A Distributed Cotton Growth Model Developed from GOSSYM and

Xin-Zhong Liang,* Min Xu, Wei Gao, K. Raja Reddy, Kenneth Kunkel,
Daniel L. Schmoldt, and Arthur N. Samel
ABSTRACT
Prediction of cotton (Gossypium hirsutum L.) production under a changing climate requires a coupled modeling system that
represents climate–cotton interactions. The existing cotton growth model GOSSYM has drawbacks that prohibit its effective
coupling with climate models. We developed a geographically distributed cotton growth model from the original GOSSYM
and optimized it for coupling with the regional Climate–Weather Research Forecasting model (CWRF). This included soft ware
redesign, physics improvement, and parameter specification for consistent coupling of CWRF and GOSSYM. Th rough incorporation of the best available physical representations and observational estimates, the long list of inputs in the original GOSSYM
was reduced to two parameters, the initial NO3 amount in the top 2 m of soil and the ratio of irrigated water amount to potential evapotranspiration. The geographic distributions of these two parameters are determined by optimization that minimizes
model errors in simulating cotton yields. The result shows that the redeveloped GOSSYM realistically reproduces the geographic
distribution of mean cotton yields in 30-km grids, within ±10% of observations across most of the U.S. Cotton Belt, whereas
the original GOSSYM overestimated yields by 27 to 135% at the state level and 92% overall. Both models produced interannual
yield variability with comparable magnitude; however, the temporal correspondence between modeled and observed interannual
anomalies was much more realistic in the redeveloped than the original GOSSYM because significant (P = 0.05) correlations
were identified in 87 and 40% of harvest grids, respectively. The redeveloped GOSSYM provides a starting point for additional
improvements and applications of the coupled CWRF–GOSSYM system to study climate–cotton interactions.
G
lobal climate change is expected to have dramatic impacts on agricultural productivity throughout
the world, including the U.S. Cotton Belt (Intergovernmental Panel on Climate Change, 2007). Long-term trends in
temperature, precipitation, growing season duration, climate
variability, and weather extremes could substantially alter the
geographic distribution of crop production (Climate Change
Science Program, 2008; Karl et al., 2009). This could have
impacts on local and regional economies and the populations
that rely on agriculture in those areas. Through a predictive
understanding of crop responses to current and future climate
change, researchers can develop new technologies for climate
X.-Z. Liang, Dep. of Atmospheric and Oceanic Science, Univ. of Maryland,
College Park, MD 20740, and Dep. of Atmospheric Sciences, Univ. of Illinois,
Urbana, IL 61801; X.-Z. Liang and M. Xu, Earth System Science Interdisciplinary
Center, Univ. of Maryland, College Park, MD 20740, and Division of Illinois
State Water Survey, Institute of Natural Resource Sustainability, Univ. of Illinois,
Champaign, IL 61820; W. Gao, USDA UV-B Monitoring and Research Program,
Natural Resource Ecology Lab., and Dep. of Ecosystem Science and Sustainability,
Colorado State Univ., Fort Collins, CO 80523; K.R. Reddy, Dep. of Plant and
Soil Sciences, Mississippi State Univ., Mississippi State, MS 39762; K. Kunkel,
Cooperative Institute for Climate and Satellites, North Carolina State Univ.,
Asheville, NC 28801, and National Oceanic and Atmospheric Administration,
National Climatic Data Center, Asheville, NC 28801; D.L. Schmoldt, USDA
National Institute of Food and Agriculture, Washington, DC 20024; and A.N.
Samel, Dep. of Geography, Bowling Green State Univ., Bowling Green, OH
43403. Received 10 Aug. 2011 *Corresponding author ([email protected]).
Published in Agron. J. 104:661–674 (2012)
Posted online 5 Mar. 2012
doi:10.2134/agronj2011.0250
Available freely online through the author-supported open access option.
Copyright © 2012 by the American Society of Agronomy, 5585 Guilford
Road, Madison, WI 53711. All rights reserved. No part of this periodical may
be reproduced or transmitted in any form or by any means, electronic or
mechanical, including photocopying, recording, or any information storage
and retrieval system, without permission in writing from the publisher.
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change adaptation, policymakers can establish necessary incentives and safety nets for producers, and producers can better
understand their risk horizons and mitigation strategies.
Crop growth models simultaneously integrate nonlinear
interactions between soil, water, plant, and weather factors as
well as management practices to determine crop productivity,
environment stresses, and water and nutrient needs (Hodges
et al., 1998; Newton et al., 2007). Regional climate processes,
including mesoscale circulations, cloud formation, radiative
transfer, as well as energy and water recycling, strongly depend
on surface heat and moisture fluxes that are controlled by vegetation and soil storage. In particular, vegetation plays a major
role in determining precipitation, interception, runoff, and the
removal of moisture from the soil by transpiration (Dirmeyer,
1994; Xue et al., 1996; Liang et al., 2003). Thus, all current
global and regional climate models incorporate comprehensive
land surface models to predict surface–atmosphere exchanges of
energy, momentum, water, and other mass constituents (Dickinson et al., 1993; Sellers et al., 1996; Dai et al., 2003). They represent key interactions between surface and atmospheric processes.
More recent land surface models depict vegetation dynamics
that include the C and N cycles (Foley et al., 1998; Dickinson
et al., 2002; Chen et al., 2004; Bonan and Levis, 2006). These
models, however, focus more on large-scale processes and longterm changes rather than the detailed daily variation characteristics of crop growth. While typical crop growth models give a
more complete treatment of the plant life cycle evolution, they
lack the feedback processes that are essential to regional climate
Abbreviations: CSSP, Conjunctive Surface–Subsurface Process; CWRF,
Climate–Weather Research Forecasting; FRIS, Farm and Ranch Irrigation
Survey; NASS, National Agricultural Statistics Service.
2 012
661
Biometry, Modeling & Statistics
A Distributed Cotton Growth Model Developed
from GOSSYM and Its Parameter Determination
variations. Thus, these climate and crop models need to be
coupled to better understand the interactions between regional
climates, ecosystems, and agricultural crops (Tsvetsinskaya et al.,
2001; Lu et al., 2001; Osborne et al., 2009). Better integration
of crop growth models with climate models can help provide the
needed understanding and predictive ability.
Our overarching goal was to couple the mesoscale regional
CWRF model (cwrf.umd.edu; Liang et al., 2012b) with the
cotton growth model GOSSYM (Gossypium—the cotton
genus) to better predict climate–cotton interactions. There
exist many challenges to reach this goal. In the past, crop
growth models were generally treated as “black boxes,” where
full two-way interactions were lacking or, if included, consistency with the host climate models in the representation of the
physical processes and soil properties that determine surface
evapotranspiration, runoff, and the energy budget was not
imposed (e.g., Heinemann et al., 2002; Doherty et al., 2003;
Challinor et al., 2005; Xiong et al., 2008). Like most crop
growth models, GOSSYM has been developed, calibrated, and
evaluated on the basis of site-specific measurements. Its application and resulting credibility across a broad region with geographically distributed grids have yet to be established. Given
the driving weather or climatic conditions, the original GOSSYM has approximately an additional 85 tunable parameters
for users to calibrate at a farm site (Boone et al., 1993). Specification for such a long list of unknown parameters is extremely
difficult to accomplish and constitutes a major obstacle that
introduces large uncertainties to the spatially distributed modeling of climate–crop interactions. Model evaluation, while
critical, has been limited and most often subjective, mainly due
to the lack of comprehensive observations and coupled predictive systems (Thorp et al., 2007; Xiong et al., 2008).
Therefore, our specific objectives to achieve the goal of coupling GOSSYM with CWRF for distributed modeling were
threefold. First, we fundamentally redesigned the soft ware to
change the original GOSSYM from running over time at a
specific location to integration over space in sequential times.
Second, we generalized the estimation of adjustable parameters
and the specification of soil properties that are geographically
distinct. This involved reducing the list, by defining most of
the parameters with best available physical representations and
observational estimates, to the final two parameters: the initial
NO3 amount in the top 2 m of soil and the ratio of irrigated
water amount to potential evapotranspiration. These parameters were derived through inverse modeling that minimizes
simulation errors for observed cotton yields across the United
States. These two parameters were validated indirectly by
comparing the model total irrigated water amounts with U.S.
statewide observations. Third, we conducted retrospective
simulations to evaluate the ability of the redeveloped GOSSYM to reproduce historical cotton yield variations as driven
by realistic climate conditions. This study, the first in a series,
addressed the first and second objectives, with a focus on
model development, including soft ware reengineering, physics
improvement, and parameter determination. A companion
study (Liang et al., 2012a) fulfi lled the third objective, where
spatiotemporal variations of cotton yields and their responses
to climate stresses simulated by the redeveloped GOSSYM
were compared with observations.
662
MATERIALS AND METHODS
Model Development
Given important differences in physics formulation and coding structure between CWRF and GOSSYM, both software
engineering and physics modeling for the critical counterparts
required appropriate modifications to ensure consistent model
coupling and realistic representation of climate–crop interactions.
Brief Description of CWRF and GOSSYM
The CWRF is the climate extension of the WRF (Weather
Research and Forecasting) model (Skamarock et al., 2005).
