Estimating crop model parameters for simulating soybean production in Iran conditions

This is anOpe Abstract – Crop modelling has the potential to contribute to food security. In this study, to provide a simple model for estimating the soybean potential yield and phenological stages in Iran, a simulation model (SSM_iCrop2) was parameterized and tested. This model estimates the soybean phenological stages and potential yield based on the weather data (minimum and maximum temperature, solar radiation and rainfall) using the phenological models such as leaf area development, mass production and partitioning and soil water balance. Regarding the model parametrization, the two maturities groups of 3 and 5 with the temperature unit of 2000 and 2400 growth degrees day (GDD) were chosen. The model evaluation results indicated that the soybean yield ranged between 1.9 and 4.8 with the average of 3.5 t.ha , while the range of simulated yield changes between 1.8 and 4.7 with the average of 3.7 t.ha . Comparing the observed yield to the simulated yield, values of r, CVand RMSE were obtained 0.84, 13%, 0.5 t.ha 1 which indicates the high accuracy of the model. All of these results indicated that the estimated model parameters are high accuracy for use in the simulation of soybean yield at the country level.


Introduction
Soybean (Glycine max) is one of the most important oilseed crops cultivated in the world. Soybean crop area and production in Iran are about 66 000 hectares and 151 000 tons, respectively which does not meet the domestic needs, so imported soybean meal to Iran amounted to 2.37 million tonnes with the worth of $1.5 billion in 2012 (Ministry of Agriculture Jihad, 2016). Also, imported soybean oil was about 800 000 tonnes worth $960 million in 2013 (FAOSTAT, 2013). So far, several attempts have been made using field experiments to better understand factors affecting crop yield per unit area. Field experiments on the crop response to various environmental conditions are laborious and costly. Due to these constraints, crop models can be useful tools to study and estimate the yield (Geerts and Raes, 2009) A mathematical model is an equation or set of equations that describes the behaviour of each system quantitatively (Soltani, 2009). To predict the crop growth, studies on phenology, mass production and partitioning, leaf area development and soil water balance are required (Dadrasi and Torabi, 2016). Precise prediction of the crop phenology is one of the essential features of the simulation models. The mass production and partitioning are largely regulated by the timing of developmental stages in crop simulation models (Soltani, 2012). Simple models can be more efficient in yield analysis and investigate the limiting factors due to easy manufacturing, testing, applying, understanding and interpretation of results; In addition it needs minimum inputs (Sinclair and Muchow, 1999). One of the other benefits of modelling is the prediction of the food production status in one area and making decisions based on environmental changes. Models apply a variety of plant and environmental parameters to simulate crop growth and they should be calibrated and evaluated before being used (Hsiao et al., 2009). In some models, the parameters related to plant characteristics may have been calculated according to the climate of a certain region, which is not usable in other regions or may not have acceptable performance. Therefore, to predict the crop growth and yield by the model, the compatibility of the equations with the relationships between the different processes of growth and yield and the climatic conditions of the study area, access to the input parameters and the model efficiency in predicting growth and yield should be considered (Torabi et al., 2011). Some used models for simulation of soybean yield and phenological stages include EPIC (Williams and Watson, 1985), SoySim (Setiyono et al., 2010), CROPGRO-Soybean (Boote et al., 1998) and APSIM (Keating et al., 2003). There is another a group of plant models, called SSM_iCrop2 . SSM_iCrop2 model simulated a large number of plant species including orchard species and perennial forages .
Therefore, the aim of this study was to determine the SSM_iCrop2 parameters in simulating main cultivars soybean growth and yield in Iran to provide a tool for analysing yieldlimiting factors, optimizing field management and identifying the factors that influence the yield increase in certain environmental conditions.

Data used
To parameterize and evaluate the model, in major areas in terms of soybean cultivation, data of various studies on soybean (treatments without any growth and development limiting factors or environmental stresses) was applied (Tab. 1). About 35% of published paper was applied to parameterize the model (include 34 situations for days to maturity and 26 situations for yield) and about 65% other was utilized to evaluate it (include 49 situations for yield). Parameterization of SSM_iCrop2 is straightforward as presented in Appendix I of Soltani and Sinclair (2012).
Briefly, the model is tested using different values for a specific parameter, then values are chosen that provide the closest match to the observations of the major outputs, frequently final yield. Also, several model parameters that are fixed within different soybean cultivars (such as cardinal temperature) were obtained from credible references.

Crop model
The model used in this study was SSM_iCrop2 1 (Soltani and Sinclair, 2012;Soltani et al., 2020a). The model includes daily phenology progress, leaf area development and senescence, dry matter production, yield formation, and soil water balance. Responses of crop processes to solar radiation, temperature, water availability, and cultivar differences are included in the model. Soil water sub-model accounts for soil water additions from precipitation or irrigation, and increasing rooting depth and water removal via deep drainage, run-off, soil evaporation, and plant transpiration. The soil profile is divided into two layers: one top layer of 15-20 cm thickness and a second layer that includes the first layer and its depth increases by root growth. Soil water balance of both layers is calculated separately. The effect of water deficit and excess on leaf area development and senescence, dry mass accumulation, and phenological development are simulated. The model also accounts for the effect of freezing temperatures on plant leaf area that might take place in early spring sowings or winter sowings. The model has been tested extensively for a wide range of plant species and proved to be robust .
Some of the parameters required in the SSM_iCrop2 model for soybean are presented in Table 2.

