Applying the SIMPLE Crop Model to Assess Soybean (Glicine max. (L.) Merr.) Biomass and Yield in Tropical Climate Variation

Abstract

Soybean Glicine max. (L.) Merr. is one of the most major food crops. In some areas, its responses to different climates have not been well studied, particularly in tropical countries where other crops are more dominant. Accordingly, we adopted the SIMPLE crop model to investigate the responses of soybeans to the climate. We conducted two experiments on crop growth in the Summer–Autumn season of 2020, and Winter–Spring 2021 in the Hoa Binh Commune, in the Mekong Delta, Vietnam, which is an area that is vulnerable to climate change impacts, to obtain data for our model input and assessment. The assessment was concerned with the effects of climate variables (temperature and CO₂) on soybean biomass and yield. The results indicated that the SIMPLE model performed well in simulating soybean yields, with an RRMSE of 9–10% overall. The drought stress results showed a negative impact on the growth and development of soybeans, although drought stress due to less rainfall seemed more serious in Spring–Winter 2021 than in Summer–Autumn 2020. This study figured out the trend that higher temperatures can shorten biomass development and lead to yield reduction. In addition, soybeans grown under high CO₂ concentrations of 600 ppm gave a higher biomass and a greater yield than in the case with 350 ppm. In conclusion, climate variance can affect the soybean yield, which can be well investigated using the SIMPLE model.

1. Introduction

Climate varies over time and can cause problems for food crops. For this reason, an assessment of the responses of crops to the climate is needed, particularly for major food crops. Soybean, a leguminous annual C3 plant in the Fabaceae family [1], is a food crop that has caused much concern due to its nutritional values for animals and humans. Soybean responses to the climate have been widely studied, but the investigation of the responses in tropical areas is uncommon. For countries where soybean is not a major crop, knowledge of soybean responses is rarely known.

Previous studies have reported the key effects of climatic factors on soybeans. For instance, the temperature can affect the soybean yield [2]; for example, an increase of 1 °C in summer led to a decrease in the yield by 16% in Wisconsin, USA [3]. For Rio Grande do Sul (southern Brazil), a subtropical area, water supply and photothermal quotient are the factors that cause yield variation [4]. As reported in the study in Matopiba, Brazil, the sowing date (in relation to climate) is the determinant of the yield changes [5]. Yield can also be affected by photoperiod and crop management, which were found in sub-Saharan Africa [6].

The soybean yield can be assessed using crop models. The models may require a large number of parameters [7], and they have particular designs and set-up, which can constrain the model and the assessment of the effects of climate change on crops. Due to model design, study purposes, and input data requirements, the applicability of the models is varied, particularly for soybeans. For instance, the model DSSAT/CROPGRO-Soybean was useful for estimating the soybean yield (i.e., in Matopiba, Brazil [5]) and the optimal management (i.e., in Phu Pha Man, Thailand [8]). ORCHIDEE-CROP, a process-oriented terrestrial biogeochemical model based on generic crop phenology [9] performs well for soybean yield simulation in China [10]. EPIC-Boku helps envision the negative effect of temperature on the yield [11]. In addition, EPIC-IIASA is applicable for studying the effects of CO₂ on yields in Argentina, Brazil, and the USA [12]. Process-based models can be coupled with artificial intelligence for crop assessment, i.e., machine learning links GEPIC to assess the effects of climate change on soybean in Argentina, Brazil, China, and the USA [13], and the application of artificial neural networks for the yield estimation in Maryland, USA [14]. The models are different from each other but geographically dependent, and thus their simulation performance levels are various. In addition, models may require many data inputs that are somehow not available; therefore, simplified models with satisfactory performance are preferred for soybean studies.

