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Citation: Li, X.; Tan, J.; Li, H.; Wang,
L.; Niu, G.; Wang, X. Sensitivity
Analysis of the WOFOST Crop Model
Parameters Using the EFAST Method
and Verification of Its Adaptability in
the Yellow River Irrigation Area,
Northwest China. Agronomy 2023,13,
2294. https://doi.org/10.3390/
agronomy13092294
Received: 24 July 2023
Revised: 14 August 2023
Accepted: 29 August 2023
Published: 30 August 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
agronomy
Article
Sensitivity Analysis of the WOFOST Crop Model Parameters
Using the EFAST Method and Verification of Its Adaptability
in the Yellow River Irrigation Area, Northwest China
Xinlong Li 1, Junli Tan 1,2,3,*, Hong Li 1, Lili Wang 1, Guoli Niu 4and Xina Wang 4
1College of Civil and Hydraulic Engineering, Ningxia University, Yinchuan 750021, China;
lixinlong9905@163.com (X.L.); 12022131197@stu.nxu.edu.cn (H.L.); 12022131213@stu.nxu.edu.cn (L.W.)
2Engineering Research Center for Efficient Utilization of Modern Agricultural Water Resources in Arid
Regions, Ministry of Education, Yinchuan 750021, China
3
Ningxia Engineering Technology Research Center of Water-Saving Irrigation and Water Resources Regulation,
Yinchuan 750021, China
4College of Agriculture, Ningxia University, Yinchuan 750021, China; 12022131564@stu.nxu.edu.cn (G.N.);
eunicexina-w@163.com (X.W.)
*Correspondence: tanjl@nxue.edu.cn; Tel.: +86-151-0961-3396
Abstract:
Sensitivity analysis, calibration, and verification of crop model parameters improve crop
model efficiency and accuracy, facilitating its application. This study selected five sites within the
Ningxia Yellow River Irrigation Area. Using meteorological data, soil data, and field management
information, the EFAST (Extended Fourier Amplitude Sensitivity Test) method was used to conduct
first-order and global sensitivity analyses of spring wheat parameters in the WOFOST (World Food
Studies Simulation) Model. A Structural Equation Model (SEM) analyzed the contribution of crop
parameters to different simulation indices, with parameter sensitivity rankings being discussed under
varying water supply and climate conditions. Finally, the adapted WOFOST model was employed to
assess its applicability in the Ningxia Yellow River Irrigation Area. TMNFTB3.0 (correction factor
of total assimilation rate at 3
◦
C), SPAN (life span of leaves growing at 35
◦
C), SLATB0 (specific leaf
area in the initial period), and CFET (correction factor transpiration rate) showed higher sensitivity
index for most simulation indices. Under the same meteorological conditions, different water supply
conditions have a limited impact on crop parameter sensitivity, mainly affecting leaf senescence,
leaf area, and assimilate conversion to storage organs. The corrected crop parameters significantly
enhanced the wheat yield simulation accuracy by the WOFOST model (
ME
= 0.9964;
RMSE
= 0.2516;
MBE
= 0.1392;
R2
= 0.0331). The localized WOFOST model can predict regional crop yield, with this
study providing a theoretical foundation for its regional application, adjustment, and optimization.
Keywords: sensitivity analysis; WOFOST model; EFAST method; structural equation model
1. Introduction
In recent years, global climate change has significantly affected wheat production due
to changes in climate factors [
1
]. Thus, accurate and rapid simulation of wheat growth,
development, and yield changes under different conditions is crucial for guiding wheat
production [
2
]. Currently, crop growth models are extensively utilized in predicting crop
yield [
3
], managing agriculture [
4
], and evaluating agricultural production potential [
5
] and
other related fields. Existing crop models (WOFOST, CERES, APSIM, etc., the full name of
models is shown in Appendix A, Table A2) are widely employed for monitoring and evalu-
ating the growth and yield of crops like wheat, rice, corn, soybean and others [
6
–
9
], due
to their strong logic and practicality. However, with time, as agriculture faces increasing
challenges, these models show higher complexity [
10
]. They mathematically represent the
intricate interplay among plants, weather, soil, and field management, requiring significant
Agronomy 2023,13, 2294. https://doi.org/10.3390/agronomy13092294 https://www.mdpi.com/journal/agronomy
Agronomy 2023,13, 2294 2 of 23
human and financial resources for parameter acquisition for model utilization [
11
]. Param-
eter estimation is crucial in model development, as it determines prediction accuracy [12].
However, focusing on sensitive parameters can enhance model calibration accuracy and
efficiency, as crop growth models often involve multiple parameters with significant impact
under certain scenarios [
13
]. Sensitivity analysis (SA) is a widely utilized tool for calibrat-
ing and developing crop growth models, enabling quantification of parameter impacts on
model output [14].
SA can allocate uncertain outcomes to various model parameters, quantify their impact
on output results, and identify and select crucial model parameters, thereby reducing the
workload in parameter optimization while minimizing output uncertainty [
15
]. SA finds
wide application in various crop models, including DSSAT [
16
], WOFOST [
17
], APSIM [
18
]
and others. It can be divided into first-order SA and global SA [
19
]. The former estimates
the impact of a single parameter on model output while keeping other parameters fixed,
and it is commonly used due to its efficiency and speed [
20
]. Global SA considers and
quantitatively represents the impact of individual parameters and their interactions [
21
].
Commonly used SA methods in crop model studies include EFAST [
22
], Morris [
23
], Fourier
Amplitude Sensitivity Test (FAST) [
24
], Sobol [
25
], and others [
26
,
27
]. Among them, the
Extended Fourier Amplitude Sensitivity Test (EFAST) method based on variance analysis
combines the advantages of FAST and Sobol methods. It calculates parameter interac-
tions and provides efficient and accurate results [
28
]. Previous studies have successfully
employed EFAST for crop growth model SA [
29
–
31
] and generated promising outcomes.
However, most existing SA studies focus on yield and above-ground biomass at maturity
as observational variables [
32
], neglecting other constantly changing variables like leaf
area index (LAI). SA can assess the impact of minor variations in parameter values on
model outcomes [
33
] or globally evaluate the interaction of the entire range of parameter
values [
34
]. The latter approach typically involves difference analysis using the Taylor
series and Monte Carlo methods [35].
Therefore, conducting SA, calibration, and validation of crop model parameters en-
hance and optimize the model’s efficiency, accuracy, and applicability. In this study, the
Yellow River irrigation area of Ningxia Hui Autonomous Region served as the research
site. Field measurements, statistical survey data on spring wheat, and local meteorological,
soil, and field management test data were utilized for an EFAST SA in the WOFOST model.