Weather data
Meteorological information of each experimental site including minimum and maximum daily temperature, daily precipitation, and solar radiation were obtained from the nearest meteorological station. Outliers and missing data were then estimated and restored using the WeatherMan program (Hoogenboom et al., 2004).

Crop management data
The required crop management information included sowing date, soil moisture content during simulation, irrigation level. This data was obtained from the articles in Table 1.
In this model, GDD was applied to determine the difference between soybean maturity groups. For this purpose, the phenological data of maturity groups 3 and 5 (major maturity groups that are grown in Iran) were used (Tab. 1). The GDD was calculated (based on soybean cardinal temperatures) for each phenological step.

Model evaluation
The statistical indices used for model evaluation were the coefficient of variation (CV), root mean square error (RMSE) and correlation coefficient (r). Also, the 1:1 line with 20% discrepancy was used to show the amount of deviation of the simulated versus the observed values. These statistical indices were calculated as follows: where x i is the observed values, y i is the simulated values, n is the number of observations, x is the mean observed values including days to maturity or grain yield in the independent experiments, and y is the mean simulated values including days to maturity or grain yield.

Sensitivity analysis
Sensitivity analysis is the study of how the different input variations of a mathematical model influence the variability of its output (Monod et al., 2006). In this research, we used local sensitivity analysis, which evaluates the local impact of the variation in the input factors on a model response, focusing on sensitivity in vicinity of a set of factor values. The evaluation is conducted through gradients or partial derivatives of the output functions at these factor values, while the values of other input factors are kept constant.
To get full coverage of parameter value space and considering that the runtime for one execution of the SSM_iCrop2 model is very short, we set the parameters for the different variation ranges, separately. In the model, about 10% of the crop parameters are approved to be varied with cultivar and environment (Bouman and van Laar, 2006;Tan et al., 2017). In previous studies, Tan et al. (2017) selected 16 parameters for uncertainty and sensitivity analysis, while Sexton et al. (2017) selected 14 parameters for this purpose. In this study, 7 parameters were used for sensitivity analysis (including tuHAR, LAIMX, KPAR, IRUE, TEC, Himax and HImin). Variation range set at ±30% perturbation of the default parameter values. The selection of perturbation range (±30%) was based on Tan et al. (2017) and Noorhosseini et al. (2018). For sensitivity analysis, grain yield (t.ha À1 ) and WTOP (accumulated above-ground dry matter, t.ha À1 ) were extracted as model outputs. Box plot (created with SAS software) was used to show changes in grain yield and WTOP under different parameter variation ranges. For create box plots, SAS 9.4 was used.
3 Results and discussion

SSM_iCrop2 model parameterization
To parameterize the SSM_iCrop2 model, common soybean cultivars in Iran (groups 3 and 5) were considered. All the parameters indicated in Table 3 were necessary for estimating soybean growth and production. Based on these parameters, SSM_iCrop2 model could simulate the yield and days to maturity. The results showed that the soybean observed yields varied between 1.9 and 4.7 with an average of 3.5 t.ha À1 and the range of simulated yield changes between 1.8 and 4.4 with an average of 3.9 t.ha À1 . The root mean square error (RMSE) was 0.48 t.ha À1 which is equivalent to 14% of both the mean of simulated and observed yields, and the correlation coefficient (r) was 0.63 (Fig. 1). The coefficient of variation in field experiments is usually between 20 to 30% (Dadrasi and Torabi, 2016). All data were within the range of ±20% of grain yield which indicates the accurate estimation of the model parameters. Regarding the phenological feature of days to maturity, the model had a good estimation so that the observed time intervals ranged from 104 to 154 days with an average of 127 days and the simulated time intervals ranged between 108 and 147 days with an average of 127 days (Fig. 2). For this feature, RMSE, the coefficient of variation (CV) and r were 12 days, 9% and 0.60, respectively. Therefore, the results of parametrization based on days to maturity are considered optimal at the country level.

Model evaluation
To evaluate the model, the values of simulated yield was compared to the observed values. For this purpose, a set of experimental data was used (Tab. 1). For simulation, required inputs for the model and the weather data of the areas in the studied years were provided as a file to the model. The values that were estimated in the parameterization section (Tab. 3) were applied as parameters. The results showed that the model had a very good prediction of the average yield. The evaluation results of yield showed that the observed yield ranged between 1.9 to 4.8 t.ha À1 with an average of 3.5 t.ha À1 and simulated yield changes between 1.8 to 4.5 t.ha À1 and with an average of 3.7 t.ha À1 . Also, RMSE, r and CV were 0.46 t.ha À1 , 0.84 and 13% (Fig. 3), which indicated a high accuracy in the soybean yield estimation in considered provinces. Therefore, this model can be applied for different purposes.