Tropical areas have particular climatic characteristics that influence soybean growth. Hence, an assessment of its responses to climate is needed to determine which crop models can help. Among tropical countries, Vietnam is currently under climatic threat [15], which is an ideal study case for the assessment. In this region, the Mekong River Delta (MRD) is widely known for being severely affected by extreme droughts [16]. Studying the responses in this area may help fulfill the knowledge of the responses to climate for decision-making. The current investigations of this crop in this area are more experimental but less modeling. Although the crop models above may be applicable to the assessment, their applications are limited. In addition, since soybean is not a major crop, studies on its responses to climate are rare, and so the input data for modeling is not always available; this issue constrains the application of these models.

In regards to data availability and climate in the Mekong Delta, Vietnam, this study adopted the SIMPLE model with simplified and open-sourced designs that performed well in terms of soybean yield estimation for temperate areas in the USA [7]. Through this pilot study, we assessed the yield and biomass of the soybean (Glycine max. (L.) Merr.) and then informed the model’s applicability and the effects of climate variation on the crop, which is necessary to help protect this crop in the context of climate change. Therefore, this study aims at (1) adopting the SIMPLE model for soybean biomass and yield estimation, and (2) using the model to assess the soybean biomass and yield under climate change in temperature and CO₂. Our final goal is to investigate how climate variation affects soybean yield to contribute to crop and food protection.

2. Methods

2.1. Field Experiments

The purpose of field experiments was to obtain data for model input supply (including parameters), model calibration, and assessment. This study includes two field experiments on soybean cultivation in 2020 and 2021. The study field is based in Hoa Binh Commune, Cho Moi district, An Giang province, Vietnam (10°23′47″ N, 105°27′41″ E), with existing soybean cultivation (Figure 1) and clay loam soil with an organic matter content of 1.6% (

Table 1. Summary of the climatic features in the experiment site.

Climatic Features	Year
	2020	2021
Total rainfall (mm)	874.1	89.1
Number of rainy days	62.0	38.0
Mean temperature (°C) *	30.5	29.0
Mean radiation (MJ m−2d−1) **	15.8	19.7

*: recorded by Thermo Recorder TR-72Ui (T&D Corp, Japan). **: data from the Agroclimatology Community of the POWER Data Access Viewer.

). In our experiments, the soybean was grown in rainy season (July to October 2020) and dry season (January to April 2021). Three soybean seeds were sown in a hole, row by row at 35 cm and plant to plant at 25 cm. After emergence, plants were thinned to one per hole. To focus on climate effects, this study used the common fertilizing including 55 kg N, 75 kg P₂O₅, and 40 kg K₂O per hectare and pesticide application schedule currently practiced in the region. The field measurement includes the following data:

-

Sowing date, flowering date, maturity date, and growing time.

-

Plant height (cm), leaves number, total vegetative biomass (t ha⁻¹) per 10 days. vegetative biomass (t ha⁻¹), and grain yield.

The soybean cultivar used in the experiment was a high-yielding variety (DT2006). Soil properties in field for the experiments are shown in

Table 2. Soil properties at the research site.

Items	Characteristics
Soil texture
Sand (%)	30
Silt (%)	42
Clay (%)	28
Soil properties or soil parameters
Total nitrogen (%)	0.17
Total phosphorus (%P2O5)	0.03
Exchangeable potassium (cmol kg−1)	0.23
Field capacity (cm3 cm−3)	0.18
Available water capacity—AWC (cm3 cm−3)	0.14
Runoff curve number—RCN	84
Deep drainage coefficient—DDC	0.18
Root zone—RZD (mm)	329
Ground water level (cm)	35.8
Fertilizer applied
N (kg)	55
P (kg)	75
K (kg)	80

.