This analysis examined the impact of crop parameters on spring wheat growth and yield
simulation results. Parameter sensitivity and their ranking consistency were discussed
under varying water supply conditions and climate scenarios, with underlying causes
being explored for sensitivity differences. Finally, the optimized model’s adaptability was
verified in the Ningxia Yellow River Irrigation Area, providing technical support for param-
eter SA to help localize the WOFOST model. Given the significant reference value of the
WOFOST model in wheat production, this study proposes a comprehensive approach to
determine model parameters by integrating actual wheat yield data. It presents sensitivity
variations of different parameters under diverse conditions, aiming to offer practical in-
sights for the application of the WOFOST model. Additionally, it offered effective methods
for crop model parameter calibration and application, and established a foundation for
future regional-scale model parameter calibration and verification.
2. Materials and Methods
2.1. Overview and Data Sources of the Study Area
Ningxia, situated in northwest China, is located between 35
◦
14
0
–39
◦
23
0
N and 104
◦
17
0
–
107
◦
39
0
E, in the upper reaches of the Yellow River. The area covers a total landmass of
~66,400 km
2
(Figure 1). This study selected five agro-meteorological testing stations in
Huinong, Yinchuan, Litong, Zhongning, and Qingtongxia as research areas due to their
significance as primary planting regions for spring wheat. Meteorological data used in
this study were sourced from the National Data Center for Meteorological Sciences (http:
//data.cma.cn), while the fundamental soil data for the model operation were obtained
Agronomy 2023,13, 2294 3 of 23
through field measurements and the China Soil Database (http://vdb3.soil.csdb.cn, China).
These details are presented in Table 1.
Figure 1. Scope of the study area and distribution of meteorological stations.
Table 1.
Information on the latitude, longitude, and fundamental physical and chemical soil proper-
ties at the experimental site.
Research Area
Organic
Carbon
Content/(g·kg−1)
Crushed Stone
Volume/%
Sand
Content/%
Silt
Content/%
Clay
Content/%
Soil Bulk
Density/g·cm−3PH Value
Yinchuan 1.12 10 29 50 21 1.38 7.8
Litong 0.46 7 41 38 21 1.4 8.1
Zhongning 1.12 10 34 45 21 1.39 7.9
Huinong 0.46 7 41 38 21 1.4 8.1
Qingtongxia 1.12 10 29 50 21 1.38 7.8
2.2. WOFOST Model
The WOFOST model, collaboratively developed by the Wageningen University and the
World Food Research Center (CWFS) in the Netherlands, is a versatile model with diverse
crop parameters applicable to various crops. Its calculation process is primarily executed
through three modules: climate, crop, and soil. By utilizing daily meteorological data, the
model establishes dynamic explanatory models for crop growth based on soil conditions,
management practices, and crop parameters [
36
]. These models simulate crop growth
under three conditions: potential, water-limited, and nutrient-limited [
37
]. The WOFOST
model incorporates major biophysical and biochemical processes. The three developmental
stages of crops (DVS) are represented by dimensionless variables: DVS 0 (represents the
seedling stage), DVS 1 (represents the flowering stage), and DVS 2 (represents the maturity
stage) [38].
For model operation, the following soil parameters are necessary: (1) soil moisture
content at wilting point (SWM; cm
3
/cm
3
), soil moisture content at field capacity (SMFCF;
cm
3
/cm
3
), soil moisture content at saturation (SM0; cm
3
/cm
3
), and hydraulic conductivity
of saturated soil (K0; cm/day). These were determined using the Van Genuchten (VG)
model [
39
], with VG parameters derived from the Rosetta model [
40
] based on the soil’s
fundamental physicochemical properties. The Mualem model [
41
] was also employed to
obtain the soil water conductivity function, calculated via Python program and converted
into the requisite soil parameters. The VG model is shown in Equation (1).
Θ=θ−θr
θs−θr
=1
1+(αh)nm
(1)
Agronomy 2023,13, 2294 4 of 23
where
Θ
is the effective soil water content at a given soil suction of h(kPa) (cm
3
/cm
3
);
θs
is saturation moisture content (cm
3
/cm
3
);
θr
is the retained water content (cm
3
/cm
3
);
α
is
scale parameter (1/kPa); and mand nare shape parameter. The meteorological parameters
necessary for model operation are computed using the Food and Agriculture Organization
of the United Nations (FAO)-recommended Penman-Monteith formula, as shown below:
Ra=24(60)
πGscdr[ωssin(ϕ)sin(δ)+cos(ϕ)cos(δ)sin(ωs)] (2)
dr=1+0.033 cos2π
365 J(3)
δ=0.409 sin2π
365 J−1.39(4)
where
Ra
is the daily solar zenith radiation (MJ
·
m
−2·
day
−1
);
Gsc
= 0.0820 is the solar
constant (MJ
·
m
−2·
min
−1
);
dr
is the reciprocal of the relative distance between the sun and
the earth;
ωs
is the solar hour angle (rad);
ϕ
is the geographical latitude (rad);
δ
is the solar
magnetic declination angle (rad);
J
is the ordinal number of a day. Solar radiation (
Rs
) and
steam pressure (es) can be obtained from the following equation:
Rs=as+bsn
NRa(5)
eO(T)=0.6108 exp17.27T
T+237.3 (6)
es=eO(Tmax)+eO(Tmin)
2(7)
where
n/N
is the relative sunshine duration;
as
and
bs
are the regression constants;
eO(T)
is
the water vapor pressure (kPa) at the air temperature T;
exp[. . .]
is an exponential function
with base 2.7183. The daily average saturated water vapor pressure should be computed as
the mean of the daily average maximum and minimum temperatures over that period.
2.3. Structural Equation Model
Structural Equation Model (SEM) is a multivariate statistical technique used to identify,
estimate, and validate various causal models [
42
]. SEM is typically applied to observe
multiple factor variables and generate corresponding observations [
43
]. It also represents
the causal process in a study through a series of structural equations, which are then
statistically tested to determine their consistency with empirical data across the entire
variable system.
Therefore, considering the potential for multiple causal relationships between simula-
tion indicators and crop parameter factors, employing SEM offers advantages in modeling
the crop growth system [
44
]. In this study, SEM was utilized to examine the contribution of
different crop parameters to various model indicators.
2.4. Research Methods
2.4.1. Crop Model Parameter Selection Method in WOFOST Model
Based on the growth and development characteristics of spring wheat and previous
studies on crop parameters of the WOFOST model for wheat [
45
–
47
], a total of 39 pa-
rameters related to different growth and development stages were selected for SA. These
parameters include assimilation, assimilate conversion, light energy utilization, extinction co-
efficient, leaf development, evapotranspiration, dry matter allocation, root system, and water use.
SA was conducted by varying the model crop parameters within
±
10% of their default values
and the default parameter range, assuming an even distribution within this range (Table 2).
Agronomy 2023,13, 2294 5 of 23
Table 2. Unit and value range of crop parameters in the WOFOST model.
