a
KCAN x SD-PM x
SLAVR 0.0010 n/a 0.0006 n/a 0.0011 n/a 0.0010 n/a
EM-FL x FL-SD x
SD-PM 0.0006 n/a 0.0006 n/a 0.0006 n/a 0.0006 n/a









Table 2-6. Global sensitivity indices for season length including


main effects and interactions


2000 Irrigated 2000 Rainfed 2003 Irrigated 2003 Rainfed
Parameter(s) Sensitivity Indices Sensitivity Indices Sensitivity Indices Sensitivity Indices
Main Main Main Effects Main
Effects & Global Effects & Global & Global Effects & Global
9 Interactions Indices Interactions Indices Interactions Indices Interactions Indices
EM-FL (e2) 0.0040 0.0339 0.0043 0.0344 0.0040 0.0343 0.0040 0.0343
FL-SD (e3) 0.1756 0.2058 0.1826 0.2127 0.1990 0.2307 0.1990 0.2307
SD-PM (e4) 0.7829 0.8142 0.7732 0.8038 0.7589 0.7896 0.7589 0.7896
EM-FL x FL-SD x
SD-PM 0.0163 n/a 0.0154 n/a 0.0165 n/a 0.0165 n/a
FL-SD x SD-PM 0.0076 n/a 0.0072 n/a 0.0077 n/a 0.0077 n/a
EM-FL x SD-PM 0.0073 n/a 0.0071 n/a 0.0064 n/a 0.0064 n/a
EM-FL x FL-SD 0.0063 n/a 0.0067 n/a 0.0074 n/a 0.0074 n/a









Table 2-7. Model parameter rankings based on local and global sensitivity indices for
dry matter yield
Parameter(s) Year 2000 Year 2003
E Irrigated Rainfed Irrigated Rainfed
Local Sensitivity Analysis Rankings
KCAN (91) 1 1 1 1
EM-FL (92) 3 4 3 3
FL-SD (93) 5 6 6 6
SD-PM (94) 4 5 4 4
SLAVR (95) 2 2 2 2
XFRT (6) 6 3 5 5
SFDUR (97) 7 7 8 8
PODUR (98) 8 8 7 7
Global Sensitivity Analysis Rankings
KCAN (91) 2 2 2 2
EM-FL (92) 6 6 6 6
FL-SD (93) 5 5 5 5
SD-PM (94) 4 4 4 4
SLAVR (95) 1 1 1 1
XFRT (6) 3 3 3 3
SFDUR (97) 8 8 8 8
PODUR (98) 7 7 7 7









Table 2-8. Model parameter rankings based on local and global sensitivity indices for
season length
Parameter(s) Year 2000 Year 2003
E Irrigated Rainfed Irrigated Rainfed
Local Sensitivity Analysis Rankings
EM-FL (92) 3 3 3 3
FL-SD (93) 2 2 2 2
SD-PM (94) 1 1 1 1
Global Sensitivity Analysis Rankings
EM-FL (92) 3 3 3 3
FL-SD (93) 2 2 2 2
SD-PM (94) 1 1 1 1









CHAPTER 3
UNCERTAINTY ANALYSIS AND PARAMETER ESTIMATION OF CROPGRO -
COTTON MODEL

Introduction

Applications of crop simulation models have become an important part of the

agricultural research process. Because decision making processes may use results

obtained from simulation models, consideration of model uncertainties in decision

making processes has become increasingly important. Uncertainties in models can be

categorized into three major sources: model parameters, model input data, and model

structure. Crop models, such as CROPGRO-Cotton are complex and have many

parameters. With limited measurement availability, estimates of model parameters are

uncertain. Model structure is uncertain since it is typically a simplified representation of

the system being studied. Lastly, model input data, such as initial conditions, are also

imperfect to some extent and hence contribute towards output uncertainty (Makowski et

al., 2006; Tolson and Shoemaker, 2008).

Different sources of uncertainties are important, however, the scope of this

research was limited to addressing parameter uncertainty. Model parameters have been

a significant source of uncertainty in model prediction in previous studies. Brazier et al.

(2000) showed that parameters such as hydraulic conductivity have been recorded with

a large variance for a single soil (Nielsen et al., 1973, Warrick and Nielsen, 1980) yet

they are often input to the model as a single value. If model output is sensitive to

hydraulic conductivity, the major portion of model output uncertainty could come from

parameter uncertainty. Wang et al. (2005) performed parameter estimation and

uncertainty analysis on crop yield and soil organic carbon simulated with the EPIC

model where only parameter uncertainty was considered. In that study, a total of nine









corn yield and soil organic carbon related parameters were used for uncertainty

analysis. Although only parameter uncertainty was considered, the observed corn yield

and soil organic carbon fell within the 95% confidence limit of the predictions.

There have been significant advances in methodologies for uncertainty

assessment. Blasone et al. (2008) referenced some of the widely used uncertainty

analysis methods that include Classical Bayesian (Vrugt et al., 2003; Thiemann et al,

2001), Pseudo-Bayesian (Beven and Binely, 1992), data assimilation (Moradkhani et al,

2005), and multi model averaging methods (Georgekakos et al., 2004; Ajami et al.,

2007). These methods differ in their underlying assumptions, complexity, and the way

different sources of error are treated. Montanari, (2007) suggested that the selection of

an uncertainty analysis method is subjective and should take into account issues such

as model complexity, type of observed dataset available, and reliability of uncertainty

assessment methods. A generalized likelihood uncertainty estimation (GLUE)

technique introduced by Beven and Binley, (1992) is one of the most widely used and

accepted uncertainty analysis techniques in environmental simulation modeling and it

has also been used in crop modeling (Wang et al., 2005; He et al., 2009; Makowski et

al., 2006). The main reasons for its popularity are its simple yet robust theory derived

from Bayesian inference and its flexibility in implementation. Stedinger et al. (2008)

counted a total of more than 500 citations of GLUE applications in various simulation

modeling studies.

The GLUE methodology was developed out of the Hornberger-Spear-Young

(HSY) method of sensitivity analysis (Whitehead and Young, 1979; Hornberger and

Spear, 1981; Young, 1983). This method works on a phenomenon called equifinality.









The equifinality thesis suggests that there may be more than one parameter set that is

acceptable for simulation and should be considered in assessing uncertainty in

predictions (Beven, 2006). In the GLUE methodology, model parameter sets are

weighted based on their agreement with related observations using subjective likelihood

measures. Beven and Binley (1992) acknowledged that the choice of likelihood function

used within the GLUE framework is subjective and the choice may greatly influence the

resulting parameters and their uncertainties. These weights or probabilities are

subsequently used to derive predictive uncertainty in output variables.

The CROPGRO-Cotton model is a part of Decision Support System for

Agrotechnology Transfer (DSSAT) software package that includes models of 21 crops

(Jones et al., 2003). It is a part of the CROPGRO family of crop models with many of

the same level of details. Pathak et al. (2007) performed a global sensitivity analysis on

the CROPGRO-Cotton model cultivar parameters and found that eight out of fifteen

cultivar parameters were important to crop yield and physiological maturity outputs of

the model. An accurate estimate of uncertainties associated with those important model

parameters is needed for model applications and improvement. It may be difficult to find

a single optimal fit of model parameters to observed datasets in complex simulation

models due to the fact that there might be more than one parameter set that gives

equally good results. This equifinality nature of this simulation model needs to be

addressed. Parameter estimates of the cotton model have only been tested a few times

under field experiments (Messina et al., 2004; Zamora et al., 2009). There have been

no studies published in referred articles to address uncertainties associated with the

CROPGRO-Cotton model.









Our main research question was, "What are the estimated values and

uncertainties in genotype parameters and how do those translate into uncertainties in

model outputs?" The objective of this research was to estimate the important model

parameters and associated uncertainties using the GLUE technique.

Materials and Methods

Description of Field Sites and Measured Datasets

Data collected on four experiments at three sites were used for this study: 1) and

2) University of Florida North Florida Research and Education Center (NFREC),

located in Quincy, Florida, 3) University of Florida Plant Science Research and

Education Unit, Citra, Florida, and 4) a cooperator's farm located in Mitchell County,

Georgia. Characteristics of the study sites including soil, weather, and management

information are shown in Table 3-1. All field plots were planted with the full season

cotton cultivar DeltaPine-555, the most widely grown cultivar in the Southeast USA. All

four experimental sites were irrigated and fertilized during the cropping season. Timing

and amounts of applied water and fertilizers were recorded.

Above ground biomass (leaf, stem, and boll) and leaf area index (LAI) were

measured at each location at an interval of approximately two to three weeks with three

to four replications. There were a total of 81 observations considered for this study

consisting of 16 LAI, 24 leaf weight, 17 boll weight, and 24 stem weight measurements

across all four experiments. In the vegetative stage sampling period, plants within one

meter of row were cut at the soil surface and separated into leaf, stem, and bolls.

Samples were then oven-dried at about 700C for 48 hours and weighed to obtain dry

biomass. LAI measurements were obtained using the LAI-2000 instrument (Li-Cor Inc.,

Lincoln, NE) for experiments 1 and 2. A leaf area meter (model LI-3100, Li-Cor Inc) was









used to measure LAI for experiments 3 and 4. Information on phenology anthesiss dates

and maturity dates) were only collected for experiments 1, 3, and 4 (Table 3-1). The

fields were visited approximately every two weeks in order to determine these dates.

The CROPGRO-Cotton Model

The CROPGRO-Cotton model is a member of the CROPGRO group of models in

DSSAT that has been tested for several crops including soybean (Boote et al., 1998)

and peanut (Boote et al., 1998; Gilbert et al., 2002). It simulates the effects of weather,

soil, and, management on crop growth and development (Boote et al., 1998; Jones et

al., 1998; Jones et al., 2003). The CROPGRO-Cotton model, using the same features

and level of details as other the CROPGRO crop models, was developed recently. Only

a few studies have been reported on this cotton model evaluation and applications

(Zamora et al., 2009, Messina et al., 2004, Guerra et al., 2005).

Soil inputs consist of one dimensional soil physical properties such as lower,

upper, and saturated water holding capacities, bulk density, and PH (Jones et al., 2003;

Jones et al., 1998). The soil module integrates information from soil temperature, soil

water, soil carbon, and nitrogen dynamics sub modules (Jones et al., 2003) to simulate

growth and yield. Weather data consisted of daily values of minimum and maximum air

temperatures, solar radiation, and precipitation. Management inputs consisted of

information on amount of irrigation, fertilization, planting dates, plant population etc. The

model was provided with information on soil, weather, and management specific to each

experiment for model simulations (Table 3-1).

The CROPGRO model has three sets of parameters that account for differences in

development, growth, and yield between species, ecotypes, and cultivars (Boote et al.,

2003). In this study, cotton cultivar parameters were estimated along with the









uncertainties associated with them. A detailed description of cultivar parameters and

uncertainty analysis procedures are given in the following sections.

Uncertainty Analysis and Parameter Estimation Procedures

The GLUE procedure was used in this study where 55,000 parameter sets were

sampled from their prior distributions using Monte-Carlo simulations, and model outputs

were obtained for each of those parameter sets. The prior distribution represents the

original information about the uncertainties of parameters based on previous studies.

The primary reason for running such a large number of simulations in GLUE is to obtain

an adequate number of acceptable parameters for estimating the posterior distribution

of parameters. Each of the model outputs was assigned likelihood based on their

agreement with related field observations. Using the likelihood values, posterior

distributions were estimated using the Bayesian approach. The GLUE procedure was

first performed on phenology parameters (EM-FL and SD-PM). Once the estimated

parameters were obtained for these phenology parameters, the GLUE procedure was

performed on the remaining cultivar parameters. This parameter estimation and

uncertainty analysis procedure was based on recommendations in Boote et al. (1998)

who suggested to first estimate phenology parameters before estimating other

parameters. Descriptions of input parameters, uncertainty ranges, prior distributions,

likelihood functions, and posterior distributions used in this research are given in the

following sections.

Parameter selection and prior distributions

A complex simulation model such as the CROPGRO-Cotton model is generally

heavily parameterized. Thorsen et al. (2001) suggested that the inclusion of a large

number of parameter sets would result in an unrealistic number of simulation runs that









would be too large to compute. A systematic way of selecting parameters for uncertainty

analysis is to perform sensitivity analysis on parameters to get information on which

parameters are important. Pathak et al. (2007) performed a global sensitivity analysis of

the CROPGRO-Cotton model to cultivar and species parameters and suggested a list of

parameters (EM-FL, FL-SD, SD-PM, SLAVAR, KCAN, SFRT, SFDUR, and PODUR) to

which important model outputs such as cotton yield and physiological maturity are

sensitive.

The CROPGRO-Cotton model was initially parameterized using data from the

literature (Messina et al., 2004; Zamora et al., 2009). Very little knowledge was

available on real ranges and distributions of these parameters. For this study, a uniform

prior distribution was assumed for each of the selected parameters as it has been the

most reported sampling distribution in similar studies reported in the literature (Beven,

2001; Stedinger et al., 2008). Because of a lack of information, it was also assumed that

the parameters are independent. The only information needed to sample parameters

from uniform distribution was their minimum and maximum values. The ranges of model

parameters should be chosen such that they represent expected extreme values of

those parameters. The ranges of model parameters (SLAVAR, KCAN, and XFRT) were

obtained from the literature (Bange and Milroy, 2000; Milroy et al., 2001; Milroy and

Bange, 2003; Reddy et al., 1992; Messina et al., 2004). Information on ranges of certain

parameters (LFMAX, EM-FL, FL-SD, and SD-PM) were not available, so in order to

make maximum use of available dataset, the percentage variance from the mean

values for the CROPGRO-Soybean (Boote et al., 2003) parameters were applied to the









base cotton model parameters. Table 3-2 shows selected parameters and their

uncertainty ranges used in the GLUE analysis.

Likelihood function

The likelihood function is a measure of how well a model outputs obtained from a

set of parameters fit to field observations. The calculation of the likelihood function is an

important part of the GLUE procedure. There have been several likelihood functions

used in previous applications of GLUE (Beven and Freer, 2001). The choice of

likelihood function should be such that it can reduce the uncertainties in parameters and

simulated outputs should provide close agreements with observed data. He et al. (2009)

compared four likelihood functions for parameter estimation of the CERES-Maize model

using the GLUE method. He found that the Gaussian likelihood function (Makowski et

al., 2006) was the best choice because the results from this function resulted in the

least uncertainties in parameters and improved model predictions more than the other

functions that were evaluated. Based on his findings, the Gaussian likelihood function

was used in this study, as is shown below.

N 1 ((0 p(0))2
L(, /O) =n exp (3-1)
,=1 2Io 20U

Where, L(O, /0) is likelihood of parameters, given the observations (0). O is a

mean of replications of observation, P (0) is ith model response, and N is the number of

observations. With complex simulation models such as the CROPGRO-Cotton model, it

is difficult to know the model error variance that is needed for the Gaussian function.

Alternatively, variances in measurements were assumed to be equal to the model error

variance in previous studies (Van Oijen et al., 2005; He et al., 2009). Another alternative









that Wang et al. (2005) used was to assume that the error variance was equal to the

error variance between observed and simulated values using the very best parameter

set. For this study, error variance o-2 was replaced with the measurement variance o-

for LAI, leaf weight, stem weight, and boll weight. Each data point in the time-series of

LAI, leaf weight, stem weight, and boll weights contained measurement variances

specific to that particular data point. The measurement variance was unknown for

anthesis date and maturity date; hence the error variance in the above equation for

anthesis and maturity date was replaced with the minimum error variance between

measured and simulated results (Wang et al., (2005). The likelihood were calculated

for each of the data points separately and were integrated together by taking the

product.

It can be seen from equation 3-1 that the likelihood values of N number of

observations were combined by taking a product to get a global likelihood. The main

benefit of using product of likelihood is that as the number of observations increases,

the global likelihood response becomes steeper. He et al. (2009) compared three

likelihood combination methods including the product and found that the Gaussian

likelihood function updated with product function provided the best combination for

CERES-Maize model.

Posterior distribution

The posterior distribution was derived from the behavioral simulations, that is, the

number of parameter sets not ruled out of the analysis by near zero likelihood. The

threshold to derive behavioral and non behavioral parameter sets is subjective in the

GLUE methodology (Beven and Binley, 1992). The common practice is to select a cutoff









for likelihood weight to identify behavioral parameters for use in determining posterior

distributions. For this study, a likelihood threshold of 0.0001 was selected. Parameter

sets having likelihood values above that cutoff limit were considered behavioral

parameters to construct the posterior distribution. Once parameter sets are

distinguished between behavioral and non behavioral by using likelihood values,

likelihood weights were calculated by normalizing behavioral likelihood values as shown

in equation 3-2.


LO L(, /0) (3-2)
L(, /O)
L, (0) N= (3-2)



Lw(0,) is the normalized likelihood weight where the sum of Lw(Oi)is equal to 1.0.

The L(O, /0) is the global likelihood value obtained by taking the product of all the

likelihood values. The expected values and variances for each parameter were

calculated using equations 3-3 and 3-4.

N
fi= L,,( ).0 (3-3)


N
= L (L0,).(0, )2 (3-4)
i=i

Uncertainty bounds for model predictions

Uncertainty bounds represent the uncertainties in model predictions that were

associated with uncertainties in model parameters. A total 5000 sets of input

parameters were sampled from their posterior distributions using Monte Carlo sampling

and the CROPGRO-Cotton model was run to obtain outputs. The uncertainties in model

outputs were estimated from their empirical cumulative distributions. An appropriate









quantiles of cumulative distribution were selected to form uncertainty bounds around the

model outputs. In this analysis 95% confidence interval (uncertainty bound) was

estimated from the values of 2.5% and 97.5% quantiles of the cumulative distribution of

model outputs. The primary reasons for obtaining 5000 simulations runs was to obtain

good estimates or prediction distributions and of prediction quantiles.

Statistical methods for model testing

The simulated values of LAI, leaf weight, stem weight, and boll weight were

analyzed using the following statistical measures:

In
MeanDeviaton = (Si Oi) (3-5)
n1l


RootMeanSquaredError(AIRSE) = (Si Oi) (3-6)
nl=1


Z(S, -,)2
d l- O1' (3-7)



Where, n is the number of observations, S, and 0, are the ith simulated value with

mean parameters and observed values, respectively. Mean deviation indicates bias in

the simulations, positive value of mean deviation corresponds to over prediction by the

model and vice versa. The RMSE corresponds to the magnitude of the mean difference

between predicted and measured values. The d-index (Willmott, 1982) corresponds to

the agreement between model simulations and observations, 0 representing no

agreement and 1 representing perfect agreement.









Results and Discussion

Simulations Using Unmodified Parameters

Simulations using unmodified cultivar parameters showed good agreement with

observed LAI, leaf weight, stem weight, and boll weight for all four experiments. The

unmodified parameters currently available in DSSAT were initially estimated using the

experimental dataset (Messina et al., 2004). Although the overall model agreement with

the measurements was fairly good, it was observed that the model over-predicted LAI

and above ground biomass when simulated using original model parameters. Figure 3-1

shows agreement between measured and simulated values with original model

parameters for LAI, leaf weight, stem weight, and boll weight for all four experiments.

Except for a few data points, the model consistently over predicted the values as the

majority of the data points fell below the 1:1 line.

Tables 3-3 summarizes the average observations, simulations, and mean

differences for LAI, leaf weight, stem weight, and boll weight for all four experiments.

The positive values of mean differences indicated that the model was over-predicting

and vice versa. For instance, the mean differences between simulated and measured

average boll weights were 1454 kg ha-1 and 1536 kg ha-1 for experiments 1 and 3,

respectively (Table 3-3). In general average observed stem weight was over predicted

by the model for all four experimental sites, average observed average LAI and leaf

weight were over predicted in three out of four experiments, and average observed boll

weight was over predicted in two out of four experiments.

Figure 3-2 shows the time series of model simulations and observed values for

LAI, leaf, stem, and boll weight at different growth stages using original model

parameters. During the early stages of crop growth the model was either under









predicting the above ground biomass and LAI or had good agreement with the

measured values. However, during the reproductive stage of crop growth, the model

over predicted them through maturity. For example, if we observe the LAI, leaf weight,

and stem weight time series plots for experiments 2, 3, and 4, the model under

predicting the first two or three measurements but then over predicted throughout the

remaining growth cycle.

In general, time series plots and statistics show that the model simulations tended

to overestimate observed LAI, leaf weight, stem weight, and boll weight for all four

experiments. Hence estimating parameters regulating the crop growth should improve

the overall model predictions.

Parameter Estimates and Uncertainties

Comparison with prior distribution

A total of eight cultivar parameters of the CROPGRO-Cotton model associated

with plant growth and development were estimated along with their uncertainties. Table

3-4 shows means, standard deviations, and coefficient of variations (CV) for prior and

posterior distributions of parameters. The prior means of model parameters shown in

Table 3-4 were based on the 55,000 randomly sampled parameter sets from their

corresponding uniform prior distributions.

The posterior distributions for all eight parameters were narrowed to smaller

ranges compared to their prior distributions (Fig. 3-3, Table 3-4). These narrower

ranges are, of course, dependent on the data from the four treatments used in this

analysis. For example, the SLAVAR had prior uncertainty range of 90-250 cm2 g-1 which

was subsequently reduced to 171-175 cm2 g-1 in its posterior distribution and the

SLAVAR coefficient of variation (CV) was changed from 27% to only 0.8%, respectively.









The KCAN parameter had a prior uncertainty range of 0.5-1, which was reduced to

0.61-0.67 and the CV was reduced from 17% to 3%. Those two parameters were the

most important parameters to simulated cotton yield according to the sensitivity analysis

results obtained by Pathak et al. (2007). Uncertainty in those parameters would

significantly affect the uncertainty in model outputs, hence predicting and reducing the

amount of uncertainty in these parameters improved the model performance. The

highest CV value among all eight parameters in the Pathak et al (2007) study was for

SLAVAR which lowered down to 0.8% in the posterior distribution compared to 27% in

the prior distribution. One of the main reasons for narrower uncertainties in posterior

distributions was the integration of the large number of observations from the four

different sites into the GLUE to estimate uncertainties. In the Gaussian likelihood

function (eq. 3-1), as the number of observations N increases the parameter space also

may tend to decrease and thus result in a narrower range. That was the primary reason

there were only 81 behavioral parameter sets that were concentrated towards the

narrower uncertainty range in this study.

Comparison with DSSAT default values

An interesting thing to notice was that the expected values of all the parameters

were not so different from their DSSAT default values except for KCAN (Table 3-4). The

estimated value for KCAN was 0.64 which was lower than its DSSAT base value of 0.8.

The KCAN is an important parameter as it is responsible for light capture by the canopy.

Hence changing the value of KCAN would have a direct impact on daily photosynthesis,

which subsequently impacts LAI and above ground biomass. As expected, the

estimated value for KCAN was lower than the DSSAT default value because it would

control the model over-prediction of LAI and above ground biomass.









Model predictions based on estimated parameters

The comparison between Figure 3-1 and 3-4 as well as Table 3-3 and 3-5 showed

that the estimated parameters improved the overall agreement of measured LAI and

above ground biomass with simulated results. Other than KCAN, no estimated

parameters were very different from their corresponding DSSAT base values. As shown

in the initial model results with unmodified parameters, the model over predicted the

observations in general. Since estimated KCAN was lower than the corresponding

DSSAT base values, the over estimation by the model was controlled significantly and

model predictions were improved.

Table 3-6 shows the comparison of RMSE and d-statistics between measured and

simulated LAI, leaf weight, stem weight, and boll weight obtained from DSSAT

parameter base values and maximum likelihood estimated parameter values,

respectively. For instance, RMSE of boll weight for default values were reduced from

1636 kg/ha to 535 kg/ha and 1842 kg/ha to 819 kg/ha for experiments 1 and 3,

respectively. This represents a reduction of RMSE of approximately 55% and 67%,

respectively. In this study, the d-statistics were improved for most of the variables

across all the experiments. The highest d-statistic value of 0.99 was obtained for stem

weight for experiments 2 and 3, which represents almost perfect agreement of

measured with simulated stem weights. The lowest d-statistic of 0.45 was obtained for

boll weight in experiment 4. The reason for a low agreement could be due to

measurement errors because the agreement of the model with other variables (LAI, leaf

weight, and stem weight) of experiment 4 was in good agreements with measured

values. The RMSE and d-statistics showed a close agreement of the measured and

simulated LAI and biomass components overall. The average RMSE of simulated LAI,









stem weight, and boll weight from all four experiments were reduced with the GLUE

estimated parameters compared to the DSSAT default parameters. The average RMSE

for leaf weight was increased; however the increase was marginal (Table 3-6). It is also

important to note that the estimated parameters generally improved the model by

reducing model error.

Model output uncertainties

Output uncertainties for LAI, leaf weight, boll weight, and stem weight were

estimated from 95% confidence interval obtained from 2.5% and 97.5% quantiles of

their cumulative distributions from 5000 simulations generated from posterior

distributions of model parameters. The output uncertainties in terms of standard

deviations (STDEV) and coefficient of variability (CV) were compared in Table 3-7 along

with the averages and ranges. The CV for model outputs obtained with prior parameter

distribution ranged between 29% and 56% which were subsequently reduced to 4-13%

with the simulated outputs obtained from the posterior distribution of parameters.

Figure 3-5 shows the simulated 95% confidence limits around the average

simulated values in addition to the measured values of LAI, leaf weight, stem weight,

and boll weight for all four sites. Results show that the 80% of the means of data from

experiment 1, 90% from experiment 2, 87% from experiment 3, and 53% of data from

experiment 4 were covered by the uncertainty bounds. Overall, approximately 79% of

the data were within the uncertainty bounds. Reasons for the remaining 21% of data

that were not within the uncertainty limits could be measurement errors also shown in

Fig 3-5 or the subjective selection of cut-off of likelihood values.

It is important to note that the output uncertainties shown in Table 3-6 only

consider uncertainties associated with eight model parameters of cotton growth and









development. The parameters and their uncertainties obtained in this analysis

considered four treatments. Results could be different if other datasets were used. This

study did not take into account the other sources of uncertainties. The uncertainties in

model structure and model input data were not within the scope of this research.

Conclusion

The mean values of parameters after estimation improved model predictions

relative to the original parameters available in DSSAT for delta pine 555 cotton cultivar.

The prior uncertainties in the most important parameters (Pathak et al., 2007), SLAVAR

and KCAN, were reduced from 27% and 13% to 0.8% and 3%, respectively. The

general agreement of the model with measurements using the GLUE estimated

parameters was good with the d-statistics ranged between 0.99 for experiments 2 and 3

and 0.45 for experiment 4. This study also demonstrated an efficient prediction of

uncertainties in model parameters and outputs using the widely accepted GLUE

technique. Overall, approximately 79% of the data were within the uncertainty bounds

that were determined from the predicted confidence interval from the uncertainty

analysis.

The limitation of this study was that the uncertainties in model structure, and

model inputs were not examined. In further research, these uncertainties should be

investigated. Also, parameter selection was concentrated only on cultivar parameters,

and one species parameter. Uncertainty analysis should be performed on other

important parameters such as soil parameters.




















AExperiment 3 v / I uuu xperimen. j
XExperiment 4 x Experiment 4

1500 x
i3 o o 10


2 x

S500
042 000






1 2 3 4 5 6 500 1000 1500 2000 2500
Simulated LAI A Simulated Leaf Weght kg ha B


8000 4000
OExperiment 1 *Experiment 1
V *Exper men t
7000 0 Experiment 2 0 Experiment 2
AExperiment 3 x AExperiment 3
6000 xExperiment 4 O 3000 xExperiment 4
xExperiment 4


5000 0 x



i2000 000



2000 4000 6000 8000 0 000 2000 3000 400
0 Z










Simulated Pod Welght kg ha C Simulated Stem Welght kg ha 1 D





weight, C) boll weight, D) stem weight for all four experiments. The simulated


results were obtained using unmodified cultivar parameters.
3000









Experiment 1


Experiment 2


Experiment 3


Experiment 4


6
5
4



25 50 75 100 125 150
25 50 75 100 125 150


4 4 -
3 -3-
2 2

0 0


25 50 75 100 125 150


25 50 75 100 125 150 A)


25 50 75 100 125 150


8000


25 50 75 100 125 150


25 50 75 100 125 150








50 100 150


25 50 75 100 125 150


8000


2000


25 50 75 100 125 150


I


2000
1500
1000
500
0
25 50 75 100 125 150 B)
8000


25 50 75 100 125 150 C)






ii


25 50 75 100 125 150 25 50 75 100 125 150 25 50 75 100 125 150 25 50 75 100 125 150 D)
Figure 3-2. Simulated and observed values for A) leaf area index, B) leaf weight (kg/ha), C) boll weight (kg/ha), and D)
stem weight (kg/ha) for experiments 1-4 using unmodified cultivar parameter values.


63


8000


i I


i--
i


~~-~







































355
EM-FL


140






93-






47-






00
380


10
LFMAX


31 U


XFRT


75 100
PODUR


350






233-






117






00
05


Figure 3-3. Posterior probability distributions of model


440
SD-PM


500


1700
SLAVAR


34 b
SFDUR


08 10
KCAN


parameters


350-





233-





117-





00
07


bU






















SExperiment 1 vlxperimen


AExperiment 3 O 2000 AExperiment 3 2
xExperiment 4 0 xExperiment 4
4E O t


o m
S500 -

000





8 0 4 x 0 0
Q o / I Uooo)














OExperiment 1 Experiment
0 Experiment 2 Experiment 2
005000



SExperiment


d Lt Expersimulaente e Weght kg ha
0 ih 0 et

Aia

4000 2000


3000 1 0 x
2o u0 o
0
2 00



X 0 O


0 2000 4000 6000 8000 0 00 2000 3000 4000 00
Simulated Pod WeLght kg ha' C Simulated Stem Weight kg ha 1 D




Figure 3-4. Scatter plot of simulated vs. measured values for A) leaf area index, B) leaf

weight, C) boll weight, D) stem weight for all four experiments. The simulated

results were obtained using estimated cultivar parameters.














7 Experiment 1
6
5
4


2 i


0 .
25 50 75 100 125 150

0 2500


25 50 75 100 125 150


25 50 75 100 125 150













25 50 75 100 125 150


Experiment 2


25 50 75 100 125 150


25 50 75 100 125 150


25 50 75 100 125 150


4 Experime-
35 -

25
2
15

05
0
25 50 75 100 125 150


25 50 75 100 125 150


6000


25 50 75 100 125 150


25 50 75 100 125 150


4 Experiment 4
35

25
2
15
1

05
0
25 50 75 100 125 150 A)

2500

2000

1500

1000

500


25 50 75 100 125 150 B)

8000


25 50 75 100 125 150 )












25 50 75 100 125 150 D)


Figure 3-5. Simulated and observed values for A) leaf area index, B) leaf weight, C) boll weight, and D) stem weight for
four experiments using estimated cultivar parameter values. Vertical bars indicate the standard deviations of

observed values. Dotted lines represent 2.5% and 97.5% confidence interval of 5000 simulations.