2.2. Modeling of Soybean Yield

This study used the SIMPLE model [7] (with daily timestep) based on crop physiology with a few parameters and equations. We assume that nutrients are given enough for soybean, and thus, this does not account for the effects of fertilizers on its growth. In this sense, this model is appropriate for assessing the climatic effects. This model considers crop yield as the product of the harvest index (HI) and the fraction of the above-ground cumulative biomass from sowing to maturity:

$$Yield=Biomass\_cum\times HI$$

(1)

where HI is the harvest index, the ratio of grain to total dry matter, and Biomass_cum is calculated using the following Euler approach:

$${Biomass\_cum}_{i+1}={Biomass\_cum}_i+{Biomass\_rate}_i$$

(2)

Biomass_rate_i is the daily biomass growth rate, and Biomass_cum_i is the cumulative biomass. Biomass_rate_i is determined in Equation (3), which depends on radiation use efficiency (RUE) of the plant canopy that intercepts daily photosynthesis active radiation (PAR) [17]. The daily change in plant biomass is affected by stress variables such as high temperatures, drought, and atmospheric CO₂ concentration [18].

$$Biomas{s}_{rate}=\begin{array}{c}Radiation\times f\left(Solar\right)\times RUE\times f\left(C{O}_2\right)\times f\left(Temp\right)\\ \times \mathrm{m}\mathrm{i}\mathrm{n}\left(\right(f\left(Heat\right),f\left(Water\right))\end{array}$$

(3)

where f(Solar) is the fraction of the solar radiation intercepted by the crop canopy regarding the Beer–Lambert law of light attenuation [19] ( as cited in Zhao et al., 2019), f(CO₂) is the CO₂ impact, f(Heat) is the heat stress function, and f(Water) is the water stress function [7,18].

f(Solar) for leaf growth and senescence period is as follows:

$$f(Solar)=\left\{\begin{array}{c}\frac{f_{Solar\_max}}{1+e^{-0.01\left(TT-I_{50A}\right)}},leaf growth period\\ \frac{f_{Solar\_max}}{1+e^{-0.01\left(TT-\left(T_{sum-}{I}_{50B}\right)\right)}},leaf senescence period\end{array}\right.$$

(4)

where I_50A is the cumulative temperature needed for leaf area development to intercept 50% of solar radiation during canopy closure; I_50B is the cumulative temperature needed from maturity to 50% of radiation interception during canopy senescence. f_{Solar_max} is the maximum fraction of radiation interception. f_{Solar_max} is used to account for different plant spacings. For most high-density crops, this value is set at 0.95 [7]. TT is the cumulative mean temperature, which is calculated as follows:

$$∆TT=\left\{\begin{array}{c}T-T_{base},\hspace{1em}\hspace{1em}T>T_{base}\\ 0,\hspace{1em}\hspace{1em}T\le T_{base}\end{array}\right.$$

(5)

$${{TT}_{i+1}=TT}_i+∆TT$$

(6)

where TT_i is the cumulative mean temperature of ith day, ΔTT is the daily added mean temperature, T is the daily average temperature (TMAX + TMIN)/2, and T_base is the base temperature for crop growth and phenological development [7,18].

Temperature stress, heat stress, drought stress, water stress, and CO₂ impact are calculated regarding the suggestions of [7,20,21,22,23,24,25,26].

$$f\left(Temp\right)=\left\{\begin{array}{c}0,\hspace{1em}\hspace{1em}\hspace{1em}T<T_{base}\\ \frac{T-T_{base}}{T_{opt}-T_{base}},\hspace{1em}\hspace{1em}\hspace{1em}{T}_{base}\le T<T_{opt}\\ 1,\hspace{1em}\hspace{1em}\hspace{1em}T\ge T_{opt}\end{array}\right.$$

(7)

where T is the daily mean temperature, and T_base and T_opt are the base and optimal temperature for biomass growth, respectively, for a given crop species.

$$f\left(Heat\right)=\left\{\begin{array}{c}1,\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{T}_{max}\le T_{heat}\\ 1-\frac{T-T_{base}}{T_{opt}-T_{base}},\hspace{1em}\hspace{1em}\hspace{1em}{T}_{heat}<T_{max}\le T_{extreme}\\ 0,\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{T}_{max}>T_{extreme}\end{array}\right.$$

(8)

where T_max is the daily maximum temperature, T_heat is the threshold temperature when biomass growth rate starts to be reduced by heat stress, and T_extreme is the extreme temperature threshold when the biomass growth rate reaches 0 due to heat stress.