This extension has been continuously refined with numerous
crucial modifications to improve interactions among land–
atmosphere–ocean, convection–microphysics, and cloud–aerosol–radiation and system consistency throughout all process
modules (Liang et al., 2005a,b,c,d, 2006, 2012b). An essential
CWRF component is the Conjunctive Surface–Subsurface
Process (CSSP) model. It predicts 11 layers of soil temperature
and moisture (liquid or ice), five layers of snow (mass, cover, and
age), and a two-leaf (sunlit or shaded) canopy of temperature,
radiation, and photosynthesis–stomatal resistance (Dai et al.,
2003, 2004). The CSSP also integrates horizontal water movement (across grids) as surface and subsurface runoff that results
from rainfall excess, saturation depletion, and lateral flows
due to resolved and subgrid topographic controls (Choi et al.,
2007; Choi and Liang, 2010). As such, the CSSP, which is most
relevant to the coupling with GOSSYM in the present study,
has outperformed major land surface models in predicting soil
temperature and moisture distributions, terrestrial hydrology
variations, and land–atmosphere exchanges (Yuan and Liang,
2011a). It also allows the CWRF to produce pronounced downscaling skill for seasonal–interannual precipitation prediction
across the continental United States (Yuan and Liang, 2011b).
Among the 15 published cotton growth models (Jallas, 1998),
GOSSYM is comprehensive and widely used in commercial
agriculture to aid in making crop management decisions. The
model formulation, development, and application of GOSSYM
have been well documented (Baker et al., 1983; McKinion et al.,
1989; Baker and Landivar, 1991; Boone et al., 1995; Hodges et
al., 1998; Reddy et al., 1997, 2002). It is a mass-balance dynamic
model that simulates C, N, and water processes in the plant and
soil root zone throughout the cotton life cycle. It predicts crop
growth (with detailed plant chemistry, morphogenesis, and phenology) and soil responses to environmental stresses, primarily
from heat, water, C, and nutrients. These stresses are determined by climate variables such as solar radiation, temperature,
rainfall, and wind, as well as by soil properties and cultural
practices including irrigation and fertilization.
GOSSYM Software Reengineering
The original GOSSYM source code was written in the
FORTRAN 77 (F77) standard and departs substantially from
the CWRF FORTRAN 90 (F90) modular designs. The F77
standard has numerous shortcomings when compared with F90.
In particular, F77 includes neither the complex data type to
describe the hierarchical structure of plant organic parts nor the
dynamic memory allocation that is desired for actual objectives
with variable dimension size such as the growing leaf, stem,
root, and boll. In addition, the original code was written for
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simulations that are site specific and in its present configuration
is not suitable for coupling with the CWRF, where simultaneous calculations across a large array of geographically distributed
grids are necessary. As such, the entire GOSSYM model soft ware
was recoded to follow the CWRF F90 modular design (Xu et al.,
2005). This enabled running the coupled system most effectively
on a parallel supercomputing environment for long-term climate
integrations across distributed grids in sequential time steps.
Soil Temperature and Moisture and Evapotranspiration
Vegetation and Soil Property Distributions
The CSSP uses the USGS land use or land cover classification with 24 categories (Liang et al., 2005a,b). Figures 1a and
1b illustrate the geographic distribution of the USGS categories identified as the dominant type (Table 1) in each CWRF
30-km grid and the USDA county-level harvested cotton
acreage averaged during 1979 to 2005. We eliminated cotton
growth in minor production areas (e.g., Kansas) where the yield
within a 30-km grid was <165 kg ha–1 and where there were
The CSSP is physically based and represents dynamic interactions between comprehensive land and atmospheric processes
through an advanced planetary boundary layer parameterization. It predicts soil temperature and moisture distributions,
terrestrial hydrology variations, and land–atmosphere flux
exchanges by strict energy conservation and mass balance.
Extensive validation against field measurements indicates
that the CSSP realistically simulates observed surface energy
and mass variations (Yuan and Liang, 2011a). In contrast, the
respective GOSSYM components are much less comprehensive, where the model formulations are generally empirical and
especially lack full interactions with atmospheric dynamics
that limit model performance (e.g., Staggenborg et al., 1996;
Khorsandi et al., 1997). Given the crucial controls that soil
temperature and moisture and evapotranspiration have on crop
growth, development, and yield, we eliminated the corresponding modules from GOSSYM and, instead, utilized the more
realistic prediction provided by the CSSP.
Soil Water Movement by Macropore Flow
The GOSSYM model treats the cotton field soil on a twodimensional mesh with 20 horizontal rows and 40 vertical
layers, where mass balances of water, NO3, NH4, and organic
matter are maintained and root growth rates are predicted
(Hodges et al., 1998). Water movement is simulated by Darcy
fluxes into each 50-mm-thick layer, starting at the surface via
infi ltration of rainfall and irrigation and moving downward by
vertical diff usion and drainage to a 2-m depth. Meanwhile, soil
moisture is transported upward to the atmospheric boundary
layer through surface evaporation and plant transpiration of
water uptake from the crop root zone. Within each layer, water
is moved laterally using the same flux equations according to
the soil water gradient and diff usivity. Any soluble chemicals,
primarily NO3–N, are assumed to move with the water fluxes.
The original GOSSYM does not consider the macropore flow
effect that is especially important in the U.S. Southeast, where
the soil contains a high percentage of sand with low soil moisture
holding capacity. We thus incorporated a macropore flow mode
to allow rapid drainage of the soil, following Theseira et al.
(2003). This mode was designed to limit the actual soil water
holding capability, increase water stress, and consequently reduce
crop yields. We kept the soil grid structure and water movement
calculation from GOSSYM to easily and intuitively incorporate
the irrigation and fertilization methods (sprinkler, furrow, drip,
broadcast, sidedress, foliar, and their alternatives). The resulting
total soil moisture tendency from field water movement and the
new macropore flow is updated at the same CSSP time interval
to provide consistent calculations, such as evaporation and runoff from CSSP, if fully coupled with the CWRF.
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Fig. 1. Geographic distributions of (a) the dominant USGS
land cover categories in the CWRF model 30-km grids, (b)
cotton harvest areas averaged during 1979 to 2005, (c) top soil
sand percentage, and (d) irrigated cotton area percentage.
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663
Table 1. The USGS land-cover categories used in the Climate–
Weather Research Forecasting model.
Type
Description
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
urban and built-up land
dryland cropland and pasture
irrigated cropland and pasture
mixed dryland and irrigated cropland and pasture
cropland–grassland mosaic
cropland–woodland mosaic
grassland
shrubland
mixed shrubland and grassland
savanna
deciduous broadleaf forest
deciduous needleleaf forest
evergreen broadleaf forest
evergreen needleleaf forest
mixed forest
water bodies
herbaceous wetland
wooded wetland
barren or sparsely vegetated
herbaceous tundra
wooded tundra
mixed tundra
bare-ground tundra
snow or ice
missing data during 1979 to 2005. Across the U.S. Cotton
Belt, the prevailing USGS categories are shrubland, grassland,
and their mixture (southwestern states: California, Arizona,
New Mexico, and Texas) as well as cropland and woodland
mosaics (Lower Mississippi River basin: Oklahoma, Louisiana,
Arkansas, Missouri, Mississippi, and Tennessee) and dryland
cropland and pasture (southeastern states: Alabama, Florida,
Georgia, South Carolina, North Carolina, and Virginia). We
first acquired the USDA data archive to define where and when
cotton grows and whether it is irrigated. The CSSP vegetation was then assigned to one of the four cropland categories
(dryland cropland and pasture, irrigated cropland and pasture,
cropland–grassland mosaic, cropland–woodland mosaic) by
the cotton dominance in each grid.
The GOSSYM model requires inputs at each cotton plot for
the soil depth and water table as well as vertical profiles that
include the following: (i) sand and clay percentages; (ii) bulk
density; (iii) volumetric water content at saturation, field capacity, permanent wilting point (water potential of –1.5 MPa),
and air dry (soil humidity in equilibrium with the surrounding
air); (iv) the water potential at field capacity; and (v) diff usivity
at the permanent wilting point. Direct measurements of these
parameters are laborious and their general application across the
U.S. Cotton Belt is limited. In contrast, CSSP uses Penn State
University 1-km soil characteristics data to define the depth to
bedrock as well as the sand (Fig. 1c) and clay profiles (Liang et
al., 2005a,b). These quantities are then used to calculate all the
other soil properties (Saxton and Rawls, 2006). The identical
CSSP representation for the geographic distributions of soil
properties was incorporated into GOSSYM to ensure consistent
coupling with CWRF and eliminate subjective calibration.
664
Cultural Practice Specifications
Cotton was planted in 2010 on >4.47 million ha in the
U.S. Cotton Belt (Fig. 1b), especially the northern Texas High
Plains, Mississippi Delta, irrigated valleys of California and
Arizona, and southeast coastal states. Approximately 4.36
million ha were harvested. In addition to planting location
and acreage, numerous other cultural or management practices
must be specified in each 30-km model grid. In particular,
timely irrigation and maintenance of soil fertility are necessary to ensure productivity and profitability because cotton is
sensitive to both water stress and N loss caused by water stress
(Reddy et al., 1997; Gerik et al., 1998). There is, however, no
systematic data archive that includes detailed records of these
practices, which differ substantially among individual farms.