66









Table 3-1. Information about the experimental sites, planting date, type of soils, and
weather characteristics


Experiment
Sites
Latitude
Longitude
Elevation (m)
Planting date

Soil type
Mean seasonal
temperature
(oC)
Mean seasonal
precipitation
(mm)
Reference of
weather data


Citra, FL
29024' N
8217' W
20
19-Jun-06

Troup Sand


2
Camilla, GA
31 11' N
8412'W
54
12-Apr-04

Troup sand


Quincy, FL
30036' N
8433' W
63
06-Jun-06
Dothan sandy
loam


22


4
Quincy, FL
30036' N
8433' W
63
05-May-06
Dothan sandy
loam


22


3.5


www.fawn.com www.aeoraiaweather.net www.fawn.com www.fawn.com









Table 3-2. The CROPGRO-Cotton parameters and uncertainty ranges used for GLUE
prior distributions.
Parameter Definition Uniform Distribution
Minimum Base Maximum
EM-FL Duration between emergence and flowering 28.00 40.00 43.00
Duration between first seed to physiological 38.00 45.00 50.00
SD-PM maturity
LFMAX Maximum leaf photosynthesis rate 0.70 1.10 1.20
Specific leaf area of cultivar under normal growth 90.00 170.00 250.00
SLAVR condition
Maximum fraction of daily growth that is 00 00
0.50 0.80 0.95
XFRT partitioned to seed+shell
Seed filling duration for boll cohort at standard 31.00 35.00 38.00
SFDUR growth condition
Time required for cultivar to reach final boll load 5.00 5.00 10.00
PODUR under optimal condition
KCAN Light Extinction Coefficient 0.50 0.80 0.95









Table 3-3. The CROPGRO-Cotton average model predictions using DSSAT default
parameters in comparison with corresponding measured data
Mean Mean Mean
Variable Name Experiment Observed Simulated Diff
First flower 1 57 51 -6
Maturity 1 142 146 4
LAI 1 3.14 2.88 -0.25
Leaf wt kg/ha 1 1354 1422 68
Stem wt kg/ha 1 2002 2073 71
Boll wt kg/ha 1 1886 3339 1454
Leaf wt kg/ha 2 909 1036 127
Stem wt kg/ha 2 1430 1955 525
Boll wt kg/ha 2 2352 2103 -249
First flower 3 65 61 -4
LAI 3 1.82 2.04 0.23
Leaf wt kg/ha 3 1031 1081 50
Stem wt kg/ha 3 1059 1305 246
Boll wt kg/ha 3 2276 3812 1536
First flower 4 64 72 8
LAI 4 1.92 2.23 0.31
Leaf wt kg/ha 4 1238 1224 -13
Stem wt kg/ha 4 1159 1495 336
Boll wt kg/ha 4 5300 4657 -644









Table 3-4. Parameter uncertainties and fundamental statistics of prior and posterior


distributions


Parameter USA I Prior Posterior
default Mean STDEV CV Mean STDEV CV
EM-FL 40 35.44 4.34 12.30% 40 0.61 1.50%
SD-PM 45 44.07 3.53 8.00% 44 2.06 4.70%
LFMAX 1.10 0.95 0.14 15.20% 1.05 0.11 5.40%
SLAVAR 170 170.00 45.91 27.10% 173 7.5 0.80%
XFRT 0.80 0.73 0.13 17.90% 0.77 0.02 2.90%
SFDUR 35 35.00 2.01 5.80% 36 0.83 2.40%
PODUR 5 7.50 1.44 19.10% 5.2 0.4 1.80%
KCAN 0.80 0.73 0.13 17.80% 0.64 0.05 3.20%










Table 3-5. The CROPGRO-Cotton average model predictions using estimated
parameters in comparison with corresponding measured data


Variable Name
First flower
Maturity
LAI
Leaf wt kg/ha
Stem wt kg/ha
Boll wt kg/ha
Leaf wt kg/ha
Stem wt kg/ha
Boll wt kg/ha
First flower
LAI
Leaf wt kg/ha
Stem wt kg/ha
Boll wt kg/ha
First flower
LAI
Leaf wt kg/ha
Stem wt kg/ha
Boll wt kg/ha


Experiment
1
1
1
1
1
1
2
2
2
3
3
3
3
3
4
4
4
4
4


Mean
Observed
57
142
3.14
1354
2002
1886
909
1430
2352
65
1.82
1031
1059
2276
64
1.92
1238
1159
5300


Mean
Simulated
52
142
2.26
1101
1559
2330
820
1412
1916
62
1.70
884
964
2572
72
1.76
954
1077
3379


Mean Diff
-5
0
-0.88
-253
-444
444
-90
-18
-436
-3
-0.12
-146
-95
296
-8
-0.16
-284
-82
-1921









Table 3-6. Comparison of RMSE, and d-statistics of simulated LAI, and biomass
components for four sites based on DSSAT default model parameters and
GLUE estimated parameters
DSSAT default GLUE estimated
Experiments Variables parameters parameters
RMSE d-statistics RMSE d-statistics
1 0.76 0.63 1.11 0.57
3 0.33 0.98 0.28 0.98
4 LAI 0.81 0.80 0.55 0.87
1 258.27 0.67 330.24 0.53
2 Leaf 333.84 0.93 287.47 0.94
3 Weight 105.69 0.99 180.87 0.98
4 Kg/ha 346.36 0.88 381.01 0.83
1 1630.34 0.75 535.15 0.95
2 Boll 497.71 0.98 681.73 0.97
3 Weight 1842.07 0.45 819.64 0.75
4 Kg/ha 1803.42 0.53 2340.07 0.45
1 229.93 0.95 474.14 0.82
2 Stem 684.69 0.94 240.62 0.99
3 Weight 316.40 0.97 116.08 0.99
4 Kg/ha 611.40 0.81 349.32 0.91









Table 3-7 Comparison of output uncertainties in model outputs
and posterior distribution


of LAI and above ground biomass components for prior


Experiments Variables Prior Posterior
STDEV (kg/ha) CV (%) STDEV (kg/ha) CV (%)
Mean Range Mean Range Mean Range Mean Range
1 1.38 1.03-1.49 56 56-58 0.26 0.12-0.34 10.7 10.1-12.0
3 0.8 0.1-1.6 47 40-52 0.14 0.01-0.28 6.97 4.29-8.75
4 LAI 0.92 0.14-1.55 51 41-56 0.18 0.02-0.31 8.79 5.64-10.0
53.76- 9.33-
1 497 360-568 44 43-45 119.13 163.2 9.98 11.35
2.13- 5.23-
2 246 0.6-481 29 10-38 62.55 114.86 7.05 11.10
6.18-
3 Leaf 302 45-594 35 32-39 67.32 136.85 6.34 3.74-8.07
Weight 11.57-
4 kg/ha 366 64-611 39 31-43 89.26 154.08 8.09 5.04-9.36
89.47- 7.64-
1 613 18-1268 45 40-61 217.26 357.21 9.71 14.92
2 562 14-917 34 20-60 87.69 0-138.13 4.58 2.74-7.01
141.68-
3 Boll 892 504-1226 36 36-37 236.75 302.59 8.57 7.83-9.07
Weight 152.24- 6.27-
4 kg/ha 1153 485-1653 38 36-42 263.43 334.50 8.19 10.82
73.77- 10.25-
1 760 478-986 46 45-50 183.94 279.83 10.98 12.45
0.39- 6.78-
2 604 2-962 43 29-62 165.83 292.98 10.14 14.19
15.78- 8.80-
3 Stem 411 57-871 53 40-75 101.05 211.07 13.02 20.88
Weight 27.42- 9.91-
4 kg/ha 501 104-896 52 44-63 125.44 220.36 12.13 15.53









CHAPTER 4
IN-SEASON UPDATES OF COTTON YIELD FORECASTS USING CROPGRO-
COTTON MODEL

Introduction

There has been significant progress in developing models to simulate growth and

development of agricultural crops (Ritchie, 1994). These crop simulation models have

shown potential for use in forecasting crop yield using weather forecasts (De Wit and

Diepen, 2007; Hansen et al., 2005; Larow et al., 2005) as well as using historical

weather records (Lembke and Jones, 1972, Wright et al., 1984). Simulation models are

usually deterministic; hence if inputs to the model and model parameters are accurately

measured, yield forecasts can be made even in abnormal climate situations, if those

can be predicted (Bannayan and Crout, 1999).

To facilitate simulation model forecasts of crop yield, daily weather data need to be

provided to the model in terms of a forecast. It is a common practice to generate

weather ensembles stochastically (Lawless and Semenove 2005; Bannayan and Crout

1999; Ahmed et al., 1976; Grondona et al., 2000; Podesta et al., 2002) to represent

uncertainty of weather conditions that are provided as an input to the model. However,

the main limitations of weather generators are that they do not simulate extreme values

well and they assume that the observed relationships between weather variables will

remain the same in the future (Jones et al., 2009). As an alternative to using generated

weather series, historical weather records could be used to represent the possible

weather for the next season. There has been handful of studies made where historical

weather data were used to simulate crop yield, which was represented as frequency

distribution of expected yields (Lembke and Jones, 1972, Wight et al., 1984).









Studies have shown that instead of using a static range of weather to forecast

yields, updating the model in-season using observed weather improves accuracy of

model forecasts (Bannayan and Crout 1999; Lawless and Semenov 2006; Semenov

and Porter 1995). Before the start of crop growing season, weather is entirely uncertain

which translates into uncertainties in crop yield forecasts. If the model is updated in-

season with observed weather data, some of the weather uncertainties are eliminated.

Since weather uncertainties early in the season are eliminated via use of observed data,

it is possible to improve accuracy of crop yield prediction by in-season updating the

model with real weather data. For example, Bannayan and Crout, (1999) clearly showed

that the in-season updating the SUCROS model improved the forecasting accuracy of

winter wheat yield.

Crop yield in southeastern United States is affected significantly by El Niio

Southern Oscillation (ENSO) (Jones et al., 2000; Hansen et al., 1998). In this region, El

Niio events are characterized by lower winter temperature and higher rainfall and La

Niia events have the opposite effects. Since ENSO influences agricultural yield in the

southeastern United States, it may be possible to forecast crop yield tailored to different

ENSO phases using in-season updates of real weather data. Royce et al. (2009)

compared the predictive potential of three different ENSO classifications on crop yields

for the Southeastern United States, including cotton. The three ENSO classifications

they used were based on Japan Meteorological Agency (JMA) index, Oceanic Nino

Index (ONI), and Multivariate ENSO index (MEI). According to that study, March-May

MEI ENSO index and January-April ONI ENSO index showed the strongest association

with cotton yield in the southeastern United States. The assumption was that the ENSO









conditions occurring immediately prior to or during the spring-summer crop season

climate influence in the southeastern United States that affects crop yields which would

not be captured by categorical annual JMA ENSO index. They found that monthly

ENSO indices were better predictors of crop yield than the JMA. That research was

based on the historical county yield data which does not distinguish between irrigated

and rain fed practices. Simulation models can be effective for more robust analysis

since they can quantify the effects under rainfed conditions alone.

The CROPGRO-Cotton model (Messina et al., 2004; Pathak et al., 2007) is a

complex simulation model that has been recently added to Decision Support System for

Agrotechnology Transfer (DSSAT) (Jones et al., 1998; Jones et al., 2003) group of

models. It has been calibrated using field conditions in the southeastern United States

but has not been utilized to obtain in-season updates of cotton yield forecasts. Specific

research questions addressed in this study were:

1). Do in-season updates of cotton yield forecasts improve accuracy over the forecast
obtained before season?

2). Which ENSO index (ONI, MEI, or JMA) provides the best cotton yield forecasting
accuracy?

3). Do in-season updates on cotton yield forecasts tailored to ENSO have better
potential in forecasting cotton yield than the cotton yield forecasts obtained using
climatology alone?

The objectives of this study were 1) to evaluate in-season updates of cotton yield

forecasts, 2) to evaluate the use of different ENSO indices in forecasting cotton yield

and 3) to compare ENSO-based forecasts with those based on climatology.









Material and Methods

Outline of the Forecasting Method

The CROPGRO-Cotton model requires daily weather data to simulate growth and

development. In order to utilize the model to forecast cotton yield, weather data inputs

must be provided in terms of a forecast. As a first step, historical weather data up to the

point when the cotton yield forecast is made were replaced with the real weather data

for that season. The process of updating the model with real weather data was repeated

two times during the season (July 1, and August 1) during 1951-2005. Cotton yield

forecasts obtained before season, and in-season using past weather data as a forecast

(climatology) were compared against their simulated cotton yields using real weather

data to evaluate an accuracy of the forecasts, to obtain cotton forecasts tailored to

ENSO phases as a next step, historical weather data for the current ENSO phase were

assumed to be a forecast of future weather. Cotton yield forecasts tailored to ENSO

were compared with the cotton yield forecasts obtained using climatology alone. This

study was focused on Quincy, Florida, as a case study of the Southeastern United

States.

Model Description and Input Data

Cotton was simulated using the CROPGRO-Cotton model under rain fed

conditions with no nitrogen stress. The planting date for all the simulations was kept on

May 1 to represent a typical planting date in the southeastern United States (Pettigrew,

2002). The model has been calibrated for Quincy, Florida location (Chapter 2) for the

Delta Pine 555 cultivar. This cultivar parameter set was used to simulate cotton yield for

this location. Site specific details including soil type and cultivar are described in detail

in Chapter 2.









Comparison between Before-Season and In-Season Cotton Yield Forecasts
Based on Climatology

Inputs of historical weather data for 1951-2005 were provided to the model to

simulate cotton yield using May 1 as a planting date for all years. The mean and

standard deviations of simulated cotton yields represent "before-season" cotton yield

forecast and associated uncertainties obtained using climatology as a forecast.

In the next step, historical weather data up to July 1 were replaced with observed

weather data up to that point for all the years. For example, in order to forecast cotton

yield for the year 1951, all the historical weather records from 1952-2005 were replaced

with 1951 observed weather up to July 1. Those updated weather data were then

provided to the model to simulate updated cotton yields on July 1. The mean and

standard deviations of those simulated cotton yields represents "in-season" updated

cotton yield forecasts and associated uncertainties using climatology as a forecast.

Another in-season update of cotton yield forecasts was obtained on August 1 for all the

years.

The residual errors of "before-season" and "in-season" updated cotton yield

forecasts were obtained by comparing with their true simulated values obtained using

observed weather data for each of the years. In order to evaluate if the forecasting

accuracy of in-season updated cotton yield was improved significantly, an F-test was

performed to see if the standard deviation of residual error (o- ) between observed and

forecasted cotton yield obtained before season was significantly different from that

obtained in-season with updated weather data. The F-test was also performed to

evaluate if the differences in average standard deviation of simulated cotton yield

forecast across all the years reflecting the uncertainties in weather (o) were









statistically significant for before season and in-season. These two F-tests provided the

basis to answer the first research question.

Comparison of Cotton Yield Forecasts Based on ENSO Indices

Royce et al, (2009) compared predictive potentials of ONI, MEI, and JMA based

ENSO classification for three crops of the southeastern United States including cotton.

Based on the findings, January-April ONI based monthly ENSO classification and

March-May MEI based monthly ENSO classification showed the strongest association

with the historic cotton yield. In this study, ONI and MEI based ENSO classification was

carried out using the approach of Royce et al, (2009). For example, under MEI

classification, historical years having El- Niio phase for March-May months were used

to create MEI El- Niio realizations as input to crop model. Similarly, under ONI

classification, historical years that had El- Niio phase for January-April months were

used to create ONI El- Niio realization as input to crop model. Similarly, La-Niia and

neutral phase realizations as input to the models were created. Since JMA is a yearly

classification for ENSO, historical years of data that fall under El- Niio, La-Niia, and

neutral phase were used to create realizations as input to the crop model, respectively.

Before-season and in-season updates of cotton yield forecasts were then obtained

under El-Niio phase, for instance, by providing the model with weather data specific to

that particular ENSO phase based on one of three ENSO indices being compared. In

order to evaluate which ENSO index showed the highest forecasting potential, the F-

test was performed to see if o- obtained by three ENSO indices were significantly

different from each other. Similarly, 5, of forecasted cotton yields obtained based on

three ENSO indices were also evaluated by the F-test to investigate if the differences









were statistically significant. These statistical evaluations were carried out to answer the

second research question.

Comparison between Climatology Based and ENSO Tailored Cotton Yield
Forecast

The particular ENSO index that showed the lowest mean standard deviations of

model simulations reflecting weather uncertainties (o ) and the lowest standard

deviation of the residual error of observed and mean simulated cotton yields (o-,) were

compare with climatology based cotton yield forecasts. Statistical comparisons between

climatology based and ENSO based cotton yield forecasts were carried out with F-test

in the same manner as described in the above two sections to answer third research

question.

Results and Discussion

Comparison between Before-Season and In-Season Cotton Yield Forecasts based
on Climatology


Cotton yield forecasts by the CROPGRO-Cotton model that were obtained before

the season for 1951-2005 using climatology are shown in Table 4-1. In-season updates

of cotton yield forecasts obtained on July 1 and August 1 over the period of 1951-2005

are shown in Table 4-2, and Table 4-3, respectively. Overall, the standard deviations of

simulated cotton yield forecasts reflecting weather uncertainties (o-) with in-season

updates on July 1, and August 1 were reduced in 80% and 90% of the years,

respectively. Similarly, the reductions in the residual errors (E) with in-season updated

cotton yield forecasts obtained on July 1 and August 1 were observed 65% and 56% of

the time compared to before season cotton yield forecasts. An example of how

uncertainties in cotton yield forecasts are reduced with in-season updates with observed









weather is shown in Figure 4-1. The average cotton yield forecast and standard

deviation around the mean were higher for forecasts obtained before the season. When,

the cotton yield forecasts were updated with observed weather data, average cotton

yield forecast approached the observed cotton yields.

Statistical comparison of mean standard deviations of simulated cotton yield

forecasts across all the years reflecting weather uncertainties (5o) and the standard

deviation of residual errors between observed and mean simulated forecast (o-0) are

shown in Table 4-4. Although the results show reductions of o-0 and J, on July 1

updated forecasts compared to the before-season cotton yield forecasts, the differences

were not statistically significant. However, o- and o, were reduced considerably for

August 1 updates. These reductions were highly significant (p<0.01). The reduction in

-, and of August 1 forecast updates relative to before-season cotton yield forecasts

were approximately 35% and 32%, respectively.

These results agree with the statement by Wright et al. (1984) that the standard

deviation decreased over time with updated forecasts. The main reason was due to the

reductions in uncertainties in the weather data over time as observed weather replaced

forecast weather.

Comparison of Cotton Yield Forecasts based on ENSO Indices

EI-Nifo phase

Measures of model deviations for cotton yield using El-Niro forecast based on

JMA, MEI, and ONI are shown in Tables 4-5, 4-6, and 4-7. In general, o and o- for

cotton yield forecasts based on MEI were lowest among three ENSO indices based

forecasts. Table 4-14 shows statistical comparison of cotton yield forecasts based on all









three ENSO indices for three phases including El-Niro phase. Results show that the

MEI was best among the three ENSO indices compared in forecasting the cotton yield

before season and in-season for El-Niro forecasts. Although o-0 of cotton yield forecast

based on MEI was 30% lower than JMA and 21% lower than ONI, the differences were

not significant. Unfortunately, between 1951 and 2005 there were only 9-12 years

classified as El-Niro under those three ENSO indices. Better statistical testing could

have been made if the sample size was larger.

La-Nina phase

Cotton yield forecasts obtained using La-Niia forecasts based on JMA, MEI, and

ONI are presented in Tables 4-8, 4-9, and 4-10. In general, MEI performed better than

other two ENSO indices based cotton yield forecasts. The o- for cotton yield forecasts

obtained using MEI based La-Niia forecasts were lowest for before season cotton yield

forecast and July 1 in-season updated cotton yield forecasts (Table 4-14) whereas, ONI

based La-Nira forecasts were lowest for August 1 in-season updated cotton yield

forecasts. But, o- and o for cotton yield forecasts for all three ENSO indices were not

statistically significant under the La-Niia phase.

Neutral phase

Interestingly, cotton yield forecasts obtained using Neutral forecasts based on

JMA index showed improved forecasting accuracy compared to the yield forecasts

based on other two ENSO indices. (Tables 4-11, 4-12, and 4-13). The o-0 of cotton yield

forecasts based on JMA was significantly different from ONI for the forecasts obtained

before the season (Table 4-14). Other than that o- and of cotton yield forecasts

based on the three ENSO indices did not show statistically significant differences.









Comparison between Climatology-Based and ENSO-Tailored Cotton Yield
Forecasts

Although cotton yield forecasting accuracy measures (o- ando,) were not

significantly different, the ENSO indices that showed the lowesto- and for a given

phase were compared with climatology based cotton yield forecast. Based on the best

results discussed above, MEI was used in the comparison for El-Niro and La-Nina

phases, and JMA was used for the Neutral phase.

Statistical comparisons between climatology based and ENSO tailored cotton yield

forecasts are shown in Table 4-15. Interestingly, ENSO tailored cotton yield forecasts

for El-Niro and La-Niia did not show improvement over climatology-based forecasts.

On the contrary, climatology-based cotton yield forecasts showed lower o-0 compared

to ENSO based cotton yield forecasts. The standard deviations were lower under the

ENSO tailored cotton yield forecasts, but those results were not significantly different.

Interestingly, the standard deviation of cotton yield forecasts obtained before the

season and on July 1 under the Neutral phase based on JMA index showed highly

statistically significant reductions compared to the climatology based cotton yield

forecasts. In general, ENSO tailored cotton yield forecasts for Neutral phase shows

better predictability compared to climatology based cotton yield forecasts. But, for El-

Niro and La-Niia phases the cotton yield forecasts did not show statistically significant

differences from climatology based forecasts.

Conclusions

Accuracy of cotton yield forecasts was improved with in-season updating the

CROPGRO-Cotton model predictions using observed weather data. The in-season

updates of cotton yield forecasts were statistically significant for August 1 forecasts but









not statistically significant for July 1 forecasts. On August 1 updates, approximately 90%

of the cotton yield forecasts showed reductions in their standard deviations, and 56% of

the cotton yield forecasts showed reductions in residual errors compared to before-

season cotton yield forecasts.

In general, ENSO indices did not show statistically significant differences in o-,

and 5 for El-Niio and La-Niia phases. For the Neutral phase, the JMA index based

cotton yield forecasts were better. The o for JMA based cotton yield forecasts was

significantly lower than ONI based cotton yield forecasts.

Comparison between climatology and ENSO based cotton yield forecast results

showed that the ENSO tailored cotton yield forecasts did not show significant

improvement for El-Niio and La-Nina phases over climatology based cotton yield

forecasts. But, under the Neutral phase, the standard deviations of ENSO tailored

cotton yield forecasts were significantly lower than climatology based cotton yield

forecasts. That shows that the in-season updates of cotton yield forecasts in neutral

phases have good potential over using climatology based cotton yield forecast.

This study was conducted with historical weather records over 1951-2005. The

limitation of this study was that there were only 9 to 12 years under El-Niio and La-Nina

categories. For better statistical comparisons, more years of weather data are needed

to increase the number of years in each ENSO phase. Also, only one location was used

as a case study in the southeastern United States. More locations should be analyzed.












4100


4000




b 3900




4 3800
0






1)
3700 -
o



3600




Before Season July 1 August 1


Figure 4-1. Distribution of forecasted cotton yields for the 1980 cotton season at
Quincy, Florida simulated using 1951-2005 historical weather data. The solid
horizontal line represents "observed" cotton yield for 1980 obtained using
model simulation using observed weather.









Table 4-1. Measures of model deviations for seed cotton yield (Quincy, FL) before
season using no forecast except climatology


Residual Residual
Year Observed Expected s Error (s) Year Observed Expected s Error (s)
kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha kg/ha kg/ha
1951 3370 3387 415 -17 1978 3947 3689 455 258
1952 2981 3393 416 -412 1979 3730 3710 459 20
1953 3448 3385 415 63 1980 3950 3735 468 215
1954 3047 3393 412 -346 1981 4286 3743 461 543
1955 3632 3382 414 250 1982 4295 3758 463 537
1956 3529 3382 419 147 1983 2494 3817 436 -1323
1957 4118 3372 402 746 1984 4123 3810 478 313
1958 3311 3393 416 -82 1985 4142 3830 476 312
1959 3671 3398 416 273 1986 4165 3846 478 319
1960 3694 3414 423 280 1987 3987 3875 483 112
1961 3420 3430 421 -10 1988 3585 3912 492 -327
1962 3623 3439 422 184 1989 3876 3930 490 -54
1963 3645 3448 424 197 1990 3463 3953 488 -490
1964 3624 3456 431 168 1991 3882 3964 495 -82
1965 3992 3457 420 535 1992 4096 3969 500 127
1966 3340 3491 428 -151 1993 4055 3978 497 77
1967 3497 3499 431 -2 1994 4382 3995 498 387
1968 3524 3515 440 9 1995 3807 4033 504 -226
1969 3576 3536 435 40 1996 4138 4044 511 94
1970 3484 3554 437 -70 1997 3699 4069 506 -370
1971 3109 3570 434 -461 1998 3599 4108 507 -509
1972 2361 3602 416 -1241 1999 4173 4114 514 59
1973 3708 3610 445 98 2001 4531 4142 516 389
1974 3014 3631 437 -617 2002 4158 4172 522 -14
1975 3990 3626 444 364 2003 5079 4187 511 892
1976 3946 3643 456 303 2004 4342 4208 529 134
1977 2132 3702 398 -1570 2005 4079 4256 529 -177










Table 4-2. Measures of model deviations for seed cotton yield (Quincy, FL) in-season
(July 1) using no forecast except climatology


Year Observed
kg/ha
1951 3370
1952 2981
1953 3448
1954 3047
1955 3632
1956 3529
1957 4118
1958 3311
1959 3671
1960 3694
1961 3420
1962 3623
1963 3645
1964 3624
1965 3992
1966 3340
1967 3497
1968 3524
1969 3576
1970 3484
1971 3109
1972 2361
1973 3708
1974 3014
1975 3990
1976 3946
1977 2132


Expected
kg/ha
3540
3316
3427
3474
3456
3474
3532
3396
3350
3382
3393
3635
3461
3522
3470
3327
3541
3521
3301
3614
3650
3535
3632
3472
3743
3603
3630


kg/ha
368
424
413
361
385
347
341
346
372
400
404
356
329
399
394
395
361
412
498
399
397
345
394
507
412
390
437


8
(Kg/ha)
-170
-335
21
-427
176
55
586
-85
321
312
27
-12
184
102
522
13
-44
3
275
-130
-541
-1174
76
-458
247
343
-1498


Year Observed
kg/ha
1978 3947
1979 3730
1980 3950
1981 4286
1982 4295
1983 2494
1984 4123
1985 4142
1986 4165
1987 3987
1988 3585
1989 3876
1990 3463
1991 3882
1992 4096
1993 4055
1994 4382
1995 3807
1996 4138
1997 3699
1998 3599
1999 4173
2001 4531
2002 4158
2003 5079
2004 4342
2005 4079


Expected
kg/ha
3665
3684
3826
3848
3811
3846
3851
3943
4043
3904
3755
3988
3915
3949
4008
3944
4077
3934
4135
4096
3766
4097
4217
4189
4321
4324
4057


(s
kg/ha
405
467
413
420
427
348
409
419
430
405
553
438
516
377
426
499
441
569
430
448
644
415
458
474
430
438
565


kg/ha
282
46
124
438
484
-1352
272
199
122
83
-170
-112
-452
-67
88
111
305
-127
3
-397
-167
76
314
-31
758
18
22












Table 4-3. Measures of model deviations for seed cotton yield (Quincy, FL) in-season
(August 1) using no forecast except climatology

Year Observed Expected as s Year Observed Expected as s

kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha kg/ha kg/ha
1951 3370 3653 287 -283 1978 3947 3735 238 212
1952 2981 2537 368 444 1979 3730 3626 311 104
1953 3448 3433 286 15 1980 3950 3867 218 83
1954 3047 3431 258 -384 1981 4286 3852 423 434
1955 3632 3525 218 107 1982 4295 4055 265 240
1956 3529 3516 246 13 1983 2494 3149 473 -655
1957 4118 3673 224 445 1984 4123 3578 286 545
1958 3311 3512 242 -201 1985 4142 4240 280 -98
1959 3671 3491 251 180 1986 4165 4236 279 -71
1960 3694 3454 290 240 1987 3987 3934 410 53
1961 3420 3585 289 -165 1988 3585 4013 388 -428
1962 3623 3540 310 83 1989 3876 3968 372 -92
1963 3645 3535 218 110 1990 3463 3251 538 212
1964 3624 3442 233 182 1991 3882 3800 254 82
1965 3992 3664 395 328 1992 4096 3852 474 244
1966 3340 3318 256 22 1993 4055 4179 357 -124
1967 3497 3593 234 -96 1994 4382 4245 406 137
1968 3524 3512 404 12 1995 3807 4362 271 -555
1969 3576 3441 237 135 1996 4138 3881 522 257
1970 3484 3735 275 -251 1997 3699 4047 313 -348
1971 3109 3577 260 -468 1998 3599 3536 194 63
1972 2361 3230 488 -869 1999 4173 4043 280 130
1973 3708 3456 353 252 2001 4531 4313 357 218
1974 3014 3301 239 -287 2002 4158 4304 314 -146
1975 3990 3894 250 96 2003 5079 4667 291 412
1976 3946 3541 457 405 2004 4342 4456 423 -114
1977 2132 2620 434 -488 2005 4079 4174 389 -95









Table 4-4. Statistical comparison of cotton yield forecasts obtained before-season with
in-season updated cotton yield forecasts. represents significant difference
in o, and SD for in-season updated cotton yield forecast with the o-0 and SD
for before season cotton yield forecasts at 0.01 probability level. The "ns"
represents non-significant correlations.


Cotton Yield Forecast based only on climatology
Before Season 01-Jul 01-Aug
Oe 457 420ns 299***
s 458 423 320***










Table 4-5. Measures of model deviations for seed cotton yield (Quincy,


Before-Season


Observed Expected
kg/ha kg/ha
2981 3197
3311 3179
3624 3213
3340 3274
3484 3323
3708 3366
2132 3571
2494 3661
3987 3607
3585 3676
4096 3700
5079 3841


"s 8
kg/ha (Kg/ha)
603 -216
605 132
614 411
623 66
632 161
638 342
492 -1439
582 -1167
689 380
718 -91
717 396
664 1238


In-Season (July 1)
Expected s,
kg/ha kg/ha
3103 659
3262 526
3274 565
3080 588
3393 568
3435 572
3469 611
3729 376
3735 596
3501 824
3789 568
4065 514


FL) using El Niro forecast based on JMA index
In-Season (August 1)


8
(Kg/ha)
-122
49
350
260
91
273
-1337
-1235
252
84
307
1014


Expected s,
kg/ha kg/ha
2466 319
3429 311
3294 308
3199 319
3634 363
3420 357
2628 413
3148 427
3880 428
3932 476
3794 520
4478 384



(Kg/ha)
515
-118
330
141
-150
288
-496
-654
107
-347
302
601


Year

1952
1958
1964
1966
1970
1973
1977
1983
1987
1988
1992
2003









Table 4-6. Measures of model deviations for seed cotton yield (Quincy, FL) using El Niro forecast based on MEI index
Before-Season In-Season (July 1) In-Season (August 1)
Year Observed Expected Qs s Expected Qs s Expected Qs s
kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha)
1953 3448 3257 429 191 3259 512 189 3343 239 105
1958 3311 3282 435 29 3229 417 82 3416 149 -105
1969 3576 3410 453 166 3084 637 492 3415 262 162
1980 3950 3591 473 360 3628 501 323 3889 162 61
1983 2494 3815 129 -1321 3786 172 -1292 2862 283 -368
1987 3987 3716 489 271 3650 444 337 3686 248 301
1992 4096 3817 510 279 3873 520 223 3607 334 490
1993 4055 3819 506 236 3755 625 300 4051 244 5
2005 4079 4118 551 -39 3836 726 243 4005 259 74









Table 4-7. Measures of model deviations for seed cotton yield (Quincy, FL) using El Niro forecast based on ONI index
Before-Season In-Season (July 1) In-Season (August 1)
Year Observed Expected Qs s Expected Qs s Expected Qs s
kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha)
1958 3311 3337 515 -26 3346 521 -35 3460 286 -149
1966 3340 3439 531 -99 3179 565 161 3254 248 86
1969 3576 3459 539 118 3157 754 420 3432 212 144
1973 3708 3528 549 180 3534 540 174 3318 448 390
1983 2494 3881 309 -1387 3800 275 -1306 2988 569 -494
1987 3987 3784 591 203 3801 589 186 3775 516 213
1992 4096 3886 636 210 3832 562 264 3698 590 398
1995 3807 3969 619 -162 3777 893 30 4350 228 -543
2003 5079 4006 524 1073 4084 514 995 4566 232 513










Table 4-8. Measures of model deviations for seed cotton yield (Quincy,


Before-Season


Observed Expected


Year

1955
1956
1957
1965
1968
1971
1972
1974
1975
1976
1989
1999


kg/ha
3384
3357
3340
3442
3499
3627
3678
3704
3629
3616
3973
4140


O"s 8


kg/ha
537
535
488
530
563
549
414
538
569
582
632
659


(Kg/ha)
248
172
778
550
25
-518
-1317
-690
361
330
-97
33


In-Season (July 1)
Expected s,
kg/ha kg/ha
3490 468
3431 474
3507 448
3488 448
3598 471
3682 505
3603 341
3610 437
3826 492
3549 508
4030 553
4070 559


FL) using La Ni~a forecast based on JMA index
In-Season (August 1)


8
(Kg/ha)
142
98
611
504
-74
-573
-1242
-596
164
397
-154
103


Expected
kg/ha
3513
3538
3715
3768
3615
3603
3415
3350
3970
3641
4043
4077


O". S


kg/ha
211
244
248
409
429
132
281
133
246
430
333
304


(Kg/ha)
119
-9
403
224
-91
-494
-1054
-336
20
305
-167
96


kg/ha
3632
3529
4118
3992
3524
3109
2361
3014
3990
3946
3876
4173









Table 4-9. Measures of model deviations for seed cotton yield (Quincy, FL) using La Ni~a forecast based on MEI index
Before-Season In-Season (July 1) In-Season (August 1)
Year Observed Expected Qs s Expected Qs s Expected Qs s
kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha)
1954 3047 3409 308 -362 3500 283 -453 3405 223 -358
1955 3632 3343 318 289 3425 294 207 3468 251 164
1956 3529 3316 337 213 3422 284 107 3498 253 31
1962 3623 3406 331 217 3639 272 -16 3536 335 87
1964 3624 3382 346 242 3530 326 94 3397 245 227
1968 3524 3455 365 69 3499 308 25 3578 431 -54
1971 3109 3593 313 -484 3650 310 -541 3550 187 -441
1974 3014 3670 276 -656 3524 352 -510 3314 212 -300
1976 3946 3561 369 385 3498 308 448 3609 434 337
1999 4173 4079 417 94 4065 337 108 4045 327 128









Table 4-10. Measures of model deviations for seed cotton yield (Quincy, FL) using La Ni~a forecast based on ONI index
Before-Season In-Season (July 1) In-Season (August 1)
Year Observed Expected s s Expected s s Expected s s
kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha)
1955 3632 3384 357 248 3500 278 132 3446 235 186
1956 3529 3352 383 177 3449 307 80 3522 261 7
1968 3524 3499 414 25 3609 312 -85 3686 227 -162
1971 3109 3662 328 -553 3748 273 -639 3550 132 -441
1974 3014 3748 269 -734 3661 299 -647 3331 150 -317
1975 3990 3623 365 367 3845 276 145 3912 280 78
1976 3946 3603 423 343 3564 312 382 3682 200 264
1999 4173 4137 448 36 4093 354 80 4072 276 101









Table 4-11. Measures of model deviations for seed cotton yield (Quincy, FL) using Neutral forecast based on JMA index
Before-Season In-Season (July 1) In-Season (August 1)
Year Observed Expected s s Expected s s Expected s s
1951 3358 3484 224 -126 3613 216 -255 3658 287 -300
1953 3449 3481 225 -32 3477 316 -28 3419 300 30
1954 3038 3495 208 -457 3563 207 -525 3503 212 -465
1959 3671 3490 225 181 3392 236 279 3484 239 187
1960 3697 3524 235 174 3465 262 232 3474 293 223
1961 3419 3528 228 -109 3494 258 -75 3641 274 -222
1962 3623 3535 230 88 3691 226 -68 3510 311 113
1963 3644 3544 231 100 3528 195 116 3567 182 77
1967 3494 3600 235 -106 3625 226 -131 3632 206 -138
1969 3575 3638 238 -63 3343 373 233 3450 229 125
1978 3947 3788 254 159 3724 248 224 3791 193 156
1979 3771 3813 258 -42 3776 317 -5 3681 275 90
1980 3949 3851 267 98 3919 274 30 3913 187 36
1981 4301 3838 248 463 3928 276 373 3834 460 467
1982 4295 3854 252 441 3848 279 447 4072 189 223
1984 4126 3926 272 200 3940 262 186 3599 296 527
1985 4143 3931 270 212 3990 258 153 4261 260 -118
1986 4165 3948 271 217 4130 290 35 4278 243 -113
1990 3472 4070 259 -598 3995 367 -523 3173 595 299
1991 3892 4074 282 -182 4012 231 -120 3801 251 91
1993 4056 4085 286 -29 4016 353 40 4209 355 -153
1994 4382 4098 282 284 4159 296 223 4272 443 110
1995 3812 4148 284 -336 4004 435 -192 4409 208 -597
1996 4160 4170 294 -10 4199 258 -39 3799 555 361
1997 3710 4187 280 -477 4201 301 -491 4138 265 -428
2001 4530 4248 299 282 4303 301 227 4332 347 198
2002 4261 4283 306 -22 4262 323 -1 4309 301 -48
2004 4347 4331 307 16 4394 261 -47 4426 433 -79
2005 4019 4374 305 -355 4137 415 -118 4162 404 -143









Table 4-12. Measures of model deviations for seed cotton yield (Quincy, FL) using Neutral forecast based on MEI index
Before-Season In-Season (July 1) In-Season (August 1)
Year Observed Expected Qs s Expected Qs s Expected Qs s
kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha)
1951 3370 3504 280 -134 3649 249 -279 3699 285 -329
1952 2981 3532 270 -551 3458 312 -477 2582 426 399
1959 3671 3504 281 167 3445 258 226 3541 267 130
1960 3694 3529 306 165 3408 232 286 3475 280 219
1961 3420 3546 286 -126 3458 238 -38 3561 282 -141
1966 3340 3616 285 -276 3416 287 -76 3353 264 -13
1970 3484 3674 297 -190 3715 265 -231 3803 251 -319
1973 3708 3727 306 -19 3738 239 -30 3538 365 170
1978 3947 3802 313 145 3779 259 168 3738 229 209
1979 3730 3832 317 -102 3782 305 -52 3703 269 27
1982 4295 3867 308 428 3937 326 358 4065 280 230
1984 4123 3933 348 190 3914 262 209 3566 276 557
1986 4165 3966 326 199 4149 296 16 4265 275 -100
1988 3585 4067 343 -482 3908 454 -323 4036 368 -451
1995 3807 4177 335 -370 4146 474 -339 4394 268 -587
2001 4531 4266 353 265 4336 291 195 4378 342 153
2003 5079 4292 307 787 4403 278 676 4693 310 386
2004 4342 4356 378 -14 4440 320 -98 4549 460 -207









Table 4-13. Measures of model deviations for seed cotton yield (Quincy, FL) using Neutral forecast based on ONI index


Before-Season In-Season (July 1) In-Season (August 1)
Expected s s Expected s s Expected s s
kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha)


Year Observed
kg/ha
1952 2981
1953 3448
1954 3047
1957 4118
1959 3671
1960 3694
1961 3420
1962 3623
1963 3645
1964 3624
1965 3992
1967 3497
1970 3484
1972 2361
1978 3947
1979 3730
1980 3950
1981 4286
1982 4295
1984 4123
1986 4165
1990 3463
1991 3882
1993 4055
1994 4382
1997 3699
2002 4158
2004 4342


3488
3462
3477
3437
3471
3498
3509
3516
3525
3543
3529
3581
3638
3716
3769
3795
3826
3820
3836
3899
3932
4055
4059
4070
4082
4171
4267
4306


358
372
362
348
372
375
377
379
380
382
372
385
390
302
409
413
421
409
412
429
429
427
442
446
445
448
470
479


-507
-14
-430
681
200
196
-89
107
120
81
463
-84
-154
-1355
178
-65
124
466
459
224
233
-592
-177
-15
300
-472
-109
36


3390
3487
3561
3580
3398
3446
3475
3681
3510
3602
3529
3621
3705
3634
3736
3776
3920
3942
3854
3930
4128
4007
4008
4038
4160
4191
4270
4405


337
338
321
291
312
367
365
312
291
364
334
336
361
265
352
407
388
388
364
380
407
404
329
418
411
427
422
391


-409
-39
-514
538
273
248
-55
-58
135
22
463
-124
-221
-1273
211
-46
30
344
441
193
37
-544
-126
17
222
-492
-112
-63


2520
3476
3529
3701
3516
3490
3634
3579
3588
3522
3681
3650
3809
3252
3804
3704
3923
3887
4119
3636
4305
3240
3848
4258
4302
4146
4359
4487


398
295
227
216
234
264
268
317
190
188
387
211
226
530
191
276
175
442
193
249
233
585
257
335
437
259
296
418


461
-28
-482
417
155
204
-214
44
57
102
311
-153
-325
-891
143
26
27
399
176
487
-140
223
34
-203
80
-447
-201
-145









Table 4-14. Statistical comparison of cotton yield forecasts tailored to ENSO forecasts by three indices. "a" represents that
the o, for JMA-Neutral is significantly lower than o- of ONI-Neutral. All other values were not statistically
different from each other.