$$f\left({CO}_2\right)=\left\{\begin{array}{c}1+S_{{CO}_2}\left({CO}_2-350\right),\hspace{1em}\hspace{1em}\hspace{1em}350 \mathrm{ppm}\le {CO}_2<700\mathrm{ppm}\\ 1+350.S_{{CO}_2},\hspace{1em}\hspace{1em}\hspace{1em}{CO}_2>700\mathrm{ppm}\end{array}\right.$$

(9)

where $S_{{CO}_2}$ is the crop-specific sensitivity of RUE to elevated CO₂, and CO₂ is the atmospheric CO₂ concentration.

$$f\left(water\right)=1-S_{water}\times ARID$$

(10)

ARID is a standardized index ranging from 0 (no water shortage) to 1 (extreme water shortage and associated drought stress). ARID is calculated based on water availability and reference evapotranspiration (Eto). S_water is the sensitivity of RUE to the ARID index.

$$ARID=1-\frac{\mathrm{m}\mathrm{i}\mathrm{n}(ETo,0.096PAW)}{ETo}$$

(11)

PAW is plant-available water content in the soil profile for the rooting depth and is obtained from a simple water balance function, including precipitation, irrigation, surface runoff, and deep drainage (see [26] for more details). ETo is the reference evapotranspiration, which is calculated using the Priestley and Taylor approach [23]. The drought stress function is similarly described by Sinclair et al. [27]. Crop stress occurs when the proportion of plant available water is smaller than 75%.

The radiation interception depends on drought stress:

$$I_{50B,\hspace{1em}i+1}=I_{50B,\hspace{1em}i}+I_{max, water}\times (1-f\left(Water\right))$$

(12)

where I_{max, water} is the maximum daily increase in I_50B due to drought stress.

The radiation interception is affected when the drought stress becomes severe enough [28].

$$fSolar\_water=\left\{\begin{array}{c}0.9+f\left(Water\right),\hspace{1em}f\left(Water\right)\le 0.1\\ 1,\hspace{1em}f\left(Water\right)>0.1\end{array}\right.$$

(13)

2.3. Model Parameters and Inputs

This study used thirteen parameters to run the SIMPLE model (

Table 3. Model parameters.

Name	Description	Range	Note
Cultivars parameters
Tsum	Thermal time requirement from sowing to maturity in daily mean (°C days).	2070–2300	*
HI	Harvest index.	0.30–0.37	*
I50A	Thermal time requirement after sowing fraction of light interception to reach 50% (°C days).	500–710	*
I50B	Represents natural senescence. Thermal time requirement from maturity backwards for light interception to reach 50% (°C days).	200–250	*
Species parameters
Tbase	Base temperature (daily mean T) for phenology development and growth (°C).	6–10	[30]
Topt	Optimal temperature (daily mean T) for biomass growth (°C).	25–30	[31]
RUE	Radiation use efficiency (above ground biomass and below ground, if harvestable, product is below ground) (g MJ−1m−2).	0.85–1.60	[32]
I50maxH	The maximum daily increase in I50B due to heat stress (°C d).	120	[7]
I50maxW	The maximum daily increase in I50B due to water stress (°C d).	20	[7]
MaxT	Threshold for daily Tmax to start accelerating senescence due to heat stress (°C).	40	[33]
ExtremeT	Daily Tmax threshold when RUE becomes 0 due to heat stress (°C).	25–40	[33]
CO2_RUE	Relative increase in RUE per 1 ppm elevated CO2 above 350 ppm.	350–600	[7]
S_Water	Sensitivity of RUE to drought stress (ARID index).	0.6–0.96	[7]

Notes: * data obtained from experiments in this study.

), including cultivar characteristics. T_sum, I_50A, and I_50B were determined from the observations of experiment data and the air temperature data. The HI was calculated as described in [29]. The remaining parameters were obtained from the literature.