Thus, we adopted the following approximations:
Cotton Type, Density, and Period. Two major types of
cotton (upland and pima) are grown in the U.S. Cotton Belt,
where upland cotton covers 5.24 million ha and pima cotton covers the remaining 0.08 million ha, as averaged during
1979 to 2005. Given its predominance, only upland cotton
was considered in this study. Because state- and county-level
data records are often missing, we chose a mid-season cotton
cultivar. A sensitivity analysis showed that the other cotton
cultivars usable in GOSSYM resulted in mean yield differences
mostly within ±20% of mean yields using the mid-season cultivar under the identical cultivation parameters calibrated for
the mid-season cultivar. The prevailing cultural information
on the plant row spacing and density as well as planting and
harvest dates are from the Agricultural Statistics Board (1997)
and State Cooperative Extension together with published
literature. They differ among the states (Table 2). For example,
row spacing ranges from 0.762 m in Missouri to 1.016 m in
Arizona, Texas, and Oklahoma, while the density (number
of plants per meter of row) varies between 4.9 in Virginia and
12.4 in New Mexico. The planting and harvest dates vary
widely among the states, where each state has a harvest window
of up to 1 mo. We used the middle of each window as the
planting and harvest dates in each state. As such, the longest
growing season spans the period from 30 April to 12 November in New Mexico. This is the window during which the
GOSSYM integration for each year is conducted. Neither plant
growth regulators nor pressure from weeds, diseases, insect
pests, or catastrophic weather events was applied anywhere.
Cotton Area. The planting and harvest areas vary greatly
from year to year. Both values were derived from the National
Agricultural Statistics Service (NASS) archive at the county
level. The GOSSYM model currently does not consider cotton
mortality: when planted, it always grows but may produce little
or no leaf, seed, and lint yield. For the purpose of validation,
we only considered the harvest acreage. Figure 1b shows the
processed harvest acreage distribution for each 30-km grid
averaged for 1979 to 2005.
Fertilization. No county-level records of actual fertilizer
application rates and dates for cotton are available. State-level
data for annual N fertilizer rates (per fertilized cotton acre
receiving N) during 1964 to 2005 are archived at the USDA
Economic Research Service. Missing records in this database
were replaced with regional averages reported by the USDA
(Potter et al., 2006, Table 34). Table 2 lists the N rate for each
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Table 2. The cultural information for each state in the U.S. Cotton Belt used by GOSSYM.
Row spacing
State
Alabama
Arizona
Arkansas
California
Florida
Georgia
Louisiana
Mississippi
Missouri
New Mexico
North Carolina
Oklahoma
South Carolina
Tennessee
Texas
Virginia
Unirrigated
Irrigated
——————— m ———————
1.003
1.003
1.016
1.016
0.965
0.965
0.986
0.965
0.914
0.914
0.914
0.914
0.983
0.983
0.965
0.965
0.762
0.762
1.007
1.007
0.965
0.965
1.016
1.016
0.965
0.965
1.003
1.003
1.016
1.016
0.838
0.838
Plant density
Unirrigated
————— no. m–1 —————
11.745
11.745
9.843
9.843
9.022
9.022
10.466
10.466
8.202
8.202
8.202
8.202
9.875
9.875
10.663
10.663
12.402
12.402
12.415
12.415
9.843
6.562
11.483
11.483
9.843
6.562
11.893
11.893
9.843
11.483
4.921
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Planting
date
Harvest date
N fertilization
9 May
15 Apr.
12 May
22 Apr.
30 Apr.
10 May
10 May
13 May
12 May
30 Apr.
10 May
31 May
10 May
12 May
21 May
30 Apr.
5 Oct.
25 Oct.
18 Oct.
23 Oct.
16 Oct.
25 Oct.
9 Oct.
20 Oct.
17 Oct.
12 Nov.
26 Oct.
16 Nov.
29 Oct.
18 Oct.
1 Nov.
10 Nov.
kg ha–1
93.071
167.827
90.893
145.530
80.960
89.903
94.325
115.819
73.700
71.225
85.360
42.493
96.140
91.718
63.118
80.960
An examination of the limited cotton farmer records from
the archive at the USDA-ARS showed that the amount of irrigated water varied substantially, ranging from as little as 12.7 to
76.2 mm in Texas to as much as 25.4 to 254 mm in California
and New Mexico, and that the dates of irrigation were irregular.
Sensitivity experiments on irrigation applications using trial
and error suggest that it is desirable to specify a unique water
amount, stress threshold, and separation period set for each
farm. This is impossible at present, given the lack of actual
data for the date of application, amount of water, and method
of irrigation (sprinkler, furrow, drip, or their alternatives).
Instead, we adopted an automatic approach based on the cotton daily water stress factor and potential evapotranspiration.
A specified amount of water, as an adjustable fraction of the
local potential evapotranspiration, is applied once the water
stress factor falls below the threshold of 0.75. Thus, we chose
the ratio of the irrigated water amount to potential evapotranspiration as another critical adjustable parameter.
state, averaged across 1979 to 2005. All N fertilizer amounts,
which vary among states and from year to year, are applied once
at the beginning of each growing season.
Initial Soil Fertility. This includes residual or initial N and
organic matter content in the soil. The geographic distribution of the annual organic matter content is specified as one of
the CWRF built-in surface boundary conditions (Liang et al.,
2005a). The initial N is an essential input factor for most crop
models and is generally measured on site before planting. Such
measurements, however, are not made publically available.
Thus, for this study, we chose the initial NO3 amount in the
top 2 m of soil in the root zone to be an adjustable parameter.
Irrigation. The annual irrigated areas for cotton were
derived mainly from the NASS archive at the county level. The
planting or harvesting fractional area of a county is treated
as being irrigated or unirrigated as indicated by the practice
record. When this information was not explicitly recorded, the
irrigated area of cotton was estimated using the NASS Farm
and Ranch Irrigation Survey (FRIS) Census of Agriculture
from 1984, 1988, 1994, 1998, and 2003. Constant extrapolation before 1984 and after 2003 and intercensus, linear
interpolation between 1984 and 2003 were used to produce the
irrigation map for each year.
Figure 1d illustrates the irrigated area percentage distribution averaged for 1979 to 2005. Irrigation was applied mostly
in the southwestern states (California, Arizona, New Mexico,
and Texas), while other states required notably less irrigation
or were entirely rainfed. Past studies (Richardson and Reddy,
2004; Potter et al., 2006) irrigated 19.1 mm of water once the
water stress factor fell below the threshold of 0.75. (The water
stress factor, used only to trigger irrigation, is the ratio of plant
water supply to demand, ranging from zero for the most severe
stress to one for no stress [Baker et al., 1983]. In addition,
GOSSYM uses the leaf water potential, which is a function
of both root zone water availability and the prevailing atmospheric moisture demand, to determine the water stress effects
on crop growth expansion, photosynthesis, and reproduction
[Reddy et al., 1997]).
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Irrigated
EXPERIMENTS AND RESULTS
Model Parameter Estimation
The two final adjustable parameters for the redeveloped
GOSSYM are: (i) the initial NO3 abundance in the top 2 m
of soil in the root zone; and (ii) the ratio of the irrigated water
amount to potential evapotranspiration. Both parameters vary
widely across the U.S. Cotton Belt. There are, however, no credible data to specify them correctly. Our strategy was to estimate
both parameters through inverse modeling by optimization that
minimizes local root mean square errors (RMSEs) of annual
cotton yields simulated from observations during 1979 to 2005.
The inverse modeling or optimization algorithm is well
accepted and widely used in calibrations of crop growth models
(Liu et al., 1989; Jones and Carberry, 1994; Calmon et al.,
1999; Irmak et al., 2000; Gauch et al., 2003; Thorp et al.,
2007; Xiong et al., 2008). For example, Liu et al. (1989) derived
the phenological coefficients for maize (Zea mays L.) through
inverse modeling by closely matching the CERES-maize
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simulated dates for silking and maturity to the observed dates.
Thorp et al. (2007) calibrate the saturated soil water conductivity of the bottom soil layer and effective tile drainage rate in the
CERES-maize model to minimize errors between simulated
and observed yields.
The use of this optimization in the current study required
a large ensemble of GOSSYM standalone simulations. They
were driven by the same set of the most realistic climate conditions during 1979 to 2005, while the two adjustable parameters listed above were altered across the ensemble to cover
their respective conceivable ranges. This standalone approach
eliminated complications from any CWRF climate biases and
nonlinear feedbacks and thus effectively confined the optimization result by reducing the physical and numerical deficiencies specific to GOSSYM.
Annual cotton yield data for each county available from the
NASS archive were used as the reference to evaluate GOSSYM
simulations. Below we describe the driving climate conditions
and model experiments to identify formulation deficiencies,
improve irrigation modeling, and achieve system optimization.
These efforts aimed to minimize cotton yield errors to derive
best estimates of the two adjustable parameters.
Driving Climate Conditions
The climate conditions driving the standalone GOSSYM
simulation were taken from the North American Regional
Reanalysis (NARR) (Mesinger et al., 2006). The NARR
provides a long-term, consistent, high-resolution climate data
set that represents the best available proxy of observations.
