Water production function of winter wheat based on root-weighted soil water availability

Abstract: In order to accurately evaluate the effects of the crop water deficit extent and the water stress sensitivity on crop yield, a novel Crop Water Production Function (CWPF) was proposed through combining a Root-Weighted Plant Water Deficit Index (PWDI) and an S-shaped cumulative function of water stress sensitivity index as a function of the normalized heat unit index in this study. Three forms of CWPFs, including Blank additive model (PWDI-B), Jensen (PWDI-J) and Rao (PWDI-R) multiplicative models, were considered. A two-year field lysimetric experiment and a one-year field drip irrigation experiment for winter wheat, respectively conducted in Changping District, Beijing (40°10′31′′N, 116°26′10′′E) from September 2014 and 2015 to June the next year and Yellow River Delta, Shandong Province, China (37°19'17"N, 118°38'41"E) from October 2020 to June 2021, were employed to optimize the fitting parameter in the nonlinear soil water stress reduction function, and to test the root-weighted PWDI estimation method and to compare and evaluate three different CWPFs. Thirteen and six irrigation treatments with various water supply levels were respectively designed in lysimetric and drip irrigation experiments. The experimental observations included meteorological data, soil water content distributions, daily transpiration, leaf area index, plant height, aboveground dry matter and grain yield of winter wheat. Three statistical indicators were used to evaluate the model performance, including the coefficient of determination (R2), Root Mean Squared Error (RMSE) and Normalized RMSE (NRMSE). Optimized using a nonlinear least-squares method by minimizing the residual between measured and estimated daily or stage-cumulative transpiration, the fitting parameter in the soil water stress reduction function was used to estimate the PWDI under various irrigation treatments. The results showed the estimated PWDIs were in a good agreement with the measured values, with an R2 of 0.78, a RMSE of 0.10, and a NRMSE of 0.16 in the lysimetric experiment, and the estimated seasonal mean PWDI was well correlated with plant height (r = ?0.95), aboveground dry matter (r = ?0.79) and final yield (r = ?0.81) of winter wheat in drip irrigation experiment, which indicates that the PWDI estimated based on root-weighted soil water availability could represent crop water deficit extent and its effects on crop growth and yields accurately. The largest daily water sensitivity index estimated was situated at the flowering-filling stage of winter wheat, implying the stages are the most sensitive period of winter wheat to water stress. By combining the daily PWDI estimated based on root-weighted soil water availability and the daily water stress sensitivity index calculated from the S-shaped cumulative function, three different forms of CWPFs were established. All CWPFs provided a reasonable estimation of yields of winter wheat, with the R2 not less than 0.78 and NRMSE not more than 0.11, respectively. By contrast, the estimation accuracy of winter wheat yield from PWDI-R was successively higher than that from PWDI-J, PWDI-B, and linear regression model (which represents the linear relationship between the seasonal mean PWDI and the yield of winter wheat) in lysimetric and drip irrigation experiments. Consequently, the combination of root-weighted PWDI and S-shaped cumulative water sensitivity index provides a reliable way to establish winter wheat water production function, and PWDI-R was found to be most suitable for winter wheat yield estimation and irrigation schedule optimization. The findings from this research may provide the theoretical basis for water management in the winter wheat field in the study regions.