Data calibration and validation of the model were implemented by carrying out a number of simulations using cultivar parameter sets within a reasonable range (excluding soil parameter, which was kept the same for all the trials). In both two experiments, the biomass was measured periodically every 10 days from sowing to maturity date. The observed data were used to validate the simulation outputs. T_sum (cumulative daily mean temperature above T_base) was set so that canopy cover at harvest date was about 80% [7]. After each model run, I_50A and I_50B were recalibrated based on daily mean temperature above T_base and iterative simulations until a good fit to the experimental results was achieved. Then, the best-fit set of cultivar parameters was used for scenario analysis.

Input variables required to run the SIMPLE model include weather (daily maximum/minimum temperature, rainfall, and solar radiation), atmospheric CO₂ concentration, sowing/harvesting date, irrigation, initial variables, and four variables characterizing the soil (Table 2 and Table 3), including fraction of plant’s available water-holding capacity (AWC; one number for entire soil profile, limited by rooting depth), runoff curve number (RCN), deep drainage coefficient (DDC), and root zone depth (RZD, a fixed maximum depth) (

Table 4. Input variables of SIMPLE model adapted from Zhao et al. [7].

Input Variables	Description	Unit
Crop management	Sowing date (SowingDate)	-
	Harvesting date (HarvestDate)	-
	Irrigation depth (Irri)	m
Initial	Biomass (InitialBio)	Ton
	Cumulative temperature (InitialTT)	°C day
	Solar radiation interception (InitialFsolar)	-
Soil characteristics	Atmospheric CO2 concentration	ppm
	Soil water-holding capacity (AWC)	-
	Runoff curve number (RCN)	-
	Deep drainage coefficient (DDC)	-
	Root zone depth (RZD)	m
Weather	Daily maximum temperature (TMAX)	°C
	Daily minimum temperature (TMIN)	°C
	Daily rainfall amount (RAIN)	m
	Daily solar radiation (SRAD)	MJ m−2 day−1

).

The daily solar radiation (MJ m⁻² day⁻¹) was collected from the Agroclimatology Community of the POWER Data Access Viewer for a period of 2 years from 2020 to 2021 at the experiment location (Figure 1). Air temperature was recorded by Thermo Recorder TR-72Ui (T&D Corp, Japan) and adapted from the POWER Data Access Viewer by the NASA Langley Research Center (LaRC) POWER Project funded through the NASA Earth Science/Applied Science Program (https://power.larc.nasa.gov/data-access-viewer/ (accessed on 1 August 2022)).

2.4. Model Assessment

Calibration was performed using the measured datasets and validation of the model was performed using measured datasets of the cropping seasons of the year 2020 and 2021. The model assessment was conducted using the root mean square of error (RMSE) criterion (Equation (14)).

$$RMSE=\sqrt{\frac{\sum _{i=1}^n{\left(Y_{sim,i}-Y_i\right)}^2}{n}}$$

(14)

where $Y_{sim,i}$ is simulated yield, $Y_i$ is observed yield, i is the data index, and n is the length of data. After that, this study calculated RRMSE, which is relative RMSE by dividing RMSE with average value of measured data as follows:

$$RRMSE=\frac{RMSE}{\sum _{i=1}^n{Y}_i}\times 100\%$$

(15)

where $RRMSE$ < 10%, 10% < $RRMSE$ < 20%, 20% < $RRMSE$ < 30%, and $RRMSE$ > 30% indicate excellent, good, fair, and poor models, respectively [34].

2.5. Scenario Analysis

The set of parameters that gave the best fit between simulation and observation was used as a control treatment to generate scenarios for the purpose of better understanding the impact of future climate change on agricultural production. Scenario analysis was implemented with the following incremental changes in mean temperature change: +1 °C, +2 °C, +3 °C, +4 °C, and +5 °C and the following atmospheric CO₂ concentration changes: +50 ppm, +100 ppm, +150 ppm, +200 ppm, and +250 ppm.