Parameter Significance Unit Lower Limiting
Value
Upper Limiting
Value Parameter Significance Unit Lower Limiting
Value
Upper Limiting
Value
AMAXTB0 Maximum CO2assimilation rate
under DVS = 0 kg·hm−2·h−132.247 39.413 TMPFTB35
Correction factor of maximum
assimilation rate under mean
temperature 25 ◦C
0 0.1
AMAXTB1.0 Maximum CO2assimilation rate
under DVS = 1.0 kg·hm−2·h−132.247 39.413 TBASE Lower threshold temperature for
emergence −2 2
AMAXTB1.3 Maximum CO2assimilation rate
under DVS = 1.3 kg·hm−2·h−132.247 39.413 TSUM1 Cumulative Temperature from
emergence to flowering
◦C·d 800 1500
AMAXTB2.0 Maximum CO2assimilation rate
under DVS = 2.0 kg·hm−2·h−14.032 4.928 TSUM2 Cumulative Temperature from
flowering to maturity
◦C·d 600 1350
CVO Efficiency of conversion into
storage organs kg·kg−10.6381 0.7799 TMNFTB0 Correction factor of total assimilation
rate under minimum temperature 0 ◦C0 0.1
CVL Efficiency of conversion into leaves kg·kg−10.6165 0.7535 TMNFTB30 Correction factor of total assimilation
rate under minimum temperature 0 ◦C0.9 1.1
CVS Efficiency of conversion into stems kg·kg−10.63 0.7282 LAIEM Leaf area index at emergence hm2·hm−20.12285 0.15015
CVR Efficiency of conversion into roots kg·kg−10.65 0.7634 FOTB1
The dry matter distribution coefficient
of storage organs increased under
DVS = 1
kg·kg−10.9 1.1
EFFTB0
Light energy utilization rate of
single leaf under
average daily
temperature 0 ◦C
kg·hm−2·h−1·J−1·m2·s0.405 0.495 CFET Correction factor transpiration rate 0.9 1.1
EFFTB40
Light energy utilization rate of
single leaf under average daily
temperature 40 ◦C
kg·hm−2·h−1·J−1·m2·s0.405 0.495 FLTB0 Leaf dry matter
distribution coefficient under DVS = 0 kg·kg−10.585 0.715
KDIFTB0 Extinction coefficient for diffuse
visible light under DVS = 0 0.54 0.66 FLTB0.25
Leaf dry matter
distribution coefficient under
DVS = 0.25
kg·kg−10.63 0.77
KDIFTB2.0 Extinction coefficient for diffuse
visible light under DVS = 2.0 0.54 0.66 FLTB0.5 Leaf dry matter
distribution coefficient under DVS = 0.5 kg·kg−10.45 0.55
SPAN Life span of leaves growing at 35
Celsius d 28.17 34.43 FLTB0.646
Leaf dry matter
distribution coefficient under
DVS = 0.646
kg·kg−10.27 0.33
SLATB0 Specific leaf area under DVS = 0 hm2·kg−10.001908 0.002332 DEPNR Crop group number for soil water
depletion 4.05 4.95
SLATB0.5 Specific leaf area under DVS = 0.5 hm2·kg−10.001908 0.002332 TDWI Initial total crop dry weight kg·hm−2180 220
SLATB2.0 Specific leaf area under DVS = 2.0 hm2·kg−10.001908 0.002332 Q10
Relative change in
respiratory rate for every 10 ◦C
temperature change
1.8 2
TMPFTB0
Correction factor of maximum
assimilation rate under mean
temperature 0 ◦C
0.009 0.1 RDI Initial rooting depth cm 10 12
TMPFTB10
Correction factor of maximum
assimilation rate under mean
temperature 0 ◦C
0.54 1 RRI Maximum daily increase in rooting
depth cm·d−11.08 1.32
TMPFTB15
Correction factor of maximum
assimilation rate under mean
temperature 15 ◦C
0.9 1 RDMCR Maximum rooting depth cm 112.5 137.5
TMPFTB25
Correction factor of maximum
assimilation rate under mean
temperature 25 ◦C
0.9 1
Agronomy 2023,13, 2294 6 of 23
2.4.2. EFAST Analysis Method
To analyze the contribution of crop input parameters to output variables and address
high-order interactions, the EFAST method was used, which is a globally applicable and
quantitative algorithm that effectively handles complex non-linear and non-monotonic
models [
48
,
49
]. This method provides first-order and global sensitivity indices for each
parameter [
50
]. EFAST combines the computational efficiency of the FAST algorithm and
the ability to calculate the total effects of the Sobol algorithm [
51
]. It has recently gained
popularity in hydrological, ecological, and meteorological modeling due to its inherent
advantages [52–55].
The EFAST algorithm comprises two main steps: sampling and sensitivity index
calculation [
56
]. First, an efficient and uniform sampling process is performed using
a transform function. Then, FAST was used to obtain a quantitative sensitivity index,
which establishes the total variance of the model determined by each parameter and their
interactions. Finally, the total variance of the model is decomposed into its constituent parts:
V(Y)=
n
∑
i=1
Vi+
n
∑
i<j≤n
Vij +· · · +V(1,2,··· ,n)(8)
Vij =VEY|xi,xj−Vi−Vj(9)
Si=Vi
V(Y)(10)
STi=V(Y)−V−i
V(Y)(11)
where
Vij ∼V(1,2,·· · ,n)
represent the variance of the interaction between parameter interac-
tions;
V−i
represents the sum of variances of all parameters excluding the parameters;
Si
represents the first-order sensitivity index of the parameter, while
STi
represents the global
sensitivity index of the parameter and its contribution rate to Yinteractions with other
parameters including
xi
. The analysis results obtained from EFAST are based on numerous
parameter samples, making it a highly accurate and comprehensive quantitative evaluation
method [57].
2.4.3. Analysis Scheme
This study collected input data from the Yongning County field trial (2021–2022) in
Yinchuan City, which included climate, soil, and field management parameters. The EFAST
method was utilized to analyze the impact of 39 input parameters on 13 yield-related
indicators, growth-related indices, and evapotranspiration-related indicators of spring
wheat in the WOFOST model. The five yield-related indicators are (1) TWRT (total root
dry weight), (2) TWLV (total leaf dry weight), (3) TWST (total stem dry weight), (4) TWSO
(storage organ dry weight), and (5) TAGP (total aboveground production). The four
growth-related indices are: (1) DUR (growth time), (2) LAIM (maximum leaf area index),
(3) HINDEX (Harvest index), and (4) GASST (total assimilation). It also measured the
sensitivity of four evapotranspiration-related indicators: (1) TRC (transpiration coefficient
rate), (2) MREST (total maintenance respiration), (3) TRANSP (total transpiration), and
(4) EVSOL (total evaporation from the soil surface). The sensitivity of crop parameters
depended upon the simulated scenarios employed. Sensitivity analysis was conducted
for four scenarios under potential and water-limited water-culture supply conditions
during two spring wheat growing seasons (2020–2021) in Yongning County. The aim was
to identify differences in parameter sensitivity between years and water-culture supply
conditions. The specific procedures were as follows:
Agronomy 2023,13, 2294 7 of 23
(1) Python 3.7 program calculated soil and meteorological files according to the test area’s
soil and meteorological conditions. The value range and distribution form of the input
crop parameters were defined in SimLab 2.2.