Type of Cotton Yield Forecast based on ENSO forecast

climate Before Season 01-Jul 01-Aug

forecast o kg/ha 5, (kg/ha) o- kg/ha a, (kg/ha) o- kg/ha a, (kg/ha)

El-Niro

JMA 716 631 660 580 398 385

MEI 517 441 533 506 241 242

ONI 636 535 606 579 383 370

La-Nira

JMA 582 550 528 475 399 283

MEI 363 338 334 307 264 289

ONI 412 373 376 301 248 220

Neutral

JMA 262a 260 246 285 264 303

MEI 330 313 289 297 312 305

ONI 403 401 373 360 309 296









Table 4-15. Statistical comparison of cotton yield forecasts using only climatology forecast with ENSO tailored cotton yield
forecasts using MEI. "***" represents that the standard deviations of expected cotton yield forecasts obtained
from JMA-Neutral is significantly lower than the standard deviations of expected cotton yield forecasts obtained
from climatology.

Type of Cotton Yield Forecast Comparison

climate Before Season 01-Jul 01-Aug

forecast ou kg/ha 5, (kg/ha) o- kg/ha 5, (kg/ha) o- kg/ha 5, (kg/ha)

Climatology 471 464 487 434 261 342

MEI-EI Niio 517 441 533 506 241 242


Climatology 324 437 299 397 274 291

MEI-La Niia 363 338 334 307 264 289


Climatology 257 467 239 430 244 314

JMA-Neutral 262 260*** 246 285*** 264 303


100









CHAPTER 5
COTTON YIELD FORECASTING FOR THE SOUTHEASTERN USA USING CLIMATE
INDICES

Introduction

Cotton is the most important fiber crop in the United States, accounting for

approximately 20% of the total production in the world and more than $25 billion in

products and services annually (USDA ERS, 2009). Cotton production in the

southeastern United States averages about 22% of the total upland cotton production in

the United States (USDA ERS, 2009). Georgia and Alabama hold the major share of

total cotton produced in the southeastern United States. Recently, there has been a

significant increase in cotton planted those two states. While comparing average

acreage planted, there was an increase of about 26% in Georgia 41% in Alabama

during the last decade (NASS, 2007).

While evidence clearly shows an increase in cotton planted over time, climate

variability is a major concern that could adversely affect its production in the

southeastern United States. An effective way to reduce agricultural vulnerability to

climate variability is through the implementation of adaptation strategies. For example

crop yield forecast could be used by farmers to mitigate negative consequences of

unfavorable climate forecast, or benefit from anticipated favorable climate conditions

(Baigorra et al., 2007). If growers know the expected cotton yield for the coming season,

they may be able to decide on alternative management strategies to reduce the cotton

production risk (Jones et al., 2000; Hansen, 2005; Vedwan et al., 2005; Jagtap et al.,

2002). For example, growers could purchase appropriate crop insurance ahead of time

in order to compensate for an adverse effect of climate variability on their cotton yields.









Given that the times at which different crop yield forecasts may be made differ, the

techniques to obtain them also vary. Seasonal cotton yield forecasts are useful if they

are available as early as February, before the growing season starts, so that growers

can make use of them to decide on purchasing seeds, fertilizers, and insurance policies

in advance (personal communication with David Wright and Clyde Fraisse). For

instance the deadline for growers to make crop insurance-related decisions in this

region is March 15. So, if they would like to make insurance decisions based on

expected yields for the coming season, then the crop yield forecasts should be available

before that date.

While the growth and development of crops are known to be influenced by

weather during the growing season, it is a common practice to predict crop yield based

on weather variables (Sakamoto, 1979; Idso et al., 1979; Walker, 1989; Alexandrove

and Hoogenboom, 2001). However, crop yield predictions based on observed weather

cannot be made available before the planting season (Kumar, 2000). Attempts to obtain

long-term forecasts using alternatives to weather variables, such as climate indices that

exhibit teleconnections with weather, are limited.

The El Niro-Southern Oscillation (ENSO) phenomenon is one of the most

significant drivers of climate and agricultural variability in the southeastern United States

(Hansen et al., 1998; Ropelewski and Halpert 1986, Kiladis and Diaz 1989; Mo and

Schemm 2008; Mennis 2001). Although, the ENSO effects in southeastern United State

are stronger during the winter, their effects are not very strong during the summer

months (Baigorria et al., 2007). Baigorria et al. (2010) also showed that cotton was not

strongly affected by ENSO itself, however, ENSO in conjunction with other oceanic


102









(Pacific and Atlantic) and atmospheric patterns may be useful for forecasting cotton

yield. In a parallel study, Martinez et al. (2009) used sea surface temperature (SST) in

the tropical North Atlantic (TNA), the Pacific-North American (PNA) index and Bermuda

High Index (BHI) along with the ENSO index to predict corn yields in the southeastern

United States. The findings of Martinez et al. (2009) showed good potential for using

climate indices to forecast corn yield in this region.

Large scale teleconnection indices greatly influence the climate and agriculture in

the southeastern United States (Stenseth et al., 2003; Enfield, 1996; Barnston et al.,

1991; Bell and Jenowiak, 1994; Martinez et al., 2009). The research question

addressed was; are there teleconnections between large scale climate indices and

cotton yield that would provide the basis for forecasting cotton yield in southeastern

United States? The objectives of this study were to evaluate the relationships between

large scale climate indices and cotton yield and to evaluate the skill of cotton yield

forecasts.

Materials and Methods

Historic Cotton Yield Data

County level yield data for cotton were obtained from National Agricultural

Statistical Services (NASS, 2008) for 57 years from 1951- 2007 for a total of 64 cotton

producing counties in Georgia and Alabama. Cotton producing counties in Florida were

not considered in this study because there was only one county, Santa Rosa that had a

county reported cotton yield available for 57 years. The NASS cotton yields did not

distinguish between irrigated and rain-fed cotton production.

The time series of historic cotton yield over the time period between 1951 and

2007 showed a gradual upward trend. The factors contributing towards this upward


103









trend likely include effects of fertilizers, pesticides, improved cultivars, and enhanced

management practices, but not necessarily climate (Wigley and Qipu, 1983). In order to

evaluate the correlations of historic cotton yield with climate indices, the effects of non

climatic influences on historic yield needed to be removed. For this study, technological

improvements in cotton yield over time was assumed to be linear, hence county cotton

yields were detrented by removing the linear trend. The percentage deviation of yield

from the trend line (% residual) was computed for each year (Eq. 4-1).


esduals observed -1 1.00 (5-1)
Trend

Climate Data

Monthly average temperature and monthly cumulative precipitation for 64 weather

stations in Georgia and Alabama were obtained from National Climatic Data Center

(NCDC) for 1966-2007. Climate data for May-September months were used in the

analysis instead of full year of data since those months typically coincides with the

cotton growing season in the southeastern United States. The main reason for limiting

the climate data to 1966-2007 instead of 1951-2007 was the fact that there were many

counties, especially in Alabama, that had missing climate data between 1951 and 1965.

Atmospheric and Oceanic Climate Indices

Stenseth et al. (2003) stated that any single climate index may possibly explain

only a relatively small part of the local climate variability. They suggested that one

should use climate indices that pick up most of the relevant climate-weather variations

for the specific system under study. In this study, a total of seven climate indices were

used: Oceanic Niio Index (ONI), Tropical North Atlantic (TNA) SST index, Atlantic

Meridional Mode (AMM) index, North Oscillation Index (NOI), North Pacific (NP) pattern,


104









Quasi-Biennial Oscillation (QBO) index, and Tropical North Hemisphere (TNH) index.

Descriptions of each of those indices as well as their effects on climate of southeastern

United States as described in the literature are as follows.

Oceanic nifo index (ONI)

The ONI anomalies are the running means of SST anomalies in the NINO 3.4

region (50N-50S, 1200-1700W) and were obtained from the NOAA climate prediction

center. The ONI has become the National Oceanic and Atmospheric Administration

(NOAA) standard for categorizing the ENSO events in the tropical pacific. However,

continuous monthly values of ONI were selected in this study and not the ENSO

phases.

ENSO exhibits strong correlations with temperature and precipitation in the United

States (Ropelewski and Halpert, 1986) and southeastern United States in particular

(Mote, 1986, Hansen et al., 1998, O'Brian et al., 1996). Since studies show clear

evidence of impact of ENSO on southeastern United States climate, ONI index was

chosen to represent ENSO index in this analysis.

Tropical north Atlantic (TNA) index

The TNA index (Enfield et al., 1999) is an anomaly of the average of the monthly

SST from 5.50N-23.50N, 150-57.50W. The TNA data were obtained from the Physical

Science Division of the Earth System Research Laboratory (ESRL) at National Oceanic

and Atmospheric Administration (NOAA).

Association of TNA with the climatic conditions of southeastern United States has

been documented in the literature. For instance, Wang et al. (2008) demonstrated that

the variability in the summer precipitation for the southeastern United States is strongly

associated with Atlantic SST. Enfield, (1996) investigated a teleconnection between


105









Atlantic SST and precipitation in the southeastern United States. Results from the study

by Martinez et al. (2009) clearly indicated an association of Atlantic SSTs with

temperature and precipitation in the southeastern United States.

Atlantic meridional mode (AMM) index

The AMM SST index is a gathering of cross equatorial meridional SST anomalies

in the tropical Atlantic index (Chiang and Vimont, 2004; Takeshi et al., 2010). The AMM

index is correlated with TNA index and plays an important role in inter-annual and

decadal climate variability and is closely linked with hurricane activities in the

southeastern United States (Xie et al., 2005; Vimont and Kossin 2007; Kossin and

Vimont 2007).

North oscillation index (NOI)

The NOI index represents differences between the sea level pressure anomalies

at the north pacific height (NPH) in the northeast Pacific and near Darwin, Australia

(Schwing et al., 2002). Monthly NOI index values were obtained from the Pacific

Fisheries Environmental Laboratory (PFEL) of NOAA.

The NOI is closely related to El Niio and La Niia events where positive values of

NOI are reflective of La Niia conditions and negative values of NOI are closely linked

with El Niio conditions (Lee and Sydeman, 2009). Since, NOI is linked closely with

ENSO events; it could impact climatic conditions of southeastern United States.

North pacific (NP) pattern

Another sea level pressure based index used in this study was NP index, that

represents area weighted SLP over the region 300N-650N, 1600E-1400W (Trenberth and

Hurrell, 1994). The positive phase of the NP pattern is associated with enhanced


106









cyclonic circulations of pacific jet stream over the southeastern United States which

affects climatic conditions in this region (Bell and Jenowiak, 1994).

Tropical north hemisphere (TNH) index

The TNH pattern, first classified by Mo and Livezey (1986) reflects large-scale

changes in both the location and eastward extent of the pacific jet stream and thus this

pattern significantly modulates the flow of marine air into the United States and to the

southeastern United States (Washington et al., 2000). Barnston et al. (1991) found that

the negative phase of TNH pattern was often observed when the pacific warm condition

(El Niio) is present, which would eventually affect the climate conditions in the

southeastern United States.

Quasi-biennial oscillation (QBO) index

The QBO represents the oscillation of zonal winds in the stratosphere (at 30 mb)

over the equator in the Pacific that blow eastward or westward in a cycle that averages

about 28 months. The effect of QBO in southeastern United States is evident due to its

close association with the ENSO (Thompson et al., 2001). For instance, during an El

Niio years with an easterly QBO the temperature tend to be below normal across the

southeastern United States (Barnston et al., 1991).

Correlation Analysis

The correlation analysis of climate indices with precipitation and temperature and

with cotton yield residuals was carried out using Pearson correlation method. The

statistical significance of the correlations was evaluated atp < 0.10 .

In the following sections correlations of climate indices with temperature,

precipitation, and cotton yield are described. The correlation analysis of cotton yield with

precipitation and temperature was not performed in this study, because in a parallel









study Baigorria et al. (2007) correlated cotton yield with surface temperature and rainfall

for 57 cotton producing counties in Georgia and Alabama. The results showed that

surface temperature and rainfall in this region were significantly correlated with cotton

yield for more than 50% of the counties processed. Results also showed that the

correlations were highly significant, especially for July rainfall for 84% of the counties.

Since the clear evidence of significant correlation of cotton yield with surface

temperature and rainfall was shown by Baigorria et al. 2007, it was not re analyzed in

this study.

Correlations of Climate Indices with Temperature and Precipitation

It was unclear whether the monthly climate indices prior to the cotton growing

season were significantly correlated with monthly temperature and precipitation during

the cotton growing season for all cotton growing counties in Georgia and Alabama

selected in this study. Climate indices for January and February were correlated with

May-September temperature and precipitation for 1966-2007.The significant

correlations of climate indices with temperature and precipitation during the cotton

growing season could provide a basis for using climate indices to forecast cotton yield.

Correlations of Climate Indices with Cotton Yield

Climate indices for January and February were correlated with county cotton yield

for 1966-2007. Correlation analyses were carried out for 64 cotton producing counties of

Georgia and Alabama. Since the correlations of cotton yield with temperature and

precipitation during the growing season is known (Baigorria et al., 2007), identifying

statistically significant correlations of climate indices with climate variables and cotton

yield would help us understand the behavior of climate- cotton yield interactions and the

forecasting of cotton yield.


108









Principal Component Regression

All climate indices were summarized using a principal component analysis (PCA).

The PCA is a data transformation technique that transforms original highly correlated

variables into a new set of independent variables in a way that the first principal

component (PC) describes the highest variance followed by the second PC and so on

(Massy, 1965).

The motivation for using principal components of climate indices instead of their

original values was because of the significant correlations among the climate indices

(Barnston et al., 1991; Barreiro et al., 2005). If highly correlated climate indices were

used in the regression model, then the assumption of mutually independent explanatory

variables is violated. Instead, the principal components of climate indices transform

them into mutually independent variables that can be effectively used in multiple linear

regression models. Another leading advantage of using PCA is that it is an efficient

data-reduction technique. For instance, if the maximum variances of two climate indices

are summarized by principal component 1, then instead of using two indices one can

use just one PC to utilize the information.

The principal component regression (PCR) model uses principal components as

explanatory variables. The dependent variable for this model was detrended historic

cotton yield and independent variables were principal components of climate indices.

The general form of model is shown below:

Yreszduals = Po + X +...+ -'X- + E (5-2)

Where, Yred,,,ua is cotton yield residual for a given county, and X ... Xp are the

principal components of climate indices retained in the PCR model based on backward


109









stepwise regressions. The residual errors from multiple regression analysis was tested

for normality. This is important because of the assumption in regression analysis that

the residual errors are normally distributed.

Leave One Out Cross Validation

The yield forecasts from different models for each county were evaluated using

cross validation. This statistical validation approach can be used to validate the model

when data are limited. With the cross validation approach, observed data are iteratively

and exhaustively used for model testing, resulting in more reliable evaluation than

getting estimates from the two-group partition method and less biased than estimates

derived from calibration-dependent dataset (Jones and Carberry, 1994). In this method,

n-1 data were used to estimate the parameters for the regression model and the one left

out data point was used for model evaluation. By an iterative process, all the data points

were used for validation. The skill of the forecast was evaluated using the statistically

significant correlations and mean squared error (MSE) between observed and

forecasted cotton yield.

Categorical Yield Forecast Contingency Table

Yield forecasts obtained from the principal component regression models were

divided into two categories; above average and below average cotton yield. A negative

cotton yield residuals falls in the below average yield category and vice versa. A 2x2

contingency table (Table 5-1) was used to evaluate the skill of the forecast. Categorical

cotton yield forecasts were evaluated for statistical significance using the Pearson's chi-

square test of association (Plackett, 1983). This method tests an association between

observed and forecasted categorical cotton yield. Statistical significance were evaluated

atp < 0.10.


110









Since it is not possible to forecast absolute cotton yields accurately, knowing

whether to expect an above average or below average yield for the coming season is

also useful information to growers. The percentages of correct yield forecasts, the

probability of detecting (POD) above average yield, and the probability of detecting

below average yields were calculated using the following equations and Table 5-1.

PercentCorrect = 100 [(A + E)/I] (5-3)

PODAboveAverge = EF (5-4)

PODBelowAverge =AIC (5-5)

The PercentCorrectin (3-3) represents the ratio of total number of correct yield

forecasts to the total number of forecasts. The PODAboveAveg (3-4) shows the ratio of

total number of correct above average forecast to the total number of observed above

average cotton yield residuals. The PODBelowAvere (3-5) shows the ratio of total number

of correct below average yield forecasts to the total number of observed below average

cotton yield residuals.

Results and Discussion

Historic Cotton Yield Data

Time-series of historic cotton yield showed a gradual upward trend over the time

period of 1951-2007. The gradual upward trend was expected due to technological

improvements over time. It was assumed that the technological trend over time was

linear; the historic cotton yield data fit well the linear trend line. Once, the trend was

removed, variability in cotton yield residuals was observed around the trend line closer

to zero. This variability in cotton yield residuals could be due to the effect of climate

variability, henceforth were analyzed for their correlations with climate indices.











Correlation Analysis

Correlations of climate indices with temperature and rainfall

Overall, the correlations of climate indices with temperature showed statistically

significant results atp < 0.10. Figure 5-1 shows the most prominent correlations of all

seven climate indices with temperature. It was interesting to note that all seven climate

indices exhibited maximum correlations with temperature during the month of July.

Climate indices such as NOI, NP, and TNH exhibited statistically significant correlations

with more counties than the other indices. Except for one county in Alabama, all seven

counties together showed statistically significant correlations with temperature in all

cotton producing counties considered in this study.

As can be seen from Figure 5-1 the NOI, NP, and TNH indices were negatively

correlated with July temperature. This means that when these climate indices are in a

negative phase during January and February, July temperature is expected to be above

average for the southeastern United States. On the other hand, AMM, QBO, TNA, and

ONI were positively correlated with July temperature. AMM, TNA, and ONI are Atlantic

and Pacific SSTs and hence, warming of the SST during January and February was

responsible for higher July temperatures.

The correlations of all seven climate indices with rainfall are shown in Figure 5-2.

The NOI and NP exhibited a negative correlations with July rainfall; opposite in sign to

their correlations with July temperature. TNH did not exhibit strong correlations with July

rainfall; however, its correlation was strong for September rainfall in a majority of the

counties in Georgia and several counties in Alabama. It was interesting to note that the

TNA showed negative correlations with June rainfall and positive correlations with


112









September rainfall. These opposite correlations with June and September could

eventually affect the cotton yield in the same manner because higher rainfall during the

early growing season is favorable to cotton but the same during the maturity would

adversely affect cotton yield.

Correlation of climate indices with cotton yield

Figure 5-3 shows correlations of climate indices with cotton yields. The NOI index

was positively correlated with cotton yield. NOI was positively correlated with July

precipitation and negatively correlated with July temperature; hence a positive

correlation with cotton yield was expected for NOI. The NP pattern had a strong

negative correlation with July temperature, but the correlations with cotton yield was

positive for all the counties. This means that during the negative phase of NP, it is likely

to have higher July temperature and lower cotton yield. The month of July typically

coincides with the flowering stage of cotton growth in southeastern United States.

Increased temperature during July stimulates the photosynthesis and leaf expansion

and crop water requirements. This could increase water stress in non-irrigated cotton

plants and also reduce the allocation of daily assimilates to the fruit. As a result, final

cotton yield could be either positively or negatively affected by July temperature.

TNA and AMM showed negative correlations with cotton yield. As mentioned in the

previous section, TNA exhibited negative correlation with June and positive correlation

with September rainfall. Both would adversely affect cotton yield and hence be

consistent with the negative correlation of TNA with cotton yield. TNH was also

negatively correlated with cotton yield while it had a positive correlation with September

rainfall. Rainfall during the late maturity stage of cotton has limited or no use to the

plant, on the contrary; it could create an adverse effect. Frequent precipitation during


113









September and October months is the main cause of one of the most common cotton

disease called hard lock of cotton, which would significantly reduce cotton yield.

It was interesting to note that NOI was significantly correlated with rainfall for more

counties than it was correlated with cotton yields. The possible explanation could be an

effect of irrigation. If irrigation is a typical practice in those counties, then the effect of

rainfall on cotton yield would be negligible and hence yield for those counties may lack

significant correlations with NOI.

As can be seen in Figure 5-3, a single month climate index alone was not

sufficient to correlate significantly with cotton yield for all counties. All seven indices

together were significantly correlated with cotton yield and climate for all the counties. In

general, the correlations of climate indices with cotton yield and climate during the

growing season showed potential use of forecasting cotton yield for the southeastern

United States.

Principal Component Regression

Table 5-3 shows significant PCs retained in the backward stepwise regression

procedure and Table 5-4 shows the loadings of climate indices in the principal

components. Principal component 1 (PC1) was retained in 44% of the regression

models for counties in Georgia. The loadings show that the TNA had the highest loading

in PC1, followed by ONI and NOI indices. In contrast, PC1 was only significant in 22%

of the counties in Alabama. Conversely, Principal Component 3 (PC3) was significant in

43% of the models for counties in Alabama but only in 20% of the models for counties in

Georgia. It can be seen from Table 5-4 that the PC3 had the highest loadings from the

QBO index. This was expected because correlations of QBO with cotton yield were

more prominent in counties of Alabama than in Georgia (Figure 5-3). Interestingly,


114









Principal Component 11 (PC 11) was significant for approximately 50% of the counties

for all the counties in Georgia and Alabama. Based on the loadings in PC 11 it can be

seen that the TNA and AMM had maximum loadings compared to other indices.

Significant PCs retained by backward stepwise regression model were not in top

to down order (Table 5-3). In other words, PC1 was not necessarily the most significant

PC for all the counties. This was due to the fact that the first PC explains the maximum

variance among the explanatory variables but not necessarily of the dependent variable

in principal component regression (Sutter et al., 1992). For example, loadings of QBO

index were higher in PC3 compared to PC1. Since QBO correlation with cotton yield

was more prominent in Alabama; PC3 was significant more times than PC1.

Leave One Out Cross Validation

The accuracy of cotton yield forecasts by principal component regression models

were evaluated with the leave one out cross validation approach. 77% of the counties in

Georgia and 70% of the counties in Alabama showed significant correlations between

observed and cross validated cotton yield residuals (Figure 5-4, Table 5-2). The highest

significant correlation of 0.50 was obtained for Shelby County in Alabama whereas the

lowest significant correlation of 0.22 was obtained for Colquitt County in Georgia and

Lee County in Alabama. A total of 8 out of 34 counties in Georgia and 9 out of 30

counties in Alabama did not show significant correlations between observed and

forecasted cotton yields. The possible reasons for this could be that the proportion of

irrigated cotton yields for those counties might be higher than rainfed cotton. The

irrigated cotton could diminish the direct impact of rainfall on the cotton yield and hence

result in non-significant correlations. For example, all seven climate indices showed

statistically significant correlations with climate during the cotton growing season in


115









Calhoun County in Georgia but did not show a significant correlation with cotton yield

and subsequently no predictability. It is possible that the climate indices show significant

correlation with climate during the cotton growing season but not with cotton yield, if the

reported cotton yield came from irrigated practices.

Baigorria et al. (2008) stated that the highest yield counties in the southeastern

United States showed weakest predictability. The speculation was that the climate

based yield predictability is weaker in counties with greater proportion of cultivated

areas under irrigation. The results obtained in this study are in agreement with that

speculation because some of the highest cotton yielding counties, such as Dooly,

Colquitt, Mitchell, and Crisp showed little or no predictability. Unfortunately, the NASS

data do not distinguish between irrigated and rainfed cotton yield, but this could be the

possible explanation of weaker predictabilities for those counties.

Figure 5-5 shows the time series comparisons between historic cotton yield

residuals and cross validated cotton yield for the highest and the lowest correlated

counties in Georgia and Alabama. It was evident that the principal components

regression models of climate indices were able to capture year-to-year variability in

cotton yield fairly well. The mean squared errors (MSE) between the historic cotton

residuals and cross validated cotton yields were within the range of 0.03-0.10. It can be

seen from Figure 5-6 that the average errors across all the counties was normally

distributed with mean being very close to 0. Overall, the cotton yield residuals

forecasted with principal components of climate indices showed good predictability of

cotton yields.


116









Categorical Yield Forecast Contingency Table

Results obtained from the contingency table are shown in Table 5-5 and Figures

5-7 and 5-8. A total 67% of the counties in Georgia and 73% of counties in Alabama

showed statistically significant association between categorical observed and cross

validated cotton yield forecast.

A total of 94% of the counties showed that the categorical cotton yield forecast

obtained from the cross validated cotton yield at the lead time of approximately two to

three months before planting (In February) was correct more than 50% of the time. The

highest percent correct score was obtained for Bulloch County in Georgia that had

correct categorical forecasts 73% of the time based on cross validated results. Figure 5-

7 shows the spatial distributions of percent correct categorical cotton yield forecasts for

counties in Georgia and Alabama. It was interesting to note that except for Thomas

County in Georgia, the categorical cotton yield forecast was correct more than 50% of

the time even though eight counties that were not significantly correlated with cross

validated cotton yields. This shows that even if the model was not able to significantly

capture the variability of the observed cotton yield residuals, a majority of forecasts

were in the right category (above average or below average) more than 50% of the

time.

As we know, the probability of detecting above average or below average yield is

50% purely by chance. With the categorical forecast of cotton yield obtained from the

principal components of climate indices, the probability of detecting above average or

below average yields was better than chance for 88% and 94% of the counties,

respectively. In applications of these results, growers might be more interested in









knowing if they would expect a better than average yield or vice versa for their decision

making processes.

Conclusions

The association of seven climate indices with climate during the cotton growing

season and with county average historic cotton yields was evaluated using Pearson's

correlations. January and February monthly climate indices, which were months prior to

the cotton growing season, exhibited statistically significant correlations with climate

during the cotton growing season as well as with cotton yields. July temperature

showed the strongest correlations with all seven climate indices whereas the strongest

correlation of climate indices with rainfall varied between June, July, August, and

September.

The accuracy of cotton yield forecasts based on principal component regressions

were evaluated with the leave one out cross validation approach. With a lead time of

approximately 2 months before the typical planting period on the southeastern United

States, about 77% of the counties in Georgia and 70% of the counties in Alabama

showed statistically significant correlations between observed and forecasted cotton

yields. The MSE between observed and cross validated cotton yield residual forecasts

were in the range of 3-11%.

Categorical cotton yield forecasts obtained from the cross validated results were

evaluated using the skill measures of percent correct forecasts, probability of detecting

above average cotton yield, and probability of detecting below average yields. 94% of

the counties showed the categorical cotton yield forecast obtained at a lead time of

approximately two months before planting (In February) was correct for more than 50%

of the time. The probabilities of detecting above and below average yields were better


118









than chance in 88% and 94% of Alabama and Georgia counties, respectively. The

principal component regression of climate indices showed potential to become a useful

tool to forecast cotton yield with a lead time of approximately two months before the

typical cotton planting time of May first week in the southeastern United States.


119





































Z Non Significant

Negative Significant (< -0.26)

Positive Significant (> 0.26)

No Data


Figure 5-1. Correlations of climate indices with temperature during the cotton growing
season. A) AMM-July temperature B) NOI-July temperature C) NP-July
temperature D) QBO-July temperature E) TNA-July temperature F) ONI-July
temperature G) TNH-July temperature. Correlations greater or less than 0.26
and -0.26 were significant atp < 0.10 .


120

















LJJ 7 A QLJ B









C D









E F









G H

Figure 5-2 Correlations of climate indices with rainfall during the cotton growing
season. A) AMM-June rainfall B) NOI-July rainfall C) NP-July rainfall D) QBO-
July rainfall E) TNA-June rainfall F) TNA-September rainfall G) ONI-August
rainfall H) TNH-September rainfall. Legends are same as Figure 3-1.
Correlations greater or less than 0.26 and -0.26 were significant atp < 0.10 .








































A Non Significant

Negative Significant (< -0.26)

Positive Significant (> 0.26)

No Data


Figure 5-3. Correlations climate indices with cotton yield. A) AMM B) NOI C) NP D)
QBO E) TNA F) ONI G) TNH. Correlations greater or less than 0.26 and -0.26
were significant atp < 0.10.


122


































K Non Significant
0.22 0.29
0.30 0.39
> 0.40
No Data

Figure 5-4. Correlations of historic cotton residuals with cross validated cotton yield
residuals using the principal component regression of January and February
climate indices. Correlations greater than 0.22 are significant at p < 0.10 (N =
57).


123











0.80
0.40
0.00 -
-0.40
-0.80 I--I-I---
1951 1961 1971 1981 1991 2001

-- Observed yield residuals -- Cross validated yield residuals
A


0.80
0.40
0.00
-0.40
-0.80 ..........
1951 1961 1971 1981 1991 2001
-- Observed yield residuals -o- Cross validated yield residuals
B


0.80
0.40
0.00 -
-0.40
-0.80 .-. .
1951 1961 1971 1981 1991 2001

-*- served yield residuals -o- Cross validated yield residuals
C


0.80
0.40
0.00-
-0.40-
-0.80 .
1951 1961 1971 1981 1991 2001
-- Served yield residuals -- Cross validated yield residuals
D

Figure 5-5. Time series comparison between observed and cross validated cotton yield
residuals for four counties of Alabama and Georgia that showed the
maximum (A and B) and minimum correlations (C and D). A) Bulloch, B)
Shelby, AL C) Colquitt, GA, and D) Lee, AL.


124














700

600

S500

S400

300 -

200

100


O Il I l ^ l ll lb
0' 0' P' P' O' 0' 0' 0'

Yield Residual Error (Kg/ha)


Figure 5-6. Histogram of residual errors across the entire cross validated county cotton
yields. The errors were normally distributed with / = -0.0001 and o- = 0.24


125






















A














B

< 50%
50% 60%
60% 70%
> 0.70%
No Data

Figure 5-7. Probability of detecting county level cotton yields using cross validated
cotton forecasts for two categories. A) Probability of detecting above average
cotton yield. B) Probability of detecting below average cotton yield.


126

























< 50%
50% 60%
60% 70%
> 0.70%
No Data

Figure 5-8. Percent correct cross validated cotton yield forecasts based on principal
components regression model of climate indices and contingency table.