The NARR adopts a 32-km grid, close to that of CWRF, and
provides 3-h atmospheric and land surface data, including
precipitation, evapotranspiration, runoff, radiation flux, surface
air temperature, humidity and wind, and soil temperature
and moisture. Daily minimum and maximum temperature
differences between NARR and the analysis based on surface
(1.5–2-m) measurements from 7235 National Weather Service
cooperative stations across the continental United States were
generally small, having RMSEs within 1°C. The NARR biases
in daily accumulative precipitation are relatively large, especially in the southeastern United States. As such, we replaced
the daily precipitation with an objective analysis based on
gauge measurements from the same cooperative stations (see
Liang et al. [2004] for the data
source and analysis procedure).
conditions: (i) one of three representative soil types (loamy
sand, sandy loam, or silt loam); (ii) with or without irrigation
application of an unstated amount (perhaps the default 19.1
mm) of water once the water stress factor dropped below 0.75;
(iii) planting on 1 May and harvesting on 20 November; (iv)
CO2 concentration fi xed at 330 μL L–1; (v) generic fertilizer
application of 165 kg ha–1 NO3; (vi) climate variations during
1960 to 1995 simulated by global and regional climate models
(containing important biases from observations). Their resulting
cotton yields were substantially greater than the observations,
with statewide overestimations ranging from 30 to 120%.
A similar experiment using the original GOSSYM was
conducted in this study to simulate cotton yield distributions
across the entire U.S. Cotton Belt during 1979 to 2005 under
more realistic conditions that include observed CO2 concentrations and climate variations, fertilizer application rates,
and irrigation area percentages (all distributed on the CWRF
30-km grid), as well as state-specific planting and harvest dates.
These driving conditions are identical to those specified for the
redeveloped GOSSYM except that a single sandy loam profi le
was chosen everywhere, no macropore flow was included, the
initial soil NO3 abundance was specified as 165 kg ha–1, and
irrigation was applied as 19.1 mm of water whenever the stress
level was <0.75, following Doherty et al. (2003).
Figure 2 illustrates serious deficiencies of the original GOSSYM in simulating cotton yields as measured by the relative
mean biases [ (Y s −Y o )/ Y o ] and standard deviation ratios (σs/
σo), where Y and σ are the mean and standard deviation of
cotton yields during 1979 to 2005 and the subscripts s and o
represent simulations and observations, respectively. The relative
mean biases measure the mean error of the simulated yields and
were scaled or normalized by the observed yield. The standard
deviation ratios are used to assess the simulated and observed
yields’ interannual variability. The relative mean biases shown
in Fig. 2a reveal that the model overestimated cotton yields
by 90 to 135, 49 to 132, 27 to 122, 27 to 135, and 92% across
the southeastern states, the Lower Mississippi River basin, the
southwestern states, the individual states, and the entire U.S.
Cotton Belt, respectively. The use of loamy sand and silt loam
soil profiles did not substantially alter this outcome, although
there were some small regional contrasts. In addition, the standard deviation ratios in Fig. 2b indicate that model cotton yield
Original GOSSYM
Deficiencies
Doherty et al. (2003) applied
GOSSYM to simulate geographic
distributions of cotton yields across
the U.S. Southeast. They used the
original GOSSYM, however, as a
“black box” model (i.e., without
the modifications outlined above)
and did not provide a direct model
validation as driven by realistic
surface and climatic conditions.
Specifically, they presented
the results under the following
666
Fig. 2. Geographic distributions of cotton yield (a) relative mean biases [( (Y s −Yo )/ Y o ] and
(b) standard deviation ratios (σs /σo) as simulated by the original GOSSYM, where Y and σ
represent cotton yield means and standard deviations during 1979 to 2005 and the subscripts
s and o indicate simulations and observations, respectively.
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amount was based only on ET and not related to current water
stress, i.e., without the max[ ] term in Eq. [1].
interannual variability was approximately 138, 90, and 43%
greater than observations in Arizona, Texas and Oklahoma,
and Louisiana and Mississippi, respectively, but 19, 21, and 27%
less in Arkansas and Tennessee, the southeastern states, and
New Mexico, respectively. These results clearly show that the
original GOSSYM contains substantial biases. This necessitated
incorporation of the key improvements outlined above into the
revised GOSSYM as well as an enhanced irrigation scheme and
optimal parameter derivation as described below.
Optimization to Minimize Yield Errors
The redeveloped GOSSYM was then subject to adjustment by an optimization procedure that focused on the two
unknown parameters: (i) the ratio of irrigated water amount
to potential evapotranspiration (across the irrigated area only);
and (ii) the initial soil NO3 abundance (everywhere). This was
accomplished via inverse modeling to determine the irrigation
ratio and initial NO3 values that minimized model biases of
observed yields, averaged across the entire integration period
(1979–2005) at each CWRF grid. Given Eq. [1], the determination of the irrigation ratio is simplified to the estimate of
parameter α. Note that other irrigation parameters, including
the stress threshold Sc, the enhancement factor β, and the application interval, also play important roles for the areas suffering
from water stress, especially in the southwestern states. Unfortunately, there exist no data to determine the accuracy of these
adjustable factors and hence they are prescribed at present.
Given that all of the above driving conditions are realistically
specified, the time-varying annual cotton yields, Yt, at each grid
modeled by the redeveloped GOSSYM depend only on the
local initial soil NO3 abundance, N0, and irrigation water ratio
parameter, α, both of which were assumed to be time invariant
in this study. Ideally, the numerical optimization is achieved
by searching from the unlimited ranges of N0 and α for the
values that minimize local RMSEs between the modeled and
observed Yt. In actual agricultural practices, the amounts of
irrigated water and applied fertilization are constrained by
the invested costs relative to the final yields. Thus, it is more
realistic to construct the optimization to account for the cost
effectiveness or efficiency of N and water application. Following the definition of agronomic efficiency (Molden, 1997;
Novoa and Loomis, 1981; Grismer, 2002), we calculated the
local N productivity, NP, and water productivity, WP, as functions of N0 and α:
Improved Autoirrigation Modeling
The redeveloped GOSSYM produced a much more realistic
simulation of the long-term mean cotton yield distribution
across the U.S. Cotton Belt. It still largely overestimated
the cotton yield interannual variability, however, mostly for
irrigated areas in the Southeast. Data analysis showed that the
existing automatic irrigation scheme, based only on the static
ratio of irrigated water amount to potential evapotranspiration
under a fi xed water stress threshold (e.g., Hillel and Guron,
1973; Fischbach and Somerholder, 1974), was likely to be the
major cause for this overestimation. During severe drought
years, simulated yields were much smaller than observations,
suggesting that plants in the model were constantly subjected
to water stress. To simulate a realistic long-term mean, the
model has to produce higher than observed yields during wet
years to balance the deficits in dry years, which results in a large
overestimation of interannual variability. Given that irrigation
is applied once per model integration interval (currently daily)
when the initial water stress drops below the threshold, the irrigated water amount in the present automatic scheme is insufficient under drought conditions for the model to maintain the
relatively wet soil that is required for high observed productivity. This problem is particularly serious in the Southeast, where
rainfed and irrigation practices often coexist, but less severe in
the Southwest, where irrigation is the predominant practice.
It is more desirable to determine the irrigation amount
based on the actual evapotranspiration (ET) and surface plus
subsurface runoff. These quantities, however, are not known
before crop growth prediction. Instead, empirical estimates
of the ratio to ET (runoff was not considered) were applied to
incorporate crop characteristics and average soil conditions
(Jensen and Heermann, 1970; Allen et al., 1998). In reality,
farmers probably irrigate with a larger amount of water per
application in dry years to reduce the overall water stress. We
therefore modified the irrigation amount ratio to include an
enhancement factor that increases with increasing departure
of the threshold from actual water stress. The irrigated water
amount, I, is expressed as a function of the daily water stress,
Sw (0.0–1.0, where the value is inversely proportional to stress),
on cotton growth and potential evapotranspiration, Ep:
I =αEp max ⎡⎣0, β(S c − S w )⎤⎦
NP =
∂Y Y ( N , α +δα )−Yt ( N 0 , α )
WP = t ≅ t 0
∂α
δα
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[1]
•
[2]
where δ denotes small increments of the adjustable parameters
N0 and α.
The constrained optimization then finds the appropriate
thresholds for NP and WP, below which further increases in
N0 and α will not result in sufficient Yt gains to justify the
N and water use. This was done by using 1979 to 2005 mean
yields. At present, the redeveloped GOSSYM applies all fertilized N (assuming in NO3–N form) once at the planting date,
while the amounts vary according to the state records (Table
1). We assumed that these actual amounts were determined
by farmers as they assessed (based on past experiences) cotton
NO3 need after accounting for initial soil fertility. As a first
approximation, we have factored yearly initial soil fertility
variations into the fertilization decision made by farmers and
hence made N0 constant with time. Moreover, the initial soil
where α is a geographically distributed coefficient for optimization to minimize local model yield biases from observations,
β is the enhancement factor (=3.0), and Sc is the water stress
threshold (=0.75) below which irrigation starts. This scheme
was designed to reduce cotton yield interannual variability
from the previous irrigation scheme, where the irrigated water
Agronomy Journal
∂Yt Yt ( N 0 +δN 0 , α )−Yt ( N 0 , α )
≅
∂N 0
δN 0
2012
667
Fig. 3. (a) Nitrogen productivity for irrigation ratios of 1.00
(blue), 0.50 (green), and 0.05 (red), and (b) water productivity
for residual NO3 values of 440 (blue), 330 (green), and 220
kg ha –1 (red) in the Southwest (California, Arizona, and
New Mexico, solid lines), Mid-South (Texas, Oklahoma,
Louisiana, Arkansas, Missouri, and Mississippi, dashed lines)
and Southeast (Tennessee, Alabama, Florida, Georgia, South
Carolina, North Carolina, and Virginia, dotted lines). The
black lines are thresholds of 0.75 kg cotton kg –1 NO3 and 100
kg ha –1 for N and water productivity, respectively.
fertility incorporates fertilization differences including timing,
amount, and composition between the reality and the model.