(2)
The Monte Carlo method randomly sampled parameters, with 2835 sampling times
taken (the EFAST method considered that the analysis results with sampling times >
number of parameters ×65 were valid).
(3)
The generated parameter set was written into the corresponding WOFOST model file.
The model was then run, and the simulation results were organized.
(4)
The simulated data was formatted into text for recognitionn by the SimLab 2.2, fol-
lowed by conducting Monte Carlo analysis through SimLab 2.2 and obtaining the
final SA result.
(5)
Based on the analysis results, parameters with a high sensitivity index were selected
to establish SEMs, which were analyzed and visualized using the RStudio2021.09.0
program.
(6)
Crop parameters were adjusted according to crop parameter sensitivity and contribu-
tion analysis. The WOFOST model was run with meteorological and soil files of other
sites for localization verification.
2.4.4. Model Consistency Test Method
Root-mean-square error (
RMSE
) quantifies the overall difference between the simulated
and measured values [
58
]. The closer the
RMSE
approaches zero, the smaller the simulation
error and the higher the model precision. Mean bias error (
MBE
) indicates the average
deviation between simulated and measured values [
59
], A value closer to zero for
MBE
indicates higher simulation accuracy. The determination coefficient (
R2
) elucidates the
extent to which changes in simulated values account for variation, with a value closer to
one signifying greater model accuracy and applicability [
60
]. The formulas for calculating
RMSE ,MBE and R2are:
RMSE =s1
n
n
∑
i=1Yai−Yobs
ai2(12)
MBE =1
n
n
∑
i=1Yai−Yobs
ai(13)
R2=n
∑
i=1Yai−YaiYobs
ai−Yobs
ai
n
∑
i−1
(Yai−Yai)2n
∑
i−1Yobs
ai−Yobs
ai2(14)
where
Yobs
ai
is the observed value at the itime;
Yai
is the simulated value at the itime;
Yobs
is the observed average;
n
is the number of sample observations. In general, the
determination coefficient tends to decrease with increasing sample size. However, a
significant correlation indicates that the model can more reliably explain the variable.
Compared to the determination coefficient affected by sample size,
RMSE
directly measures
the deviation between simulated and observed values, with a smaller value indicating a
low error [61].
3. Results and Analysis
3.1. Spring Wheat Crop Parameter Sensitivity
Using randomly generated parameters, the model simulation was conducted under
four conditions: 2021 and 2022 potential and water-limited supply scenarios. The Monte
Carlo algorithm based on the extended Fourier series sensitivity test method analyzed
the 15 simulation indicators and their corresponding 39 crop parameters (Figure 2). The
results indicate a consistent trend between first-order sensitivity and global sensitivity.
TMNFTB3.0, SPAN, SLATB0, and CFET have higher sensitivity indices for most simulation
indices, among which TMNFTB3.0 has higher sensitivity indices for TAGP, GASST, TRC,
Agronomy 2023,13, 2294 8 of 23
and MREST. The first-order and global sensitivity indices of SPAN to EVSOL and CFET
to TRANSP are both >0.7, indicating that these crop parameters are dominant in the
simulation of the corresponding indicators and can explain
≥
70% of the variance variation
of the results. The study conducted by Xing et al. [
47
] demonstrated that CEFT exhibited
the highest sensitivity among crop parameters in relation to wheat yield, with a global
sensitivity index of 0.56, which aligns with the findings of this investigation.
Figure 2. Cont.
Agronomy 2023,13, 2294 9 of 23
Figure 2.
First-order and global sensitivities of crop parameters under the conditions of potential (
A
),
water restriction (B) in 2021, potential (C), and water restriction (D) in 2022.
Assuming fixed meteorological, soil and field management conditions, a slight dis-
crepancy exists between first-order sensitivity and global sensitivity of crop parameters for
the same model simulation index (Figure 3). The global sensitivity surpasses the first-order
sensitivity by a 1–8% margin, except for indicators with negligible disparities in simulation
outcomes, such as DUR, where the disparity between first-order and global sensitivity is
substantial, exceeding 30%.
Figure 3. Cont.
Agronomy 2023,13, 2294 10 of 23
Figure 3. Cont.
Agronomy 2023,13, 2294 11 of 23
Figure 3.
Difference of crop parameter sensitivity under the conditions of potential (
A
), water
restriction (B) in 2021, potential (C) and water restriction (D) in 2022.
Under identical meteorological conditions, varying water supply has a limited impact
on crop parameter sensitivity. In 2021, the changes in water supply only affected the
first-order and global sensitivities of five crop parameters: CVO, EFFTB40, KDIFTB0, SPAN,
and SLATB0, with those of CVO, EFFTB40, KDIFTB0, KDIFTB2.0, SPAN, SLATB0 and
TDWI being impacted by varying water supply conditions in 2022. Among the first-order
sensitivities, significant changes are observed for SLATB0 in 2021 and TDW1 in 2022.
Notably, KDIFTB0 and SLATB0 exhibited substantial changes in terms of global SA in 2021
(Figure 4).
Under the meteorological conditions of 2021, the sensitivity ranking of wheat yield-
related indicators (TWRT, TWLV, TWST, TWSO and TAGP) shows that TMNFTB3.0 >
CVS > AMAXTB1.0 > SPAN > AMAXTB0 > CVL exhibited greater sensitivity among crop
parameters with slightly varying specific circumstances. SPAN was the most sensitive to
TWSO, followed by TMNFTB3.0 and KDIFTB2.0. Furthermore, CVS was the most sensitive
to TWRT, followed by AMAXTB0. TMNFTB3.0 was the most sensitive to TAGP, followed
by AMAXTB1.0. Changes in the water supply have little effect on the sensitivity ranking of
the parameter sensitivity index, with the water limit only affecting the sensitivity ranking
of KDIFTB2.0 to TWSO and SLATB0 to TAGP.
Under meteorological conditions of 2022, the ranking of crop parameters with greater
sensitivity generally was TMNFTB 3.0 > CVS > SPAN > AMAXTB 1.0 > CVL, similar
to 2021. However, there are slight differences in the parameters of crops with greater
sensitivity to TWSO. TMNFTB 3.0 > CVO > KDIFTB2.0 > AMAXTB1.0 exhibited a higher
global sensitivity to TWST and Q10 to TAGP as compared to first-order sensitivity, while
the sensitivity ranking of crop parameters remained unaffected by changes in water supply
conditions.
Agronomy 2023,13, 2294 12 of 23
Figure 4. Cont.
Agronomy 2023,13, 2294 13 of 23
Figure 4.
Changes of first-order parameter sensitivity in 2021 (
A
) and 2022 (
B
) and changes of global
parameter sensitivity in 2021 (C) and 2022 (D).
For crop growth-related indices DUR, LAIM, HINDEX, and GASST under the me-
teorological conditions of 2021, the crop parameters with greater sensitivity are ranked
as TMNFTB3.0 > SPAN > CVO > CVS > SLATB0, consistent with the ranking of GASST.