Table 5-1. A 2x2 contingency table for categorical cotton yields.
Observed Forecasted Yield Total
Yield Below Above
Below A B C
Above D E F
Total G H I


128










Table 5-2. Pearson's correlations and MSE for cross validated cotton yields for the
counties in Georgia and Alabama. The and represents significance at


0.01, 0.05, and 0.1 probability
correlations.


levels. The "ns" represents non-significant


Counties
BEN HILL
BLECKLEY
BROOKS
BULLOCH
BURKE
CALHOUN
CHANDLER
CLAY
COFFEE
COLQUITT
CRISP
DODGE
DOOLY
EARLY
EMANUEL
HOUSTON
IRWIN
JEFFERSON
JENKINS
LAURENS
LEE
MACON
MITCHELL
PULASKI
RANDOLPH
SCREEN
SUMTER
TERRELL
THOMAS
TIFT
TURNER
WASHINGTON
WILCOX
WORTH


Georgia
Correlations
0.42
0.23
0.42
0.46
0.30*
0.33*
ns
0.48
0.28
0.22
ns
0.28
ns
0.37
0.42
ns
0.35
0.29*
0.31
ns
0.33
0.37
ns
0.35
0.37
ns
0.34
0.31
ns
0.46
0.40
0.29*
ns
0.30*


MSE
0.07
0.07
0.04
0.06
0.06
0.03
0.08
0.04
0.10
0.04
0.05
0.06
0.09
0.05
0.07
0.06
0.05
0.08
0.08
0.08
0.07
0.06
0.06
0.06
0.05
0.08
0.07
0.04
0.05
0.04
0.06
0.07
0.06
0.05


Counties
AUTAUGA
BARBOUR
BLOUNT
CALHOUN
CHEROKEE
COFFEE
COLBERT
COVINGTON
CULLMAN
DALE
DALLAS
ELMORE
ESCAMBIA
ETOWAH
FAYETTE
HOUSTON
LAUDERDALE
LAWRENCE
LEE
LIMESTONE
LOWNDES
MACON
MADISON
MARENGO
MONROE
MONTGOMER'
PICKENS
SHELBY
TALLADEGA
TUSCALOOSA


Alabama
Correlations
0.47
0.30
0.38
ns
0.44
ns
0.25
0.29
ns
0.45
0.46
0.42
0.25
ns
0.46
0.35*
ns
0.30
0.23
0.37
0.49
0.28
ns
ns
0.29
Y 0.30
0.44
0.50
ns
ns


129


MSE
0.07
0.08
0.03
0.09
0.06
0.11
0.06
0.07
0.07
0.09
0.06
0.10
0.07
0.06
0.10
0.09
0.08
0.08
0.06
0.08
0.07
0.05
0.09
0.09
0.05
0.07
0.05
0.05
0.04
0.06










Table 5-3. Significant principal components (PCs) of principal component regression
models for cotton producing counties of Georgia and Alabama


Georgia

Counties
BEN HILL
BLECKLEY
BROOKS
BULLOCH
BURKE
CALHOUN
CHANDLER
CLAY
COFFEE
COLQUITT
CRISP
DODGE
DOOLY
EARLY
EMANUEL
HOUSTON
IRWIN
JEFFERSON
JENKINS
LAURENS
LEE
MACON
MITCHELL
PULASKI
RANDOLPH
SCREEN
SUMTER
TERRELL
THOMAS
TIFT
TURNER
WASHINGTON
WILCOX
WORTH


Significant
PCs
3,5,12,13,14
11,12
5,8,13
1,9,13,14
1,6,11
5,8,11
1,9
1,5,6,11
7,9,13
3,14
3,6
5,11,12
11
1,3,8,14
1,5,9,12,13
1,11
9,12
1,7,11,13
1,2,13
12
6,9,13
1,3,11,14
1
3,6,11
1,5,6,11
12
1,6,11,13
5,11,12
1
2,8,11,12,14
1,6,8,11,12,14
6,11
5,6,14
3.5.12.14


Alabama

Counties
AUTAUGA
BARBOUR
BLOUNT
CALHOUN
CHEROKEE
COFFEE
COLBERT
COVINGTON
CULLMAN
DALE
DALLAS
ELMORE
ESCAMBIA
ETOWAH
FAYETTE
HOUSTON
LAUDERDALE
LAWRENCE
LEE
LIMESTONE
LOWNDES
MACON
MADISON
MARENGO
MONROE
MONTGOMERY
PICKENS
SHELBY
TALLADEGA
TUSCALOOSA


Significant
PCs
2,4,5,9,11
8,11
12
1
2,3,5,11,12
3,7
3,6,11
3,5
2
1,5,7,8,11,14
4,5,9,11
1,2,5,9,11
1
2,3
3,8,9,11
3,4,5,7,11
3
3,6,11
5,11
3
1,2,3,4,9,11
5,11,13
3
6
6
2,7,8
1,3,6,9,11
2,4,5,9,10,11
1
6


130










Table 5-4. Loadings of principal components (PCs) of climate indices
Indices PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
ONIJan 0.73 0.44 0.30 0.13 -0.20 -0.32 -0.03 0.09 0.03 -0.01
ONIFeb 0.74 0.45 0.33 0.10 -0.17 -0.32 0.00 0.05 0.01 -0.02
AMMJan 0.30 -0.89 -0.15 0.04 -0.02 0.18 0.12 -0.07 0.02 -0.11
AMMFeb 0.56 -0.77 -0.08 0.03 -0.02 0.10 0.08 0.01 -0.06 0.23
NOIJan -0.72 -0.40 0.04 0.28 -0.22 -0.13 -0.06 0.23 -0.33 -0.05
NOIFeb -0.56 -0.45 -0.16 -0.40 -0.36 -0.15 -0.03 0.31 0.23 0.02
NPJan -0.46 -0.25 0.00 0.54 0.55 -0.25 0.15 0.14 0.17 0.02
NPFeb -0.55 -0.37 0.15 -0.28 -0.04 -0.52 0.33 -0.29 -0.06 0.02
QBO_Jan 0.15 0.28 -0.91 0.11 -0.07 -0.15 -0.01 -0.04 -0.04 -0.01
QBO_Feb 0.16 0.23 -0.92 0.09 -0.11 -0.15 0.04 -0.02 0.01 0.02
TNAJan 0.61 -0.72 0.00 0.14 -0.15 -0.03 0.07 -0.04 0.07 -0.23
TNAFeb 0.80 -0.52 0.05 0.12 -0.10 -0.08 0.08 0.07 -0.02 0.13
TNHJan -0.26 0.54 0.08 0.21 -0.35 0.30 0.61 0.05 0.03 0.01
TNH Feb -0.58 -0.17 0.14 0.48 -0.46 0.02 -0.30 -0.24 0.14 0.07


PC11
0.07
0.07
0.15
0.09
0.01
0.01
0.01
0.00
0.02
-0.02
-0.09
-0.16
0.00
0.00


PC12 PC13 PC14
0.02 0.00 0.07
-0.01 0.01 -0.07
0.03 0.07 0.00
-0.02 -0.06 0.00
0.01 0.00 0.00
-0.01 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
-0.14 0.02 0.01
0.14 -0.02 -0.01
-0.02 -0.06 0.00
0.00 0.06 0.00
-0.01 0.00 0.00
0.00 0.00 0.00









Table 5-5. Skills of categorical cross validated cotton yield forecasts for
Georgia and Alabama.


Georgia
%
Counties correct
BEN HILL*** 71.93
BLECKLEY** 61.40
BROOKS 56.14
BULLOCH*** 73.21
BURKE* 59.65
CALHOUN 57.89
CANDLER** 61.40
CLAY*** 68.52
COFFEE 56.36
COLQUITT* 59.65
CRISP* 57.89
DODGE** 63.16
DOOLY** 64.91
EARLY*** 68.42
EMANUEL*** 62.50
HOUSTON 52.73
IRWIN*** 68.42
JEFFERSON 56.14
JENKINS 51.85
LAURENS 54.39
LEE 58.18
MACON*** 66.07
MITCHELL 54.39
PULASKI** 63.16
RANDOLPH** 63.64
SCREEN 52.63
SUMTER** 61.40
TERRELL*** 66.67
THOMAS 28.07
TIFT*** 71.93
TURNER*** 66.67
WASHINGTON** 59.26
WILCOX 54.39
WORTH*** 71.93


POD
Above
0.72
0.57
0.56
0.70
0.57
0.62
0.57
0.69
0.53
0.62
0.57
0.62
0.57
0.71
0.67
0.48
0.68
0.57
0.52
0.59
0.59
0.68
0.65
0.62
0.62
0.59
0.64
0.62
0.23
0.75
0.59
0.62
0.52
0.69


POD
Below
0.71
0.66
0.56
0.76
0.62
0.55
0.66
0.68
0.62
0.57
0.59
0.64
0.72
0.66
0.59
0.57
0.69
0.56
0.52
0.50
0.58
0.64
0.39
0.64
0.65
0.46
0.59
0.71
0.32
0.70
0.75
0.57
0.57
0.75


Counties
AUTAUGA*
BARBOUR**
BLOUNT***
CALHOUN
CHEROKEE**
COFFEE**
COLBERT**
COVINGTON**
CULLMAN
DALE
DALLAS***
ELMORE**
ESCAMBIA***
ETOWAH*
FAYETTE**
HOUSTON**
LAUDERDALE**
LAWRENCE**
LEE**
LIMESTONE***
LOWNDES***
MACON
MADISON*
MARENGO*
MONROE
MONTGOMERY
PICKENS**
SHELBY**
TALLADEGA
TUSCALOOSA***


Alabama

% correct
55.77
60.78
64.58
38.46
61.11
61.11
61.11
59.62
47.92
53.19
64.15
55.56
59.26
51.85
64.58
61.54
61.11
64.81
58.82
66.67
70.83
53.85
59.26
55.32
50.00
54.35
63.83
63.46
48.98
50.00


counties of


POD
Above
0.48
0.67
0.71
0.64
0.65
0.58
0.58
0.54
0.56
0.48
0.58
0.61
0.59
0.62
0.57
0.69
0.56
0.60
0.61
0.63
0.68
0.58
0.54
0.59
0.50
0.63
0.58
0.61
0.64
0.44


POD
Below
0.64
0.57
0.58
0.08
0.57
0.64
0.63
0.64
0.39
0.58
0.69
0.52
0.59
0.43
0.70
0.54
0.66
0.69
0.57
0.70
0.74
0.50
0.65
0.52
0.50
0.48
0.71
0.67
0.33
0.56


132









CHAPTER 6
CONCLUSIONS AND FUTURE WORK

The main focus of this dissertation was to use climate forecasts and climate

indices to forecast cotton yield for the southeastern United States using the CROPGRO-

Cotton model and an empirical model. Overall, the use of climate information provided

significant skill in forecasting cotton yield for the southeastern United States.

In order to achieve the overall research question presented in Chapter 1, the

dissertation research was organized into four specific objectives under four main

chapters; global sensitivity analysis of CROPGRO-Cotton model (Chapter 2), parameter

estimation and uncertainty analysis (Chapter 3), In-season updates of cotton yield

forecasts using the CROPGRO-Cotton model (Chapter 4), and cotton yield forecasting

for the southeastern United States using climate indices (Chapter 5).

The global sensitivity analysis results improved our understanding of how sensitive

the CROPGRO-Cotton model is to the selected parameters over the range of parameter

uncertainties. The specific leaf area (SLAVR) followed by extinction coefficient (KCAN),

and fraction of daily assimilates allocated to seed (XFRT) were important model

parameters that influenced the simulated cotton yield. The duration between emergence

and flowering (EM-FL), and first seed to physiological maturity (SD-PM) parameters

were most important parameters for physiological maturity. Results also showed that

global sensitivity analysis was a better method than local sensitivity analysis due to the

fact that local sensitivity analysis did not take into account the interactions among the

parameters.

Results from global sensitivity analysis were utilized to estimate parameters and

perform an uncertainty analysis in Chapter 3. The parameter estimates obtained by the


133









generalized likelihood uncertainty estimation technique represented an improvement in

the parameters previously available in DSSAT for DP-555 cotton cultivar. The output

uncertainty confidence intervals at 95% limit covered approximately 80% of the

measurements. This study also demonstrated an efficient prediction of uncertainties in

model parameters and outputs using the widely accepted GLUE technique. There was

good overall agreement of the CROPGRO-Cotton model with the field measurements

using the estimated parameters.

The parameter estimation and uncertainties of the CROPGRO-Cotton model in

chapter 3 provided the basis in using it for cotton yield forecasting. In-season updating

the CROPGRO-cotton model with observed weather data along with the climatology

improved the accuracy of the cotton yield forecasts over time. The reduction in the

residual errors and standard deviations were statistically significant with in-season

updates. Approximately 90% of the cotton yield forecasts showed reduction in standard

deviations and 56% of the cotton yield forecasts showed reduction in residual errors

among the 55 years tested. In general, three ENSO indices among them selves and the

comparison between climatology based and ENSO tailored cotton yield forecasts did

not show statistically significant differences in the standard deviations and residual

errors of forecasted cotton yield.

As an alternative of using the crop model, cotton yield forecasts were also

evaluated using historical county yield and climate data in an empirical model in this

dissertation. Chapter 5 was mainly focused on forecasting county cotton yield using

climate indices. The empirical principal component regression models of climate indices

provided significant skills in forecasting cotton yield for the southeastern United States.


134









In general, with a lead time of approximately 2 months before the typical planting period

in the southeastern United States in May, about 77% of the counties in Georgia and

70% of the counties in Alabama showed statistically significant correlations between

observed and forecast cotton yields. The MSE between observed and cross validated

cotton yield forecasts were in the range of 0.03-0.11. In addition to that, the skills of

categorical cotton yield forecasts were evaluated with a contingency table. 94% of the

counties showed the categorical cotton yield forecast obtained at a lead time of

approximately two months before planting (In February) was correct more than 50% of

the time.

In general, results showed potential for significant skill in using climate forecasts to

forecast cotton yield for the southeastern United States. Improvements to the current

forecasts can be made as and when climate forecasts are improved. However, in order

to use these forecasts in decision making, users must integrate their perceptions of

forecast uncertainty in the context of their goals, constraints, and risk tolerance as they

manage their agricultural production systems (Jones et al., 2003).


135









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BIOGRAPHICAL SKETCH

Tapan Pathak was born in a city called Vadodara and grew up in a beautiful city

and a Gujarat state capitol Gandhinagar, India. He went to St.Xavier's High School. He

earned his Bachelors degree in Agricultural Engineering from Gujarat Agricultural

University in 2000. In January, 2001 he joined Utah State University for MS program

and earned his MS degree in Irrigation Engineering in 2004. After completion of MS

degree program, he joined UF for the Ph.D. in 2005 and finished his Ph.D. in 2010. He

is currently working as a faculty in the school of natural resources at the University of

Nebraska, Lincoln.


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1 COTTON YIELD FOR ECASTING FOR THE SOUTHEASTERN UNITED STATES By TAPAN BHARATKUMAR PATHAK A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE O F DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010

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2 2010 T apan Pathak

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3 To, my loving wife my parents, and my f amily

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4 ACKNOWLEDGMENTS My PhD dissertation was one of the most important life changing journeys of my life I have seen good time s as well as hard times throughout my PhD student life I enjoyed the good times and tried to learn and improve from the experiences of hard time. PhD degree was like a dream for me and this dream would not have been possible without constant high quality guidance and support from my major advisor Dr. James W. Jones. He is one of the best advisors and I was fortunate to have him as my PhD supervisor. He always encouraged me to explore innovative ideas but at the same time made sure that those ideas are exec uted in a systematic scientific manner. I have seen so much professional improvement in myself in last 5 years, which was solely due to his valuable guidance There is so much to say about Dr. Jones and it is hard to narrate on a single page, but I must sa y that I will have my deepest respect for him throughout my career and will always try to follow his advice for my own professional development. I would also like to express my deepest respect and gratitude towards my PhD co advisor Dr. Clyde W. Fraisse. He was always helpful in providing me with new research ideas. His enthusiasm over implementing them always motivated me. I have a lot to learn from him and this dissertation would not have been possible without his support. I would like to thank my commit tee members, Dr. David Wright, Dr. James Heaney, and Dr. Gregory Kiker for their valuable guidance and recommendations. I am also thankful to Dr. Kenneth Boote for allowing me use his lab instruments for my research and also for his valuable advice. I woul d also like to extend my acknowledgement to Dr. Hoogenboom and Dr. Jasmeet Judge for providing me with experimental data to run my analyses. I am greatly thankful to all my friends at McNair

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5 Bostick Simulation Laboratory (MBSL) for keeping cheerful yet non disturbing work environment. I really enjoyed working with them I will always miss him I would like to thank all my family members for their constant support and motivation throughout my PhD. I wish I could list out and thank all of them individually, but I am afraid that it will take up many more pages. I would like thank my mom and dad for their blessings, inspiration, and unconditional care. No words are enough to show my gratitude towards t hem. Finally, I have an opportunity to thank the most beautiful, loving, caring woman of my life, Rucha for her countless sacrifices and constant support throughout my PhD. She has seen all the ups and downs with me and I could not have done my PhD without her company. At the end, I would like to acknowledge our little lucky charm who is soon to arrive in this world

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 9 LIST OF FIGURES ................................ ................................ ................................ ........ 12 ABSTRACT ................................ ................................ ................................ ................... 14 1 INTRODUCTION ................................ ................................ ................................ .... 15 2 Use of Global Sensitivity Analysis for CROPGRO Cotton Model Development ...... 19 Introduction ................................ ................................ ................................ ............. 19 Materials and Methods ................................ ................................ ............................ 23 Overview of CSM CROPGRO Cotton Model ................................ .................... 23 Site and Experiment Description ................................ ................................ ...... 24 Sensitivity Analysis ................................ ................................ ........................... 25 Local sensitivity ................................ ................................ .......................... 26 Global sensitivity ................................ ................................ ........................ 26 Results and Discussion ................................ ................................ ........................... 30 Local Sensitivity Analysis ................................ ................................ ................. 30 Global Sensitivity Analysis ................................ ................................ ................ 30 Conclusions ................................ ................................ ................................ ............ 33 3 Uncertainty Analysis and Parameter Estimation of CROPGRO Cotton Model .... 45 Introduction ................................ ................................ ................................ ............. 45 Materials and Methods ................................ ................................ ............................ 48 Description of Field Sites and Measured Datasets ................................ ........... 48 The CROPGRO Cotton Model ................................ ................................ ......... 49 Uncertainty Analysis and Parameter Estimation Procedures ........................... 50 Parameter selection and prior distributions ................................ ................ 50 Likelihood function ................................ ................................ ..................... 52 Posterior distribution ................................ ................................ .................. 53 U ncertainty bounds for model predictions ................................ .................. 54 Statistical methods for model testing ................................ ......................... 55 Results and Discussion ................................ ................................ ........................... 56 Simulations Using Unmodified Parameters ................................ ...................... 56 Parameter Estimates and Uncertainties ................................ ........................... 57 Comparison wi th prior distribution ................................ .............................. 57 Comparison with DSSAT default values ................................ .................... 58 Model predictions based on estimated parameters ................................ .... 59 Model output uncertainties ................................ ................................ ......... 60 Conclusion ................................ ................................ ................................ .............. 61

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7 4 In Season Updates of Cotton yield forecasts u sing cropgro cotton model .............. 74 Introduction ................................ ................................ ................................ ............. 74 Material and Methods ................................ ................................ ............................. 77 Outl ine of the Forecasting Method ................................ ................................ ... 77 Model Description and Input Data ................................ ................................ .... 77 Comparison between Before Season and In Season Cotton Yield Forec asts Based on Climatology ................................ ................................ ................... 78 Comparison of Cotton Yield Forecasts Based on ENSO Indices ..................... 79 Comparison Between Climatology Based and EN SO Tailored Cotton Yield Forecast ................................ ................................ ................................ ........ 80 Results and Discussion ................................ ................................ ........................... 80 Comparison between Before Season and In Season Cotton Yield Forecasts b ased on Climatology ................................ ................................ .................... 80 Comparison of Cotton Yield Forecasts based on ENSO Indices ...................... 81 El Nio phase ................................ ................................ ............................ 81 La Nia phase ................................ ................................ ............................ 82 Neutral phase ................................ ................................ ............................. 82 Comparison Between Climatology Based and ENSO Tailored Cotton Yield For ecast ................................ ................................ ................................ ........ 83 Conclusions ................................ ................................ ................................ ............ 83 5 Cotton Yield forecasting for the Southeastern USa using climate indices ............. 101 Introduction ................................ ................................ ................................ ........... 101 Materials and Methods ................................ ................................ .......................... 103 Historic Cotton Yield Data ................................ ................................ .............. 103 Climate Data ................................ ................................ ................................ ... 104 Atmospheric and Oceanic Climate Indices ................................ ..................... 104 Oceanic nio index (ONI) ................................ ................................ ......... 105 Tropical north Atlantic (TNA) index ................................ .......................... 105 Atlantic meridional mode (AMM) index ................................ .................... 106 North oscillation index (NOI) ................................ ................................ .... 106 North pacific (NP) pattern ................................ ................................ ......... 106 Tropical north hemisphere (TNH) index ................................ ................... 107 Quasi biennial oscillation (QBO) index ................................ .................... 107 Correlation Analysis ................................ ................................ ....................... 107 Correlations of Climate Indices with T emperature and Precipitation .............. 108 Correlations of Climate Indices with Cotton Yield ................................ ........... 108 Principal Component Regression ................................ ................................ ... 109 Leave One Out Cross Validation ................................ ................................ .... 110 Categorical Yield Forecast Contingency Table ................................ ............ 110 Results and Discussion ................................ ................................ ......................... 111 Historic Cotton Yield Data ................................ ................................ .............. 111 Correlation Analysis ................................ ................................ ....................... 112 Correlations of climate indices with temperature and rainfall ................... 112 Correlation of climate indices with cotton yield ................................ ......... 113

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8 Prin cipal Component Regression ................................ ................................ ... 114 Leave One Out Cross Validation ................................ ................................ .... 115 Categorical Yield Forecast Contingency Table ................................ ............ 117 Conclusions ................................ ................................ ................................ .......... 118 6 CONCLUSIONS AND FUTURE WORK ................................ ............................... 133 LIST OF REFERENCES ................................ ................................ ............................. 136 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 146

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9 LIST OF TABLES Table page 2 1. List of cultivar parameters in CSM CROPGRO Cotton M odel .............................. 37 2 2. Local sensitivity indices with respect to selected model parameters for dry matter yield ................................ ................................ ................................ ......... 38 2 3. Local sensitivity indi ces with respect to selected model parameters for season length ................................ ................................ ................................ .................. 39 2 4. Model parameters and their range of uncertainty selected for the global sensitivity analysis ................................ ................................ .............................. 40 2 5. Global sensitivity indices for dry matter yield including main effects and interactions ................................ ................................ ................................ ......... 41 2 6. Global sensitivity indices for season length including ma in effects and interactions ................................ ................................ ................................ ......... 42 2 7. Model parameter rankings based on local and global sensitivity indices for dry matter yield ................................ ................................ ................................ ......... 43 2 8. Model parameter rankings based on local and global sensitivity indices for season length ................................ ................................ ................................ ..... 44 3 1. Information about the experimental sites, planting date, type of soils, and weather character istics ................................ ................................ ....................... 67 3 2. The CROPGRO Cotton parameters and uncertainty ranges used for GLUE prior distributions ................................ ................................ ................................ 68 3 3. The CROPGRO Cotton avera ge model predictions using DSSAT default parameters in comparison with corresponding measured data .......................... 69 3 4. Parameter uncertainties and fundamental statistics of prior and posterior distributions ................................ ................................ ................................ ........ 70 3 5. The CROPGRO Cotton average model predictions using estimated parameters in comparison with corresponding measured data ................................ ............. 71 3 6. Comparison of RMSE, and d statistics of simulated LAI, and biomass components for four sites based on DSSAT default model parameters and GLUE estimated parameters ................................ ................................ .............. 72 3 7 Comparison of output un certainties in model outputs of LAI and above ground biomass components for prior and posterior distribution ................................ .... 73

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10 4 1. Measures of model deviations for seed cotton yield (Quincy, FL) before season using no forecast except climatology ................................ ................................ .. 86 4 2. Measures of model deviations for seed cotton yield (Quincy, FL) in season (July 1) using no forecast except climatology ................................ ..................... 87 4 3. Measures of model deviations for seed cotton yield (Quincy, FL) in season (August 1) using no forecast except climatology ................................ ................ 88 4 4. Statistical comparison of cotton yield forecasts obtained before season with in season updated cotton yield forecasts.. ................................ ............................. 89 4 5. Measures of model deviations for seed cotton yield (Quincy, FL) using El Nio forecast based on JMA index ................................ ................................ ............. 90 4 6. Measures of model deviations for seed cotton yield (Quincy, FL) using El Nio forecast based on MEI index ................................ ................................ .............. 91 4 7. Measures of model deviations for seed cotton yield (Quincy, FL) using El Nio forecast based on ONI index ................................ ................................ .............. 92 4 8. Measures of model deviations for seed cotton yield (Quincy, FL) using La Nia fo recast based on JMA index ................................ ................................ ............. 93 4 9. Measures of model deviations for seed cotton yield (Quincy, FL) using La Nia forecast based on MEI index ................................ ................................ .............. 94 4 10. Measures of model deviations for seed cotton yield (Quincy, FL) using La Nia forecast based on ONI index ................................ ................................ ...... 95 4 11. Measures of model deviations for seed cotton yield (Quincy, FL) u sing Neutral forecast based on JMA index ................................ ................................ ............. 96 4 12. Measures of model deviations for seed cotton yield (Quincy, FL) using Neutral forecast based on MEI index ................................ ................................ .............. 97 4 13. Measures of model deviations for seed cotton yield (Quincy, FL) using Neutral forecast based on ONI index ................................ ................................ .............. 98 4 14. Statistical comparison of cotton yield forecasts tailored to ENSO forecasts by three indices. ................................ ................................ ................................ ...... 99 4 15. Statistical comparison of cotton yield forecasts using only climatology forecast with ENSO tailored cotton yield forecasts using MEI.. ................................ ...... 100 5 1. A 2x2 contingency table for categorical cotton yields. ................................ ......... 128 5 or the counties in Georgia and Alabama.. ................................ ................................ ... 129

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11 5 3. Significant principal components (PCs) of principal component regression models for cotton producing counties of Georgia and Alabama ....................... 130 5 4. Loadings of principal components (PCs) of climate indices ................................ 131 5 5. Skills of categorical cross validated cotton yield forecasts for count ies of Georgia and Alabama. ................................ ................................ ...................... 132

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12 LIST OF FIGURES Figure page 2 1. Local Sensitivity indices for irrigated and rainfed conditions for 2000 (top) and 20 03 (bottom). ................................ ................................ ................................ .... 35 2 2. Global Sensitivity indices for irrigated and rainfed conditions for the year 2000 (top) and 2003 (bottom). ................................ ................................ ..................... 36 3 1. Scatter plot of simulated vs. measured values for A) leaf area index, B) leaf weight, C) boll weight, D) stem weight for all four experiments.. ........................ 62 3 2. Simulated and observed values for A) l eaf area index, B) leaf weight (kg/ha), C) boll weight (kg/ha), and D) stem weight (kg/ha) for experiments 1 4 using unmodified cultivar parameter values. ................................ ................................ 63 3 3. Posterior probability distribut ions of model parameters ................................ ......... 64 3 4. Scatter plot of simulated vs. measured values for A) leaf area index, B) leaf weight, C) boll weight, D) stem weight for all four experiments.. ........................ 65 3 5. Simulated and observed values for A) leaf area index, B) leaf weight, C) boll weight, and D) stem weight for four experiments using estimated cultivar parameter values.. ................................ ................................ .............................. 66 4 1. Distribution of forecasted cotton yields for the 1980 cotton season at Quincy, Florida simulated using 1951 2005 historical weather data. .............................. 85 5 1. Correlati ons of climate indices with temperature during the cotton growing season.. ................................ ................................ ................................ ............ 120 5 2 Correlations of climate indices with rainfall during the cotton growing season.. ... 121 5 3. Correlations climate indices with cotton yield.. ................................ .................... 122 5 4. Correlations of historic cotton residuals with cross validated cotton yield residuals using the principal component regression of January and February climate indices. ................................ ................................ ................................ 123 5 5. Time series comparison between observed and cross validated cotton yield residuals for four counties of Alabama and Georgia that showed the maximum (A and B) and minimum correlations (C and D).. .............................. 124 5 6. Histogram of residual errors across the entire cross validated county cotton yields. ................................ ................................ ................................ ............... 125

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13 5 7. Probability of detecting county level cotton yields using cross validated cotton forecasts for two categories.. ................................ ................................ ............ 126 5 8. Percent correct cro ss validated cotton yield forecasts based on principal components regression model of climate indices and contingency table. ........ 127

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14 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 COTTON YIELD FOR ECASTING FOR T HE SOUTHEASTERN UNITED STATES By Tapan Bharatkumar Pathak August 2010 Chair: James W. Jones Cochair: Clyde W. Fraisse Major: Agricul tural and Biological Engineering Cotton is the most important fiber crops in the United States, accounting for approximately 20% of the total production in the world and more than $25 billion in products and services annually. The Southeastern United Stat es holds a major share of total cotton production of the country. While evidence clearly show s an increase in cotton planted over the time, climate variability is a major concern that could adversely affect its production in the southeastern United States. An effective way to reduce agricultural vulnerability to climate variability is through the implementation of adaptation strategies such as crop yield forecast s to mitigate negative consequences or take advantage of favorable conditions. The u se of climat e forecasts and climate indices to forecast cotton yield using the CROPGRO Cotton model and principal component regression model respectively, were assessed in this study Using the crop model, in season updating of the cotton yield forecast with real wea ther data along with the climatology significantly improved the accuracy of the forecast. With principal component regression models, cotton yield forecasts with significant skills were obtained with a lead time of approximately two months before cotton pl anting Results indicated good potential for forecasting cotton yield for the southeastern United States.

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15 CHAPTER 1 INTRODUCTION Cotton is the single mo st important fiber crop in the w orld, accounting for more than 35% of the total fiber production. In t erms of the world rankings, t he United States is ranked second in cotton production, accounting for 19.9% of total world production ( USDA ERS, 2009). The United States cotton industry is one of the major economic drivers of the country accounting for more than $25 billion in products and services annually. The Southeastern United States holds a major share of total cotton production in the United States ; a pproximately one fourth of total produced comes from this region. For instance, Georgia is ranked seco nd to Texas in total cotton produced in the United States. In recent years, there has been an increased need for fiber supply which has triggered increased cotton production in this region. Increase s in acreage planted to cotton in Georgia and Alabama wer e approximately 26% and 41% in the last decade respectively (NASS, 2007). Although cotton is considered as a drought tolerant crop, climate variability may adversely impact cotton production. Especially, cotton produced under rain fed conditions could be sever ely affected by a variable climate. El Ni o Southern Oscillation (ENSO) is a dominant phenomenon of climate variability in this region and other locations worldwide. The ENSO phenomenon is governed by the shift in sea surface temperature (SST) in the Pacific which affects inter annual climate variability across most parts of the world including the southeastern United States ( Hansen et al., 1998; Jones et al., 2003; Ropelewski and Halpert 198 6 Kiladis and Diaz 1989; Mo and Schemm 2008; Mennis 2001) Hansen et al. (1998) showed that ENSO phase significantly influenced six major crops including cotton in the southeastern United

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16 States. Their results showed that cotton area harvested in Alabama, Georgia, Florida, and South Carolina were significantly influenced by ENSO. Jones et al. (2003) stated that the main reason that the climate variability is often so devastating to agriculture is that we do not know what to expect in the next growing season. Effective application of climate forecast and climate indices may provide an opportunity to tailor agricultural decisions for higher economic returns to growers. There ha ve been many studies that evaluated the potential benefits of using climate forecasts on decision making processes in agriculture as a way to adapt to climate variability (Hansen et al., 200 5 ; Podesta et al., 200 2 ; Jones et al., 2003; Hansen et al., 1998). An effective way to reduce agricultural vulnerability to climate variability is through an effective use of climate forecast s One potenti al adaptation tool is yield forecasting based on climate information. Crop yield forecast s could be used by farmers to mitigate negative consequences of unfavorable climate, or benefit from anticipated favorable climate conditions (Baigorra et al., 20 10 ). If growers know the expected cotton yield for the coming season, they may be able to decide on alternative management strategies to reduce the production risk s (Jones et al., 2000; Hansen, 2005; Vedwan et al., 2005; Jagtap et al., 2002 ). Crane et al. (2010 ) conducted a research study to explore the s Their r esearch adjusting their decisions using climate forecasts to help them adapt to climate variabi lity. Some of the documented long term decisions were crop type, buying appropriate crop insurance, and areas to plant Pre season c rop yield forecasts would help growers in making the above mentioned decisions. For example, growers could purchase higher c rop insurance coverage, plant different crop,

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17 plant less etc. in order to compensate for an adverse effect of climate variability on their cotton yields. Crop models have shown potential for use in forecasting crop yield if climate data are provided to the model is in terms of a forecast. The m ain advantage of a crop model is that it can produce a range of possible climate forecasts using uncertain climate forecasts Before the start of crop growing season, weather is entirely uncertain this translates int o uncertainties in crop yield. If the model is updated during a season with observed weather data, some of the weather uncertainties are eliminated. Although weather uncertainties at the later stages of crop growth still impact the final crop yield, it may be possible to improve th e accuracy of crop yield prediction by in season updating the model with real weather data. A model to simulate cotton growth and development has recently been developed for the Decision Support System for Agrotechnology Transfer (DSSAT) called CROPGRO Cotton model (Jones et al., 1998; Hoogenboom et al., 2004). Since the CROPGRO Cotton model is relatively new it is important to calibrate and evaluate the model for t field conditions before it can be used for forecasting cotton yi eld. Hence, determining and understanding how sensitive the simulations of certain model processes are with respect to model parameters and estimating them is useful for model improvements. While growth and development of crops are known to be influenced by weather during the growing season, it is a common practice to predict crop yield based on weather variables (Sakamoto, 1979; Idso et al., 1979; Walker, 1989; Alexandrove and Hoogenboom, 2001). However, crop yield predictions based on observed weather

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18 ca nnot be made available before the planting season (Kumar, 2000). Attempts to obtain long te r m forecasts using alternatives to weather variables such as climate indices that exhibit teleconnections with weather are limited. Large scale teleconnection indice s greatly influence the climate and agriculture in the southeastern United States (Stenseth et al., 2003; Enfield, 1996; Bell and Jenowiak, 199 4 ; Martinez et al., 2009) Using those large scale climate indices as an early indicator to cotton yield could pr ovide valuable information to the growers in the Southeastern United States. climate forecasts and climate indices by crop model and empirical models provide potential in forec objectives include: Objective 1: To conduct a global sensitivity analysis of the CROPGRO Cotton model Objective 2: To estimate model parameters and conduct an uncertainty analysis of the C ROPGRO Cotton model Objective 3: To evaluate the use of in season updates of cotton yield forecasts using the climate forecasts Objective 4: To evaluate the use of climate indices for cotton yield forecasting in the Southeastern United States

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19 CHAPTER 2 USE OF GLOBAL SENSIT IVITY ANALYSIS FOR CROPGRO COTTON MODEL DEVELOPMENT Introduction The need for information in agriculture is increasing due to market and economic pressures combined with the need for better management of our natural resources. Crop m odels, widely used as research and teaching tools, are now becoming important tools for agricultural decision makers, as the need for information in agriculture increases. Crop models range in complexity from simple ones with a few state variables to compl ex ones having large numbers of model parameters and state variables. The Decision Support System for Agrotechnology Transfer (DSSAT) (Jones et al., 1998; Hoogenboom et al. 2004) contains complex dynamic models that simulate crop growth and yield as a func tion of soil and weather conditions and crop management regimes. DSSAT can also be used to help researchers, extension agents, growers, and other decision makers to analyze complex alternate decisions (Tsuji et al., 1998). Cotton ( Gossypium hirsutum L.) i s the single most important textile fiber in the world, accounting for over 40 percent of total world fiber production. While some 80 countries from around the globe produce cotton, the United States, China, and India together provide over half the world's cotton. The United States, while ranking second to China in production, is the leading exporter, accounting for over one third of global trade in raw cotton (MacDonald, 2000). Due to the importance of cotton in the world in general, and in the southeaster n USA in particular, a model to simulate cotton growth and development is currently being developed by the DSSAT crop modeling group. The Cropping System Model (CSM, Jones et al., 2003) contains models of 21 crops based on the CROPGRO, CERES and other mode ls. The new cotton model has been

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20 developed using the CSM CROPGRO crop template that allows its integration with other modules of the cropping system (Messina et al., 2004). The CROPGRO development team has used this approach in creating models for differe nt species, including brachiaria grass (Giraldo et al., 1998), tomato (Scholberg et al., 1997), and velvet bean (Hartkamp et al., 2002, Boote et al., 2002). CROPGRO was originally developed as a process oriented model for grain legumes, based on the SOYGRO PNUTGRO, and BEANGRO models that consider crop carbon, water, and nitrogen balances (Boote et al., 1998). Its ability to represent different crops is attained through input files that define species traits and cultivar attributes (Boote et al., 2002). O utputs from CROPGRO models depend on a large number of model parameters associated with the species traits and cultivar attributes. Determining and understanding how sensitive the simulations of certain model processes are with respect to model parameters is useful for guiding model developers. The effects of particular model parameter on a given output can be determined by measuring the relative influence of the model parameter on model output. Sensitivity analysis is useful for identifying the most and t he least important model parameters to the given model output so that it can contribute to the simplification of a model (Saltelli et al., 2000). There are a number of methods and techniques available for performing sensitivity analysis (Saltelli et al., 2 004), local and global sensitivity analyses are the most commonly used methods. Ruget et al. (2002) performed a local sensitivity analysis on the STICS crop simulation model (Brisson et al., 1998) to determine how sensitive the simulation of processes in each module was to the model parameters. Leaf area index was sensitive

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21 to all the model parameters of the leaf area index module (crop density, rate of LAI growth, and density effect on tillering), the cumulated root length was sensitivity to two of the m odel parameters of the root module (rooting depth for half water absorption, and rate of root deepening), whereas mineralization was most sensitive to humification depth. Xie et al. (2003) conducted local sensitivity analysis of the ALMANAC model (Kiniry et al., 1992) to input variables such as solar radiation, rainfall, soil depth, soil plant available water, and runoff curve number and the impact on grain yield of sorghum and maize. They found that runoff curve number change had the greatest impact on si mulated yield. Global sensitivity analysis differs from local methods by accounting for the variance of the model output associated with model parameters over their entire range of uncertainty. Homma and Saltelli (1996) explored methods of global sensit ivity analysis of nonlinear models to calculate the fractional contribution of model parameters to the variance of model predictions. Makowski et al. (2004) used global sensitivity analysis to determine the contribution of generic model parameters to the v ariance of crop model predictions. A sensitivity analysis was performed for three output variables of the AZODYN wheat model (Jeuffroy and Recous, 1999) that included grain yield, grain protein content, and the nitrogen nutrition index. Out of thirteen dif ferent model parameters, five were found to have the most influence on grain yield and grain protein content. The only model parameter that affected the nitrogen nutrition index was the ratio of leaf area index to critical nitrogen concentration. This stud y concluded that model parameters with the least influence on important simulated processes may not need to be accurately estimated.