Figure 3a depicts the NP statistics averaged for 1979 to
2005 over the Southwest, Mid-South, and Southeast regions
in terms of varying N0 from 110 to 440 kg ha–1 (in increments
of 27.5 kg ha–1) for α values of 0.05, 0.50, and 1.00. The results
indicate that NP decreases in each region as N0 increases and α
decreases; however, there exist important regional differences in
NP sensitivity to α variations. The greatest sensitivity occurred
in the Southwest, where productivity exceeded that of any other
region when α = 1.0 but was zero when α = 0.05. Although
productivity in the Mid-South is also sensitive to α, NP was
less than that across the Southwest for the larger α values, while
there was a low level of productivity when α = 0.05 and N0 was
<250 kg ha–1. The value of NP across the Southeast was less
sensitive to α variations than in the other regions, and there
was substantial productivity when α = 0.05. The results show
that, while cotton growth is a function of both N0 and α, the
importance of these stress factors varies among regions. For the
Southwest and Mid-South (mainly Texas), rainfall is insufficient
668
and irrigation is the primary water source for crops. Thus,
water availability is the key limiting factor for NP, regardless of
N0. In the Southeast, however, where rainfall is much greater,
irrigation has a relatively small impact on productivity. Thus,
NP in the Southwest responds strongly to increased irrigation,
while productivity in the Southeast is much greater than in the
other regions when irrigated water is low. Given interstate and
regional differences, we chose the NP optimization threshed
to be 0.75 kg cotton kg–1 NO3. This corresponds to the lowest
observed value reported by Bronson et al. (2003).
Figure 3b shows the WP statistics averaged during 1979 to
2005 across the Southwest, Mid-South, and Southeast in terms
of varying α from 0.1 to 0.9 in increments of 0.05 for N0 values
of 440, 330, and 220 kg ha–1. The results indicate substantial
regional WP differences, where productivity was greatest in
the Southwest and least in the Southeast. Productivity in the
Southwest increased sharply from 971 to 4275 kg ha–1 for all
N0 values as α increased from 0.1 to 0.15, and then decreased
when α exceeded 0.20. The WP in the Mid-South increased
from 1100 to 2123 kg ha–1 for all N0 when α increased from
0.1 to 0.15, and then decreased when α exceeded 0.15. Maximum productivity in the Southeast, 709 kg ha–1, occurred
when α was 0.1. The WP then decreased as α increased.
In addition to these regional differences, productivity in
each region was greatest (least) when N0 = 440 kg ha–1
(220 kg ha–1), where WP sensitivity to N0 variations was
greatest (least) in the Southwest (Southeast). These results
illustrate that productivity in the Southwest and Mid-South is
highly dependent on water availability when α is small. When
irrigated water is sufficient, however, additional water leads
to a decrease in WP. This is particularly true in the Southeast,
where rainfall is sufficient to maximize water production, and
the addition of irrigated water causes WP to decrease for all α.
These results are consistent with those of Zwart and Bastiaanssen (2004), who reported WP increases with fertilization
for wheat (Triticum aestivum L.) yields in Niger, Syria, and
Uruguay, and Singh et al. (2010), who found significant WP
rises for cotton seeds in response to increased fertilization
rates of 80 to 200 kg ha–1 under deficit irrigation. Finally,
note in Fig. 3b that, when α becomes large, WP approaches
100 kg ha–1. This means that for large α, an increase in
irrigated water amount will not significantly impact water use
efficiency. Thus, we chose the WP optimization threshold to be
100 kg ha–1 to ensure a high sensitivity of cotton yields to the
irrigation water ratio.
Optimal Parameter Distribution and Validation
To examine the responses of the redeveloped GOSSYM to
the optimization method described above, we conducted five
experiments:
1. CNTL: optimize both the irrigation ratio and initial NO3
with WP >100 kg ha–1 and NP >0.75 kg cotton kg–1 NO3
2. OPTI: optimize the irrigation ratio only and hold the
residual NO3 constant at 176 kg ha–1
3. OPTN: optimize the initial soil NO3 only and apply the
original GOSSYM irrigation scheme, i.e., apply irrigation
with 19 mm of water whenever the water stress level is
<0.75 following Doherty et al. (2003)
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4. ULMT: optimize both the
irrigation ratio and initial soil
NO3 without any limitation on
WP and NP
5. NOOP: apply the original
GOSSYM irrigation scheme
and initial soil NO3 of 176 kg
ha–1 instead of optimizing them
by inverse modeling
The relative mean biases and
ratios of standard deviations of
simulated to observed cotton
yields are shown for each experiment in Fig. 4. The CNTL simulation performed well, where the
long-term mean modeled yields
were within ±10% of observations in the 30-km grids across
major areas of the U.S. Cotton
Belt (Fig. 4a). Compared with
the CNTL mean biases, both
OPTI (Fig. 4b) and OPTN (Fig.
4c) reduced the underestimations
in north-central Texas, but they
increased overestimations by 4 to
17 and 6 to 15%, respectively, in
the southeastern states, with averages of 12 and 7%, respectively.
Moreover, OPTI significantly
underestimated long-term mean
yields along the Mississippi River
and Sacramento Valley in California by 11 to 27%, and OPTN
overestimated yields by about 17%
in areas of North Texas along the
New Mexico border. The NOOP
simulation (Fig. 4e) systematically underestimated the observed
yields in the southwestern states
and along sections of the Mississippi River but overestimated
yields in the other regions.
The OPTI underestimations
that occurred in heavily irrigated
regions were caused primarily
by insufficient soil NO3 because
the irrigated water amounts are
Fig. 4. Geographic distributions of cotton yield relative mean biases and standard
deviation ratios, respectively, for (a) and (f) the control (CNTL), i.e., optimization with
adjustable, while the overestimawater productivity >100 kg ha –1 and N productivity >0.75 kg cotton kg –1 NO3, (b) and (g)
tions in the southeastern states
irrigation optimization only (OPTI), (c) and (h) fertilization optimization only (OPTN); (d)
indicate that the soil initial NO3
and (i) optimization without limits on water and N productivity (ULMT); and (e) and (j) no
optimization (NOOP).
of 176 kg ha–1 is too large for
this region. The major cottonproducing areas in the southeastern states and North Texas
use of the old irrigation scheme and initial NO3 of 176 kg ha–1
along the New Mexico border are rainfed, with only limited
generates excessive yield overestimations by 17 and 38% in the
areas receiving irrigation. The OPTN overestimations show
southeastern states and Texas rainfed fields, respectively, as well
that the old irrigation scheme is not suitable and that irrigated
as substantial underestimations in the more heavily irrigated
cotton yields are far too large and disproportionately impact
regions of the southwestern states (38% in California, 65% in
grid area-weighted yields. The NOOP result also shows that
Arizona, and 18% in the Mississippi Delta).
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669
Among the five experiments, ULMT (Fig. 4d) produced
the best results because it optimized both the irrigation ratio
and initial NO3 without placing limitations on WP and NP.
Compared with the CNTL experiment, ULMT produced
slight improvements in the Southeast and Texas by reducing
the underestimation by approximately 3%. This indicates that
constraints on water and N productivities in the mathematical and statistical optimizing processes, which account for the
actual cropping practices, do not decrease model performance
substantially. The improvements generated by OPTI and
OPTN in Texas also resulted from the removal of WP and NP
constraints, respectively. By optimizing only one key parameter,
however, either the irrigation ratio or initial NO3, both OPTI
and OPTN simulated larger biases than the control experiment in key regions of the U.S. Cotton Belt.
When the experimental long-term standard deviations were
compared with observations, CNTL (Fig. 4f) produced overestimations of 28 to 118% along the Mississippi River, southeastern states, and the southern part of Arizona, with an average
of 64%. On the other hand, the average standard deviation
was 27% smaller in New Mexico, the Texas High Plains, and
southeast Texas. This pattern was produced in all experiments.
The reduced variability probably occurred because the observed
Fig. 5. Geographic distributions of (a) initial soil N abundance
consequences of pest damage and improved management pracin the top 2 m of soil (kg ha –1) and (b) the ratio of irrigated
tices were not considered.
water amount to potential evapotranspiration from the
Figure 5 illustrates the geographic distribution of initial soil
control (CNTL) experiment. Both quantities varied across
space but remained invariant during 1979 to 2005.
NO3 abundance in the top 2 m of soil in the root zone and the
ratio of irrigated water amount to potential evapotranspiration derived from inverse modeling in the CNTL experiment.
The initial soil NO3 abundances were <103 kg ha–1 in the
southeastern states and the Texas High Plains but >210 kg ha–1
along the Mississippi River and in the southwestern states. The
ratio of irrigated water amount to potential evapotranspiration
obtained by optimization did not
vary with time. The heaviest irrigation, where the ratio of irrigated
water amount was >0.8, occurred
along the Arizona–California
border. The areas with the greatest
irrigation normally coincide with
those that have largest initial soil
NO3 abundances. Moderate irrigation (irrigated ratio of 0.6–0.7)
is located in the Sacramento and
San Joaquin valleys in California
and isolated areas of the MidSouth states, while relatively little
irrigation (irrigated ratio <0.6)
occurs across the remainder of the
U.S. Cotton Belt.
