Simulation of plant height of winter wheat under soil Water stress using modified growth functions

Plant height is an important trait that influences the yield and sustainability of wheat productions. It is also an important objective for agronomic breeding and a critical indicator to represent the status of crop growth and nitrogen absorption in the vegetative stage. Wheat is the main crop in arid regions. However, there is insufficient understanding of wheat plant height response to soil water stress. In this study, we tried to explore a new algorithm for simulating dynamics of winter wheat height under different scenarios of soil water stress based on soil column and field experiments conducted under rainout shelters between 2012 and 2016 at Yangling, Shaanxi province, China. First, we established a temperature response function of wheat plant height based on four cardinal temperatures (i.e. base temperature, lower optimal temperature, higher optimal temperature, and ceiling temperature). And we also constructed a water stress response function of wheat plant height using relative soil water availability (Aw) as water stress index. Then, these two functions were used as multipliers to modify the first-order derivative of six distinct growth functions (i.e. Gompertz, Logistic, Mischerlich, Richards, Von Bertalanffy, and Weibull) to represent the elongation rate of wheat plant height under soil water stresses. Consequently, six modified simulation models for wheat plant height were established and identified as Mod-Geo, Mod-Log, Mod-Mis, Mod-Ric, Mod-Von, and Mod-Wei, respectively, among which an optimal simulation model was selected for winter wheat growth under soil water stresses. Based on experimental data of 2014–2015 used for model calibration, it was found that when Aw was greater than 0.65, elongation rate of wheat height was not influenced by soil water content; when Aw was between 0.3 and 0.65, elongation rate of wheat height gradually reduced following an exponential function driven by water stress; when Aw was less than 0.30, elongation rate of wheat height rapidly and linearly reduced driven by water stress until Aw was close to 0 at which the elongation stopped. After that, the data of soil column experiment of 2014–2015 growing season were used to assess the parameters of the six newly established models. The results of model calibration showed that the mean value of the Willmott Index of Agreement (WIA) between measured and simulated wheat heights of the six cultivars were all less than 0.90 for all treatments in the experiment, except for the Mod-Log model (0.95). The data of soil column experiment in 2015–2016 seasons were used to validate the six calibrated new models. The results of model validation with mean value of WIA 0.93 which were even better than model calibration. Finally, the data of two growing seasons (2012–2013 and 2013–2014) of field experiments conducted under a giant rainout shelter were used for further verification of the six new models under field conditions. Among the six different plant height simulation model, Mod-Log model obtained the best values of RMSE and WIA.