Improvement of HLM Modeling for Winter Wheat Yield Estimation Under Drought Conditions

[Objective] Winter wheat yield is crucial for national food security and the standard of living of the population. Existing crop yield prediction models often show low accuracy under disaster-prone climatic conditions. This study proposed an improved hierarchical linear model (IHLM) based on a drought weather index reduction rate, aiming to enhance the accuracy of crop yield estimation under drought conditions. [Methods] HLM was constructed using the maximum enhanced vegetation index-2 (EVI2max), meteorological data (precipitation, radiation, and temperature from March to May), and observed winter wheat yield data from 160 agricultural survey stations in Shandong province (2018－2021). To validate the model's accuracy, 70% of the data from Shandong province was randomly selected for model construction, and the remaining data was used to validate the accuracy of the yield model. HLM considered the variation in meteorological factors as a key obstacle affecting crop growth and improved the model by calculating the relative meteorological factors. The calculation of relative meteorological factors helped reduce the impact of inter-annual differences in meteorological data. The accuracy of the HLM model was compared with that of the random forest (RF), Support Vector Regression (SVR), and Extreme Gradient Boosting (XGBoost) models. The HLM model provided more intuitive interpretation, especially suitable for processing hierarchical data, which helped capture the variability of winter wheat yield data under drought conditions. Therefore, a drought weather index reduction rate model from the agricultural insurance industry was introduced to further optimize the HLM model, resulting in the construction of the IHLM model. The IHLM model was designed to improve crop yield prediction accuracy under drought conditions. Since the precipitation differences between Henan and Shandong provinces were small, to test the transferability of the IHLM model, Henan province sample data was processed in the same way as in Shandong, and the IHLM model was applied to Henan province to evaluate its performance under different geographical conditions. [Results and Discussions] The accuracy of the HLM model, improved based on relative meteorological factors (rMF), was higher than that of RF, SVR, and XGBoost. The validation accuracy showed a Pearson correlation coefficient (r) of 0.76, a root mean squared error (RMSE) of 0.60 t/hm2, and a normalized RMSE (nRMSE) of 11.21%. In the drought conditions dataset, the model was further improved by incorporating the relationship between the winter wheat drought weather index and the reduction rate of winter wheat yield. After the improvement, the RMSE decreased by 0.48 t/hm2, and the nRMSE decreased by 28.64 percentage points, significantly enhancing the accuracy of the IHLM model under drought conditions. The IHLM model also demonstrated good applicability when transferred to Henan province. [Conclusions] The IHLM model developed in this study improved the accuracy and stability of crop yield predictions, especially under drought conditions. Compared to RF, SVR, and XGBoost models, the IHLM model was more suitable for predicting winter wheat yield. This research can be widely applied in the agricultural insurance field, playing a significant role in the design of agricultural insurance products, rate setting, and risk management. It enables more accurate predictions of winter wheat yield under drought conditions, with results that are closer to actual outcomes.