Sensitivity analysis of model parameters
The comparison of the averages presented in Figures 4 and  5 showed that the change in the values of the tuHAR, LAIMX and KPAR parameters in the SSM_iCrop2 model caused a difference in the total dry matter predicted by the model (Figs. 4 and 5). Among these parameters, the change in the amount of KPAR caused a difference in the amount of simulated dry matter, increasing and decreasing the amount of KPAR by 30% changed the total dry matter from 11.1 t.ha À1 (constant and unchanged parameter) to 14.4 (increase in KPAR value) and 7.8 t.ha À1 (decrease in KPAR value). Also, in terms of grain yield (considering 13% moisture content at the harvest time), changes in the values of tuHAR, LAIMX, KPAR and HImax parameters caused differences in predicted yield by model. Among these parameters, KPAR and HImax caused the highest difference in the predicted total dry matter. Analysis of the KPAR parameter showed that by increasing and decreasing KPAR about 30%, the grain yield varied from 4.6 t.ha À1 (constant and unchanged parameter) to 6.0 (increase in KPAR value) and 3.2 t.ha À1 (decrease in the amount of KPAR). Also, Increasing and decreasing the HImax parameter value by 30% changed the grain yield from 4.6 t.ha À1 to 6.0 and 3.2 t.ha À1 , respectively. The most sensitive parameters for the total dry matter were tuHAR, LAImax, and KPAR. The increase and decrease of 30% in the values of these three parameters changed the total dry matter. In terms of grain yield sensitivity to the change of parameters, different results were achieved,  so that, in addition to the parameters affecting the dry matter, increasing and decreasing the total amount of HImax by 30% caused the most significant difference on grain yield simulated by the model. An interesting point about the grain yield was the effect of the 30% change in the tuHAR parameter, which appears to be due to the increase and decrease in the growth period of the soybean. By 30% increase in the amount of tuHAR, the vegetative growth period was increased and reproductive stage (seed filling) starts in the undesirable temperatures so yield decreased. A 30% decrease in the tuHAR amount resulted in yield reduction due to the decrease in the vegetation and reproductive growth periods which causes less dry matter transfer to the seed. Our results indicated the SSM_iCrop2 model simulates growth and yield with reasonable accuracy across a wide range of environments in the Iran. For example, in the validation data set, observed grain yields ranged from 1.9 to 4.8 t.ha À1 , sowing dates were as April 8 to July 31, and cultivars differed in maturity from MG 3 and MG 5. SSM_iCrop2 achieves this robust simulation capability with only 9 parameters variable. SSM_iCrop2 model has considerable advantages compared with other models. Although SSM_iCrop2 requires a maximum of 37 parameters, the actual relevant number of parameters is about half of the total number (i.e., between 15 and 20 depending on plant species) because many parameters are interconnected and some parameters are not important for some species . Whereas, the APSIM and DSSAT models needed 292 and 211 parameters to estimate the potential yield and phenological stages, respectively. (Noorhosseini et al., 2018). Due to the number of required parameters, the SSM_iCrop2 model can simulate the phenological stages of growth in a large area such as a country.
It is worth noting that, in the model can easily use an Excel spreadsheet to provide input and produce output, and also it is open source.
The studies that have been done using SSM_iCrop2 model include the following: Soltani et al. (2020b) estimated total plant production at province and country levels by SSM_iCrop2 and a bottom-up scaling protocol (GYGA). They provided a framework within which assessing the possibility of increasing national plant production via intensification, optimizing water allocation across plant species at province and country levels by changing the cropping pattern, and assessing and prioritizing possible ways of adapting a country's agriculture to limited land and water resources and climate change. Alizadeh Dehkordi et al. (2020) evaluated potential yield of wheat by using the SSM_iCrop2 model in the Northwest of Iran. Nehbandani et al. (2020a) estimated soybean potential yield, amount of net irrigation water, evapotranspiration, vapour-pressure deficit, and soybean water productivity using the SSM_iCrop2 model in Iran. Also, they investigated relationships between potential yield and environmental factors (accumulated solar radiation, rainfall, maximum temperature, and minimum temperature during the soybean growing season).

Conclusion
Crop models are essential in undertaking large scale estimation of crop production of diverse crop species, especially in assessing food availability and climate change impacts. In this research, crop simulation model (SSM_iCrop2) parameters were estimated and evaluated. The model requires limited, readily available input information. The simulations account for plant phenology, leaf area development and senescence, dry matter accumulation, yield formation, and soil water balance in a daily time step. Parameterization of this model is easy and straightforward. The results of this study showed that the SSM_iCrop2 model provides reasonable prediction of development stages and yield for the soybean in Iran. The sensitivity analysis of the parameter values showed that the most effective parameter on the total dry matter and grain yield are KPAR and HImax, respectively. This model can help find the best management plans to achieve the potential yield for different regions of the country. Fig. 5. The ranking of influential cultivar-specific parameters for grain yield (t.ha À1 ) under different parameter variation ranges included þ30% (White), À30% (Grey) and Standard (Dotted line).