Among these parameters, CVL and TMNFTB3.0 have the most significant influence on
LAIM, followed by SLATB0.5. CVO is identified as the most influential parameter on
HINDEX, followed by SPAN and TMPFTB25. Changes in water supply conditions signifi-
cantly affect the degree ranking of DUR and the sensitivity index of SLATB0. Under the
Agronomy 2023,13, 2294 14 of 23
meteorological circumstances of 2022, TMNFTB3.0 > SPAN > CVO > TBASE > CVS are
generally ranked as crop parameters with higher sensitivity, while the rank of HINDEX
and GASST exhibited similar parameter sensitivity indices to those observed in 2021. The
sensitivity index of crop parameters for LAIM follows the order of TBASE > TMNFTB3.0
> SLATB0.5 > CVL > CVS, with changes in water supply conditions greatly affecting the
ranking of parameter degrees for DUR.
In 2021, the evapotranspiration-related indices TRC, MREST, TRANSP, and EVSOL
were analyzed under meteorological conditions. The crop parameters with greater sensitiv-
ity are ranked as TMNFTB3.0 > SPAN > CFET > SLATB0 > CVL. Specifically, TMNFTB3.0
showed the highest sensitivity to TRC. The second factor is the sensitivity index ranking
of various parameters to different environmental stressors. TMNFTB3.0 exhibited the
highest sensitivity to MREST, followed by SPAN and AMAXTB1.0. CFET showed the
highest sensitivity to TRANSP, followed by TMNFTB3.0 and SPAN. In terms of EVSOL,
SPAN had the greatest impact on parameter sensitivity, followed by SLATB0 and CVL.
Changes in water supply conditions significantly affected the sensitivity index ranking of
SLATB0 but maintained consistent rankings for first-order and global parameters. Under
the meteorological conditions of 2022, the sensitivity index ranking slightly differed from
that of 2021. Only Q10 and TMPFTB0 displayed a global sensitivity ranking for MREST and
TRANSP, respectively, with KDIFTB0 showing a first-order and global sensitivity ranking
to EVSOL. Changes in water supply conditions had a negligible effect on the parameter
sensitivity index ranking.
In summary, crop parameters with high overall sensitivity often exhibit greater sensi-
tivity towards a single model index, with certain specific parameters possibly displaying
higher sensitivity towards particular model indices, thus affecting the parameter sensitivity
index ranking. Table A1 lists the detailed rankings. Therefore, when considering model
simulation for a specific index, priority should be given to adjusting parameters with the
highest sensitivity index ranking.
3.2. SEM of Degree of Contribution of Crop Parameters to Different Simulation Indices
SA conducted a comprehensive selection of 11 representative crop parameters: CEFT,
CVS, TBASE, EFFTB0, SLATB0, CVL, SPAN, TMNFTB3.0, CVO, AMAXTB0, and AMAXTB1.
TRANSP was chosen as the representative evapotranspiration index, while LAIM and
TWSO represented the crop growth index and yield, respectively. These parameters were
analyzed using a SEM. The SEM diagram under varying water supply conditions is omitted
(Figure 5), as different water supply conditions minimally affect the contribution of crop
parameters to simulation indicators, TRANSP, LAIM and TWSO.
The model demonstrated that CFET had the highest path coefficients of 0.69 and 0.75,
followed by SPAN with path coefficients of 0.48 and 0.5, indicating they independently
affected the evapotranspiration index TRANSP at rates of 69%, 75%, 48%, and 50%, re-
spectively. Conversely, CVO negatively contributed to TRANSP. Furthermore, TMNFTB3,
with path coefficients of 0.67 and 0.56, significantly impacted LAIM and independently
accounted for 67% and 56% of the changes in LAIM, respectively. Negative contribution
parameters are identified as CVO and TBASE. Regarding the yield index TWSO, TMNFTB3
had the highest impact with path coefficients of 0.66 and 0.62, followed by SPAN with
path coefficients of 0.52 and 0.55, independently affecting 66%, 62%, 52%, and 55% of
TWSO changes, respectively. However, SLATB0 has a negative contribution. Therefore,
these results indicate that diverse meteorological conditions exert varying impacts on the
positive and negative degrees of crop parameters’ contributions while negligibly affecting
the ranking of parameter contribution degrees.
Agronomy 2023,13, 2294 15 of 23
Figure 5. SEM of spring wheat in Yinchuan in 2021 (A) and 2022 (B).
3.3. Adaptability Verification of the Modified WOFOST Model in the Ningxia Yellow River
Irrigation Area
Crop parameters are adjusted based on the growth, development, and yield of spring
wheat in Yinchuan in 2021 as a benchmark. Considering actual weather conditions and soil
data from other research sites, the simulation results obtained are as follows (Table 3):
Agronomy 2023,13, 2294 16 of 23
Table 3. Parameter values of WOFOST model crops.
Crop
Parameter Value Crop
Parameter Value Crop
Parameter Value Crop
Parameter Value
AMAXTB0 35.2528 CVS 0.724642 KDIFTB2 0.654335 TMPFTB0 0.099835
AMAXTB1 39.0031 CVR 0.667882 SPAN 33.0204 TMPFTB10 0.56683
AMAXTB1.3 38.1757 EFFTB0 0.487338 SLATB0 0.002004 TMPFTB15 0.937174
CVO 0.765686 EFFTB40 0.476887 SLATB0.5 0.001944 TMPFTB25 0.956712
CVL 0.667321 KDIFTB0 0.573685 SLATB2 0.002072 TMPFTB35 0.015039
TBASE −1.53077 LAIEM 0.129034 FLTB0.5 0.450768 RDI 11.9468
TSUM1 1269.89 FOTB1 0.956577 FLTB0.646 0.296593 RRI 1.29025
TSUM2 1263.68 CFET 0.929755 DEPNR 4.64869 RDMCR 122.543
TMNFTB0 0.078391 FLTB0 0.601276 TDWI 182.62 AMAXTB2 4.84661
TMNFTB3 0.913048 FLTB0.25 0.641849 Q10 1.87027
For TAGP simulation using field trials in Yongning County, Yinchuan City, during 2021
and 2022, the model evaluation standards were:
RMSE
= 0.2516;
MBE
= 0.1392;
R2= 0.9976
.
Similarly, for LAI simulation using field trials in Yongning County during 2021 and 2022,
the model evaluation standards were:
RMSE
= 0.4533;
MBE
= 0.1283;
R2
= 0.2877. Finally,
Figure 6shows the simulated outputs for Yinchuan (2019–2022) and Zhongning, Qing-
tongxia, Litong and Huinong (2019–2020). Thus, the simulation demonstrates that the dry
matter accumulation of spring wheat in Yongning County, Yinchuan City (with an error
rate below 7%) outperforms the leaf area index (with an error rate below 20%). The rectified
model can simulate the Yellow River diversion irrigation region in Ningxia with a <8%
deviation.
Figure 6. Cont.
Agronomy 2023,13, 2294 17 of 23
Figure 6.