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22 A sensitivity analysis allows modelers to rank model parameters in order of their influence on model output. Based on the rankings it can be used to identify model parameters that need a high accuracy in their estimates. Sensitivity analysis can also be used to check whether the behavior of the model output is as expected with respect to change in the input. For the CSM crop models, it is practically impossible to measure or estimate all the model parameters with a high level of accuracy. The CSM CROPGRO Cotton model under development was initially parameterized using data from the literature (Messina et al., 2004) and evalua ted for different environmental conditions using those parameters. Thus, there was uncertainty in the values of model parameters and how they may affect the output. This study was conducted for two purposes. The first objective was to determine whether th e global sensitivity analysis method would provide information on model performance that differs from the simpler local sensitivity method. This type of sensitivity analysis had not been used in the past with the CSM model. The central hypothesis in this c ase was that global sensitivity analysis will lead to improved understanding of the importance of model parameters since it accounts for the variance of model output associated with the variance of model parameters over the range on uncertainty in each par ameter. The second objective was to determine how sensitive the prototype cotton model predictions are to an important subset of its crop growth and development parameters. Although the prototype model was based on an existing crop model it was not clear h ow these model parameters would affect the most critical outputs, such as yield and season length. We also did not know how these effects would differ between

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23 rainfed and irrigated conditions. We hypothesized that the sensitivity of yield and season length to changes in model parameters does not vary with weather and irrigation. Results from this study were needed to guide further model parameter estimation efforts for improving the cotton model. Materials and Methods Overview of CSM CROPGRO Cotton Model Th e cotton model is based on the modular code of the CSM CROPGRO model (Jones et al., 2003). This model simulates crop growth and development independent of location, season, and crop management system. Its flexible physiological framework provides a conveni ent template to implement a cotton model that can be immediately integrated with other crop models (Messina et al., 2004) CSM CROPGRO is composed of several modules that make up a land unit in a cropping system. The primary modules are crop, soil, weather soil plant atmosphere, and management. The soil module integrates information from four sub modules: soil water, soil temperature, soil carbon, and nitrogen dynamics. The soil is represented by a one dimensional profile, consisting of a number of vertica l soil layers. The main function of the weather module is to read or generate daily weather data required by the model, including minimum and maximum air temperatures, solar radiation, and precipitation. The soil plant atmosphere module computes daily soil evaporation and plant transpiration while the management module determines when field operations are performed by calling sub modules related to planting, harvesting, inorganic fertilization, irrigation, and application of crop residues or organic materia ls. The Crop module can predict the growth and development of a number of different crops, each crop has its own model parameter files. These modules describe the time changes that occur in a land unit due to management and weather.

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2 4 The CSM CROPGRO model h as three sets of parameters that account for differences in development, growth, and yield between species, ecotypes, and cultivars (Boote et al., 2003). Cultivar parameters are specific to a particular variety, Ecotype parameters are for a group of cultiv ars, and Species parameters are common to all cultivars. Mainly the model cultivar parameters ( Table 2 1) are vital to consider for sensitivity analysis. Site and Experiment Description Sensitivity analyses were conducted for two cropping seasons, 2003 fo r which we had observed data collected in an experiment conducted at the C.M. Stripling Irrigation Research Park (SIRP), Camilla, GA (31 o 11N, 84 o 12W), and 2000 which was a dry year to compare the results from irrigated and rainfed conditions. Daily weath er data consisting of maximum and minimum temperature, solar radiation, precipitation, and wind speed were obtained from a local weather station at SIRP. Maximum temperatures varied from 24 to 33C; the minimum temperatures varied from 10 to 22C; and the average temperatures varied from 18 to 27C. The extremes for minimum temperatures occurred at the end of the growing season. Long term average precipitation (1939 to 2003) for June and July were 131.1 mm and 150.9 mm, respectively. During the 2000 croppin g season the total precipitation for June and July were 63.2 mm and 102.4 mm, respectively. In 2003, June and July precipitation totaled 139.9 mm and 203.6 mm, respectively. Unlike 2003, no field experiment was conducted during 2000. The main reason of per forming the sensitivity analysis for this year was to include a dry cropping season. Comparison of dry and wet years would allow us to evaluate the hypothesis that the importance of model parameters do not vary with irrigated and rainfed conditions.

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25 A 34 ha field was planted with a late maturing cotton variety, DP 555, using a conventional tillage system. The field was sown during the first week of May with a plant population of approximately 110,000 plants per hectare. The soil type at the study site was classified as an Orangeburg loamy sand (Fine loamy, siliceous, thermic Typic Paleudults) (Source Mitchell County SCS Map, Soil Conservations Service). The experiment had two treatments; one was rainfed and the other was irrigated. All other inputs were t he same for both treatments. Sensitivity Analysis The principle of sensitivity analysis is firstly to generate output variability associated with the variability of input, and secondly to assign the simulated output variability to the model parameters tha t affect it the most (Ruget et al., 2002). The most crucial step in sensitivity analysis is the selection of the model parameters and their uncertainty ranges. Including a large number of model parameters for global sensitivity analysis would result in an unrealistically high number of simulation runs and impractical computational load (Thorsen et al., 2001). Local sensitivity analysis was performed on the entire set of culti var model parameters listed in T able 2 1 and also on one of the species parameters light extinction coefficient (KCAN). Messina et al. (2004) recommended that KCAN should be considered as a cultivar or ecotype parameter because initial estimates of KCAN from literature data showed variations between and within seasons, with planting da tes, and between cultivars (Rosenthal and Gerik, 1991; Milroy et al., 2001; Milroy and Bange, 2003; Bange and Milroy, 2004). The main reason for including KCAN in the sensitivity analysis was to help answer the question whether KCAN was sufficiently import ant parameter to warrant its inclusion as an ecotype parameter. Results from this local

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26 sensitivity analysis were used to select model parameters for the global sensitivity analysis. Local s ensitivity Local sensitivity is often used to provide a normaliz ed measure for comparing sensitivity of a model to several parameters. In order to measure relative sensitivity of an output relative to a particular model parameter, only that parameter is changed in the vicinity of a base value; all other parameters are fixed to their base values. Local sensitivity was calculated for model responses using the base and + and 5% changes in the base value. Sensitivity indices were obtained by computing the change in the output relative to changes in parameters. Relative se nsitivities for dry ma tter yield and season length were defined as follows: ( 2 1) ( 2 2) Where Y is simulated dry matter yield and M is simulated length of the growing season obtain other model parameters at their base values. and represent fraction changes in simulated outputs for dry matter and season length relativ e to the fraction changes in inputs respectively. and represent local sensitivities for the dry matter and season length, respectively. Global s ensitivity Measuring model sensitivity f model parameters fixed at their single base values prevents the detection and

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27 quantification of interactions. A key aspect of most global sensitivity methods is the ability to take these interactions into account. Factorial design is a method of global sensitivity analysis that allows for simultaneous evaluation of the influence of many model parameters. It follows the classical theory of experimental design where nature is replaced by the simulated crop model (Box and Draper, 1987). In this study, selection of model parameters for global sensitivity analysis was based on results from the local sensitivity analysis. A simplification of the deterministic model can be used to represent the two output state v ariables, dry matter yield (Y) and season length (M), as a function of mode l parameters: and ( 2 3) Complete factorial design uses all possible combinations of chosen factor s and levels. For example, eight model parameters and three levels would create 3 8 combinations. For such a factorial experiment, the analysis can be expressed by decomposing the function Y= f f Y abcde fgh = + a + b abcdefgh ( 2 4) M abcdefgh = + a + b abcdefgh ( 2 5) Y abcdefgh = f (a,b,c,d,e,f,g,h) and M abcdefgh = f (a,b,c,d,e,f,g,h) denote the model responses of dry matter yield and growing season length, respec 1 2 = 3 4 5 6 7 8 = h; is the overall mean of the model responses; a b h represent the 1 2 8

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28 1 2 8 = h; ab is the interaction betwee n a and b gh is the interaction between g and h and so on The overall response variability can be separated into factorial terms as follows: ( 2 6) Where or total sum of squares (SS T ), represents th e total variability in the model responses, is the sum of squares (SS 1 ) associated with the main effect of m 1, and so on. The NCSS (Hintze, 2004) statistical software was used for calculating the sum of squares of the main effects for the complete factorial design. For the sensitivity analysis of a deterministic model, the main int erest lies in comparing the contributions of the factorial terms to the total variability. The main effect sensitivity (S i=1 to 8 ) indicates the relative importance of individual model parameter uncertainty and can be calculated by dividing the correspondi ng main effect sum of squares by the total sum of squares (Equation 7). ( 2 7) Interaction sensitivity indices are measures of the interactive influences of the model parameters on the output variance and were calculated by dividing the interaction sum of squares of the model parameters by the total sum of squares. Global sensitivity indices indicate the overall impact of model parameters on the output variance when model parameters vary over their entire range of unce rtainty.

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29 Global sensitivity indices for selected model parameters were calculated by following equation (Equation 8). ( 2 8) Where, indicates global sensitivity index, is the m ain effect sum of squares, is interaction sum of squares, and is total sum of squares, for parameters i = 1 to 8. Global sensitivity analysis apportions the output variability to the variability in model param eters covering their entire range space, and hence it was important to decide the range of selected model parameters. The ranges of model parameters should be chosen such that they represent the expected extreme values of those parameters. The ranges of some of the model parameters SLAVR, KCAN, and XFRT were obtained from the literature (Bange and Milroy, 2000; Milroy et al., 2001; Milroy and Bange, 2003; Reddy et al. 1993; Reddy et al., 1992; Reddy et al., 1991; Messina et al., 2004). Published data by Wright and Sprenkel (2006) on the ranges of different growth stages were used to determine the ranges of the model parameters that deal with crop growth duration. Information on certain crop growth stages was not available in the published literature so i n order to make maximum use of available dataset it was assumed that the ratio of parameters on crop growth stages for the cotton model were same as the ratio of those parameters for the soybean model. Data for soybean parameters were obtained from Boote e t al. (2003). In the case of SFDUR and PODUR, no information on ranges was available. Instead of using an arbitrary range, the

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30 percentage variance from the mean value for soybean parameters was applied to the base cotton model parameters. Results and Dis cussion Local Sensitivity Analysis Model parameters that were selected for global sensitivity analysis based on the initial local sensitivity analysis are shown in Tables 2 2 and 2 3. Sensitivity indices of the other parameters were either zero or very sma ll. For both treatments and years, KCAN was the parameter that most affected the dry matter yield. For the 2000 rainfed condition, magnitudes and orders of local sensitivity indices were different from 2000 irrigated condition and 2003 irrigated and rainfe d conditions (Table 2 2, Figure 2 1). As an example, dry matter yield was more sensitive to XFRT than EM FL for 2000 rainfed condition whereas it was vice versa for all other cases. One reason for such differences could be because the model is non linear i n its responses and local sensitivity analysis does not consider the range of uncertainty. Only three model parameters, EM FL, FL SD and SD PM, affected the response of season length. The time between first seed and maturity (SD PM) was the model paramete r that influenced season length the most (Table 2 3). Global Sensitivity Analysis Based on the local sensitivity analysis results of all the cultivar model parameters and one species model parameter, eight parameters were selected for global sensitivity an alysis (Table 2 4). Table 2 5 and 2 6 shows the calculated global sensitivity indices for dry matter yield and season length taking into account all main effects and interactions related to corresponding model parameter. The first ten interaction terms in order of their magnitudes of sensitivity indices are listed in Table 2 5.

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31 Unlike local sensitivity indices, global sensitivity indices were consistent in terms of order of sensitivity across rainfed and irrigated conditions and years. For a given manageme nt condition and year, SLAVR had the highest sensitivity index followed by KCAN. Two model parameters, PODUR and SFDUR, showed the least influence on dry matter yield across both treatments and years. For lower specific leaf areas, thicker and smaller leav es would reduce light capture and net photosynthesis. On the other hand for higher specific leaf areas, leaves are thinner and larger resulting in increased light capture and hence increased net photosynthesis. Thus changing SLAVR would indirectly affect c anopy net photosynthesis which eventually affects growth and yield. KCAN was the second most important parameter for dry matter yield. The light extinction coefficient, KCAN, is used to compute light interception depending on leaf area index. The highest i nteraction effect was obtained between KCAN and SLAVR. The model parameter XFRT was the third most important model parameter for crop yield. Parameter values of SLAVR and KCAN mainly control leaf expansion and light capture and hence control daily assimila tes. XFRT regulates the partitioning of daily assimilates that goes to seed. XFRT being the third most important parameter, its interaction with SLAVR and KCAN being the second and third most important interactions was logical. For 2000, irrigated and ra infed conditions provided similar sensitivity indices ( Figure 2 2). There were small differences in the values due to irrigation and year; however the order of importance of model parameters was consistent. Year 2003 was a wet year and hence even with the rainfed conditions, the indices were consistent in

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32 terms of values and order. Overall, global sensitivity indices did not show variations in order of importance with different treatments. Season length was sensitive to only three model parameters, EM FL, FL SD, and SD PM. Season length is mostly determined by parameters that control the duration of different crop growth stages. In our study three duration model parameters were selected that covered the whole crop season length. SD PM was the most important model parameter, partly due to greater uncertainty in this parameter, affecting season length, followed by FL SD, and EM FL respectively ( Table 2 6). Comparison of Local and Global Sensitivity Analysis Results For comparing local and global sensitivity a nalysis results, only rankings were taken into consideration. The reason for that was because local sensitivity index is the ratio of percentage change in the output response to the percentage change in the model parameter, whereas the global sensitivity i ndex is the measure of percentage contribution of an individual model parameter to overall output variance. Based on local sensitivity results, KCAN was the most important model parameter for cotton dry matter yield followed by SLAVR, which was opposite to global sensitivity results. The main reason for these differences was because local sensitivity analysis focuses on local impact of the model parameter on the model response where model parameters varied in small intervals around the base value of the mod el parameter. For nonlinear models, finding the most important model parameter with such sparse domain coverage may be misleading. On the other hand, global sensitivity analysis takes into account the main effects and interactions between parameters over t heir entire uncertainty ranges.

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33 For this study, irrigated and rainfed conditions for dry and wet years were used to compare local sensitivity and global sensitivity analyses results. The model parameter rankings did not change with years and treatments fo r global sensitivity analysis, whereas they varied among the years and treatments for local sensitivity analysis. Both methods provided similar results for two variables (PODUR and SFDUR) showing that model sensitivity over the range of parameter uncertain ty was small. Such information can be useful to focus additional research and possibly to simplify the model by reducing the number of model parameters that one has to estimate. Season length response was sensitive to only three model parameters, EM FL, F L SD, and SD PM. Out of these three SD PM was the most important model parameter followed by FL SD, and EM FL, respectively. These rankings were the same for both sensitivity analysis methods. The reason for season length response being sensitive to only t hree model parameters was because those model parameters were the crop growth duration model parameters selected for this analysis. Conclusions This study evaluated how sensitive the cotton model predictions were to a selected set of model parameters. L ocal and global sensitivity analyses were used to determine dry matter yield and season length sensitivity to model parameters under irrigated and rainfed conditions for two cropping seasons. Results demonstrated that, in accordance with our first hypothe sis, global sensitivity analysis improved our understanding of how sensitive the prototype cotton model was to the selected set of parameters over the ranges of parameter uncertainties. In addition to accounting for the variance of model output associated with the variance of model parameters over the entire range on uncertainty, it had an advantage of considering the interactions among

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34 model parameters. The most influencing model parameter on dry matter yield was the specific leaf area (SLAVR). Local sensi tivity analysis indicated that the extinction coefficient (KCAN) was the most influencing model parameter. The global sensitivity analysis results also demonstrated that, consistent with our second hypothesis, sensitivity of dry matter yield and season le ngth to the selected set of model parameters did not vary between irrigated and rainfed conditions or with years. However, that was not true for local sensitivity analysis. Results from this study indicated that more research is needed to reduce the range of uncertainties of both KCAN and SLAVR. Experiments have shown variations in KCAN values for different cultivars and hence it was suggested that it should be included in ecotype set of model parameters rather than in species file. That suggestion was supp orted from the results of this study. The parameters selected for this study were associated with crop growth and development. Additional studies are needed to assess model sensitivity to soil water and nitrogen parameters which were held constant for this study. Global sensitivity analysis can be a valuable tool for application with large, highly non linear models, such as the DSSAT CSM models. However, the use of a complete factorial design and analysis of variance can result in a large number of simulat ion runs when there are many model parameters. The choice of model parameters to be evaluated should be considered with care, taking into account available resources.

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35 Figure 2 1. Local Sensitivity indices for seed cotton yield for irrigated and rain fed conditions for 2000 (top) and 2003 (bottom).

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36 Figure 2 2. Global Sensitivity indices for seed cotton yield for irrigated and rainfed conditions for the year 2000 (top) and 2003 (bottom).

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37 Table 2 1. List of cultivar parameters in CSM CROPGRO Cotton Model Numbers Parameters Definitions 1 CSDL Critical Short Day Length below which reproductive development progresses with no day length effect (for short day plants) (hour) 2 PPSEN Slope of the relative response of development to photoperiod with tim e (positive for short day plants) (1/hour) 3 EM FL Time between plant emergence and flower appearance (R1) (photothermal days) 4 FL SH Time between first flower and first boll (R3) (photothermal days) 5 FL SD Time between first flower and first se ed (R5) (photothermal days) 6 SD PM Time between first seed (R5) and physiological maturity (R7) (photothermal days) 7 FL LF Time between first flower (R1) and end of leaf expansion (photothermal days) 8 LFMAX Maximum leaf photosynthesis rate at 3 0 C, 350 ppm CO2, and high light (mg CO2/m2 s) 9 SLAVR Specific leaf area of cultivar under standard growth conditions (cm2/g) 10 SIZLF Maximum size of full leaf (three leaflets) (cm2) 11 XFRT Maximum fraction of daily growth that is partitioned t o seed + shell 12 WTPSD Maximum weight per seed (g) 13 SFDUR Seed filling duration for boll cohort at standard growth conditions (photothermal days) 14 SDPDV Average seed per boll under standard growing conditions (#/ boll ) 15 PODUR Time required for cultivar to reach final boll load under optimal conditions (photothermal days) 16 KCAN* Canopy light extinction coefficient (* species parameter)

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38 Table 2 2. Local sensitivity indices with respect to selected model parameters for dry matter yiel d Parameter(s) Base Year 2000 Year 2003 Value Irrigated Rainfed Irrigated Rainfed 1 ) 0.72 3.11 2.65 3.32 3.32 EM 2 ) 27.87 1.45 0.83 1.76 1.76 FL 3 ) 11.65 0.43 0.44 0.34 0.34 SD 4 ) 27.68 0.62 0.69 0.79 0.79 5 ) 170.00 1.76 0.99 1.91 1.91 6 ) 0.72 0.40 0.84 0.37 0.37 7 ) 35.00 0.21 0.19 0.03 0.03 8 ) 8.00 0.09 0.12 0.13 0.13

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39 Table 2 3. Local sensitivity indices with respect to selected model parameters for season length Parameter(s) Base Year 2000 Year 2003 Value Irrigated Rainfed Irrigated Rainfed 1 ) 0.72 0 .00 0 .00 0 .00 0 .00 EM 2 ) 27.87 0.31 0.32 0.32 0.32 FL 3 ) 11.65 0.10 0.10 0.10 0.10 SD 4 ) 27.68 0.42 0.43 0.43 0.43 5 ) 170 .00 0 .00 0 .00 0 .00 0 .00 6 ) 0.72 0 .00 0 .00 0 .00 0 .00 7 ) 35 .00 0 .00 0 .00 0 .00 0 .00 8 ) 8 .00 0 .00 0 .00 0 .00 0 .00

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40 Table 2 4. Model parameters and their range of uncertainty selected for the global sensitivity analysis Parameter(s) Uncertainty Range Reference Minimum Base Maximum For Uncertainty Range 1 ) 0.5 0 0.72 0.95 Rosenthal and Gerik, 1991;Milroy et al., 2001; Milroy and Bange, 2003; Bange and Milroy, 2004 EM 2 ) 27.72 27.87 28.02 Wright and Sprenkel, 2006 FL 3 ) 9.03 11.65 14.27 Wright and Sprenkel, 2006; Boote et al., 2003 SD 4 ) 21.46 27.68 33.91 Wright and Sprenkel, 2006; Boote et al., 2003 5 ) 90 .00 170 .00 250 .00 Reddy et al. 1993; Reddy et al., 1992; Reddy et al., 1991 6 ) 0.5 0 0.72 0.95 Reddy et al. 1993; Reddy et al., 1992; Reddy et al., 1991 SF 7 ) 31.12 35 .00 38.88 Boote et al., 2003 8 ) 5.82 8 .00 10.18 Boote et al., 2003

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41 Table 2 5. Global sensitivity indices for dry matter yield including main effects and interactions Parameter(s) 2000 Irrigated Sensitivity Indices 2000 Rain fed Sensitivity Indices 2003 Irrigated Sensitivity Indices 2003 Rainfed Sensitivity Indices Main Effects & Interactions Global Indices Main Effects & Interactions Global Indices Main Effects & Interactions Global Indices Main Effects & Interactions Glob al Indices 1 ) 0.3848 0.4802 0.4109 0.4976 0.3761 0.4832 0.3762 0.4832 EM 2 ) 0.0002 0.0022 0.0002 0.0022 0.0002 0.0023 0.0002 0.0023 FL 3 ) 0.0057 0.0122 0.0065 0.0131 0.0058 0.0132 0.0058 0.0132 SD 4 ) 0.0203 0.0359 0.0196 0.0325 0. 0165 0.0311 0.0165 0.0310 5 ) 0.4491 0.5451 0.4262 0.5132 0.4549 0.5631 0.4550 0.5631 6 ) 0.0224 0.0479 0.0291 0.0532 0.0182 0.0400 0.0182 0.0400 7 ) 0.0002 0.0009 0.0001 0.0010 0.0000 0.0011 0.0000 0.0011 8 ) 0.0004 0.002 0 0.0007 0.0027 0.0010 0.0029 0.0010 0.0029 KCAN x SLAVR 0.0716 n/a 0.0651 n/a 0.0855 n/a 0.0855 n/a KCAN x XFRT 0.0107 n/a 0.0100 n/a 0.0089 n/a 0.0089 n/a SLAVR x XFRT 0.0096 n/a 0.0102 n/a 0.0082 n/a 0.0082 n/a SD PM x SLAVR 0.0065 n/a 0.0045 n/a 0. 0059 n/a 0.0059 n/a KCAN x SD PM 0.0053 n/a 0.0046 n/a 0.0047 n/a 0.0047 n/a KCAN x SD PM x XFRT 0.0038 n/a 0.0029 n/a 0.0034 n/a 0.0034 n/a FL SD x SLAVR 0.0018 n/a 0.0017 n/a 0.0020 n/a 0.0020 n/a KCAN x FL SD 0.0015 n/a 0.0016 n/a 0.0016 n/a 0.0016 n/a KCAN x SD PM x SLAVR 0.0010 n/a 0.0006 n/a 0.0011 n/a 0.0010 n/a EM FL x FL SD x SD PM 0.0006 n/a 0.0006 n/a 0.0006 n/a 0.0006 n/a

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42 Table 2 6. Global sensitivity indices for season length including main effects and interactions Parameter(s) 2000 Irrigated Sensitivity Indices 2000 Rainfed Sensitivity Indices 2003 Irrigated Sensitivity Indices 2003 Rainfed Sensitivity Indices Main Effects & Interactions Global Indices Main Effects & Interactions Global Indices Main Effects & Interactions Global Indices Main Effects & Interactions Global Indices EM 2 ) 0.0040 0.0339 0.0043 0.0344 0.0040 0.0343 0.0040 0.0343 FL 3 ) 0. 1756 0.2058 0.1826 0.2127 0.1990 0.2307 0.1990 0.2307 SD 4 ) 0.7829 0.8142 0.7732 0.8038 0.7589 0.7896 0.7589 0.7896 EM FL x FL SD x SD PM 0.0163 n/a 0.0154 n/a 0.0165 n/a 0.0165 n/a FL SD x SD PM 0.0076 n/a 0.0072 n/a 0.0077 n/a 0.0077 n/a EM FL x SD PM 0.0073 n/a 0.0071 n/a 0.0064 n/a 0.0064 n/a EM FL x FL SD 0.0063 n/a 0.0067 n/a 0.0074 n/a 0.0074 n/a

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43 Table 2 7. Model parameter rankings based on local and global sensitivity indices for dry matter yield Parameter(s) Year 2000 Year 2003 Ir rigated Rainfed Irrigated Rainfed Local Sensitivity Analysis Rankings 1 1 1 1 EM 3 4 3 3 FL 5 6 6 6 SD 4 5 4 4 2 2 2 2 6 3 5 5 7 7 8 8 8 8 7 7 Global Sensitivity Anal ysis Rankings 2 2 2 2 EM 6 6 6 6 FL 5 5 5 5 SD 4 4 4 4 1 1 1 1 3 3 3 3 8 8 8 8 7 7 7 7

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44 Table 2 8. Model parameter rankings based on local an d global sensitivity indices for season length Parameter(s) Year 2000 Year 2003 Irrigated Rainfed Irrigated Rainfed Local Sensitivity Analysis Rankings EM 3 3 3 3 FL 2 2 2 2 SD 1 1 1 1 Global Sensitivity Analysis Rankings E M 3 3 3 3 FL 2 2 2 2 SD 1 1 1 1

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45 CHAPTER 3 UNCERTAINTY ANALYSIS AND PARAMETER ESTIMA TION OF CROPGRO COTTON MODEL Introduction Applications of crop simulation models have become an important part of the agricultural research pro cess. Because decision making processes may use results obtained from simulation models, consideration of model uncertainties in decision making processes has become increasingly important. Uncertainties in models can be categorized into three major source s: model parameters, model input data, and model structure. Crop models, such as CROPGRO Cotton are complex and have many parameters. With limited measurement availability, estimates of model parameter s are uncertain. Model structure is uncertain since it is typically a simplified representation of the system being studied. Lastly, model input data, such as initial conditions, are also imperfect to some extent and hence contribute towards output uncertainty (Makowski et al., 2006; Tolson and Shoemaker, 2008 ). Different sources of uncertainties are important, however, the scope of this research was limited to address ing parameter uncertainty. Model parameters have been a significant source of uncertainty in model prediction in previous studies. Brazier et al (2000) showed that parameters such as hydraulic conductivity have been recorded with a large variance for a single soil (Nielsen et al., 1973, Warrick and Nielsen, 1980) yet they are often input to the model as a single value. If model output is sensitiv e to hydraulic conductivity, the major portion of model output uncertainty c ould come from parameter uncertainty. Wang et al. (2005) performed parameter estimation and uncertainty analysis on crop yield and soil organic carbon simulated with the EPIC model where only parameter uncertainty was considered. In that study, a total of nine

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46 corn yield and soil organic carbon related parameters were used for uncertainty analysis. Although only parameter uncertainty was considered, the observed corn yield and soil organic carbon fell within the 95% confidence limit of the predictions. There ha ve been significant advance s in methodologies for uncertainty assessment. Blasone et al. (2008) referenced some of the widely used uncertainty analysis methods that include Cl assical Bayesian (Vrugt et al., 2003; Thiemann et al, 2001), Pseudo Bayesian (Beven and Binely, 1992), data assimilation (Moradkhani et al, 2005), and multi model averaging methods (Georgekakos et al., 2004; Ajami et al., 2007). These methods differ in the ir underlying assumptions, complexity, and the way different sources of error are treated. Montanari, (2007) suggested that the selection of an uncertainty analysis method is subjective and should take into account issues such as model complexity, type of observed dataset available, and reliability of uncertainty assessment methods. A generalized likelihood uncertainty estimation (GLUE) technique introduced by Beven and Binley, (1992) is one of the most widely used and accepted uncertainty analysis techniq ues in environmental simulation modeling and it has also been used in crop modeling (Wang et al., 2005; He et al., 2009; Makowski et al., 2006). The main reasons for its popularity are its simpl e yet robust theory derived from Bayesian inference and its fl exibility in implementation. Stedinger et al. (2008) counted a total of more than 500 citations of GLUE applications in various simulation modeling studies The GLUE methodology was developed out of the Hornberger Spear Young (HSY) method of sensitivity an alysis (Whitehead and Young, 1979; Hornberger and Spear, 1981; Young, 1983). This method works on a phenomenon called equifinality.

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47 The equifinality thesis suggests that there may be more than one parameter set that is acceptable for simulation and should be considered in assessing uncertainty in predictions (Beven, 2006). In the GLUE methodology, model parameter sets are weighted based on their agreement with related observations using subjective likelihood measures. Beven and Binley (1992) acknowledged th at the choice of likelihood function used within the GLUE framework is subjective and the choice may greatly influence the resulting parameters and their uncertainties. These weights or probabilities are subsequently used to derive predictive uncertainty i n output variables. The CROPGRO Cotton model is a part of Decision Support System for Agrotechnology Transfer (DSSAT) software package that includes models of 21 crops (Jones et al., 2003). It is a part of the CROPGRO family of crop models with many of the same level of details. Pathak et al. (2007) performed a global sensitivity analysis on the CROPGRO Cotton model cultivar parameters and found that eight out of fifteen cultivar parameters were important to crop yield and physiological maturity outputs of the model. An accurate estimate of uncertainties associated with those important model parameters is needed for model applications and improvement. It may be difficult to find a single optimal fit of model parameters to observed datasets in complex simulat ion models due to the fact that there might be more than one parameter set that give s equally good results. This equifinality nature of this simulation model needs to be addressed. Parameter estimates of the cotton model have only been tested a few times u nder field experiments (Messina et al., 2004; Zamora et al., 2009). There have been no studies published in referred articles to address uncertainties associated with the CROPGRO Cotton model.