Given that accurate geographical distributions of observed
initial soil NO3 and irrigated
water amount are not available, we
compared the simulated state-level
irrigated water amount with data
from the 1984, 1988, 1994, 1998,
Fig. 6. Total simulated (black dot) and observed (bar) irrigated water amounts in the U.S.
and 2003 USDA FRIS to indiCotton Belt states in 1984, 1988, 1994, 1998, and 2003.
rectly validate the optimization
670
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the model simulates more grids with smaller errors relative
to observations, and hence is more realistic. The redeveloped
GOSSYM has a peak frequency of 40% at the relative mean
bias of –0.05, while the peak frequency of the original model is
7.5% at the relative mean bias of 1.05. This result clearly shows
that the redeveloped GOSSYM substantially improved the
simulation of long-term mean cotton yields. For the standard
deviation ratio, simulation agreement with observations
improves as the peak frequency approaches 1.0 on the horizontal axis. The frequency distribution difference of this ratio
between the redeveloped and original GOSSYM is relatively
small when compared with their relative mean bias contrasts.
Thus, the two models produced interannual yield variability
with comparable magnitudes.
A more important capability in modeling variability is the
temporal correspondence between GOSSYM and observed
anomalies from 1 yr to another. Th is can be measured by
correlating the time series. For this measure, the closer the
peak frequency is to 1.0 on the horizontal axis, the better
the model captures the observed variations. The redeveloped
GOSSYM generates its peak frequency at 17% when the
correlation coefficient is 0.65, whereas the original model has
its peak value at 16% when the correlation coefficient is 0.25.
Based on the Student t-test and assuming yearly independence, correlation coefficients >0.32 are statistically significant at the 0.05 level. Significant correlations were simulated
by the redeveloped and original GOSSYM in 87 and 40% of
harvest grids, respectively. Therefore, the redeveloped GOSSYM substantially improved the simulation of the observed
yield anomaly interannual variability.
method used in this study (Fig. 6). We did not validate the
initial soil NO3 because credible initial NO3 information is
unavailable and its yearly variation is factored into the farmers’ fertilization decisions. The results showed that simulated
annual irrigated water amounts were in good agreement with
the FRIS data in the Southwest and Mid-South during the
survey years. In the Southeast, however, FRIS irrigated water
amounts had larger uncertainties due to the small fraction of
irrigated cotton and large spatial and interannual variations in
irrigation practices. Thus, in some survey years, the FRIS irrigated water amounts were zero, such as for Tennessee in 1984,
1988, and 1994. We assumed that the differences between
modeled and FRIS irrigated water amounts in the Southeast
resulted mainly from FRIS data uncertainties.
Result Improvement from the Original
to Redeveloped GOSSYM
When compared with the original GOSSYM (Fig. 2a), the
redeveloped GOSSYM (Fig. 4a) substantially reduced longterm yield mean biases from 92 to 4% when averaged across the
entire U.S. Cotton Belt. The standard deviation (Fig. 2b vs. 4f)
overestimations in Arizona and southwest Texas were reduced
from 138 and 90% to 33 and –21%, respectively. In addition,
the redeveloped (original) model overestimated (underestimated) standard deviations in the southeastern states by 71%
(27%). The larger value (i.e., 71% vs. 27%) does not imply that
the redeveloped model has diminished capabilities. In fact, the
underestimation produced by the original GOSSYM in this
region probably occurred because cotton experiences small N
and water stresses (without imposing physical constraints) that
cause substantial mean yield overestimations that approximate
the optimal values for the cotton cultivar (Fig. 2a). The standard deviation overestimation by
the redeveloped model occurred
because cotton yields were overestimated (underestimated) during
wet (dry) years. In wet (dry) years,
the irrigated cotton fraction in
a grid is smaller (larger) and less
(more) irrigated water is required.
Given that the southeastern states
contain a mixture of rainfed
and irrigated cotton fields, the
new autoirrigation scheme can
only partially solve this problem
because the actual irrigated cotton
fraction varies annually and has a
large uncertainty due to a lack of
creditable data.
Figure 7 compares the spatial
frequency distributions of all
cotton-grid pointwise relative
mean biases, standard deviation
ratios, and correlation coefficients
of the original and redeveloped
GOSSYM. For the relative mean
Fig. 7. Spatial frequency distributions of all cotton-grid pointwise relative mean biases (black;
bias, the occurrence of a larger
bottom and left axes), standard deviation ratios (red; top and right axes), and correlation
coefficients (green; bottom and left axes) of cotton yields between observations and
frequency closer to 0.0 on the
simulations by the original (dashed lines) and redeveloped (solid lines) GOSSYM.
horizontal axis indicates that
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DISCUSSION AND CONCLUSIONS
This study focused on the development of the geographically
distributed cotton growth model GOSSYM for coupling with
the regional climate model CWRF. The redeveloped GOSSYM includes improved physics and interface development,
where its key parameters are determined by an optimization
method. In particular, model formulation consistency between
GOSSYM and CWRF is incorporated for the physical representations of vegetation and soil properties, soil temperature
and moisture, evaporation and transpiration, and photosynthesis radiation, as well as the numerical implementation of the
dynamic coupling and soft ware engineering. The redeveloped
GOSSYM then integrates the best available cultural practice
specifications. As a result, the geographic distribution of irrigation practices and initial soil N content remain unknown due
to the lack of credible observations.
To close the system, we incorporated an improved autoirrigation model that computes the irrigated water amount once the
water stress factor falls below a threshold of 0.75 on the basis
of the simultaneous water stress and the ratio of the irrigated
water amount to potential evapotranspiration. Hence, inverse
modeling (with minimized modeled cotton yield errors) is
used to optimize the geographic distributions of the final two
key parameters: the ratio of the irrigated water amount to
potential evapotranspiration, as a surrogate for the unknown
actual irrigation practice (stress threshold, water amount, and
application interval), and the initial soil NO3 abundance in
the top 2 m of soil. The optimization also includes water and
N productivities to account for actual cropping practices and
showed that N productivity decreases as N0 increases and α
decreases. The sensitivity to α varied across the U.S. Cotton
Belt and was strongest (weakest) in the Southwest (Southeast),
where water productivity is greatest (least). Productivity in each
region increased when α was small and then decreased to a near
constant value when α became large. Given regional variations
in WP and NP, we chose the NP optimization threshold to be
0.75 kg cotton kg–1 NO3 and the WP optimization threshold
to be 100 kg ha–1.
Inclusion of the above improvements and optimizations in
the redeveloped GOSSYM produced good agreement with
observations, where simulated 1979 to 2005 mean yields were
within ±10% of observed values across almost the entire U.S.
Cotton Belt. In contrast, the redeveloped GOSSYM with the
old irrigation scheme and fi xed initial soil NO3 of 176 kg ha–1
generated substantial biases, with systematic cotton yield overestimations in the southeastern states, Mississippi River Delta,
and Texas High Plains (heavily irrigated regions). Sensitivity
studies further showed that optimizing only the irrigation ratio
or initial NO3 increased the mean biases across major cotton
growing areas of the U.S. Cotton Belt, including the southeastern states, northern Texas along the New Mexico border, and
the Sacramento Valley in California. Introducing the water
and N productivity constraints to the optimization process
to account for actual cropping practices did not substantially
impact the results.
The redeveloped GOSSYM realistically reproduced the geographic distribution of mean annual yields across the U.S. Cotton Belt. Good agreement between simulated annual irrigated
water amounts and observations from FRIS data in the major
672
irrigated cotton regions illustrates the improvements that
resulted from use of the new irrigation scheme and optimized
irrigation ratio. In the companion study (Liang et al., 2012a),
the redeveloped GOSSYM was used to study the responses
of cotton growth to climatic stresses in the U.S. Cotton Belt
and thereby to evaluate its ability to reproduce the observed
cotton–climate relationships. The interactive GOSSYM, as
coupled with the CWRF model, can be used in future studies
to provide more credible and detailed depictions of cotton–
climate interactions. The coupled modeling system will have
wide applications in the fields of precision farming and policy
development as they relate to food security.
ACKNOWLEDGMENTS
This study benefited from constructive discussions with Carl J.
Bernacchi on crop modeling. We thank David Kristovich for valuable
comments on the manuscript. This research was mainly supported by
the USDA UV-B Monitoring and Research Program, Colorado State
University, USDA-CREES-2009-34263-19774 (subawards to the
University of Illinois, G-1449-1), USDA-NIFA-2010-34263-21075
(subawards to the University of Maryland, G-1470-3), and USDANRI-2008-35615-04666 (subawards to the University of Maryland,
G-1469-3). The modeling was conducted on the National Center for
Supercomputing Applications facility. The views expressed are those
of the authors and do not necessarily reflect those of the sponsoring
agencies or the affiliating institutions of the authors.
REFERENCES
Agricultural Statistics Board. 1997. Usual planting and harvesting dates for
U.S. field crops. Agric. Handbk. 628. Natl. Agric. Stat. Serv., Washington, DC. www.nass.usda.gov/Publications/Usual_Planting_and_Harvesting_Dates/uph97.pdf.
Allen, R.G., L.S. Pereira, D. Raes, and M. Smith. 1998. Crop evapotranspiration: Guidelines for computing crop water requirements. Irrig. Drain.
Pap. 56. FAO, Rome.