The fitting of TAGP (
A
), LAI (
C
), TAGP (
B
), and LAI (
D
) in 2021 in Yongning County,
Yinchuan City, and the fitting of yield (E) simulation in other regions.
4. Discussion
4.1. Analysis of Crop Parameter Sensitivity and its Response to Different Water Supply Conditions
In this study, EFAST was used to analyze the sensitivity indices of 39 WOFOST crop
parameters with respect to 13 model simulation outputs under potential and water-limited
conditions. The results indicate that among the yield-related outputs, TMNFTB3.0, CVS,
AMAXTB1.0, and SPAN showed the highest sensitivity indices. Furthermore, moisture
restriction increases the sensitivity index of AMAXTB0 while decreasing that of SLATB0.
Regarding growth-related indices, TMNFTB3.0, SPAN, CVO, TBASE, and SLATB0 exhibit
the highest sensitivity index values. Additionally, meteorological conditions in different
years significantly impact the sensitivity index. Moisture restriction increases the sensitivity
index of SLATB0 and SPAN while decreasing that of CVO.
Regarding evapotranspiration-related indices, TMNFTB3.0, SPAN, CEFT, SLATB0
and CVL exhibited the highest sensitivity levels. However, water restriction reduces the
sensitivity index for SLATB0. These findings highlight the crucial role of crop parameters
like TMNFTB3.0, SPAN, CVS, and AMAXTB1.0 in spring wheat’s growth and development.
Water restriction significantly impacts growth-related indicators, particularly leaf aging,
leaf area, and assimilate conversion to storage organs. These findings align with those
of a previous report [
62
]. Leaf senescence, initial specific leaf area, and assimilation rate
at 30
◦
C significantly impact crop yield, growth, and evapotranspiration. The allocation
of assimilates to stems, storage organs, and leaves also impacts crop yield, growth, and
evapotranspiration. The CO
2
assimilation rate, the low-temperature threshold for leaf
aging, and the correction factor for evapotranspiration independently and significantly
impact crop yield, growth, and evapotranspiration. This aligns with Xing et al. [
47
]
and underscores the sensitivity and importance of these parameters, as demonstrated
previously [
62
]. Currently, in this study, the parameter CFET, often overlooked in most SA
studies, significantly affects crop yield under water-limited conditions. Therefore, accurate
verification of this parameter can be highly valuable for simulating crop yield in the Yellow
River diversion irrigation area.
Zhang et al. [
63
] identified TSUM1, FRTB, CVO, CVS, DVSI, SPAN, and SLATB as
higher sensitivity parameters in the WOFOST model. The global sensitivity index exceeds
0.5. Similarly, Chen et al. [
45
] found that TSUM1, SLATB1, SLATB2, SPAN, EFFTB3 and
TMPF4 were more sensitive parameters of the WOFOST models. Their global sensitivity
indexes were 0.271, 0.237, 0.49, 0.191, 0.126 and 0.149. However, Li et al. [
53
] reported that
SPAN was the most sensitive parameter for dry matter accumulation, differing slightly
from the results of this study. This discrepancy might be attributed to crop type and study
Agronomy 2023,13, 2294 18 of 23
area variations, as varying crop types could generate different value ranges for different
parameters. Xu et al. [
64
] demonstrated that leaf area index (SLATB), maximum leaf as-
similation rate (AMAXTB), and extinction coefficient (KDIFTB2.0) were more sensitive
to varying water conditions due to the WOFOST model’s canopy division into distinct
leaf layers for calculating each layer’s assimilation rate. Consequently, upper leaves easily
achieve their maximum assimilation rates under stronger radiation. Since the light energy
utilization efficiency is reduced, particularly in water-scarce conditions where parameter
sensitivity changes are more pronounced [
65
], this aligns with this study’s findings. Fur-
thermore, [
45
] discovered minimal disparity in the maximum leaf area and above-ground
biomass sensitivity to parameters under potential and water-limited cultivation supply
conditions. This may be attributed to regional scale, simulated meteorological conditions,
and environment or field management measures. This also highlights the significance of
conducting SA before model implementation in a specific operational context [66].
4.2. Analysis of Degree of Contribution of SEM to Model Parameters
SA improves the understanding of process variables in a model [
66
], while SEM
visually illustrates the impact of different parameters on various simulation outcomes.
The findings indicate that CFET, followed by SPAN and CVO, significantly impacts the
evapotranspiration index TRANSP, indicating that higher assimilate conversion to storage
organs causes lower evapotranspiration. TMNFTB3, followed by SPAN, has the greatest
impact on LAIM and TWSO, highlighting their significant contribution to wheat growth
and yields. This finding aligns with the EFAST SA results mentioned above, reinforcing
our conclusion. Notably, few studies have reported SEM-based SA of the WOFOST model.
However, Wu et al. [
67
] used SEM analysis to examine the impact of meteorological
drought conditions on wheat yield and investigated how climate change and human
activities contributed to meteorological droughts and affected the net wheat primary
production loss. Temperature, wind, and total solar radiation emerged as primary drivers
of agricultural drought due to their high correlation with evapotranspiration. Dewitt
et al. [
68
] utilized SEM to construct an SEM based on yield components and plant growth
data. They deciphered the relationship between quantitative trait loci, yield components,
and total panicle yield. They also explored how diverse developmental processes that
interacted with the environment impacted wheat yield and plant growth. Additionally,
Vargas et al. [
69
] used SEM to analyze the effects of wheat genotypes and climate variables
on wheat growth and development. They found that external climate variables were related
to the final yield composition, with most process variables like ear number being affected
by low temperature and radiation during the early stage of plant development.
4.3. Localization of the WOFOST Model
The localized WOFOST model demonstrated superior reliability in wheat yield predic-
tion compared to its non-localized counterpart, as validated against official statistical wheat
yield data. This aligns with previous research findings [
70
], highlighting the effectiveness of
data localization in reducing wheat yield prediction errors. Although the calibration of crop
parameters and meteorological conditions improved overall model performance, further
enhancements are required for water-related aspects. Notably, simulations of potential crop
yield showed a slightly better correlation with recorded yields than those under water-
limited conditions [
62
]. This discrepancy may be attributed to various extreme processes,
including the impact of hot and dry winds, waterlogging, pest infestations, diseases, weeds,
and field management challenges, which can potentially reduce crop growth and yields.
However, some modeling studies have not fully addressed the impact of extreme
weather events on crop production [
71
]. Extreme events, such as heat waves, cold snaps,
droughts, floods, and frosts, directly and indirectly, affect crop systems by altering plant
physiology and behavior, growth periods, product quality, and yield [
72
]. To address
this issue, most current crop models require adjustments or updates to formalize the
biophysical interactions between crops and their environment, inevitably increasing the
Agronomy 2023,13, 2294 19 of 23
number of input factors (variables and parameters) needed for the model to account for
this complex interaction. It also involves parameter value distribution intervals, driving
variables (climate, soil, and management), and model structure [
73
]. Therefore, conducting
SA is crucial to adapt the model to a specific environment. Moreover, performing SA on
the model under various production levels and complex influencing factors can provide
deeper insights into the model and enhance its regional applicability.