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48 and uncertainties in genotype parameters and how do those translate into uncertainties in The objective of this research was to estimate the important model parameters and associated uncertainties using the GLUE technique. Materials and M ethods Description of Field Sites and Measured Datasets Data collected on four experiments at three sites were used for this study: 1) and 2) University of Florida North Florida Research and Education Center (NFREC), located in Quincy, Florida, 3) Univer sity of Florida Plant Science Research and Education Unit, Citra, Florida, and 4) a Georgia. Characteristics of the study sites including soil, weather, and management information are shown in T able 3 1. All fi eld plots were planted with the full season cotton cultivar DeltaPine 555, the most widely grown cultivar in the Southeast USA. All four experimental sites were irrigated and fertilized during the cropping season. Timing and amounts of applied water and fe rtilizers were recorded. Above ground biomass (leaf, stem, and boll) and leaf area index (LAI) were measured at each location at an interval of approximately two to three weeks w ith three to four replications. There were a total of 81 observations conside red for this study consisting of 1 6 LAI, 24 leaf weight 17 boll weight, and 24 stem weight measurements across all four experiments. In the vegetative stage sampling period, plants within one meter of row were cut at the soil surface and separated into le af, stem, and bolls. Samples were then oven dried at about 70 o C for 48 hours and weighed to obtain dry biomass. LAI measurements were obtained using the LAI 2000 instrument (Li Cor Inc., Lincoln, NE) for experiments 1 and 2. A leaf area meter (model LI 310 0, Li Cor Inc) was

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49 used to measure LAI for experiments 3 and 4. Information on phenology (anthesis dates and maturity dates) were only collected for experiments 1, 3, and 4 (Table 3 1). The fields were visited approximately every two weeks in order to dete rmine these dates. The CROPGRO Cotton Model The CROPGRO Cotton model is a member of the CROPGRO group of models in DSSAT that has been tested for several crops including soybean (Boote et al., 1998) and peanut (Boote et al., 1998; Gilbert et al., 2002). I t simulates the effects of weather, soil, and, management on crop growth and development (Boote et al., 1998; Jones et al., 1998; Jones et al., 2003). The CROPGRO Cotton model, using the same features and level of details as other the CROPGRO crop models was developed recently O nly a few studies have been reported on this cotton model eva luation and applications (Zamora et al., 200 9 Messina et al., 2004, Guerra et al., 2005). Soil inputs consist of one dimensional soil physical properties such as lower, upper, and saturated water holding capacities, bulk density, and PH (Jones et al., 2003; Jones et al., 1998). The soil module integrates information from soil temperature, soil water, soil carbon, and nitrogen dynamics sub modules (Jones et al., 2003) to s imulate growth and yield. Weather data consist ed of daily values of minimum and maximum air temperatures, solar radiation, and precipitation. Management inputs consist ed of information on amount of irrigation, fertilization, plantin g dates, plant populatio n etc. The m odel was provided with information on soil, weather, and management specific to each experimen t for model simulations (Table 3 1). The CROPGRO model has three sets of parameters that account for differences in development, growth, and yield bet ween species, ecotypes, and cultivars (Boote et al., 2003). In this study, cotton cultivar parameters were estimated along with the

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50 uncertainties associated with them. A detailed description of cultivar parameters and uncertainty analysis procedures are gi ven in the following sections. Uncertainty Analysis and Parameter Estimation Procedure s The GLUE procedure wa s used in this study where 55,000 parameter set s were sampled from their prior distributions using Monte Carlo simulations and model outputs were obtained for each of those parameter set s The prior distribution represents the original information about the uncertainties of parameters based on previous studies The primary reason for running such a large number of simulations in GLUE is to obtain a n adequate number of acceptable parameters for estimating the posterior distribution of parameters Each of the model outputs was assigned likelihoods based on their agreement with related field observations. Using the likelihood values, posterior distribu tions were estimated using the Bayesian approach. The GLUE procedure was first performed on phenology parameters (EM FL and SD PM). Once the estimated parameters were obtained for these phenology parameters, the GLUE procedure was performed on the remainin g cultivar parameters. This parameter estimation and uncertainty analysis procedure was based on recommendations in Boote et al. ( 199 8) who suggested to first estimate phenology parameters before estimating other parameters. Descriptions of input parameter s, uncertainty ranges, prior distributions, likelihood functions, and posterior distributions used in this research are given in the following sections. Parameter selection and prior d istributions A complex simulation model such as the CROPGRO Cotton model is generally heavily parameterized. Thorsen et al. (2001) suggested that the inclusion of a large number of parameter sets would result in an unrealistic number of simulation runs that

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51 would be too large to compute. A systematic way of selecting parameter s for uncertainty analysis is to perform sensitivity analysis on parameters to get information on which parameters are important. Pathak et al. (2007) performed a global sensitivity analysis of the CROPGRO Cotton model to cultivar and species parameters an d suggested a list of parameters (EM FL, FL SD, SD PM, SLAVAR, KCAN, SFRT, SFDUR, and PODUR) to which important model outputs such as cotton yield and physiological maturity are sensitive. The CROPGRO Cotton model was initially parameterized using data fro m the literature (Messina et al., 2004 ; Zamora et al., 2009). Very little knowledge was available on real ranges and distributions of these parameters. For this study, a uniform prior distribution was assumed for each of the selected parameters as it has b een the most reported sampling distribution in similar studies reported in the literature (Beven, 2001; Stedinger et al., 2008). Because of a lack of information, it was also assumed that the parameters are independent. The only information needed to sampl e parameters from uniform distribution was their minimum and maximum values. The ranges of model parameters should be chosen such that they represent expected extreme values of those parameters. The ranges of model parameters (SLAVAR, KCAN, and XFRT) were obtained from the literature (Bange and Milroy, 2000; Milroy et al., 2001; Milroy and Bange, 2003; Reddy et al., 1992; Messina et al., 2004). Information on ranges of certain parameters (LFMAX, EM FL, FL SD, and SD PM) were not available, so in order to ma ke maximum use of available dataset, the percentage variance from the mean values for the CROPGRO Soybean (Boote et al., 2003) parameters were applied to the

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52 base cotton model parameters. Table 3 2 shows selected parameters and their uncertainty ranges use d in the GLUE analysis. Likelihood f unction The likelihood function is a measure of how well a model outputs obtained from a set of parameters fit to field observations. The calculation of the likelihood function is an important part of the GLUE procedure. There have been several likelihood functions used in previous applications of GLUE (Beven and Freer, 2001). The choice of likelihood function should be such that it can reduce the uncertaint ies in parameters and simulated output s should provide close agre ements with observed data He et al. (2009) compared four likelihood functions for parameter estimation of the CERES Maize model using the GLUE method. He found that the Gaussian likelihood function (Makowski et al., 2006) was the best choice because the r esults from this function resulted in the least uncertainties in parameters and improved model predictions more than the other functions that were evaluated Based on his findings the Gaussian likelihood function was used in this study as is shown below (3 1) Where, is likelihood of parameters, given the observations (O). is a mean of replications of observation, is i th model response, and N is the number of observations. With complex simulation models such as the CROPGRO Cotton model, it is difficult to know the model error variance that is needed for the Gaussian function Alternatively, variance s in m easurements w ere assumed to be equal to the model error variance in previous studies (Van Oijen et al., 2005; He et al., 2009). Another alternative

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53 that Wang et al. (2005) used was to assume that the error variance was equal to the error variance between o bserved and simulated values using the very best parameter set For this study, error variance was replaced with the measurement variance for LAI, leaf weight, stem weight, and boll weight. Each data point in th e time series of LAI, leaf weight, stem weight, and boll weights contained measurement variances specific to that particular data point. The measurement variance was unknown for anthesis dat e and maturity date; hence the error variance in the above equatio n for anthesis and maturity date was replaced with the minimum error variance between measured and simulated results (Wang et al., (2005) The likelihoods were calculated for each of the data points separately and were integrated together by taking the pro duct. It can be seen from equation 3 1 that the likelihood values of N number of observations were combined by taking a product to get a global likelihood. The main benefit of using product of likelihoods is that as the number of observations increases, the global likelihood response becomes steeper. He et al. (2009) compared three likelihood combination methods including the product and found that the Gaussian likelihood function updated with product function provided the best combination for CERES Maize model. Posterior d istribution The posterior distribution was derived from the behavioral simulations, that is, the number of parameter sets not ruled out of the analysis by near zero likelihood The threshold to derive behavioral and non behavioral para meter sets is subjective in the GLUE methodology (Beve n and Binley, 1992). The common practice is to select a cutoff

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54 for likelihood weight to identify behavioral parameters for use in determining posterior distributions For this study a likelihood thresh old of 0.0001 was se lected. Parameter sets having likelihood values above that cutoff limit were considered behavioral parameters to construct the posterior distribution. Once parameter sets are distinguished between behavioral and non behavioral by using likelihood values, likelihood weights were calculated by normalizing behavioral likelihood values as shown in equation 3 2. ( 3 2) is the normalized likelihood weight where the sum of is equal to 1.0. The is the global likelihood value obtained by taking the product of all the likelihood values. The expected values and variances f or each parameter were calculated using equations 3 3 and 3 4. (3 3) (3 4) Uncertainty bounds for m odel p redictions Uncertainty bounds represent the uncertainties in model predictions that were associated with uncertainties in model parameters. A total 5000 sets of input paramete rs were sampled from their posterior distribution s using Monte Carlo sampling and the CROPGRO Cotton model was run to obtain outputs. The uncertainties in model outputs were estimated from the ir empirical cumulative distributions. An appropriate

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55 quantiles of cumulative distribution were selected to form uncertainty bounds around the model outputs. In this analysis 95% confidence interval (uncertainty bound) was estimated from the values of 2.5% and 97.5% quantiles of the cumulative distribution of model out puts. The primary reason s for obtaining 5000 simulations runs was to obtain good estimate s or prediction distributions and of prediction quantiles. Statistical methods for model testing The simulated values of LAI, leaf weight, stem weight, and boll weigh t were analyzed using the following statistical measures: (3 5) ( 3 6) (3 7) Where, n is the number of observations, and are the i th simulated value with mean parameters and observed values respective ly Mean deviation indicates bias in the simulations, positive value of mean deviation corresponds to over prediction by the model and vice versa. The RMSE corresponds to the magnitude of the mean difference between predicted and measured values. The d ind ex (Willmott, 1982) corresponds to the agreement between model simulations and observations, 0 representing no agreement and 1 representing perfect agreement.

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56 Results and Discussion Simulations U sing U nmodified P arameters Simulations using unmodified cult ivar parameters showed good agreement with observed LAI, leaf weight, stem weight, and boll w eight for all four experiments. The unmodified parameters currently available in DSSAT were initially estimated using the experimental dataset (Messina et al., 200 4). Although the overall model agreement with the measurements was fairly good it was observed that the model over predicted LAI and above ground biomass when simulated using ori ginal model parameters. Figure 3 1 shows agreement between measured and simul ated values with original model parameters for LAI, leaf weight, stem weight, and boll weight for all four experiments. Except for a few data points, the model consistently over predicted the values as the majority of the data points f e ll below the 1:1 lin e. Tables 3 3 summarizes the average observations, simulations, and mean differences for LAI, leaf weight, stem weight, and boll weight for all four experiments. The positive values of mean differences indicated that the model was over predicting and vice versa. For instance, the mean differences between simulated and measured average boll weights were 1454 kg ha 1 and 1536 kg ha 1 for experimen ts 1 and 3 respectively (Table 3 3). In general average observed stem weight was over predicted by the model for all four experimental sites, average observed average LAI and leaf weight were over predicted in three out of four experiments, and average observed boll weight was over predicted in two out of four experiments. Figure 3 2 shows the time series of model s imulations and observed values for LAI, leaf, stem, and boll weight at different growth stages using original model parameters. During the early stages of crop growth the model wa s either under

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57 predicting the above ground biomass and LAI or ha d good agreem ent with the measured values. However, during the reproductive stage of crop growth, the model over predict ed them through maturity. For example, if we observe the LAI, leaf weight, and stem weight time series plots for experiments 2, 3, and 4, the model u nder predicting the first two or three measurements but then over predict ed throughout the remaining growth cycle. In general, time series plots and statistics show that the model simulations tended to overestimate observed LAI, leaf weight, stem weight, and boll weight for all fo ur experiments. Hence estimating parameters regulating the crop growth should improve the overall model predictions. Parameter Estimates and Uncertainties Comparison with prior distribution A total of eight cultivar parameters of the CROPGRO Cotton model associated with plant growth and development were estimated along with their uncer tainties. Table 3 4 shows mean s standard deviation s and coefficient of variation s (CV) for prior and posterior distributions of parameters. The pr ior mean s of model parameters shown in T able 3 4 were based on the 55,000 randomly sampled parameter sets from their corresponding uniform prior distributions. The posterior distributions for all eight parameters were narrowed to smaller ranges compared t o their prior distributions (Fig. 3 3, Table 3 4). These narrower ranges are, of course, dependent on the data from the four treatments used in this analysis. For example, the SLAVAR had prior uncertainty range of 90 250 cm 2 g 1 which was subsequently redu ced to 171 175 cm 2 g 1 in its posterior distribution and the SLAVAR coefficient of variation (CV) was changed from 27% to only 0.8% respectively.

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58 The KCAN parameter had a prior uncertainty range of 0.5 1 which was reduced to 0.61 0.67 and the CV was redu ced from 17% to 3%. Those two parameters were the most important parameters to simulated cotton yield according to the sensitivity analysis results obtained by Pathak et al. (2007). Uncertainty in those parameters would significantly affect the uncertainty in model outputs, hence predicting and reducing the amount of uncertainty in these parameters improved the model performance. The highest CV value among all eight parameters in the Pathak et al (2007) study was for SLAVAR which lowered down to 0.8% in the posterior distribution compared to 27% in the prior distribution. One of the main reasons for narrower uncertainties in posterior distributions was the integration of the large number of observations from the four different sites into the GLUE to estimate uncertainties. In the Gaussian likelihood function (eq. 3 1), as the number of observations N increases the parameter space also may tend to decrease and thus result in a narrower range That was the primary reason there were only 81 behavioral parameter sets that were concentrated towards the narrower uncertain ty range in this study Comparison with DSSAT default values An interesting thing to notice was that the expected values of all the parameters were not so different from their DSSAT default values e xcept for KCAN (Table 3 4). The estimated value for KCAN was 0.64 which was lower than its DSSAT base value of 0.8. The KCAN is an important parameter as it is responsible for light capture by the canopy. Hence changing the value of KCAN would have a direc t impact on daily photosynthesis which subsequently impacts LAI and above ground biomass. As expected the estimated value for KCAN was lower than the DSSAT default value because it would control the model over prediction of LAI and above ground biomass.

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59 Model predictions based on estimated p arameters The comparison between F igure 3 1 and 3 4 as well as Table 3 3 and 3 5 showed that the estimated parameters improved the overall agreement of measured LAI and above ground biomass with simulated results. Othe r than KCAN, no estimated parameters were very different from their corresponding DSSAT base values. As shown in the initial model results with unmodified parameters the model over predict ed the observations in general Since estimated KCAN was lower than the corresponding DSSAT base values, the over estimation by the model was controlled significantly and model predictions were improved. Table 3 6 shows the comparison of RMSE and d stat istics between measured and simulated LAI, leaf weight, stem weight, and boll weight obtained from DSSAT parameter base values and maximum likelihood estimated parameter values, respectively. For instance, RMSE of boll weight for default values were reduced from 1636 kg/ha to 535 kg/ha and 1842 kg/ha to 819 kg/ha for experi ments 1 and 3 respectively. This represents a reduction of RMSE of approximately 55% and 67% respectively. In this study, the d statistics were improved for most of the variables across all the experiments. The highest d statistic value of 0.99 was obtai ned for stem weight for experiment s 2 and 3 which represents almost perfect agreement of measured with simulated stem weights. The lowest d statistic of 0.45 was obtained for boll weight in experiment 4. The reason for a low agreement could be due to meas urement errors because the agreement of the model with other variables (LAI, leaf weight, and stem weight) of experiment 4 w as in good agreement s with measured values. The RMSE and d statistics showed a close agreement of the measured and simulated LAI and biomass components overall. The average RMSE of simulated LAI,

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60 stem weight, and boll weight from all four experiments were reduced with the GLUE estimated parameters compared to the DSSAT default parameters T he average RMSE for leaf weight was increased; however the incre ase was marginal (Table 3 6). It is also important to note that the estimated parameters generally improved the model by reducing model error. Model output u ncertainties Output uncertainties for LAI, leaf weight, boll weight, and stem wei ght were estimated from 95% confidence interval obtained from 2.5% and 97.5% quantiles of their cumulative distributions from 5 000 simulations generated from posterior distributions of model parameters. The output uncertainties in terms of standard deviati ons ( STDEV ) and coefficient of variability ( CV ) were compared in Table 3 7 along with the average s and ranges. The CV for model outputs obtained with prior parameter distribution ranged between 29% and 56% which were subsequently reduced to 4 13 % with the simulated outputs obtained from the posterior distribution of parameters. Figure 3 5 shows the simulated 95% confidence limits around the average simulated values in addition to the measured values of LAI, leaf weight, stem weight, and boll weight for all four sit es. Results show that the 80 % of the means of data from experiment 1, 90 % from experiment 2, 87% from experiment 3, and 53 % of data from experiment 4 were covered by the uncertainty b ounds. Overall, approximately 79 % of the data were within the un certainty bounds. Reason s for the remaining 21 % of data that were not within the uncertainty limits could be measurement errors also shown in Fig 3 5 or the subjective selection of cut off of likelihood values It is important to not e that the output un ce rtainties shown in T able 3 6 only consider uncertainties associated with eight model parameters of cotton growth and

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61 development. The parameter s and their uncertainties obtained in this analysis considered four treatments. Results could be different if oth er datasets were used. This study did not take into account the other sources of uncertainties. The uncertainties in model structure and model input data were not within the scope of this research. Conclusion The mean values of parameters after estimation improved model predictions relative to the original parameters available in DSSAT for delta pine 555 cotton cultivar. The prior uncertaint ies in the most important parameters (Pathak et al., 2007), SLAVAR and KCAN, w ere reduced from 27% and 13% to 0.8% and 3%, respectively. The general agreement of the model with measurements using the GLUE estimated parameters was good with the d statistics ranged between 0.99 for experiments 2 and 3 and 0.45 for experiment 4. This study also demonstrated an efficient pred iction of uncertainties in model parameters and outputs using the widely accepted GLUE technique. Overall, approximately 79% of the data were within the uncertainty bounds that were determined from the predicted confidence interval from the uncertainty ana lysis The limitation of this study was that the uncertainties in model structure, and model inputs were not examined. In further research, th ese uncertainties should be investigated. Also, parameter selection was concentrated only on cultivar parameters, and one species parameter. Uncertainty analysis should be performed on other important parameters such as soil parameters.

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62 A B C D Figure 3 1. Scatter plot of simulated vs. measured values for A) leaf area index, B) leaf weight, C) boll weight, D) stem weight for all four experiments. The simulated results were obtained using unmodified cultivar parameters.

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63 A) B) C) D) Figure 3 2. Simulated and observed values for A) leaf area i ndex, B) leaf weight (kg/ha), C) boll weight (kg/ha), and D) stem weight (kg/ha) for experiments 1 4 using unmodified cultivar parameter values. Experiment 1 Experiment 2 Experiment 3 Experiment 4

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64 Figure 3 3. Posterior probability distributions of model parameters

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65 A B C D Figure 3 4. Scatter plot of simulated vs. measured values for A) leaf area index, B) leaf weight, C) boll weight, D) stem weight for all four experiments. The simulated results were obtained using estimated cultivar parameters.

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66 A) B) C) D) Figure 3 5. Simulated and observed values for A) leaf area index, B) leaf weight, C) boll weight, and D) stem weight for four experiments using estimated cultivar parameter values. Vertic al bars indicate the standard deviations of observed values. Dotted lines represent 2.5% and 97.5% confidence interval of 5000 simulations. Experiment 1 Experiment 2 Experiment 3 Experiment 4

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67 Table 3 1. Information about the experimental sites, planting date, type of soils, and weather characteristics Exp eriment 1 2 3 4 Sites Citra, FL Camilla, GA Quincy, FL Quincy, FL Latitude 2924' N 3111' N 3036' N 3036' N Longitude 8217' W 8412'W 8433' W 8433' W Elevation (m) 20 54 63 63 Planting date 19 Jun 06 12 Apr 04 06 Jun 06 05 May 06 Soil type Trou p Sand Troup sand Dothan sandy loam Dothan sandy loam Mean seasonal temperature ( o C) 27 25 22 22 Mean seasonal precipitation (mm) 2.4 3.7 3.5 3.5 Reference of weather data www.fawn.com www.georgiaweather.net www.fawn.com www.fawn.com

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68 Table 3 2. The CROPGRO Cotton parameters and uncertainty ranges used for GLUE prior distributions. Parameter Definition Uniform Distribution Minimum Base Maximum EM FL Duration between emergence and flowering 28 .00 40 .00 43 .00 SD PM Duration between first s eed to physiological maturity 38 .00 45 .00 50 .00 LFMAX Maximum leaf photosynthesis rate 0.7 0 1.10 1.2 0 SLAVR Specific leaf area of cultivar under normal growth condition 90 .00 170 .00 250 .00 XFRT Maximum fraction of daily growth that is partitioned to see d+shell 0.5 0 0.80 0.95 SFDUR Seed filling duration for boll cohort at standard growth condition 31 .00 35 .00 38 .00 PODUR Time required for cultivar to reach final boll load under optimal condition 5 .00 5 .00 10 .00 KCAN Light Extinction Coefficient 0.5 0 0 .80 0.95

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69 Table 3 3. The CROPGRO Cotton average model predictions using DSSAT default parameters in comparison with corresponding measured data Variable Name Experiment Mean Observed Mean Simulated Mean D iff First flower 1 57 51 6 Maturity 1 142 146 4 LAI 1 3.14 2.88 0.25 Leaf wt kg/ha 1 1354 1422 68 Stem wt kg/ha 1 2002 2073 71 Boll wt kg/ha 1 1886 3339 1454 Leaf wt kg/ha 2 909 1036 127 Stem wt kg/ha 2 1430 1955 525 Boll wt kg/ha 2 23 52 2103 249 First flower 3 65 61 4 LAI 3 1.82 2.04 0.23 Leaf wt kg/ha 3 1031 1081 50 Stem wt kg/ha 3 1059 1305 246 Boll wt kg/ha 3 2276 3812 1536 First flower 4 64 72 8 LAI 4 1.92 2.23 0.31 Leaf wt kg/ha 4 1238 1224 13 Stem wt kg/ha 4 1159 1495 336 Boll wt kg/ha 4 5300 4657 644

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70 Table 3 4. Parameter uncertainties and fundamental statistics of prior and posterior distributions Parameter DSSAT Prior Posterior default Mean STDEV CV Mean STDEV CV EM FL 40 35.44 4.34 1 2.30% 40 0.61 1.50% SD PM 45 44.07 3.53 8.00% 44 2.06 4.70% LFMAX 1.10 0.95 0.14 15.20% 1.05 0.11 5.40% SLAVAR 170 170.00 45.91 27.10% 173 7.5 0.80% XFRT 0.80 0.73 0.13 17.90% 0.77 0.02 2.90% SFDUR 35 35.00 2.01 5.80% 36 0.83 2.40% PODUR 5 7.50 1.44 19.10% 5.2 0.4 1.80% KCAN 0.80 0.73 0.13 17.80% 0.64 0.05 3.20%

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71 Table 3 5. The CROPGRO Cotton average model predictions using estimated parameters in comparison with corresponding measured data Variable Name Experiment Mean Observed Mean S imulated Mean Diff First flower 1 57 52 5 Maturity 1 142 142 0 LAI 1 3.14 2.26 0.88 Leaf wt kg/ha 1 1354 1101 253 Stem wt kg/ha 1 2002 1559 444 Boll wt kg/ha 1 1886 2330 444 Leaf wt kg/ha 2 909 820 90 Stem wt kg/ha 2 1430 1412 18 Boll wt kg/ha 2 2352 1916 436 First flower 3 65 62 3 LAI 3 1.82 1.70 0.12 Leaf wt kg/ha 3 1031 884 146 Stem wt kg/ha 3 1059 964 95 Boll wt kg/ha 3 2276 2572 296 First flower 4 64 72 8 LAI 4 1.92 1.76 0.16 Leaf wt kg/ha 4 123 8 954 284 Stem wt kg/ha 4 1159 1077 82 Boll wt kg/ha 4 5300 3379 1921

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72 Table 3 6. Comparison of RMSE, and d statistics of simulated LAI, and biomass components for four sites based on DSSAT default model parameters and GLUE estimated parameters E xperiments Variables DSSAT default parameters GLUE estimated parameters RMSE d statistics RMSE d statistics 1 LAI 0.76 0.63 1.11 0.57 3 0.33 0.98 0.28 0.98 4 0.81 0.80 0.55 0.87 1 Leaf Weight Kg/ha 258.27 0.67 330.24 0.53 2 333.84 0.93 287.47 0.94 3 105.69 0.99 180.87 0.98 4 346.36 0.88 381.01 0.83 1 Boll Weight Kg/ha 1630.34 0.75 535.15 0.95 2 497.71 0.98 681.73 0.97 3 1842.07 0.45 819.64 0.75 4 1803.42 0.53 2340.07 0.45 1 Stem Weight Kg/ha 229.93 0.95 474.14 0.82 2 684.69 0.94 2 40.62 0.99 3 316.40 0.97 116.08 0.99 4 611.40 0.81 349.32 0.91

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73 Table 3 7 Comparison of output uncertainties in model outputs of LAI and above ground biomass components for prior and posterior distribution Experiments Variables Prior Post erior STDEV (kg/ha) CV (%) STDEV (kg/ha) CV (%) Mean Range Mean Range Mean Range Mean Range 1 LAI 1.38 1.03 1.49 56 56 58 0.26 0.12 0.34 10.7 10.1 12.0 3 0.8 0.1 1.6 47 40 52 0.14 0.01 0.28 6.97 4.29 8.75 4 0.92 0.14 1.55 51 41 56 0.18 0.02 0. 31 8.79 5.64 10.0 1 Leaf Weight kg/ha 497 360 568 44 43 45 119.13 53.76 163.2 9.98 9.33 11.35 2 246 0.6 481 29 10 38 62.55 2.13 114.86 7.05 5.23 11.10 3 302 45 594 35 32 39 67.32 6.18 136.85 6.34 3.74 8.07 4 366 64 611 39 31 43 89.26 11.57 154.08 8. 09 5.04 9.36 1 Boll Weight kg/ha 613 18 1268 45 40 61 217.26 89.47 357.21 9.71 7.64 14.92 2 562 14 917 34 20 60 87.69 0 138.13 4.58 2.74 7.01 3 892 504 1226 36 36 37 236.75 141.68 302.59 8.57 7.83 9.07 4 1153 485 1653 38 36 42 263.43 152.24 334.50 8 .19 6.27 10.82 1 Stem Weight kg/ha 760 478 986 46 45 50 183.94 73.77 279.83 10.98 10.25 12.45 2 604 2 962 43 29 62 165.83 0.39 292.98 10.14 6.78 14.19 3 411 57 871 53 40 75 101.05 15.78 211.07 13.02 8.80 20.88 4 501 104 896 52 44 63 125.44 27.42 220 .36 12.13 9.91 15.53

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74 CHAPTER 4 IN SEASON UPDATES OF CO TTON YIELD FORECASTS USING CROPGRO COTTON MODEL Introduction There has been significant progress in developing models to simulate growth and development of agricultural crops (Ritchie, 1994). These cr op simulation models have shown potential f or use in forecasting crop yield using weather forecasts (De Wit and Diepen, 2007; Hansen et al., 200 5 ; Larow et al., 2005 ) as well as using historical weather records (Lembke and Jones, 1972, W r ight et al., 1984) Simulation models are usually deterministic; hence if inputs to the model and model parameters are accurately measured, yield forecasts can be made even in abnormal climate situations, if those can be predicted (Bannayan and Crout, 1999). To facilitate simulation model forecasts of crop yield, daily weather data need to be provided to the model in terms of a forecast. It is a common practice to generate weather ensembles stochastically (Lawless and Semenove 2005; Bannayan and Crout 1999; Ahmed et al., 19 76; Grondona et al., 2000; Podesta et al., 2002) to represent uncertainty of weather conditions that are provided as an input to the model. However, the main limitations of weather generators are that they do not simulate extreme values well and they assum e that the observed relationships between weather variables will remain the same in the future (Jones et al., 2009). As an alternative to using generated weather series, historical weather records could be used to represent the possible weather for the nex t season. There has been handful of studies made where historical weather data were used to simulate crop yield which was represented as frequency distribution of expected yields (Lembke and Jones, 1972, Wight et al., 1984).

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75 Studies have shown that inste ad of using a static range of weather to forecast yields, updating the model in season using observed weather improves accuracy of model forecasts (Bannayan and Crout 1999; Lawless and Semenov 2006; Semenov and Porter 1995). Before the start of crop growin g season, weather is entirely uncertain which translates into uncertainties in crop yield forecast s If the model is updated in season with observed weather data, some of the weather uncertainties are eliminated. Since weather uncertainties early in the se ason are eliminated via use of observed data, it is possible to improve accuracy of crop yield prediction by in season updating the model with real weather data. For example, Bannayan and Crout, (1999) clearly showed that the in season updating the SUCROS model improved the forecasting accuracy of winter wheat yield. Crop yield in southeastern United States is affected significantly by El Nio Southern Oscillation (ENSO) (Jones et al., 2000; Hansen et al., 1998). In this region, El Nio events are characte rized by lower winter temperature and higher rainfall and La Nia events have the opposite effects. Since ENSO influences agricultural yield in the southeastern United States, it may be possible to forecast crop yield tailored to different ENSO phases usin g in season updates of real weather data. Royce et al. (2009) compared the predictive potential of three different ENSO classifications on crop yields for the Southeastern United States, including cotton. The three ENSO classifications they used were based on Japan Meteorological Agency (JMA) index, Oceanic Nio Index (ONI), and Multivariate ENSO index (MEI). According to that study, March May MEI ENSO index and January April ONI ENSO index showed the strongest association with cotton yield in the southeast ern United States. The assumption was that the ENSO

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76 conditions occurring immediately prior to or during the spring summer crop season climate influence in the southeastern United States that affects crop yields which would not be captured by categorical an nual JMA ENSO index. They found that monthly ENSO indices we re better predictors of crop yield than the JMA. Th at research was based on the historic al county yield data which does not distinguish between irrigated and rain fed practices. Simulation models can be effective for more robust analysis since they can quantify the effects under rainfed condition s alone. The CROPGRO Cotton model (Messina et al., 2004; Pathak et al., 2007) is a complex simulation model that has been recently added to Decision Suppo rt System for Agrotechnology Transfer (DSSAT) (Jones et al., 1998; Jones et al., 2003) group of models. It has been calibrated using field conditions in the southeastern United States but has not been utilized to obtain in season updates of cotton yield fo recasts. Specific research questions addressed in this study were: 1). Do in season updates of cotton yield forecasts improve accuracy over the forecast obtained before season? 2). Which ENSO index (ONI, MEI, or JMA) provide s the best cotton yield forecas ting accuracy? 3). Do in season updates on cotton yield forecast s tailored to ENSO ha ve better potential in forecasting cotton yield than the cotton yield forecasts obtained using climatology alone? The objectives of this study were 1) to evaluate in sea son updates of cotton yield forecasts, 2) to evaluate the use of different ENSO indices in forecasting cotton yield and 3) to compar e ENSO based forecasts with those based on climatology.

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77 Material and Methods Outline of the Forecasting Method The CROPGRO Cotton model requires daily weather data to simulate growth and development. In order to utilize the model to forecast cotton yield weather data input s must be provided in terms of a forecast. As a first step, historical weather data up to the point when the cotton yield forecast is made were replaced with the real weather data for that season. The process of updating the model with real weather data w as repeated two times during the season (July 1, and August 1) during 1951 2005. Cotton yield forecasts ob tained before season, and in season using past weather data as a forecast (climatology) were compared against their simulated cotton yields using real weather data to evaluate an accuracy of the forecasts, to obtain cotton forecasts tailored to ENSO phases as a next step historical weather data for the current ENSO phase were assumed to be a forecast of future weather. Cotton yield forecasts tailored to ENSO were compared with the cotton yield forecasts obtained using climatology alone. This study was focu sed on Quincy, Florida, as a case study of the Southeastern United States. Model Description and Input Data Cotton was simulated using the CROPGRO Cotton model under rain fed conditions with no nitrogen stress. The planting date for all the simulations wa s kept on May 1 to represent a typical planting date in the southeastern United States (Pettigrew, 2002). The model has been calibrated for Quincy, Florida location (Chapter 2) for the Delta Pine 555 cultivar. Th is cultivar parameter set was used to simula te cotton yield for this location. Site specific details including soil type and cultivar are described in detail in Chapter 2.