Baker, D.N., J.R. Lambert, and J.M. McKinion. 1983. GOSSYM: A simulator
of cotton crop growth and yield. Tech. Bull. 1089. South Carol. Agric.
Exp. Stn., Clemson.
Baker, D.N., and J.A. Landivar. 1991. The simulation of plant development in
GOSSYM. In: T. Hodges, editor, Predicting crop phenology. CRC Press,
Boca Raton, FL. p. 153–170.
Bonan, G.B., and S. Levis. 2006. Evaluating aspects of the Community Land
and Atmosphere models (CLM3 and CAM3) using a dynamic global
vegetation model. J. Clim. 19:2290–2301. doi:10.1175/JCLI3741.1
Boone, M.Y.L., D.O. Porter, J.M. McKinion. 1993. Calibration of GOSSYM: Theory and practice. Comput. Electron. Agric. 9:193–203
doi:10.1016/0168-1699(93)90038-3
Boone, M.Y.L., D.O. Porter, and J.M. McKinion. 1995. RHIZOS 1991: A simulator of row crop rhizospheres. USDA-ARS Bull. 113. U.S. Gov. Print.
Office, Washington, DC.
Bronson, K.F., T.T. Chua, J.D. Booker, J.W. Keeling, and R.J. Lascano. 2003.
In-season nitrogen status sensing in irrigated cotton: II. Leaf nitrogen and biomass. Soil Sci. Soc. Am. J. 67:1439–1448. doi:10.2136/
sssaj2003.1439
Calmon, M.A., J.W. Jones, D. Shinde, and J.E. Specht. 1999. Estimating
parameters for soil water balance models using adaptive simulated
annealing. Appl. Eng. Agric. 15:703–713.
Challinor, A.J., T.R. Wheeler, J.M. Slingo, P.Q. Craufurd, and D.I.F. Grimes.
2005. Simulation of crop yields using ERA-40: Limits to skill and nonstationarity in weather–yield relationships. J. Appl. Meteorol. Climatol.
44:516–531. doi:10.1175/JAM2212.1
Chen, M., D. Pollard, and E.J. Barron. 2004. Regional climate change in East
Asia simulated by an interactive atmosphere–soil–vegetation model. J.
Clim. 17:557–572. doi:10.1175/1520-0442(2004)0172.0.CO;2
Agronomy Journal
•
Volume 104, Issue 3
•
2012
Choi, H.I., P. Kumar, and X.-Z. Liang. 2007. Th ree-dimensional volumeaveraged soil moisture transport model with a scalable parameterization of subgrid topographic variability. Water Resour. Res. 43:W04414.
doi:10.1029/2006WR005134
Choi, H.I., and X.-Z. Liang. 2010. Improved terrestrial hydrologic representation in mesoscale land surface models. J. Hydrometeorol. 11:797–809.
doi:10.1175/2010JHM1221.1
Climate Change Science Program. 2008. The effects of climate change on agriculture, land resources, water resources, and biodiversity in the United
States. Synthesis and Assessment Product 4.3. U.S. Climate Change Science Program, Washington, DC.
Dai, Y., R.E. Dickinson, and Y.-P. Wang. 2004. A two-big-leaf model for
canopy temperature, photosynthesis, and stomatal conductance. J. Clim.
17:2281–2299. doi:10.1175/1520-0442(2004)0172.0.CO;2
Dai, Y., X. Zeng, R.E. Dickinson, I. Baker, G. Bonan, M. Bosilovich, et al.
2003. The Common Land Model (CLM). Bull. Am. Meteorol. Soc.
84:1013–1023. doi:10.1175/BAMS-84-8-1013
Dickinson, R.E., J.A. Berry, G.B. Bonan, G.J. Collatz, C.B. Field, I.Y. Fung, M.
Goulden, W.A. Hoffman, R.B. Jackson, R. Myneni, P.J. Sellers, and M.
Shaikh. 2002. Nitrogen controls on climate model evapotranspiration. J.
Clim. 15:278–295. doi:10.1175/1520-0442(2002)0152.0.CO;2
Dickinson, R.E., A. Henderson-Sellers, P.J. Kennedy, and M.F. Wilson. 1993.
Biosphere-Atmosphere Transfer Scheme (BATS) for NCAR community
climate model. NCAR Tech. Note NCAR/TN-387+STR. Natl. Ctr. for
Atmos. Res., Boulder, CO.
Dirmeyer, P.A. 1994. Vegetation stress as a feedback mechanism in midlatitude drought. J. Clim. 7:1463–1483.
doi:10.1175/1520-0442(1994)0072.0.CO;2
Doherty, R.M., L.O. Mearns, K.R. Reddy, M.W. Downton, and L. McDaniel. 2003. Spatial scale effects of climate scenarios on simulated cotton
production in the southeastern U.S.A. Climatic Change 60:99–129.
doi:10.1023/A:1026030400826
Fischbach, P.E., and B.R. Somerholder. 1974. Irrigation design requirement for
corn. Trans ASAE 17:162–171
Foley, J.A., S. Levis, I.C. Prentice, D. Pollard, and S.L. Thompson. 1998. Coupling dynamic models of climate and vegetation. Global Change Biol.
4:561–579. doi:10.1046/j.1365-2486.1998.t01-1-00168.x
Gauch, H.G., Jr., J.T.G. Hwang, and G.W. Fick. 2003. Model evaluation by
comparison of model‐based predictions and measured values. Agron. J.
95:1442–1446. doi:10.2134/agronj2003.1442
Gerik, T.J., D.M. Oosterhuis, and H.A. Torbet. 1998. Managing cotton nitrogen
supply. Adv. Agron. 64:115–147. doi:10.1016/S0065-2113(08)60503-9
Grismer, M.E. 2002. Regional cotton lint yield, ETc and water value in Arizona and California. Agric. Water Manage. 54:227–242. doi:10.1016/
S0378-3774(01)00174-3
Heinemann, A.B., G. Hoogenboom, and R.T. de Faria. 2002. Determination
of spatial water requirements at county and regional levels using crop
models and GIS: An example for the state of Parana, Brazil. Agric. Water
Manage. 52: 177–196. doi:10.1016/S0378-3774(01)00137-8
Hillel, D., and Y. Guron. 1973. Relation between evapotranspiration
rate and maize yield. Water Resour. Res. 9:743–748 doi:10.1029/
WR009i003p00743
Hodges, H.F., F.D. Whisler, S.M. Bridges, K.R. Reddy, and J.M. McKinion.
1998. Simulation in crop management: GOSSYM/COMAX. In: R.M.
Peart and R.B. Curry, editors, Agricultural systems modeling and simulation. Marcel Dekker, New York. p. 235–282.
Intergovernmental Panel on Climate Change. 2007. Climate Change 2007:
Impacts, adaptation, and vulnerability. Contribution of Working Group
II to the Th ird Assessment Report of the Intergovernmental Panel on
Climate Change. Cambridge Univ. Press, Cambridge, UK.
Irmak, A., J.W. Jones, T. Mavromatis, S.M. Welch, K.J. Boote, and G.G.
Wilkerson. 2000. Evaluating methods for simulating soybean cultivar
responses using cross validation. Agron. J. 92:1140–1149. doi:10.2134/
agronj2000.9261140x
Jallas, E. 1998. Improved model-based decision support by modeling cotton
variability and using evolutionary algorithms. Ph.D. diss. Mississippi
State Univ., Mississippi State, MS (Diss. Abstr. 9829786).
Jensen, M.E., and D.F. Heermann. 1970. Meteorological approaches to irrigation scheduling. In: Proceedings of the National Irrigation Symposium,
Lincoln, NE. 10–13 Nov. 1970. Am. Soc. Agric. Eng., St. Joseph, MI. p.
NN1–NN10.
Agronomy Journal
•
Volume 104, Issue 3
•
2012
Jones, P.N., and P. S. Carberry. 1994. A technique to develop
and validate simulation models. Agric. Syst. 46:427–442.
doi:10.1016/0308-521X(94)90105-O
Karl, T.R., J.M. Melillo, and T.C. Peterson, editors. 2009. Global climate
change impacts in the United States. Cambridge Univ. Press, New York.
Khorsandi, F., M.Y.L. Boone, G. Weerakkody, and F.D. Whisler. 1997. Validation of the soil temperature subroutine HEAT in the cotton simulation
model GOSSYM. Agron. J. 89:415–420. doi:10.2134/agronj1997.0002
1962008900030008x
Liang, X.-Z., H. Choi, K.E. Kunkel, Y. Dai, E. Joseph, J.X.L. Wang, and P.
Kumar. 2005a. Development of the regional Climate–Weather Research
and Forecasting model (CWRF): Surface boundary conditions. ISWS
SR 2005-01. Ill. State Water Surv., Champaign.
Liang, X.-Z., H. Choi, K.E. Kunkel, Y. Dai, E. Joseph, J.X.L. Wang, and P.
Kumar. 2005b. Surface boundary conditions for mesoscale regional climate models. Earth Interact. 9:1–28. doi:10.1175/EI151.1
Liang, X.-Z., W. Gao, K.E. Kunkel, J. Slusser, X. Pan, H. Liu, and Y. Ma. 2003.
Sustainability of vegetation over Northwest China, Part 1: Climate
response to grassland. Proc. SPIE 4890:29–44.
Liang, X.-Z., L. Li, K. E. Kunkel, M. Ting, and J. X. L. Wang. 2004.