3. Results and Discussions

3.1. Model Assessment

The model evaluation results showed that the SIMPLE model was applicable to estimate the biomass and grain yield of soybean. The simulated biomass fit well to the observed biomass for the two crops (Figure 2). The simulated growing season length was 96 days for Summer–Autumn 2020 and 88 days for Spring–Winter 2021; this is consistent with that of the soybean cultivar used for the experiments (85–95 days). Significantly positive relationships were found between the observed and simulated yields for the Summer–Autumn 2020 season (Figure 3a) and the Spring–Winter 2021 season (Figure 3b).

The results show that the biomass and yield were well simulated using the SIMPLE model (

Table 5. Observed and simulated biomass and yields.

Season Crop	Observation (t ha−1)		Simulation (t ha−1)
	Biomass	Yield	Biomass	Yield
2020	4.801	2.101	5.005	1.852
2021	4.739	2.225	5.466	2.023

). In this study, model performance testing resulted in an RRMSE of 9–10% overall for the biomass and yield, which indicates that the applied SIMPLE model is an excellent model regarding the category described by Jamieson et al. [34]. In a similar case study in the USA for soybeans with the same modeling approach, the obtained RRMSE value was about 25.4% [7], which is higher than in our case. Models simulating soybean yields may perform in various ways (regarding RRMSE values), which depends on the data availability and study location. For instance, the RRMSE was 3% for the model AquaCrop for the case in Ile-Ife, Nigeria [35] while 20% for the model CROPGRO-Soybean in northeast China [36]. The performance may also rely on modeling approaches. For instance, SAFY with satellite data of leaf area index (LAI) can help obtain the soybean yield in the southwest of France with an RRMSE of 2.5%, while coupling Sentinel-2 LAI with crop modeling can result in an RRMSE of 35.8% overall for the case in Uruguay [37]. Results from this study show that the adapted SIMPLE model is proper for soybean biomass and yield estimation.

3.2. Effects of Climate Variation

3.2.1. Growth Stages

This study figured out the growing season and growth stages of soybean observed from the two experiments in 2020 and 2021 (

Table 6. Growth stages of soybean crop in 2020 and 2021.

Stages	Year
	2020	2021
Growing period	21 July to 24 October	20 January to 17 April
Bloom	20 August (31 DAP)	18 February (30 DAP)
Seed fill	2 September (44 DAP)	28 February (40 DAP)
Mat	12 October (84 DAP)	7 April (78 DAP)
Harvest date	25 October (96 DAP)	17 April (88 DAP)

Note: DAP—day after planting.

). The results showed that the growth stages for the Summer–Autumn season 2020 were almost longer compared to the Spring–Winter 2021, with a variation from 1 to 7 days, depending on each stage of growth.

3.2.2. Rainfall and Drought

The weather pattern at the experimental site, in general, was different between the Summer–Autumn season in 2020 and the Spring–Winter season in 2021, especially concerning the rainfall amount and the number of rainy days, which are also similar to solar radiation (Table 1 and Figure 4). This may affect the biomass and yield of the soybean crop. The total biomass of the Summer–Autumn 2020 growing season was 4.801 t ha⁻¹, which was slightly higher than that in the Spring–Winter 2021 (4.739 t ha⁻¹) (Table 5). The yield was 2.101 t ha⁻¹ and 2.225 t ha⁻¹ for the Summer–Autumn 2020 and the Spring–Winter 2021, respectively (Table 5).

More rainfall concentrated during 10–21 and 56–90 days after planting for the 2020 period (Table 1 and Figure 4b), which may prolong the vegetative and R5–R7 stages, and thus lead to the delay of blooming and development, which was similar to [38]. Aberrant rainfall may shorten or extend the flowering stage [39]. In addition, the solar radiance was lower than that in the Spring–Winter 2021 (Figure 4a) and thus this may result in the reduction of solar radiation use efficiency (RUE) and finally the yield.