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78 Comparison between Before Season and In Season Cotton Yield Forecasts B ased on Climatology Inputs of historical weather data fo r 1951 2005 were provided to the model to simulate cotton yield using May 1 as a planting date for all years. The mean and forecast and associated uncertainties obtained using climatology as a forecast. In the next step, historical weather data up to July 1 were replaced with observed weather data up to that point for all the years. For example, in order to forecast cotton yield for the year 1951, all the historical weath er records from 1952 2005 were replaced with 1951 observed weather up to July 1. Those updated weather data were then provided to the model to simulate updated cotton yields on July 1. The mean and standard deviations of those simulated cotton yields repre cotton yield forecasts and associated uncertainties using climatology as a forecast. Another in season update of cotton yield forecasts was obtained on August 1 for all the years. se forecasts were obtained by comparing with their true simulated values obtained using observed weather data for each of the years In order to evaluate if the forecasting accuracy of in season updated cotton yield was improved sig nificantly, an F test was performed to see if the standard deviation of residual error ( ) between observed and forecasted cotton yield obtained before season was significantly different from that obtained in season with updated weathe r data. The F test was also performed to evaluate if the differences in average standard deviation of simulated cotton yield forecast across all the years reflecting the uncertainties in weather ( ) were

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79 statistically significant for b efore season and in season These two F tests provided the basis to answer the first research question. Compar ison of Cotton Yield Forecasts B ased on ENSO Indices Royce et al, (2009) compared predictive potentials of ONI, MEI, and JMA based ENSO classific ation for three crops of the southeastern United States including cotton. Based on the findings, January April ONI based monthly ENSO classification and March May MEI based monthly ENSO classification showed the strongest association with the historic cot t on yield In this study, ONI and MEI based ENSO classification was carried out using the approach of Royce et al, (2009). For example, under MEI classification, historical years having El Nio phase for March May months were used to create MEI El Nio re alizations as input to crop model. Similarly, under ONI classification, historical years that had El Nio phase for January April months were used to create ONI El Nio real ization as input to crop model. Similarly, La Ni a and neutral phase realizations as input to the models were created. Since JMA is a yearly classification for ENSO historical years of data that fall under El Nio La Ni a, and neutral phase were used to create realizations as input to the crop model, respectively. Before season and in season updates of cotton yield forecasts were then obtained under El Nio phase, for instance, by providing the model with weather data specific to that particular ENSO phase based on one of three ENSO indices being compared. In order to evaluate which ENSO index showed the highest forecasting potential, the F test was performed to see if obtained by three ENSO indices were significantly different from each other. Similarly, of forecasted cotton yields obtain ed based on three ENSO indices were also evaluated by the F test to investigate if the differences

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80 were statistically significant. These statistical evaluations were carried out to answer the second research question. Comparison between Climatology B ased and ENSO Tailored Cotton Yield Forecast The particular ENSO index that showed the lowest mean standard deviations of model simulations reflecting weather uncertainties ( ) and the lowest standard deviation of the residual error of obse rved and mean simulated cotton yields ( ) were compare with climatology based cotton yield forecasts. Statistical comparison s between climatology based and ENSO based cotton yield forecasts were carried out with F test in the same mann er as described in the above two sections to answer third research question. Results and Discussion Comparison between Before Season and In Season Cotton Yield Forecasts based on Climatology C otton yield forecasts by the CROPGRO Cotton model that were o btained before the season for 1951 2005 using climatology are shown in Table 4 1. In season updates of cotton yield forecasts obtained on July 1 and August 1 over the period of 1951 2005 are shown in Table 4 2, and Table 4 3, respectively. Overall, the sta ndard deviations of simulated cotton yield forecast s reflecting weather uncertainties ( ) with in season updates on July 1, and August 1 were reduced in 80% and 90% of the years respectively Similarly, the reductions in the residual errors ( ) with in season updated cotton yield forecasts obtained on July 1 and August 1 were observed 65% and 56% of the time compared to before season cotton yield forecasts. An example of how uncertainties in cotton yield forecasts are reduced with in season updates with observed

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81 weather is shown in Figure 4 1. The average cotton yield forecast and standard deviation around the mean w ere higher for forecasts obtained before the season. Wh en the cotton yield forecasts were updated wi th observed weather data average cotton yield forecast approached the observed cotton yield s Statistical comparison of mean standard deviations of simulated cotton yield forecasts across all the years reflecting weather uncertainties ( ) and the standard deviation of residual errors between observed and mean simulated forecast ( ) are shown in Table 4 4. Although the results show reductions of and on July 1 update d fo recasts compared to the before season cotton yield forecasts, the differences were not statistically significant. However, and were reduced considerably for August 1 updates. These reductions were highly signif icant (p<0.01). The reduction in and of August 1 forecast updates relative to before season cotton yield forecasts were approximately 35% and 32%, respectively. These results agree with the statement by Wright et al. (1984) that the standard deviation decreased over time with updated forecasts. The main reason was due to the reductions in uncertainties in the weather data over time as observed weather replaced forecast weather Comparison of Cotton Yield Forec asts based on ENSO Indices El Nio phase Measure s of model deviations for cotton yield using El Nio forecast based on JMA, ME I, and ONI are shown in Tables 4 5, 4 6, and 4 7. In general, and for cotton yield fo recasts based on MEI were lowest among three ENSO indices based forecasts. Table 4 14 shows statistical comparison of cotton yield forecasts based on all

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82 three ENSO indices for three phases including El Nio phase. Results show that the MEI was best among the three ENSO indices compared in forecasting the cotton yield before season and in season for El Nio forecasts. Although of cotton yield forecast based on MEI was 30% lower than JMA and 21% lower than ONI, the differences were not significant. Unfortunately, between 1951 and 2005 there were only 9 12 years classified as El Nio under those three ENSO indices. Better statistical testing could have been made if the sample size was larger. La Nia phase Cotton yield forecasts obtaine d using La Nia forecasts based on JMA, MEI, a nd ONI are presented in Tables 4 8, 4 9, and 4 10. In general, MEI performed better than other two ENSO indices based cotton yield forecasts. The for cotton yield forecasts obtained using MEI based La Nia forecasts were lowest for before season cotton yield forecast and July 1 in season updated cotton yield forecasts (Table 4 14) whereas, ONI based La Nia forecasts were lowest for August 1 in season updated cotton yield forecasts. But, and for cotton yield forecasts for all three ENSO indices were not statistically significant under the La Nia phase. Neutral phase Interestingly, cotton yield forecasts obtained using Neutral forecasts based on JMA index showed improved forecasting accuracy compared to the yield forecasts based on o ther two ENSO indices. (Tables 4 11, 4 12, and 4 13). The of cotton yield forecasts based on JMA was significantly different from ONI for the fo recasts obt ained before the season (Table 4 14). Other than that and of cotton yield forecasts based on the three ENSO indices did not show statistically significant differences.

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83 Comparison between Climatology B ased and ENSO Tailored Cotton Yield Forecast s Although cotton yield forecasting accuracy measures ( and ) were not significantly different, the ENSO indices that showed the lowest and for a given phase were compared with climatology based cotton yield forecast. Based on the best results discussed above MEI was used in the comparison for El Nio and La Nia phases, and JMA was used for the Neutral phase. Statistical compa rison s between climatology based and ENSO tailored cotton yiel d forecasts are shown in Table 4 15. Interestingly, ENSO tailored cotton yield forecasts for El Nio and La Nia did not show improvement over climatology based forecast s On the contrary clima tology based cotton yield forecasts showed lower compared to ENSO based cotton yield forecasts. T he standard deviations were lower under the ENSO tailored cotton yield forecasts but those results were not significantly different. In terestingly, the standard deviation of cotton yield forecasts obtained before the season and on July 1 under the Neutral phase based on JMA index showed highly statistically significant reduction s compared to the climatology based cotton yield forecasts. I n general, ENSO tailored cotton yield forecasts for Neutral phase shows better predictability compared to climatology based cotton yield forecasts. But, for El Nio and La Nia phases the cotton yield forecasts did not show statistically significant differ ences from climatology based forecasts. Conclusions Accuracy of cotton yield forecasts was improved with in season updating the CROPGRO Cotton model predictions using observed weather data. The in season updates of cotton yield forecasts were statisticall y significant for August 1 forecasts but

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84 not statistically significant for July 1 forecasts. On August 1 updates approximately 90% of the cotton yield forecasts showed reduction s in their standard deviations and 56% of the cotton yield forecasts showed r eductions in residual errors compared to before season cotton yield forecasts. In general, ENSO indices did not show statistically significant differences in and for El Nio and La Nia phases. For the Neutral phase, the JMA index based cotton yield forecasts were better. The for JMA based cotton yield forecasts was significantly lower than ONI based cotton yield forecasts. Comparison between climatology and ENSO based cotton yield forecast results showed that the ENSO tailored cotton yield forecasts did not show significant improvement for El Nio and La Nia phases over climatology based cotton yield forecasts. But, under the Neutral phase, the standard deviations of ENSO tailored cotton y ield forecasts were significantly lower than climatology based cotton yield forecasts. That shows that the in season updates of cotton yield forecasts in neutral phase s have good potential over using climatology based cotton yield forecast. This study was conducted with historical weather records over 1951 2005. The limitation of this study was that there were only 9 to 12 years under El Nio and La Nia categor ies For better statistical comparison s more years of weather data are needed to increase the n umber of years in each ENSO phase. Also, only one location was used as a case study in the southeastern United States. M ore locations should be analyzed.

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85 Figure 4 1. Distribution of forecasted cotton yields for the 1980 cotton season at Quincy, Fl orida simulated using 1951 2005 historical weather data. The s olid horizontal line represents observed cotton yield for 1980 obtained using model simulation using observed weather. Before Season July 1 August 1

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86 Table 4 1. Measures of model deviations for seed cotton yield (Quincy, FL) before season usi ng no forecast except climatology Year Observed Expected Residual Error ( ) Year Observed Expected Residual Error ( ) kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha kg/ha kg/ha 1951 3370 3387 415 17 1978 3947 3689 455 258 1952 2981 3393 416 412 1979 3730 3710 45 9 20 1953 3448 3385 415 63 1980 3950 3735 468 215 1954 3047 3393 412 346 1981 4286 3743 461 543 1955 3632 3382 414 250 1982 4295 3758 463 537 1956 3529 3382 419 147 1983 2494 3817 436 1323 1957 4118 3372 402 746 1984 4123 3810 478 313 1958 3311 339 3 416 82 1985 4142 3830 476 312 1959 3671 3398 416 273 1986 4165 3846 478 319 1960 3694 3414 423 280 1987 3987 3875 483 112 1961 3420 3430 421 10 1988 3585 3912 492 327 1962 3623 3439 422 184 1989 3876 3930 490 54 1963 3645 3448 424 197 1990 3463 3953 488 490 1964 3624 3456 431 168 1991 3882 3964 495 82 1965 3992 3457 420 535 1992 4096 3969 500 127 1966 3340 3491 428 151 1993 4055 3978 497 77 1967 3497 3499 431 2 1994 4382 3995 498 387 1968 3524 3515 440 9 1995 3807 4033 504 226 1969 357 6 3536 435 40 1996 4138 4044 511 94 1970 3484 3554 437 70 1997 3699 4069 506 370 1971 3109 3570 434 461 1998 3599 4108 507 509 1972 2361 3602 416 1241 1999 4173 4114 514 59 1973 3708 3610 445 98 2001 4531 4142 516 389 1974 3014 3631 437 617 2002 4158 4172 522 14 1975 3990 3626 444 364 2003 5079 4187 511 892 1976 3946 3643 456 303 2004 4342 4208 529 134 1977 2132 3702 398 1570 2005 4079 4256 529 177

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87 Table 4 2. Measures of model deviations for seed cotton yield (Quincy, FL) in season (July 1) using no forecast except climatology Year Observed Expected Year Ob served Expected kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha kg/ha kg/ha 1951 3370 3540 368 170 1978 3947 3665 405 282 1952 2981 3316 424 335 1979 3730 3684 467 46 1953 3448 3427 413 21 1980 39 50 3826 413 124 1954 3047 3474 361 427 1981 4286 3848 420 438 1955 3632 3456 385 176 1982 4295 3811 427 484 1956 3529 3474 347 55 1983 2494 3846 348 1352 1957 4118 3532 341 586 1984 4123 3851 409 272 1958 3311 3396 346 85 1985 4142 3943 419 199 19 59 3671 3350 372 321 1986 4165 4043 430 122 1960 3694 3382 400 312 1987 3987 3904 405 83 1961 3420 3393 404 27 1988 3585 3755 553 170 1962 3623 3635 356 12 1989 3876 3988 438 112 1963 3645 3461 329 184 1990 3463 3915 516 452 1964 3624 3522 399 102 1991 3882 3949 377 67 1965 3992 3470 394 522 1992 4096 4008 426 88 1966 3340 3327 395 13 1993 4055 3944 499 111 1967 3497 3541 361 44 1994 4382 4077 441 305 1968 3524 3521 412 3 1995 3807 3934 569 127 1969 3576 3301 498 275 1996 4138 4135 430 3 1 970 3484 3614 399 130 1997 3699 4096 448 397 1971 3109 3650 397 541 1998 3599 3766 644 167 1972 2361 3535 345 1174 1999 4173 4097 415 76 1973 3708 3632 394 76 2001 4531 4217 458 314 1974 3014 3472 507 458 2002 4158 4189 474 31 1975 3990 3743 41 2 247 2003 5079 4321 430 758 1976 3946 3603 390 343 2004 4342 4324 438 18 1977 2132 3630 437 1498 2005 4079 4057 565 22

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88 Table 4 3. Measures of model deviations for seed cotton yield (Quincy, FL) in season (August 1) using no forecas t except climatology Year Observed Expected Year Observed Expected kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha kg/ha kg/ha 1951 3370 3653 287 283 1978 3 947 3735 238 212 1952 2981 2537 368 444 1979 3730 3626 311 104 1953 3448 3433 286 15 1980 3950 3867 218 83 1954 3047 3431 258 384 1981 4286 3852 423 434 1955 3632 3525 218 107 1982 4295 4055 265 240 1956 3529 3516 246 13 1983 2494 3149 473 655 1957 4118 3673 224 445 1984 4123 3578 286 545 1958 3311 3512 242 201 1985 4142 4240 280 98 1959 3671 3491 251 180 1986 4165 4236 279 71 1960 3694 3454 290 240 1987 3987 3934 410 53 1961 3420 3585 289 165 1988 3585 4013 388 428 1962 3623 3540 310 83 1 989 3876 3968 372 92 1963 3645 3535 218 110 1990 3463 3251 538 212 1964 3624 3442 233 182 1991 3882 3800 254 82 1965 3992 3664 395 328 1992 4096 3852 474 244 1966 3340 3318 256 22 1993 4055 4179 357 124 1967 3497 3593 234 96 1994 4382 4245 406 137 1968 3524 3512 404 12 1995 3807 4362 271 555 1969 3576 3441 237 135 1996 4138 3881 522 257 1970 3484 3735 275 251 1997 3699 4047 313 348 1971 3109 3577 260 468 1998 3599 3536 194 63 1972 2361 3230 488 869 1999 4173 4043 280 130 1973 3708 3456 35 3 252 2001 4531 4313 357 218 1974 3014 3301 239 287 2002 4158 4304 314 146 1975 3990 3894 250 96 2003 5079 4667 291 412 1976 3946 3541 457 405 2004 4342 4456 423 114 1977 2132 2620 434 488 2005 4079 4174 389 95

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89 Table 4 4. Statistical c omparison of cotton yield forecasts obtained before season with in season updated cotton yield forecasts. *** represents significant difference in and SD for in season updated cotton yield forecast with the and S D represents non significant correlations. Cotton Yield Forecast based only on climatology Before Season 01 Jul 01 Aug 457 420 ns 299*** 458 423 320***

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90 Table 4 5. Measures of model deviations for seed cotton yield (Quincy, FL) using El Nio forecast based on JMA index Before Season In Season (July 1) In Season (August 1) Year Observed Expected Expected Expected kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) 1952 2981 3197 603 216 3103 659 122 2466 319 515 1958 3311 3179 605 132 3262 526 49 3429 311 118 1964 3624 3213 614 411 3274 565 350 3294 308 330 1966 3340 3274 623 66 3080 588 260 3199 319 141 1970 3484 3323 632 161 3393 568 91 3634 363 150 1973 3708 3366 638 342 3435 572 273 3420 357 288 1977 2132 3571 492 1439 3469 611 1337 2628 413 496 1983 2494 3661 582 1167 3729 376 1235 3148 427 654 1987 3987 3607 689 380 3735 596 252 3880 428 107 1988 3585 3676 718 91 3501 824 84 3932 476 347 1992 4096 3700 717 396 3 789 568 307 3794 520 302 2003 5079 3841 664 1238 4065 514 1014 4478 384 601

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91 Table 4 6. Measures of model deviations for seed cotton yield (Quincy, FL) using El Nio forecast based on MEI index Before Season In Season (July 1) In Season (August 1) Year Observed Expected Expected Expected kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) 1 953 3448 3257 429 191 3259 512 189 3343 239 105 1958 3311 3282 435 29 3229 417 82 3416 149 105 1969 3576 3410 453 166 3084 637 492 3415 262 162 1980 3950 3591 473 360 3628 501 323 3889 162 61 1983 2494 3815 129 1321 3786 172 1292 2862 283 368 1987 3987 3716 489 271 3650 444 337 3686 248 301 1992 4096 3817 510 279 3873 520 223 3607 334 490 1993 4055 3819 506 236 3755 625 300 4051 244 5 2005 4079 4118 551 39 3836 726 243 4005 259 74

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92 Table 4 7. Measures of model deviations for seed cotton yield (Quincy, FL) using El Nio forecast based on ONI index Before Season In Season (July 1) In Season (August 1) Year Observed Expected Expected Expected kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) 1958 3311 3337 515 26 3346 521 35 3460 286 149 1966 3340 3439 531 99 3179 565 161 3254 248 86 1969 3576 3459 539 118 3157 754 420 3432 2 12 144 1973 3708 3528 549 180 3534 540 174 3318 448 390 1983 2494 3881 309 1387 3800 275 1306 2988 569 494 1987 3987 3784 591 203 3801 589 186 3775 516 213 1992 4096 3886 636 210 3832 562 264 3698 590 398 1995 3807 3969 619 162 3777 893 30 4350 22 8 543 2003 5079 4006 524 1073 4084 514 995 4566 232 513

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93 Table 4 8. Measures of model deviations for seed cotton yield (Quincy, FL) using La Nia forecast based on JMA index Before Season In Season (July 1) In Season (August 1) Year Observed Expec ted Expected Expected kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) 1955 3632 3384 537 2 48 3490 468 142 3513 211 119 1956 3529 3357 535 172 3431 474 98 3538 244 9 1957 4118 3340 488 778 3507 448 611 3715 248 403 1965 3992 3442 530 550 3488 448 504 3768 409 224 1968 3524 3499 563 25 3598 471 74 3615 429 91 1971 3109 3627 549 518 3682 505 573 3603 132 494 1972 2361 3678 414 1317 3603 341 1242 3415 281 1054 1974 3014 3704 538 690 3610 437 596 3350 133 336 1975 3990 3629 569 361 3826 492 164 3970 246 20 1976 3946 3616 582 330 3549 508 397 3641 430 305 1989 3876 3973 632 97 4 030 553 154 4043 333 167 1999 4173 4140 659 33 4070 559 103 4077 304 96

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94 Table 4 9. Measures of model deviations for seed cotton yield (Quincy, FL) using La Nia forecast based on MEI index Before Season In Season (July 1) In Season (August 1) Ye ar Observed Expected Expected Expected kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) 195 4 3047 3409 308 362 3500 283 453 3405 223 358 1955 3632 3343 318 289 3425 294 207 3468 251 164 1956 3529 3316 337 213 3422 284 107 3498 253 31 1962 3623 3406 331 217 3639 272 16 3536 335 87 1964 3624 3382 346 242 3530 326 94 3397 245 227 1968 3524 3455 365 69 3499 308 25 3578 431 54 1971 3109 3593 313 484 3650 310 541 3550 187 441 1974 3014 3670 276 656 3524 352 510 3314 212 300 1976 3946 3561 369 385 3498 308 448 3609 434 337 1999 4173 4079 417 94 4065 337 108 4045 327 128

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95 Table 4 10 Measures of model deviations for seed cotton yield (Quincy, FL) using La Nia forecast based on ONI index Before Season In Season (July 1) In Season (August 1) Year Observed Expected Expected Expected kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) 1955 3632 3384 357 248 3500 278 132 3446 235 186 1956 3529 3352 383 177 3449 307 80 3522 261 7 1968 3524 3499 414 25 3609 312 85 3686 227 162 1971 3109 3662 328 553 3748 273 639 3550 132 441 1974 3014 3748 269 734 3661 299 647 3331 150 317 1975 3990 3623 365 367 3845 276 145 3912 280 78 1976 3946 3603 423 343 3564 312 382 3682 200 264 1999 4173 4137 448 36 4093 354 80 4072 276 101

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96 Table 4 11. Measures of model deviations for seed cotton yield (Quincy, FL) using Neutral forecast based on JMA index Before Season In Season (July 1) In Season (August 1) Year Observed Expected Expected Expected 1951 3358 3484 224 126 3613 216 255 3658 287 300 1953 3449 3481 225 32 3477 316 28 3419 300 3 0 1954 3038 3495 208 457 3563 207 525 3503 212 465 1959 3671 3490 225 181 3392 236 279 3484 239 187 1960 3697 3524 235 174 3465 262 232 3474 293 223 1961 3419 3528 228 109 3494 258 75 3641 274 222 1962 3623 3535 230 88 3691 226 68 3510 311 113 1963 3644 3544 231 100 3528 195 116 3567 182 77 1967 3494 3600 235 106 3625 226 131 3632 206 138 1969 3575 3638 238 63 3343 373 233 3450 229 125 1978 3947 3788 254 159 3724 248 224 3791 193 156 1979 3771 3813 258 42 3776 317 5 3681 275 90 1980 3949 3851 267 98 3919 274 30 3913 187 36 1981 4301 3838 248 463 3928 276 373 3834 460 467 1982 4295 3854 252 441 3848 279 447 4072 189 223 1984 4126 3926 272 200 3940 262 186 3599 296 527 1985 4143 3931 270 212 3990 258 153 4261 260 118 1986 4165 394 8 271 217 4130 290 35 4278 243 113 1990 3472 4070 259 598 3995 367 523 3173 595 299 1991 3892 4074 282 182 4012 231 120 3801 251 91 1993 4056 4085 286 29 4016 353 40 4209 355 153 1994 4382 4098 282 284 4159 296 223 4272 443 110 1995 3812 4148 2 84 336 4004 435 192 4409 208 597 1996 4160 4170 294 10 4199 258 39 3799 555 361 1997 3710 4187 280 477 4201 301 491 4138 265 428 2001 4530 4248 299 282 4303 301 227 4332 347 198 2002 4261 4283 306 22 4262 323 1 4309 301 48 2004 4347 4331 30 7 16 4394 261 47 4426 433 79 2005 4019 4374 305 355 4137 415 118 4162 404 143

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97 Table 4 12. Measures of model deviations for seed cotton yield (Quincy, FL) using Neutral forecast based on MEI index Before Season In Season (July 1) In Season (Aug ust 1) Year Observed Expected Expected Expected kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (K g/ha) 1951 3370 3504 280 134 3649 249 279 3699 285 329 1952 2981 3532 270 551 3458 312 477 2582 426 399 1959 3671 3504 281 167 3445 258 226 3541 267 130 1960 3694 3529 306 165 3408 232 286 3475 280 219 1961 3420 3546 286 126 3458 238 38 3561 28 2 141 1966 3340 3616 285 276 3416 287 76 3353 264 13 1970 3484 3674 297 190 3715 265 231 3803 251 319 1973 3708 3727 306 19 3738 239 30 3538 365 170 1978 3947 3802 313 145 3779 259 168 3738 229 209 1979 3730 3832 317 102 3782 305 52 3703 26 9 27 1982 4295 3867 308 428 3937 326 358 4065 280 230 1984 4123 3933 348 190 3914 262 209 3566 276 557 1986 4165 3966 326 199 4149 296 16 4265 275 100 1988 3585 4067 343 482 3908 454 323 4036 368 451 1995 3807 4177 335 370 4146 474 339 4394 268 587 2001 4531 4266 353 265 4336 291 195 4378 342 153 2003 5079 4292 307 787 4403 278 676 4693 310 386 2004 4342 4356 378 14 4440 320 98 4549 460 207

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98 Table 4 13. Measures of model deviations for seed cotton yield (Quincy, FL) using Neutral forecas t based on ONI index Before Season In Season (July 1) In Season (August 1) Year Observed Expected Expected Expected kg/ha kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) kg/ha kg/ha (Kg/ha) 1952 2981 3488 358 507 3390 337 409 2520 398 461 1953 3448 3462 372 14 3487 338 39 3476 295 28 1954 3047 3477 362 430 3561 321 514 3529 227 482 1957 4118 3437 348 681 3580 291 538 3701 216 417 1959 3671 3471 372 200 3398 312 273 3516 234 155 1960 3694 3498 375 196 3446 367 248 3490 264 204 1961 3420 3509 377 89 3475 365 55 3634 268 214 1962 3623 3516 379 107 3681 312 58 3579 317 44 1963 3645 3525 380 120 3510 291 135 3588 190 57 1964 3624 3543 382 81 3602 364 22 3522 188 102 1965 3992 3529 372 463 3529 334 463 3681 387 311 1967 3497 3581 385 84 3621 336 124 3650 211 153 1970 3484 3638 390 154 3705 361 221 3809 226 325 1972 2361 3716 302 1355 3634 26 5 1273 3252 530 891 1978 3947 3769 409 178 3736 352 211 3804 191 143 1979 3730 3795 413 65 3776 407 46 3704 276 26 1980 3950 3826 421 124 3920 388 30 3923 175 27 1981 4286 3820 409 466 3942 388 344 3887 442 399 1982 4295 3836 412 459 3854 364 441 4119 193 176 1984 4123 3899 429 224 3930 380 193 3636 249 487 1986 4165 3932 429 233 4128 407 37 4305 233 140 1990 3463 4055 427 592 4007 404 544 3240 585 223 1991 3882 4059 442 177 4008 329 126 3848 257 34 1993 4055 4070 446 15 4038 418 17 4258 335 203 1994 4382 4082 445 300 4160 411 222 4302 437 80 1997 3699 4171 448 472 4191 427 492 4146 259 447 2002 4158 4267 470 109 4270 422 112 4359 296 201 2004 4342 4306 479 36 4405 391 63 4487 418 145

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99 Table 4 14. Statistical comparison of the for JMA Neutral is significantly lower than of ONI Neutral. All other values were not statistically different from each other. Type of Cotton Yield Forecast based on ENSO forecast climate Before Season 01 Jul 01 Aug forecast kg/ha (kg/ha) kg/ha (kg/ha) kg/ha (kg/ha) El Nio JMA 716 631 660 580 398 385 MEI 517 441 533 506 241 242 ONI 636 535 606 579 383 370 La Nia JMA 582 550 528 475 399 283 MEI 363 338 334 307 264 289 ONI 412 373 376 301 248 220 Neutral JMA 262 a 260 246 285 264 303 MEI 330 313 289 297 312 305 ONI 403 401 373 360 309 296

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100 Table 4 15. Statistical comparison of cotton yield forecasts using only climatology forecast with ENSO tailored cotton yield hat the standard deviations of expected cotton yield forecasts obtained from JMA Neutral is significantly lower than the standard deviations of expected cotton yield forecasts obtained from climatology. Type of Cotton Yield Forecast Comparison climat e Before Season 01 Jul 01 Aug forecast kg/ha (kg/ha) kg/ha (kg/ha) kg/ha (kg/ha) Climatology 471 464 487 434 261 34 2 MEI El Nio 517 441 533 506 241 242 Climatology 324 437 299 397 274 291 MEI La Nia 363 338 334 307 264 289 Climatology 257 467 239 430 244 314 JMA Neutral 262 260*** 246 285*** 264 303

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101 CHAPTER 5 COTTON YIELD FORECAS TING FOR THE S OUTHEASTERN USA USIN G CLIMATE INDICES Introduction Cotton is the most important fiber crop in the United States, accounting for approximately 20% of the total production in the world and more than $25 billion in products and services annually (USDA ERS, 20 09 ). C otton production in the southeastern United States averages about 22% of the total upland cotton production in the United States (USDA ERS 2009). Georgia and Alabama hold the major share of total cotton produced in the southeastern United States. Re cently, there has been a significant increase in cotton planted those two states. While comparing average acreage planted, there was an increase of about 26% in Georgia 41% in Alabama during the last decade (NASS, 2007). While evidence clearly shows an in crease in cotton planted over time, climate variability is a major concern that could adversely affect its production in the southeastern United States. An effective way to reduce agricultural vulnerability to climate variability is through the implementat ion of adaptation strategies. For example crop yield forecast could be used by farmers to mitigate negative consequences of unfavorable climate forecast, or benefit from anticipated favorable climate conditions (Baigorra et al., 2007). If growers know the expected cotton yield for the coming season, they may be able to decide on alternative management strategies to reduce the cotton production risk (Jones et al., 2000; Hansen, 2005; Vedwan et al., 2005; Jagtap et al., 2002). For example, growers could purch ase appropriate crop insurance ahead of time in order to compensate for an adverse effect of climate variability on their cotton yields.

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102 Given that the time s at which different crop yield forecasts may be made differ, the techniques to obtain them also va r y Seasonal cotton yield forecasts are useful if they are available as early as February, before the growing season starts, so that growers can make use of them to decide on purchasing seeds, fertilizers, and insurance policies in advance (personal commun ication with David Wright and Clyde Fraisse). For instance the deadline for growers to make crop insurance related decisions in this region is March 15. So, if they would like to make insurance decisions based on expected yields for the coming season, then the crop yield forecasts should be available before that date. While the growth and development of crops are known to be influenced by weather during the growing season, it is a common practice to predict crop yield based on weather variables (Sakamoto, 1979; Idso et al., 1979; Walker, 1989; Alexandrove and Hoogenboom, 2001). However, crop yield predictions based on observed weather cannot be made available before the planting season (Kumar, 2000). Attempts to obtain long te r m forecasts using alternatives to weather variables such as climate indices that exhibit teleconnections with weather are limited. The El Nio Southern Oscillation (ENSO) phenomenon is one of the most significant drivers of climate and agricultural variability in the southeastern Un ited States (Hansen et al., 1998; Ropelewski and Halpert 198 6 Kiladis and Diaz 1989; Mo and Schemm 2008; Mennis 2001). Although, the ENSO effects in southeastern United State are stronger during the winter, their effects are not very strong during the sum mer months (Baigorria et al., 2007). Baigorria et al. (2010) also showed that cotton was not strongly affected by ENSO itself, however, ENSO in conjunction with other oceanic

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103 (Pacific and Atlantic) and atmospheric patterns may be useful for forecasting cot ton yield. In a parallel study, Martinez et al. (2009) used sea surface temperature (SST) in the tropical North Atlantic (TNA), the Pacific North American (PNA) index and Bermuda High Index (BHI) along with the ENSO index to predict corn yields in the sout heastern United States. The findings of Martinez et al. (2009) showed good potential for using climate indices to forecast corn yield in this region. Large scale teleconnection indices greatly influence the climate and agriculture in the southeastern Unite d States (Stenseth et al., 2003; Enfield, 1996; Barnston et al., 1991; Bell and Jenowiak, 199 4 ; Martinez et al., 2009) The research question addressed was; are there teleconnections between large scale climate indices and cotton yield that would provide t he basis for forecasting cotton yield in southeastern United States? The objectives of this study were to evaluate the relationships between large scale climate indices and cotton yield and to evaluate the skill of cotton yield forecasts. Materials and Met hods Historic Cotton Yield Data County level yield data for cotton were obtained from National Agricultural Statistical Services (NASS, 2008) for 57 years from 1951 2007 for a total of 64 cotton producing counties in Georgia and Alabama. Cotton producing counties in Florida were not considered in this study because there was only one county, Santa Rosa that had a county reported cotton yield available for 57 years. The NASS cotton yields did not distinguish between irrigated and rain fed cotton production The time series of historic cotton yield over the time period between 1951 and 2007 show ed a gradual upward trend. The factors contributing towards this upward

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104 trend likely include effects of fertilizers, pesticides, improved cultivars, and enhanced mana gement practices, but not necessarily climate (Wigley and Qipu, 1983). In order to evaluate the correlations of historic cotton yield with climate indices, the effects of non climatic influences on historic yield needed to be removed. For this study, techn ological improvements in cotton yield over time was assumed to be linear, hence county cotton yields were detrented by removing the linear trend. The percentage deviation of yield from the trend line (% residual) was computed for each year (Eq. 4 1). (5 1) Climate Data Monthly average temperature and monthly cumulative precipitation for 64 weather stations in Georgia and Alabama were obtained from National Climat ic Data Center (NCDC) for 1966 2007. Climate data for May September months were used in the analysis instead of full year of data since those months typically coincides with the cotton growing season in the southeastern United States. The main reason for l imiting the climate data to 1966 2007 instead of 1951 2007 was the fact that there were many counties, especially in Alabama, that had missing climate data between 1951 and 1965. Atmospheric and Oceanic Climate Indices Ste n seth et al. (2003) stated that an y single climate index may possibly explain only a relatively small part of the local climate variability. They suggested that one should use climate indices that pick up most of the relevant climate weather variations for the specific system under study. In this study, a total of seven climate indices were used: Oceanic Nio Index (ONI), Tropical North Atlantic (TNA) SST index, Atlantic Meridional Mode (AMM) index, North Oscillation Index (NOI), North Pacific (NP) pattern,

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105 Quasi Biennial Oscillation (QBO) index, and Tropical North Hemisphere (TNH) index. Descriptions of each of those indices as well as their effects on climate of southeastern United States as described in the literature are as follows. Oceanic nio i ndex (ONI) The ONI anomalies are the run ning means of SST anomalies in the NIO 3.4 region ( 5 o N 5 o S, 120 o 170 o W) and were obtained from the NOAA climate prediction center The ONI has become the National Oceanic and Atmospheric Administration (NOAA) standard for categorizing the ENSO events in t he tropical pacific. However, continuous monthly values of ONI were selected in this study and not the ENSO phases. ENSO exhibits strong correlations with temperature and precipitation in the United States (Ropelewski and Halpert, 1986) and southeastern U nited States in particular (Mote, 1986, Hansen et al., 1998 evidence of impact of ENSO on southeastern United States climate, ONI index was chosen to represent ENSO index in this analysis. Tropical north At lantic (TNA) index The TNA index (Enfield et al., 1999) is an anomaly of the average of the monthly SST from 5.5 o N 23.5 o N, 15 o 57.5 o W. The TNA data were obtained from the Physical Science Division of the Earth System Research Laboratory (ESRL) at National Oceanic and Atmospheric Administration (NOAA). Association of TNA with the climatic conditions of southeastern United States has been documented in the literature. For instance, Wang et al. (2008) demonstrated that the variability in the summer precipitat ion for the southeastern United States is strongly associated with Atlantic SST. Enfield, (1996) investigated a teleconnection between

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106 Atlantic SST and precipitation in the southeastern United States. Results from the study by Martinez et al. (2009) clearl y indicated an association of Atlantic SSTs with temperature and precipitation in the southeastern United States. Atlantic meridional m ode (AMM) index The AMM SST index is a gathering of cross equatorial meridional SST anomalies in the tropical Atlantic i ndex (Chiang and Vimont, 2004; Takeshi et al., 2010). The AMM index is correlated with TNA index and plays an important role in inter annual and decadal climate variability and is closely linked with hurricane activities in the southeastern United States ( Xie et al., 2005; Vimont and Kossin 2007; Kossin and Vimont 2007). North oscillation i ndex (NOI) The NOI index represents differences between the sea level pressure anomalies at the north pacific height (NPH) in the northeast Pacific and near Darwin, Aus tralia (Schwing et al., 2002). Monthly NOI index values were obtained from the Pacific Fisheries Environmental Laboratory (PFEL) of NOAA. The NOI is closely related to El Nio and La Nia events where positive values of NOI are reflective of La Nia condit ions and negative values of NOI are closely linked with El Nio conditions (Lee and Sydeman, 2009). Since, NOI is linked closely with ENSO events; it could impact climatic conditions of southeastern United States. North p acific (NP) pattern Another sea le vel pressure based index used in this study was NP index that represents area weighted SLP over the region 30 o N 6 5 o N 160 o E 140 o W ( Trenberth and Hurrell, 1994 ). The positive phase of the NP pattern is associated with enhanced

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107 cyclonic circulations of paci fic jet stream over the southeastern United States which affects climatic conditions in this region (Bell and Jenowiak, 199 4 ). Tropical north h emisphere (TNH) index The TNH pattern, first classified by Mo and Livezey (1986) reflects large scale changes in both the location and eastward extent of the pacific jet stream and thus this pattern significantly modulates the flow of marine air into the United States and to the southeastern United States (Washington et al., 2000 ). Barnston et al. (1991) found that t he negative phase of TNH pattern was often observed when the pacific warm condition (El Nio) is present, which would eventually affect the climate conditions in the southeastern United States. Quasi biennial o scillation (QBO) index The QBO represents the oscillation of zonal winds in the stratosphere (at 30 mb) over the equator in the Pacific that blow eastward or westward in a cycle that averages about 28 months. The effect of QBO in southeastern United States is evident due to its close association with the ENSO (Thompson et al., 2001). For instance, during an El Nio years with an easterly QBO the temperature tend to be below normal across the southeastern United States ( Bar nston et al., 1991). Correlation Analysis The correlation analysis of climate in dices with precipitation and temperature and with cotton yield residuals was carried out using Pearson correlation method. The statistical significance of the correlations was evaluated at In the following sections correlations of c limate indices with temperature, precipitation, and cotton yield are described. The correlation analysis of cotton yield with precipitation and temperature was not performed in this study, because in a parallel

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108 study Baigorria et al. (2007) correlated cott on yield with surface temperature and rainfall for 57 cotton producing counties in Georgia and Alabama. The results showed that surface temperature and rainfall in this region were significantly correlated with cotton yield for more than 50% of the countie s processed. Results also showed that the correlations were highly significant, especially for July rainfall for 84% of the counties. Since the clear evidence of significant correlation of cotton yield with surface temperature and rainfall was shown by Bai gorria et al. 2007, it was not re analyzed in this study. Correlations of Climate Indices with Temperature and Precipitation It was unclear whether the monthly climate indices prior to the cotton growing season were significantly correlated with monthly te mperature and precipitation during the cotton growing season for all cotton growing counties in Georgia and Alabama selected in this study. Climate indices for January and February were correlated with May September temperature and precipitation for 1966 2 007.The significant correlations of climate indices with temperature and precipitation during the cotton growing season could provide a basis for using climate indices to forecast cotton yield. Correlations of Climate Indices with Cotton Yield Climate ind ices for January and February were correlated with county cotton yield for 1966 2007. Correlation analyses were carried out for 64 cotton producing counties of Georgia and Alabama. Since the correlations of cotton yield with temperature and precipitation d uring the growing season is known (Baigorria et al., 2007), identifying statistically significant correlations of climate indices with climate variables and cotton yield would help us understand the behavior of climate cotton yield interactions and the fo recasting of cotton yield.