Regional climate model simulation of U.S. precipitation during 1982–2002, Part 1: Annual cycle. J. Clim. 17:3510–3528.
doi:10.1175/1520-0442(2004)0172.0.CO;2
Liang, X.-Z., M. Xu, H.I. Choi, K.E. Kunkel, L. Rontu, J.-F. Geleyn, M.D.
Müller, E. Joseph, and J.X.L. Wang. 2006. Development of the regional
Climate–Weather Research and Forecasting model (CWRF): Treatment
of subgrid topography effects. In: Proceedings of the 7th Annual WRF
User’s Workshop, Boulder, CO. 19–22 June 2006. http://www.mmm.
ucar.edu/wrf/users/workshops/WS2006/abstracts/Session07/7_3_
Liang.pdf.Natl. Ctr. for Atmos. Res., Boulder, CO.
Liang, X.-Z., M. Xu, W. Gao, K.E. Kunkel, J. Slusser, Y. Dai, Q. Min, P.R.
Houser, M. Rodell, C.B. Schaaf, and F. Gao. 2005c. Development of land
surface albedo parameterization bases on Moderate Resolution Imaging Spectroradiometer (MODIS) data. J. Geophys. Res. 110:D11107.
doi:10.1029/2004JD005579
Liang, X.-Z., M. Xu, W. Gao, K.R. Reddy, K.E. Kunkel, D.L. Schmoldt, and
A.N. Samel. 2012a. Physical modeling of U.S. cotton yields and climate
stresses during 1979 to 2005. Agron. J. 675–683 (this issue).
Liang, X.-Z., M. Xu, X. Yuan, T. Ling, H.I. Choi, F. Zhang, et al. 2012b. Climate–Weather Research and Forecasting model (CWRF). Bull. Am.
Meteorol. Soc. (in press).
Liang, X.-Z., M. Xu, J. Zhu, K.E. Kunkel, and J.X.L. Wang. 2005d. Development of the regional Climate–Weather Research and Forecasting model
(CWRF): Treatment of topography. In: Proceedings of the 2005 WRF/
MM5 User’s Workshop, Boulder, CO. 27–30 June 2005. Univ. Corp. for
Atmos. Res., Boulder, CO. Pap. 9.3. www.mmm.ucar.edu/wrf/users/
workshops/WS2005/abstracts/Session9/3-Liang.pdf
Liu, W.T.H., D.M. Botner, and C.M. Sakamoto. 1989. Application of CERES‐
Maize model to yield prediction of a Brazilian maize hybrid. Agric. For.
Meteorol. 45:299–312. doi:10.1016/0168-1923(89)90050-6
Lu, L., R.A. Pielke, Sr., G.E. Liston, W.J. Parton, D. Ojima, and M. Hartman.
2001. Implementation of a two-way interactive atmospheric and ecological model and its application to the central United States. J. Clim.
14:900–919. doi:10.1175/1520-0442(2001)0142.0.CO;2
McKinion, J.M., D.N. Baker, F.D. Whisler, and J.R. Lambert. 1989. Application of GOSSYM/COMAX system to cotton crop management. Agric.
Sys. 31:55–65. doi:10.1016/0308-521X(89)90012-7
Mesinger, F., G. DiMego, E. Kalnay, K. Mitchell, P.C. Shafran, W. Ebisuzaki,
et al. 2006. North American regional reanalysis. Bull. Am. Meteorol.
Soc. 87:343–360. doi:10.1175/BAMS-87-3-343
Molden, D. 1997. Accounting for water use and productivity. System-wide Initiative for Water Management (SWIM) Pap. 1. Int. Irrig. Manage. Inst.,
Colombo, Sri Lanka.
Newton, P.C.D., R.A. Carran, G.R. Edwards, and P.A. Niklaus, editors. 2007.
Agroecosystems in a changing climate. CRC Press, Boca Raton, FL.
Novoa, R., and R.S. Loomis. 1981. Nitrogen and plant production. Plant Soil
58:177–204. doi:10.1007/BF02180053
Osborne, T.M., J.M. Slingo, D.M. Lawrence, and T.R. Wheeler. 2009.
Examining the interaction of growing crops with local climate
using a coupled crop–climate model. J. Clim. 22:1393–1411.
doi:10.1175/2008JCLI2494.1
673
Potter, S.R., S. Andrews, J.D. Atwood, R.L. Kellogg, J. Lemunyon, L. Norfleet,
and D. Oman. 2006. Model simulation of soil loss, nutrient loss and soil
organic carbon associated with crop production. U.S. Gov. Print. Office,
Washington, DC. www.nrcs.usda.gov/Internet/FSE_DOCUMENTS/
nrcs143_013138.pdf
Reddy, K.R., H.F. Hodges, and J.M. McKinion. 1997. Modeling temperature
effects on cotton internode and leaf growth. Crop Sci. 37:503–509.
doi:10.2135/cropsci1997.0011183X003700020032x
Reddy, K.R., V.G. Kakani, J.M. McKinion, and D.N. Baker. 2002. Applications of a cotton simulation model, GOSSYM, for crop management,
economic and policy decisions. In: L.R. Ahuja et al., editors, Agricultural
System Models in Field Research and Technology Transfer. CRC Press,
Boca Raton, FL. p. 33–73.
Richardson, A.G., and K.R. Reddy. 2004. Assessment of solar radiation models and temporal averaging schemes in predicting radiation and cotton production in the southern United States. Clim. Res. 27:85–103.
doi:10.3354/cr027085
Saxton, K.E., and W.J. Rawls. 2006. Soil water characteristic estimates by
texture and organic matter for hydrologic solutions. Soil Sci. Soc. Am. J.
70:1569–1578. doi:10.2136/sssaj2005.0117
Sellers, P.J, D.A. Randall, G.J. Collatz, J.A. Berry, C.B. Field, D.A. Dazlich,
C. Zhang, G.D. Collelo, and L.B. Bounoua. 1996. A revised land surface
parameterization (SiB2) for atmospheric GCMs, Part I: Model formulation. J. Clim. 9:676–705. doi:10.1175/1520-0442(1996)0092.0.CO;2
Singh, Y., S.S. Rao, and P.L. Regar. 2010. Deficit irrigation and nitrogen effects
on seed cotton yield, water productivity, and yield response factor in shallow soils of semi-arid environment. Agric. Water Manage. 97:965–970.
doi:10.1016/j.agwat.2010.01.028
Skamarock, W.C., J.B. Klemp, J. Dudhia, D.O. Gill, D.M. Barker, W. Wang,
and J.G. Powers. 2005. A description of the advanced research WRF version 2. Tech. Note NCAR/TN-468+STR. Natl. Ctr. for Atmos. Res.,
Boulder, CO. www.wrf-model.org/wrfadmin/docs/arw_v2.pdf
674
Staggenborg, S.A., R J. Lascano, and D.R. Krieg. 1996. Determining cotton
water use in a semiarid climate with the GOSSYM cotton simulation
model. Agron. J. 88:740–745. doi:10.2134/agronj1996.000219620088
00050010x
Theseira, G.W., G.E. Host, J.G. Isebrands, and F.D. Whisler. 2003. SOILPSI:
A potential-driven three-dimensional soil water redistribution model:
Description and comparative evaluation. Environ. Modell. Soft w. 18:13–
23. doi:10.1016/S1364-8152(02)00040-3
Thorp, K., W. Batchelor, J. Paz, A. Kaleita, and K. DeJonge. 2007. Using crossvalidation to evaluate CERES-Maize yield simulations within a decision
support system for precision agriculture. Trans. ASABE 50:1467–1479.
Tsvetsinskaya, E.A., L.O. Mearns, and W.E. Easterling. 2001. Investigating the effects of seasonal plant growth and development in
three-dimensional atmospheric simulations: Part II. Atmospheric
response to crop growth and development. J. Clim. 14:711–729.
doi:10.1175/1520-0442(2001)0142.0.CO;2
Xiong, W., I. Holman, D. Conway, E. Lin, and Y. Li. 2008. A crop model cross
calibration for use in regional climate impacts studies. Ecol. Modell.
213:365–380. doi:10.1016/j.ecolmodel.2008.01.005
Xu, M., X.-Z. Liang, W. Gao, K.R. Reddy, J. Slusser, and K.E. Kunkel. 2005.
Preliminary results of the coupled CWRF–GOSSYM system. Proc.
SPIE 5884:68–74.
Xue, Y., M.J. Fennessy, and P.J. Sellers. 1996. Impact of vegetation properties
on U.S. summer weather prediction. J. Geophys. Res. 101:7419–7430.
doi:10.1029/95JD02169
Yuan, X., and X.-Z. Liang. 2011a. Evaluation of a conjunctive surface–subsurface process model (CCSP) over the United States. J. Hydrometeorol.
12:579–599. doi:10.1175/2010JHM1302.1.
Yuan, X., and X.-Z. Liang. 2011b. Improving cold season precipitation prediction by the nested CWRF-CFS system. Geophys. Res. Lett. 38:L02706.
doi:10.1029/2010GL046104
Zwart, S.J., and W.G.M. Bastiaanssen. 2004. Review of measured crop water
productivity values for irrigated wheat, rice, cotton and maize. Agric.
Water Manage. 69:115–133. doi:10.1016/j.agwat.2004.04.007
Agronomy Journal
•
Volume 104, Issue 3
•
2012