The development of the WOFOST model is based on the agricultural planting condi-
tions in Europe, so the simulation effect of the adjusted model in other regions is not very
ideal, which may be caused by the different meteorological and geographical conditions in
the different areas and the different ability of crops to resist cold and drought. Therefore,
we suggest that in the actual implementation process, local crops’ yield and planting condi-
tions over the years should be referred to determine and calibrate the model parameters. In
addition, sub-models of the impact of pests and weed competition can be considered in the
development process of the model.
5. Conclusions
(1) The first-order and global sensitivity trends of spring wheat parameters in the WOFOST
model showed consistent results. TMNFTB3.0, SPAN, SLATB0, and CFET exhibited
higher sensitivity for most simulation indices. The impact of different water supply
conditions on crop parameter sensitivity in the WOFOST model was limited under
identical meteorological conditions. SA of crop parameters in the WOFOST model
revealed that TMNFTB3.0, SPAN, CVS, AMAXTB1.0 and other crop parameters
significantly affect the growth and development of spring wheat. Furthermore, water
restriction severely impacted the growth-related indices, particularly leaf senescence,
leaf area, and the assimilate allocation to storage organs.
(2)
The SEM identified CFET is the crop parameter with the highest contribution to
the evapotranspiration index TRANSP, while TMNFTB3 have the highest impact on
LAIM. TMNFTB3 is the most influential crop parameter for the yield index TWSO.
(3) The TAGP simulation results from field trials conducted in Yongning County, Yinchuan
City, during 2021 and 2022 met the model evaluation standards as evident from
RMSE = 0.2516
;
MBE
= 0.1392;
R2
= 0.9976. For LAI results from the same field trials,
the model evaluation standards were:
RMSE
= 0.4533;
MBE
= 0.1283;
R2
= 0.2877.
Therefore, the corrected model demonstrates improved simulation accuracy for the
Ningxia Yellow River diversion irrigation area, with errors <8%.
Author Contributions:
Conceptualization, X.L. and J.T.; Data curation, X.L., H.L., L.W. and G.N.;
Funding acquisition, X.W.; Investigation, X.W., J.T., X.L., X.L., H.L., L.W. and G.N.; Methodology, X.L.;
Software, X.L.; Supervision, X.W. and J.T.; Writing—original draft, X.L.; Writing—review and editing,
X.L. and J.T. All authors have read and agreed to the published version of the manuscript.
Funding:
This work was supported by the National Key Research and Development Program
of China [grant numbers 2018YFD0200405], the National Key Research and Development Plan
Project Topic [2021YFD1900605], the National Natural Science Foundation of China [52369010], the
Natural Science Foundation of Ningxia [grant numbers 2022AAC02013], the National Natural Science
Foundation of China [grant numbers 31860590], and the Ningxia University First-class Discipline
Construction (Hydraulic Engineering) Project [grant numbers NXYLXK2021A03].
Data Availability Statement:
Data relevant to this study are available on request from the corre-
sponding author.
Conflicts of Interest:
The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported in this paper.
Agronomy 2023,13, 2294 20 of 23
Appendix A
Table A1. Sensitivity ranking of first-order and global parameters of crops under different water supply and meteorological conditions.
Water
Supply
Conditions
and
Meteorolog-
ical
Conditions
TotalRoot Dry Weight Total Leaf Dry Weight Total Stem Weight Storage Organ Dry Weight Total Above-Ground
Production
Yield-
Related
Index
SimulatedTime Maximum Leaf Area Index HarvestIndex Total Assimilation
Growth-
Related
Index
TranspirationRate
Coefficient TotalMaintenance
Respiration TotalTranspiration TotalSurface Evaporation Evapotranspiration
RelatedIndex
First-Order
Sensitivity
Indexof
TWRT
Global
Sensitivity
Indexof
TWRT
First-Order
Sensitivity
Indexof
TWLV
Global
Sensitivity
Indexof
TWLV
First-Order
Sensitivity
Indexof
TWST
Global
Sensitivity
Indexof
TWST
First-Order
Sensitivity
Indexof
TWSO
Global
Sensitivity
Indexof
TWSO
First-Order
Sensitivity
indexof
TAGP
GlobalSensitivity Index of TAGP
First-Order
Sensitivity
Indexof
DUR
Global
Sensitivity
Indexof
DUR
First-Order
Sensitivity
Indexof
LAIM
Global
Sensitivity
Indexof
LAIM
First-Order
Sensitivity
Indexof
HINDEX
Global
Sensitivity
Indexof
HINDEX
First-Order
Sensitivity
Indexof
GASST
TheGlobal Sensitivity Index of
GASST
First-
ORDER
Sensitivity
Indexof
TRC
Global
Sensitivity
Indexof
TRC
First-Order
Sensitivity
Indexof
MREST
Global
Sensitivity
Indexof
MREST
First-order
Sensitivity
Indexof
TRANSP
Global
Sensitivity
Indexof
TRANSP
First-Order
Sensitivity
Indexof
EVSOL
GlobalSensitivity Index of EVSOL
Potential
conditionof
2021
CVS CVS TMNFTB3.0 TMNFTB3.0 CVS CVS SPAN SPAN TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 SPAN SPAN TMNFTB3.0 CVL CVO CVO TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 CFET CFET SPAN SPAN TMNFTB3.0
