基于基因表达式编程的作物水分生产函数构建

作物水分生产函数的确定是农业水资源优化配置的关键。该研究采用农业水文生态系统模型（Agro-Hydrological & Chemical and Crop systems simulator, AHC）与基因表达式编程（Gene Expression Programming, GEP）相结合的方法构建作物水分生产函数。以河套灌区3种主要作物（葵花、玉米、小麦）为研究对象，采用AHC模型模拟作物产量等，构建基于GEP算法的作物水分生产函数，探讨考虑盐分胁迫的作物水分生产函数构建的思路与方法。结果表明：1）作物模拟产量与地下水埋深、地下水矿化度和灌水量等因素有关。2）构建作物水分生产函数的最优输入因子组合为地下水埋深、灌溉量、蒸散发、地下水矿化度、土壤根层盐分对作物胁迫因子、土壤根层含水率。3）应用作物水分生产函数估算不同灌溉定额条件下作物产量（预测产量），并与AHC模型计算的产量（模拟产量）进行比较，玉米、葵花、小麦预测产量与模拟产量具有很好一致性，其决定系数分别是0.96、0.93、0.96，平均相对误差均小于5%，满足计算精度要求。因此，该研究所构建的作物水分生产函数可以较准确地估算盐分胁迫下作物产量，为农业节水与灌溉水高效利用提供科学参考。

Crop water production function based on gene expression programming

A crop water production function has been one of the most significant parameters to improve the use efficiency of agricultural water in irrigation districts. A quantitative relationship between agricultural hydrological elements and yield can be established for the influence of the agricultural hydrological process on crop growth. However, the determination of parameters in the water production function requires a great deal of field experimental data in the water- salt stress gradient treatment. At the same time, there is the complex response of crop yield to the water-salt dynamic processes with the water production function. Therefore, it is necessary to construct the water production functions for the quantitative influence of hydrological factors on the crop yield using soil water-salt dynamic processes. In this study, the new crop water production function was established to integrate the Agro-Hydrological & chemical and Crop systems simulator (AHC) and Gene Expression Programming (GEP), particularly for the water saving and higher yield. The main crops were taken as the research objects, including maize, sunflower, and wheat, which were widely planted in the Hetao Irrigation District. The AHC was selected to simulate the agro-hydrological process and crop growth under different scenarios. Simulation results were used as the input data of the GEP algorithm. Subsequently, the optimal input factor combination was determined to compare the evaluation indexes of the generated data from the GEP algorithm. As such, the crop water production functions were established. Results showed that the optimal input combinations included the groundwater depth, irrigation amount, evapotranspiration (ET), total dissolved solids of groundwater, salt stress, and water content in the root zone soil. Specifically, the sensitive environmental factors varied greatly in the different crop yields. The maize yield was related to the groundwater depth, salt stress in the sowing- jointing stage and the filling-harvest stage, and the soil water content in the jointing-trumpet stage and the trumpet- tasseling stage. The sunflower yield was closely related to the groundwater depth, evapotranspiration, and the salt stress in the sowing-seedling stage, the seedling-budding stage, and the flowering-filling stage, while the soil water content in the budding-flowering stage and the filling-harvest stage. The wheat yield was related to the evapotranspiration, and salt stress in the jointing- heading stage, while the soil water content in the filling-harvest stage. Furthermore, the groundwater was the main water supply source during the maize growth period, when the maize was less resistant to the salt. By contrast, the less irrigation amount resulted in the soil salt accumulation and the salt stress in the initial and end stage of maize growth. Correspondingly, the effect of groundwater on the sunflower yield was similar to the maize, whereas, the sunflower yield was affected by the evapotranspiration, which was related to the dry aboveground biomass accumulation and yield. In addition, the effect of evaporation on the wheat yield was consistent with the effect on sunflower yield. The excessive salt accumulation and water deficit were reduced the wheat yield during the jointing-heading stage and the filling-harvest stage, which were the main growth periods. Meanwhile, the crop yield (predicted yield) was estimated under different irrigation quantities using the crop water production function. The determination of coefficient values between the predicted yields of maize, sunflower, and wheat and their simulated ones by AHC were 0.96, 0.93, and 0.96, respectively, and the mean relative errors were both less than 5%. Therefore, the water production function can be used to accurately estimate the crop yield under the salinity stress. The finding can provide strong references for agricultural water saving and efficient use of irrigation water.