Drought stress can affect crop growth. The findings in this study reported that the drought stress simulated by the SIMPLE model was low to medium during the whole season for both experiments, especially during the 6–84 days after planting for the Spring–Winter season 2021 (Figure 5a,b). The drought stress was higher during the first 10 days and 27–54 days after planting in the Summer–Autumn 2020, f(Water) ranged from 0.44 to 1.0, while for the Spring–Winter season of 2021, f(Water) ranged from 0.52 to 1.0 and widely distributed during almost all growth stages of the plant. Overall, drought stress had a relative effect on the growth and development of the soybean; however, during the Spring–Winter 2021 it seems to be more serious than the Summer–Autumn 2020 because it is usually less rainy in the dry season (from November to the end of April in the Mekong delta).

More rainfall during the late stage may cause the green canopy to be maintained for a longer period of time and result in a decrease in time from maturity backwards for the light interception to reach 50%; this means that the value of I_50B becomes lower, and therefore, the initial development and middle stages may need more time to be completed. It was quite clearly reflected in the dynamics of the fraction of radiation interception (fSolar) in the SIMPLE model (Figure 6b). As shown in Figure 6b, increasing I_50B caused an acceleration of canopy senescence and consequently led to the maturity date for the Spring–Winter 2021 being advanced by about 7 days compared to the Summer–Autumn 2020. The impact of heat stress is similar to that of drought stress.

3.2.3. Temperature Effects

The observed daily temperature varied from 29.8 °C to 40.7 °C for Summer–Autumn season 2020 (Figure 6a), and from 23.2 °C to 34.7 °C for the Spring–Winter 2021 (Figure 6b). The average daily temperature in the Summer–Autumn 2020 crop (30.5 °C) was slightly higher than that in the Spring–Winter 2021 (29.0 °C). Particularly, the number of days in which maximum temperature above 35 °C were 62 days (Figure 6a) and 44 days (Figure 6b) during the growing seasons; thus, the extended time of maximum temperature was also longer and quite higher than that in the Spring–Winter 2021.

The total simulated biomass dynamics for the two crop seasons are shown in Figure 7. The results from the SIMPLE model showed that a temperature increase caused a significant decline in the final cumulative biomass. The yield declined by approximately 32% and 14% compared with the observed yield for the Summer–Autumn and the Spring–Winter 2021 periods, respectively.

The findings from this study show that temperature significantly affects the soybean yield, and an elevated temperature can cause a yield reduction. As reported, mid- and high-latitude areas may benefit from warming temperatures, in which the warming outside of the core of the growing season is the most beneficial to the yield increase [3]. However, the benefit of warming depends on how soybeans respond to the change. Indeed, this study shows that the increase in temperature can lead to a yield reduction, which was similarly reported in the case in the USA [7]. The effect of temperature on soybeans is caused by their physiological characteristics. The optimum growth takes place at temperatures between 20 and 30 °C [40]. The yield gradually increases with temperatures up to 29 °C to 32 °C and then sharply decreases as temperatures exceed this threshold [41]. In another case, seed set on sterile male and fertile female soybeans decreased as the daytime temperatures increased from 30 to 35 °C [42], which was alsoS mentioned by Caviness and Fagala [43]. Overall, a sustained increase in ambient temperature would likely threaten soybean yields [44].

This study confirms the effects of temperature on the yield. The analyses of 51 stations in China from 1992 to 2011 showed that an increasing temperature can change soybean phenology and shorten its growth stages [45]. For this reason, warming temperatures may reduce the yield of soybeans [46]. For instance, a canopy temperature over 20.9 °C in central Illinois can lead to a yield reduction [47]. As predicted, climate change (primarily temperature change) may result in potential yield losses in the USA, Russia, and India by 15.1–16.1% by the end of the 21st century [48]. This spectrum could also be a potential problem in Matopiba, Brazil, where meets the predicted yield reductions of over 23% under RCP 8.5 (2041–2070) due to temperature increases above 3 °C [49]. In principle, the warming temperature during pod filling can inhibit transgenerational seed germination, particularly for 37 °C/29 °C (day/time) [50] and then cause a reduction in the seed mass, seeds per pod, and seeds per plant [47]. For soybean genotype EC 538828, high temperatures up to 42/28 °C (day/night) can decrease its photosynthesis, stomatal conductance, and seed yield [51]. The evidence above implies that tropical areas, such as Vietnam, with potential temperature increases in the future can encounter risks of the yield reduction. For this reason, climate change adaptations in this area should consider not only soybean genotypes that are tolerant to high temperatures [50] but also cultivation areas (with climatic conditions) [48]. Since the yield is dependent on temperature, future adaptations to this issue should consider selecting proper planting dates to avoid temperature extremes [52]; in other words, a cropping calendar change.