AMAXTB0 AMAXTB0 CVS CVS TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 AMAXTB1.0 AMAXTB1.0 CVS TMNFTB3.0 TMNFTB3.0 CVL TMNFTB3.0 SPAN SPAN AMAXTB1.0 AMAXTB1.0 SPAN CFET CFET SPAN SPAN TMNFTB3.0 TMNFTB3.0 SLATB0 SLATB0 SPAN
TMNFTB3.0 TMNFTB3.0 AMAXTB1.0 AMAXTB1.0 AMAXTB1.0 AMAXTB1.0 CVO SLATB0 SPAN SPAN AMAXTB1.0 CVS CVS SLATB0.5 SLATB0.5 TMPFTB25 TMPFTB25 SPAN SPAN CVO EFFTB0 SPAN AMAXTB1.0 AMAXTB1.0 SPAN SPAN CVL CVL CFET
CVL CVL AMAXTB0 AMAXTB0 CVL SLATB0 KDIFTB2.0 KDIFTB2.0 CVS SLATB0 SPAN TSUM2 TSUM2 CVS SLATB0 TBASE TBASE CVL SLATB0 CVS CVL CVL CVL SLATB0 SLATB0 SLATB0 KDIFTB2.0 KDIFTB2.0 SLATB0
AMAXTB1.0 AMAXTB1.0 CVL CVL AMAXTB0 CVL AMAXTB1.0 CVO CVL CVS AMAXTB0 SLATB2.0 SLATB2.0 AMAXTB0 TBASE AMAXTB1.3 AMAXTB1.3 AMAXTB0 AMAXTB2.0 AMAXTB1.0 SPAN TMPFTB0 CVS CVL TDWI TDWI TMNFTB3.0 TMNFTB3.0 CVL
Water
restriction
conditionof
2021
CVS CVS TMNFTB3.0 TMNFTB3.0 CVS CVS SPAN SPAN TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 SPAN SPAN TMNFTB3.0 CVL CVO CVO TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 CFET CFET SPAN SPAN TMNFTB3.0
AMAXTB0 AMAXTB0 CVS CVS TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 AMAXTB1.0 AMAXTB1.0 CVS SLATB0 SLATB0 CVL TMNFTB3.0 SPAN SPAN AMAXTB1.0 AMAXTB1.0 SPAN CFET CFET SPAN SPAN TMNFTB3.0 TMNFTB3.0 SLATB0 SLATB0 SPAN
TMNFTB3.0 TMNFTB3.0 AMAXTB1.0 AMAXTB1.0 AMAXTB1.0 AMAXTB1.0 KDIFTB2.0 KDIFTB2.0 SPAN SPAN AMAXTB1.0 KDIFTB0 KDIFTB0 SLATB0.5 SLATB0.5 TMPFTB25 TMPFTB25 SPAN SPAN CVO EFFTB0 SPAN AMAXTB1.0 AMAXTB1.0 SPAN SPAN CVL CVL CFET
CVL CVL AMAXTB0 AMAXTB0 CVL CVL CVO CVO CVS CVS SPAN TMNFTB3.0 TMNFTB3.0 CVS SLATB0 TBASE TBASE CVL AMAXTB2.0 SLATB0 CVL CVL CVL CVL TDWI SLATB0 KDIFTB2.0 KDIFTB2.0 CVL
AMAXTB1.0 AMAXTB1.0 CVL CVL AMAXTB0 SLATB0 AMAXTB1.0 CVR CVL CVL AMAXTB0 CVS CVS AMAXTB0 TBASE AMAXTB1.3 AMAXTB1.3 AMAXTB0 SLATB0 CVS SPAN TMPFTB0 CVS CVS CVL TDWI TMNFTB3.0 TMNFTB3.0 SLATB0
Potential
conditionof
2022
TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 SPAN SPAN TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 SPAN KDIFTB0 TBASE TBASE CVO CVO TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 CFET CFET SPAN SPAN TMNFTB3.0
CVL CVS CVS CVS CVS CVS TMNFTB3.0 TMNFTB3.0 AMAXTB1.0 AMAXTB1.0 CVS KDIFTB0 CVS TMNFTB3.0 TMNFTB3.0 SPAN SPAN AMAXTB1.0 AMAXTB1.0 SPAN CFET CFET SPAN SPAN TMNFTB3.0 TMNFTB3.0 SLATB0 SLATB0 SPAN
CVS CVL AMAXTB0 AMAXTB0 AMAXTB1.0 AMAXTB1.0 CVO CVO SPAN SPAN SPAN CVS TDWI SLATB0.5 SLATB0.5 TBASE TBASE SPAN SPAN CVO CVL SPAN AMAXTB1.0 AMAXTB1.0 SPAN TDWI TMNFTB3.0 KDIFTB0 CFET
AMAXTB0 AMAXTB0 CVL TBASE CVL RDI KDIFTB2.0 KDIFTB2.0 CVS Q10 AMAXTB1.0 TDWI SPAN CVL CVL TMPFTB25 TMPFTB25 KDIFTB2.0 KDIFTB2.0 TBASE EFFTB0 TMPFTB0 CVS Q10 TDWI SPAN KDIFTB0 TMNFTB3.0 SLATB0
TMPFTB15 TBASE TBASE CVL TBASE TBASE AMAXTB1.0 TBASE CVL CVS CVL TMNFTB3.0 TMNFTB3.0 CVS SLATB0 AMAXTB1.3 TMPFTB15 AMAXTB0 Q10 CVS SPAN CVL CVL CVS CVL TMPFTB0 KDIFTB2.0 KDIFTB2.0 CVL
Water
restriction
conditionof
2022
TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 SPAN SPAN TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 SPAN SPAN TBASE TBASE CVO CVO TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 TMNFTB3.0 CFET CFET SPAN SPAN TMNFTB3.0
CVL CVS CVS CVS CVS CVS TMNFTB3.0 TMNFTB3.0 AMAXTB1.0 AMAXTB1.0 CVS CVS CVS TMNFTB3.0 TMNFTB3.0 SPAN SPAN AMAXTB1.0 AMAXTB1.0 SPAN CFET CFET SPAN SPAN TMNFTB3.0 TMNFTB3.0 SLATB0 SLATB0 SPAN
CVS CVL AMAXTB0 AMAXTB0 AMAXTB1.0 AMAXTB1.0 CVO CVO SPAN SPAN SPAN TMNFTB3.0 KDIFTB0 SLATB0.5 SLATB0.5 TBASE TBASE SPAN SPAN CVO CVL SPAN AMAXTB1.0 AMAXTB1.0 SPAN SPAN TMNFTB3.0 KDIFTB0 CFET
AMAXTB0 AMAXTB0 CVL TBASE CVL RDI KDIFTB2.0 KDIFTB2.0 CVS Q10 AMAXTB1.0 TSUM2 TMNFTB3.0 CVL CVL TMPFTB25 TMPFTB25 KDIFTB2.0 KDIFTB2.0 TBASE EFFTB0 TMPFTB0 CVS Q10 TDWI TDWI KDIFTB0 TMNFTB3.0 CVL
TMPFTB15 TBASE TBASE CVL TBASE TBASE AMAXTB1.0 TBASE CVL CVS CVL KDIFTB0 TSUM2 CVS SLATB0 AMAXTB1.3 TMPFTB15 AMAXTB0 Q10 CVS SPAN CVL CVL CVS CVL TMPFTB0 KDIFTB2.0 KDIFTB2.0 SLATB0
Table A2. The meaning of some abbreviations that appear in this article.
Abbreviations Meaning Abbreviations Meaning Abbreviations Meaning
EFAST Extended Fourier Amplitude
Sensitivity Test SWM soil moisture content at the
wilting point TAGP total aboveground
production
WOFOST World Food Studies
Simulation DVS developmental stages of
crops DUR growth time
SEM Structural Equation Model SMFCF the soil moisture content at
field capacity LAIM maximum leaf area index
CERES Crop Environment Resource
Synthesis SM0 the soil moisture content at
saturation HINDEX Harvest index
APSIM Agricultural Production
Systems sIMulator K0 hydraulic conductivity of
saturated soil GASST total assimilation
DSSAT Decision Support System for
Agrotechnology Transfer TWRT total root dry weight TRC transpiration coefficient rate
RMSE Root-mean-square error TWLV total leaf dry weight MREST total maintenance respiration
MBE Mean bias error TWST total stem dry weight TRANSP total transpiration
R2determination coefficient TWSO storage organ dry weight EVSOL total evaporation from the
soil surface
Agronomy 2023,13, 2294 21 of 23
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