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109 Principal Component Regression All climate indices were summarized using a principal component analysis (PCA). The PCA is a data transformation technique that transforms original highly correlated variables into a new set of ind ependent variables in a way that the first principal component (PC) describes the highest variance followed by the second PC and so on (Massy, 1965). The motivation for using principal components of climate indices instead of their original values was beca use of the significant correlations among the climate indices ( Barnston et al., 1991; Barreiro et al., 2005 ). If highly correlated climate indices were used in the regression model, then the assumption of mutually independent explanatory variables is viola ted. Instead, the principal components of climate indices transform them into mutually independent variables that can be effectively used in multiple linear regression models. Another leading advantage of using PCA is that it is an efficient data reduction technique. For instance, if the maximum variances of two climate indices are summarized by principal component 1, then instead of using two indices one can use just one PC to utilize the information. The principal component regression (PCR) model uses pr incipal components as explanatory variables. The dependent variable for this model was detrended historic cotton yield and independent variables were principal components of climate indices. The general form of model is shown below: (5 2) Where, is cotton yield residual for a given county, and are the principal components of climate indices retained in the PCR m odel based on backward

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110 stepwise regressions. The residual error from multiple regression analysis was tested for normality. This is important because of the assumption in regression analysis that the residual errors are normally distr ibuted. Leave One Out Cross Validation The yield forecasts from different models for each county were evaluated using cross validation. This statistical validation approach can be used to validate the model when data are limited. With the cross validation approach, observed data are iteratively and exhaustively used for model testing, resulting in more reliable evaluation than getting estimates from the two group partition method and less biased than estimates derived from calibration dependent dataset (Jo nes and Carberry, 1994). In this method, n 1 data were used to estimate the parameters for the regression model and the one left out data point was used for model evaluation. By an iterative process, all the data points were used for validation. The skill of the forecast was evaluated using the statistically significant correlations and mean squared error (MSE) between observed and forecasted cotton yield. Categorical Yield Forecast Contingency Table Yield forecasts obtained from the principal component r egression models were divided into two categories; above average and below average cotton yield. A negative cotton yield residuals falls in the below average yield category and vice versa. A 2x2 contingency table (Table 5 1) was used to evaluate the skill of the forecast. Categorical square test of association (Plackett, 1983). This method tests an association between observed and forecasted categorical cotton yield. Statistical significance were evaluated at

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111 Since it is not possible to forecast absolute cotton yields accurately, knowing whether to expect an above average or below average yield for the coming season is also useful information to growers. The percentages of correct yield forecasts, the probability of detecting (POD) above average yield, and the probability of detecting below average yields were calculated using the following equations and Table 5 1. (5 3) (5 4) (5 5) The in (3 3) represents the ratio of total number of correct yield forecasts to the total number of forecasts. The (3 4) shows the ratio of total number of correct above average forecast to th e total number of observed above average cotton yield residuals. The (3 5) shows the ratio of total number of correct below average yield forecasts to the total number of observed below average cotton yield residuals. Results and Di scussion Historic Cotton Yield Data Time series of historic cotton yield showed a gradual upward trend over the time period of 1951 2007. The gradual upward trend was expected due to technological improvements over time. It wa s assumed that the technologic al trend over time was linear; the historic cotton yield data fit well the linear trend line. Once, the trend was removed, variability in cotton yield residuals was observed around the trend line closer to zero. This variability in cotton yield residuals c ould be due to the effect of climate variability, henceforth were analyzed for their correlations with climate indices.

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112 Correlation Analysis Correlations of climate indices with temperature and r ainfall Overall, the correlations of climate indices with t emperature showed statistically significant results at Figure 5 1 shows the most prominent correlations of all seven climate indices with temperature. It was interesting to note that all seven climate indices exhibited maximum correl ations with temperature during the month of July. Climate indices such as NOI, NP, and TNH exhibited statistically significant correlations with more counties than the other indices. Except for one county in Alabama, all seven counties together showed stat istically significant correlations with temperature in all cotton producing counties considered in this study. As can be seen from Figure 5 1 the NOI, NP, and TNH indices were negatively correlated with July temperature. This means that when these climate indices are in a negative phase during January and February, July temperature is expected to be above average for the southeastern United States. On the other hand, AMM, QBO, TNA, and ONI were positively correlated with July temperature. AMM, TNA, and ONI are Atlantic and Pacific SSTs and hence, warming of the SST during January and February was responsible for higher July temperatures. The correlations of all seven climate indices with rainfall are shown in Figure 5 2. The NOI and NP exhibited a negative correlations with July rainfall; opposite in sign to their correlations with July temperature. TNH did not exhibit strong correlations with July rainfall; however, its correlation was strong for September rainfall in a majority of the counties in Georgia and several counties in Alabama. It was interesting to note that the TNA showed negative correlations with June rainfall and positive correlations with

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113 September rainfall. These opposite correlations with June and September could eventually affect the cott on yield in the same manner because higher rainfall during the early growing season is favorable to cotton but the same during the maturity would adversely affect cotton yield. Correlation of climate indices with cotton y ield Figure 5 3 shows correlation s of climate indices with cotton yields. The NOI index was positively correlated with cotton yield. NOI was positively correlated with July precipitation and negatively correlated with July temperature; hence a positive correlation with cotton yield was ex pected for NOI. The NP pattern had a strong negative correlation with July temperature, but the correlations with cotton yield was positive for all the counties. This means that during the negative phase of NP, it is likely to have higher July temperature and lower cotton yield. The month of July typically coincides with the flowering stage of cotton growth in southeastern United States. Increased temperature during July stimulates the photosynthesis and leaf expansion and crop water requirements. This coul d increase water stress in non irrigated cotton plants and also reduce the allocation of daily assimilates to the fruit. As a result, final cotton yield could be either positively or negatively affected by July temperature. TNA and AMM showed negative cor relations with cotton yield. As mentioned in the previous section, TNA exhibited negative correlation with June and positive correlation with September rainfall. Both would adversely affect cotton yield and hence be consistent with the negative correlation of TNA with cotton yield. TNH was also negatively correlated with cotton yield while it had a positive correlation with September rainfall. Rainfall during the late maturity stage of cotton has limited or no use to the plant, on the contrary; it could cre ate an adverse effect. F requent precipitation during

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114 September and October months is the main cause of one of the most common cotton disease called hard lock of cotton, which would significantly reduce cotton yield. It was interesting to note that NOI was significantly correlated with rainfall for more counties than it was correlated with cotton yields. The possible explanation could be an effect of irrigation. If irrigation is a typical practice in those counties, then the effect of rainfall on cotton yie ld would be negligible and hence yield for those counties may lack significant correlations with NOI. As can be seen in Figure 5 3, a single month climate index alone was not sufficient to correlate significantly with cotton yield for all counties. All s even indices together were significantly correlated with cotton yield and climate for all the counties. In general, the correlations of climate indices with cotton yield and climate during the growing season showed potential use of forecasting cotton yield for the southeastern United States. Principal Component Regression Table 5 3 shows significant PCs retained in the backward stepwise regression procedure and Table 5 4 shows the loadings of climate indices in the principal components. Principal component 1 (PC1) was retained in 44% of the regression models for counties in Georgia. The loadings show that the TNA had the highest loading in PC1, followed by ONI and NOI indices. In contrast PC1 was only significant in 22% of the counties in Alabama. Converse ly, Principal Component 3 (PC3) was significant in 43% of the models for counties in Alabama but only in 20% of the models for counties in Georgia It can be seen from Table 5 4 that the PC3 had the highest loadings from the QBO index. This was expected be cause correlations of QBO with cotton yield were more prominent in counties of Alabama than in Georgia (Figure 5 3). Interestingly,

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115 Principal Component 11 (PC 11) was significant for approximately 50% of the counties for all the counties in Georgia and Ala bama. Based on the loadings in PC 11 it can be seen that the TNA and AMM had maximum loadings compared to other indices. Significant PCs retained by backward stepwise regression model were n ot in top to down order (Table 5 3). In other words, PC1 was not necessarily the most significant PC for all the counties. This was due to the fact that the first PC explains the maximum variance among the explanatory variables but not necessarily of the dependent variable in principal component regression (Sutter et al ., 1992). For example, loadings of QBO index were higher in PC3 compared to PC1. Since QBO correlation with cotton yield was more prominent in Alabama; PC3 was significant more times than PC1. Leave One Out Cross Validation The accuracy of cotton yield fo recasts by principal component regression models were evaluated with the leave one out cross validation approach. 77% of the counties in Georgia and 70% of the counties in Alabama showed significant correlations between observed and cross validated cotton yiel d residuals (Figure 5 4, Table 5 2). The highest significant correlation of 0.50 was obtained for Shelby County in Alabama whereas the lowest significant correlation of 0.22 was obtained for Colquitt County in Georgia and Lee County in Alabama. A total of 8 out of 34 counties in Georgia and 9 out of 30 counties in Alabama did not show significant correlations between observed and forecasted cotton yields. The possible reasons for this could be that the proportion of irrigated cotton yields for those cou nties might be higher than rainfed cotton. The irrigated cotton could diminish the direct impact of rainfall on the cotton yield and hence result in non significant correlations. For example, all seven climate indices showed statistically significant corre lations with climate during the cotton growing season in

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116 Calhoun County in Georgia but did not show a significant correlation with cotton yield and subsequently no predictability. It is possible that the climate indices show significant correlation with cl imate during the cotton growing season but not with cotton yield, if the reported cotton yield came from irrigated practices. Baigorria et al. (2008) stated that the highest yield counties in the southeastern United States showed weakest predictability. T he speculation was that the climate based yield predictability is weaker in counties with greater proportion of cultivated areas under irrigation. The results obtained in this study are in agreement with that speculation because some of the highest cotton yielding counties, such as Dooly, Colquitt, Mitchell, and Crisp showed little or no predictability. Unfortunately, the NASS data do not distinguish between irrigated and rainfed cotton yield, but this could be the possible explanation of weaker predictabil ities for those counties. Figure 5 5 shows the time series comparisons between historic cotton yield residuals and cross validated cotton yield for the highest and the lowest correlated counties in Georgia and Alabama. It was evident that the principal com ponents regression models of climate indices were able to capture year to year variability in cotton yield fairly well. The mean squared errors (MSE) between the historic cotton residuals and cross validated cotton yields were within the range of 0.03 0.10 It can be seen from Figure 5 6 that the average errors across all the counties was normally distributed with mean being very close to 0. Overall, the cotton yield residuals forecasted with principal components of climate indices showed good predictabilit y of cotton yields.

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117 Categorical Yield Forecast Contingency Table Results obtained from the contingency table are shown in Table 5 5 and Figures 5 7 and 5 8. A total 67% of the counties in Georgia and 73% of counties in Alabama showed statistically signi ficant association between categorical observed and cross validated cotton yield forecast. A total of 94% of the counties showed that the categorical cotton yield forecast obtained from the cross validated cotton yield at the lead time of approximately tw o to three months before planting (In February) was correct more than 50% of the time. The highest percent correct score was obtained for Bulloch County in Georgia that had correct categorical forecasts 73% of the time based on c ross validated results. Fig ure 5 7 shows the spatial distributions of percent correct categorical cotton yield forecasts for counties in Georgia and Alabama. It was interesting to note that except for Thomas County in Georgia, the categorical cotton yield forecast was correct more t han 50% of the time even though eight counties that were not significantly correlated with cross validated cotton yields. This shows that even if the model was not able to significantly capture the variability of the observed cotton yield residuals, a majo rity of forecasts were in the right category (above average or below average) more than 50% of the time. As we know, the probability of detecting above average or below average yield is 50% purely by chance. With the categorical forecast of cotton yield o btained from the principal components of climate indices, the probability of detecting above average or below average yields was better than chance for 88% and 94% of the counties, respectively. In applications of these results, growers might be more inter ested in

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118 knowing if they would expect a better than average yield or vice versa for their decision making processes. Conclusions The association of seven climate indices with climate during the cotton growing season and with county average historic cotton correlations. January and February monthly climate indices, which were months prior to the cotton growing season, exhibited statistically significant correlations with climate during the cotton growing season as well a s with cotton yields. July temperature showed the strongest correlations with all seven climate indices whereas the strongest correlation of climate indices with rainfall varied between June, July, August, and September. The accuracy of cotton yield forec asts based on principal component regressions were evaluated with the leave one out cross validation approach. With a lead time of approximately 2 months before the typical planting period on the southeastern United States, about 77% of the counties in Geo rgia and 70% of the counties in Alabama showed statistically significant correlations between observed and forecasted cotton yields. The MSE between observed and cross validated cotton yield residual forecasts were in the range of 3 11 % Categorical cotto n yield forecasts obtained from the cross validated results were evaluated using the skill measures of percent correct forecasts, probability of detecting above average cotton yield, and probability of detecting below average yields. 94% of the counties sh owed the categorical cotton yield forecast obtained at a lead time of approximately two months before planting (In February) was correct for more than 50% of the time. The probabilities of detecting above and below average yields were better

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119 than chance in 88% and 94% of Alabama and Georgia counties, respectively. The principal component regression of climate indices showed potential to become a useful tool to forecast cotton yield with a lead time of approximately two months before the typical cotton plant ing time of May first week in the southeastern United States.

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120 A B C D E F G Figure 5 1. Correlations of climate indices with temperature during the cotton growing season. A) AMM July temperature B) NOI July temperature C) NP July temperature D) QBO July temperature E) TNA July temperature F) ONI July temperature G) TNH July temperature. Correlations greater or less than 0.26 and 0.26 were significant at Non Significant Negative Significant (< 0.26) No Data Positive Significant (> 0.26)

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121 A B C D E F G H Figure 5 2 Correlations of climate indices with rainfall during the cotton growing season. A) AMM June rainfall B) NOI July rainfall C) NP July rainfall D) QBO July rainfall E) TNA June rainfall F) TNA September rainfall G) ONI August rainfall H) TNH September rainfall. Legends are same as Figure 3 1. Correlations greater or less than 0.26 and 0.26 were significant at

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122 A B C D E F G Figure 5 3. Correlations climate indices with cotton yield. A) AMM B) NOI C) NP D) QBO E) TNA F ) ONI G) TNH. Correlations greater or less than 0.26 and 0.26 were significant at Non Significant N egative Significant (< 0.26) No Data Positive Significant (> 0.26)

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123 Figure 5 4. Correlations of historic cotton residuals with cross validated cotton yield residuals using the principal component regression of Jan uary and February climate indices. Correlations greater than 0.22 are significant at (N = 57). Non Significant 0.22 0.29 0.30 0.39 > 0.40 No Data

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124 A B C D Figure 5 5. Time series comparison between observed and cross validated cotton yield residuals for four counties of Al abama and Georgia that showed the maximum (A and B) and minimum correlations (C and D). A) Bulloch, B) Shelby, AL C) Colquitt, GA, and D) Lee, AL.

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125 Figure 5 6. Histogram of residual errors across the entire cross validated county cotton yields. The er rors were normally distributed with and

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126 A B Figure 5 7. Probability of detecting c ounty level cotton yields using cross validated cotton forecasts for two categories. A) Probability of detecting above average cotton yield. B) Probability of detecting below average cotton yield. < 50% 50% 60% 60% 70% > 0.70% No Data

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127 Figure 5 8. Percent correct cross validated cotton yield forecasts based on principal components regression model of climate indices and contingency table. < 50% 50% 60% 60% 70% > 0.70% No Data

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128 Table 5 1. A 2x2 contin gency table for categorical cotton yields. Observed Forecasted Yield Total Yield Below Above Below A B C Above D E F Total G H I

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129 Table 5 counties in Geor gia and Alabama. The *** ** and represents significance at significant correlations. Georgia Alabama Counties Correlations MSE Counties Correlations MSE BEN HILL 0.42 *** 0.07 AUTAUGA 0. 47 *** 0.07 BLECKLEY 0.23 0.07 BARBOUR 0.30 ** 0.08 BROOKS 0.42 *** 0.04 BLOUNT 0.38 *** 0.03 BULLOCH 0.46 *** 0.06 CALHOUN ns 0.09 BURKE 0.30 ** 0.06 CHEROKEE 0.44 *** 0.06 CALHOUN 0.33 ** 0.03 COFFEE ns 0.11 CANDLER ns 0.08 COLBERT 0.25 0.06 CLAY 0.48 ** 0.04 COVINGTON 0.29 ** 0.07 COFFEE 0.28 ** 0.10 CULLMAN ns 0.07 COLQUITT 0.22 0.04 DALE 0.45 *** 0.09 CRISP ns 0.05 DALLAS 0.46 *** 0.06 DODGE 0.28 ** 0.06 ELMORE 0.42 *** 0.10 DOOLY ns 0.09 ESCAMBIA 0.25 0.07 EARLY 0.37 *** 0.05 ETOWAH ns 0.06 EMANUEL 0.42 *** 0.07 FAYETTE 0.46 *** 0.10 HOUSTON ns 0.06 HOUSTON 0.35 ** 0.09 IRWIN 0.35 *** 0.05 LAUDERDALE ns 0.08 JEFFERSON 0.29 ** 0.08 LAWRENCE 0.30 ** 0.08 JENKINS 0.31 ** 0.08 LEE 0.23 0.06 LAURENS ns 0.08 LIMESTONE 0.37 *** 0.08 LEE 0.33 ** 0.07 LOWNDES 0.49 *** 0.07 MACON 0.37 *** 0.06 MACON 0.28 ** 0.05 MITCHELL ns 0.06 MADISON ns 0.09 PULASKI 0.35 *** 0.06 MARENGO ns 0.09 RANDOLPH 0.37 *** 0.05 MONROE 0.29 ** 0.05 SCREVEN ns 0.08 MONTGOMERY 0.30 ** 0.07 SUMTER 0.34 *** 0.07 PICKENS 0.44 *** 0.05 TERRELL 0.31 ** 0.04 SHELBY 0.50 *** 0.05 THOMAS ns 0.05 TALLADEGA ns 0.04 TIFT 0.46 *** 0.04 TUSCALOOSA ns 0.06 TURNER 0.40 *** 0.06 WASHINGTON 0.29 ** 0.07 WILCOX ns 0.06 WORTH 0.30 ** 0.05

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130 Table 5 3. Significant principal components (PCs) of pr incipal component regression models for cotton producing counties of Georgia and Alabama Georgia Alabama Counties Significant PCs Counties Significant PCs BEN HILL 3,5,12,13,14 AUTAUGA 2,4,5,9,11 BLECKLEY 11,12 BARBOUR 8,11 BROOKS 5,8,13 BLOUNT 12 B ULLOCH 1,9,13,14 CALHOUN 1 BURKE 1,6,11 CHEROKEE 2,3,5,11,12 CALHOUN 5,8,11 COFFEE 3,7 CANDLER 1,9 COLBERT 3,6,11 CLAY 1,5,6,11 COVINGTON 3,5 COFFEE 7,9,13 CULLMAN 2 COLQUITT 3,14 DALE 1,5,7,8,11,14 CRISP 3,6 DALLAS 4,5,9,11 DODGE 5,11,12 ELMORE 1,2,5,9,11 DOOLY 11 ESCAMBIA 1 EARLY 1,3,8,14 ETOWAH 2,3 EMANUEL 1,5,9,12,13 FAYETTE 3,8,9,11 HOUSTON 1,11 HOUSTON 3,4,5,7,11 IRWIN 9,12 LAUDERDALE 3 JEFFERSON 1,7,11,13 LAWRENCE 3,6,11 JENKINS 1,2,13 LEE 5,11 LAURENS 12 LIMESTONE 3 LEE 6,9,1 3 LOWNDES 1,2,3,4,9,11 MACON 1,3,11,14 MACON 5,11,13 MITCHELL 1 MADISON 3 PULASKI 3,6,11 MARENGO 6 RANDOLPH 1,5,6,11 MONROE 6 SCREVEN 12 MONTGOMERY 2,7,8 SUMTER 1,6,11,13 PICKENS 1,3,6,9,11 TERRELL 5,11,12 SHELBY 2,4,5,9,10,11 THOMAS 1 TALL ADEGA 1 TIFT 2,8,11,12,14 TUSCALOOSA 6 TURNER 1,6,8,11,12,14 WASHINGTON 6,11 WILCOX 5,6,14 WORTH 3,5,12,14

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131 Table 5 4. Loadings of principal components (PCs) of climate indices Indices PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 PC12 P C13 PC14 ONI_Jan 0.73 0.44 0.30 0.13 0.20 0.32 0.03 0.09 0.03 0.01 0.07 0.02 0.00 0.07 ONI_Feb 0.74 0.45 0.33 0.10 0.17 0.32 0.00 0.05 0.01 0.02 0.07 0.01 0.01 0.07 AMM_Jan 0.30 0.89 0.15 0.04 0.02 0.18 0.12 0.07 0.02 0.11 0.15 0.03 0.07 0 .00 AMM_Feb 0.56 0.77 0.08 0.03 0.02 0.10 0.08 0.01 0.06 0.23 0.09 0.02 0.06 0.00 NOI_Jan 0.72 0.40 0.04 0.28 0.22 0.13 0.06 0.23 0.33 0.05 0.01 0.01 0.00 0.00 NOI_Feb 0.56 0.45 0.16 0.40 0.36 0.15 0.03 0.31 0.23 0.02 0.01 0.01 0.00 0.00 NP_Jan 0.46 0.25 0.00 0.54 0.55 0.25 0.15 0.14 0.17 0.02 0.01 0.00 0.00 0.00 NP_Feb 0.55 0.37 0.15 0.28 0.04 0.52 0.33 0.29 0.06 0.02 0.00 0.00 0.00 0.00 QBO_Jan 0.15 0.28 0.91 0.11 0.07 0.15 0.01 0.04 0.04 0.01 0.02 0.14 0.02 0. 01 QBO_Feb 0.16 0.23 0.92 0.09 0.11 0.15 0.04 0.02 0.01 0.02 0.02 0.14 0.02 0.01 TNA_Jan 0.61 0.72 0.00 0.14 0.15 0.03 0.07 0.04 0.07 0.23 0.09 0.02 0.06 0.00 TNA_Feb 0.80 0.52 0.05 0.12 0.10 0.08 0.08 0.07 0.02 0.13 0.16 0.00 0.06 0 .00 TNH_Jan 0.26 0.54 0.08 0.21 0.35 0.30 0.61 0.05 0.03 0.01 0.00 0.01 0.00 0.00 TNH_Feb 0.58 0.17 0.14 0.48 0.46 0.02 0.30 0.24 0.14 0.07 0.00 0.00 0.00 0.00

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132 Table 5 5. Skills of categorical cross validated cotton yield forecasts f or counties of Georgia and Alabama. Georgia Alabama Counties % correct POD Above POD Below Counties % correct POD Above POD Below BEN HILL*** 71.93 0.72 0.71 AUTAUGA* 55.77 0.48 0.64 BLECKLEY** 61.40 0.57 0.66 BARBOUR** 60.78 0.67 0.57 BROOKS 56.14 0.5 6 0.56 BLOUNT*** 64.58 0.71 0.58 BULLOCH*** 73.21 0.70 0.76 CALHOUN 38.46 0.64 0.08 BURKE* 59.65 0.57 0.62 CHEROKEE** 61.11 0.65 0.57 CALHOUN 57.89 0.62 0.55 COFFEE** 61.11 0.58 0.64 CANDLER** 61.40 0.57 0.66 COLBERT** 61.11 0.58 0.63 CLAY*** 68.52 0. 69 0.68 COVINGTON** 59.62 0.54 0.64 COFFEE 56.36 0.53 0.62 CULLMAN 47.92 0.56 0.39 COLQUITT* 59.65 0.62 0.57 DALE 53.19 0.48 0.58 CRISP* 57.89 0.57 0.59 DALLAS*** 64.15 0.58 0.69 DODGE** 63.16 0.62 0.64 ELMORE** 55.56 0.61 0.52 DOOLY** 64.91 0.57 0.72 ESCAMBIA*** 59.26 0.59 0.59 EARLY*** 68.42 0.71 0.66 ETOWAH* 51.85 0.62 0.43 EMANUEL*** 62.50 0.67 0.59 FAYETTE** 64.58 0.57 0.70 HOUSTON 52.73 0.48 0.57 HOUSTON** 61.54 0.69 0.54 IRWIN*** 68.42 0.68 0.69 LAUDERDALE** 61.11 0.56 0.66 JEFFERSON 56.14 0.57 0.56 LAWRENCE** 64.81 0.60 0.69 JENKINS 51.85 0.52 0.52 LEE** 58.82 0.61 0.57 LAURENS 54.39 0.59 0.50 LIMESTONE*** 66.67 0.63 0.70 LEE 58.18 0.59 0.58 LOWNDES*** 70.83 0.68 0.74 MACON*** 66.07 0.68 0.64 MACON 53.85 0.58 0.50 MITCHELL 54.39 0.65 0 .39 MADISON* 59.26 0.54 0.65 PULASKI** 63.16 0.62 0.64 MARENGO* 55.32 0.59 0.52 RANDOLPH** 63.64 0.62 0.65 MONROE 50.00 0.50 0.50 SCREVEN 52.63 0.59 0.46 MONTGOMERY 54.35 0.63 0.48 SUMTER** 61.40 0.64 0.59 PICKENS** 63.83 0.58 0.71 TERRELL*** 66.67 0. 62 0.71 SHELBY** 63.46 0.61 0.67 THOMAS 28.07 0.23 0.32 TALLADEGA 48.98 0.64 0.33 TIFT*** 71.93 0.75 0.70 TUSCALOOSA*** 50.00 0.44 0.56 TURNER*** 66.67 0.59 0.75 WASHINGTON** 59.26 0.62 0.57 WILCOX 54.39 0.52 0.57 WORTH*** 71.93 0.69 0.75

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133 CHAPTER 6 CONCLUSIONS AND FUTU RE WORK The main focus of this dissertation was to use climate forecasts and climate indices to forecast cotton yield for the southeastern United States using the CROPGRO Cott on model and an empirical model. Overall, the use of climate information provided significant skill in forecasting cotton yield for the southeastern United States. In order to achieve the overall research question presented in Chapter 1, the dissertation research was organized into four specific objectives under four main chapters; global sensitivity analysis of CROPGRO Cotton model (Chapter 2), parameter estimation and uncertainty analysis (Chapter 3), In season updates of cotton yield forecasts using the CROPGRO Cotton model (Chapter 4), and cotton yield forecasting for the southeastern United States using climate indices (Chapter 5). The global sensitivity analysis results improved our understanding of how sensitive the CROPGRO Cotton model i s to the se lected parameters over the range of parameter uncertainties. The specific leaf area (SLAVR) followed by extinction coefficient (KCAN), and fraction of daily assimilates allocated to seed (XFRT) were important model parameters that influenced the simulated cotton yield. The duration between emergence and flowering (EM FL), and first seed to physiological maturity (SD PM) parameters were most important parameters for physiological maturity. Results also showed that global sensitivity analysis was a better met hod than local sensitivity analysis due to the fact that local sensitivity analysis did not take into account the interactions among the parameters. Results from global sensitivity analysis were utilized to estimate parameter s and perform an uncertainty a nalysis in Chapter 3. The parameter estimates obtained by the

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134 generalized likelihood uncertainty estimation technique represented an improvement in the parameters previously available in DSSAT for DP 555 cotton cultivar. The output uncertainty confidence i ntervals at 95% limit covered approximately 80% of the measurements. This study also demonstrated an efficient prediction of uncertainties in model parameters and outputs using the widely accepted GLUE technique. The re was good overall agreement of the CRO PGRO Cotton model with the field measurements using the estimated parameters. The parameter estimation and uncertainties of the CROPGRO C otton model in chapter 3 provided the basis in using it for cotton yield forecasting. I n season updating the CROPGRO co tton model with observed weather data along with the climatology improved the accuracy of the cotton yield forecasts over time The reduction in the residual errors and standard deviations were statistically significant with in season updates. Approximatel y 90% of the cotton yield forecasts showed reduction in standard deviations and 56% of the cotton yield forecasts showed reduction in residual errors among the 55 years tested In general, three ENSO indices among them selves and the comparison between cli matology based and ENSO tailored cotton yield forecasts did not show statistically significant differences in the standard deviations and residual errors of forecasted cotton yield. As an alternative of using the crop model, cotton yield forecasts were al so evaluated using historical county yield and climate data in an empirical model in this dissertation. Chapter 5 was mainly focused on forecasting county cotton yield using climate indices. The empirical principal component regression models of climate in dices provided significant skills in forecasting cotton yield for the southeastern United States.

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135 In general, with a lead time of approximately 2 months before the typical planting period i n the southeastern United States in May, about 77% of the counties in Georgia and 70% of the counties in Alabama showed statistically significant correlations between observed and forecast cotton yields. The MSE between observed and cross validated cotton yield forecasts were in the range of 0.03 0.11. In addition to that the skills of categorical cotton yield forecasts were evaluated with a contingency table. 94% of the counties showed the categorical cotton yield forecast obtained at a lead time of approximately two months before planting (In February) was correct more than 50% of the time. In general, results showed potential for significant skill in using climate forecasts to forecast cotton yield for the southeastern United States. Improvements to the current forecasts can be made as and when climate forecasts are imp roved. However, in order to use these forecasts in decision making, user s must integrate their perceptions of forecast uncertainty in the context of their goals, constraints, and risk tolerance as they manage their agricultural production system s (Jones et al., 2003).

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136 LIST OF REFERENCES Ahmed, J., C.H.M. Van Bavel, and E.A. Hiller. 1976. Optimizing of crop irrigation strategy under a stochastic weather regime: a simulation study. Water Resource Res. 12(6): 1241 1247. Ajami, N.K., Q. Duan, and S. Sorooshian. 2007. An integrated hydrologic Bayesian multi model combination framework: confronting input, parameter and model structural uncertainty. Water Resource Res 43:W01403. doi:10.1029/2005WR004745. Alexandrov, V.A., and G. Hoogenboom. 2001. Climat e variation and crop production in Georgia, USA, during the twentieth century. Clim Res. 17:33 43. predictability of cotton yields in the southeastern USA based on atmosp heric circulation and surface temperatures. J of Applied Meteorology and Climatology. 47: 76 91. uncertainties in crop model simulations using daily bias corrected regiona l circulation model outputs. Clim Res. 34:211 222. Higgins. 2010. Agron. J. 102: 187 196. Bange, M. P., and S. P. Milroy. 2000. Timing of crop maturity in cotton impac t of dry matter production and partitioning. Field Crops Res 68: 143 155. Bange, M. P., and S. P. Milroy. 2004. Growth and dry matter partitioning of diverse cotton genotypes. Field Crops Res. 87: 73 87. Bannayan, M., and N.M.J. Crout. 1999. A stochastic modelling approach for real time forecasting of winter wheat yield. Field crop res. 62: 85 95. Barnston, A.G., R.E. Livezey, and M.S. Halpert. 1991. Modulation of Southern Oscillation North Hemisphere mid winter climate relationships by the QBO. J. of Cl imate. 4: 203 217. Barreiro, M., P. Chang, L. Ji, R. Saravanan, and A. Giannini. 2005. Dynamical elements of predicting boreal spring tropical Atlantic sea surface temperatures. Dyn. Atmos. Oceans 39: 61 85. Bell, G. D. and J. E. Janowiak. 1994. Atmospher ic circulation during the Midwest floods of 1993. Bull. Amer. Met. Soc 76: 681 696. Beven, K.J. 2001. How far can we go in distributed hydrological modelling ?. Hydrology and Earth System Sciences 5(1): 1 12.

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146 BIOGRAPHICAL SKETCH Tapan Pathak was born in a city called Vadodara and grew up in a beautiful city and a Gujarat state capitol Gandhinagar earned his Bachelors degree in Agricultural Engineering fr om Gujarat Agricultural University in 2000. In January, 2001 he joined Utah State University for MS program and earned his MS degree in Irrigation Engineering in 2004. After completion of MS degree program, he joined UF for the Ph.D. in 2005 and finished h is Ph.D. in 2010. He is currently working as a faculty in the school of natural resources at the University of Nebraska, Lincoln.