3.2.4. CO₂ Fertilization Effect

This study simulated total biomass from a free-air CO₂ enrichment (Figure 8). The results indicated that for the control (350 ppm) and high CO₂ (600 ppm), the simulations reproduced the difference in total biomass dynamics, and the 250-ppm enrichment of CO₂ concentration increased the simulated final biomass by 2% and 9% for the Summer–Autumn 2020 and the Spring–Winter 2021, respectively, which led to the yield increase.

Relative yield changes were simulated with increasing temperatures and CO₂ concentrations, as shown in Figure 9. The soybean yield rapidly decreased in the Summer–Autumn of 2020 with about a 7% reduction per °C increase, while in the Spring–Winter of 2021, this reduction was about 2.3% (Figure 9a). With an increase in the CO₂ concentration, the yield increased by about 14% and 16% per 100 ppm for the Summer–Autumn 2020 and the Spring–Winter 2021, respectively (Figure 9b).

Besides temperature, CO₂ is an influencing factor on the yield. This study reported the yield enhancement by the CO₂ increase, which agreed with the report from historical analysis of the effects of CO₂ on the yield [53]. Zhao et al. [7] found a yield increase of 7% per 100 ppm CO₂ in the USA, which is lower than the case in our study. The yield can increase by up to 26–31% as the free-air CO₂ is enriched [54]. The phenomenon of the increase was also recorded in Pradesh, India [55], and Iowa, USA [56], particularly in major soybean production countries such as the USA, Brazil, and China [53].

The effects of elevated CO₂ on yield are fundamental to the fertilization effect [53]. Historical data analyses showed that the average yields for the USA, Brazil, and China in 2002–2006 (377 ppm CO₂ in 2006) were 4.34%, 7.57%, and 5.10% higher, respectively, than that in 1980 (338 ppm CO₂) [53]. In other words, fertilization can increase the yield, i.e., the level of 370 ppm CO₂ triggered the yield increase for Iowa, USA [57], and the soybean productivity enhancement [58]. The mechanism of this effect is that rising CO₂ levels can affect the photosynthesis capacity, photosynthetic pigment, and antioxidant levels at flowering stages, particularly at 400 ppm and 600 ppm levels of CO₂ [59]. In addition, the rising levels of CO₂ from 400 to 600 ppm can reduce Fe (negative correlation with the yield) in soybean seeds, which is the opposite to the elevated temperature [60]. In co-effects, the increase of 2.1 °C together with CO₂ of 700 ppm can increase the yield by 31% [61]. Such evidence showed that elevated CO₂ levels may boost the yield increase, which could be a potential benefit for future climates with high CO₂ concentrations in terms of soybean production. However, soybeans may be co-affected by temperature and CO₂, which further studies should consider.

4. Conclusions

The SIMPLE model performed well in assessing the soybean biomass and yield in this case study. It is a generic and simple dynamic model based on the known principles of crop physiology with a few equations and parameters. This model was competent for estimating the soybean yield under different weather conditions. This study found that drought stress inhibited the soybean growth, and although drought stress due to less rainfall seemed to be more serious in Spring–Winter 2021 than in Summer–Autumn 2020, the soybeans grown in rainy months have a longer growing period and lower yield than those planted in less rainy months under the same environmental conditions. An increase in temperature can lead to a yield reduction, while an increase in CO₂ can be followed by a yield increase. Modeling using the SIMPLE model is useful for assessing the responses of soybeans to climate impacts, which can be applicable to other studies, particularly in tropical areas with similar climates.