Machine learning-enhanced 4DVar assimilation for winter wheat yield estimation

Abstract

Context Accurate crop yield estimation is crucial for ensuring food security, promoting sustainable agriculture, and optimizing management practices. However, integrating remote sensing data with crop models remains challenging, largely due to the inability of traditional data assimilation methods to adequately represent complex, spatiotemporally variable error covariance structures. Objective This study aims to improve crop yield prediction by addressing the persistent challenge of error covariance specification in data assimilation. We seek to establish a more rigorous and adaptive approach for determining error covariance, thereby enhancing the accuracy and reliability of yield estimates. Methods We developed a machine learning–enhanced four-dimensional variational data assimilation algorithm (ML-4DVar), in which ML models (Random Forest, Extreme Gradient Boosting, and Long Short-Term Memory) dynamically estimate error covariance matrices for both crop model outputs and remote sensing observations. Comparative experiments were conducted against conventional 4DVar and Ensemble Kalman Filter (EnKF) approaches for yield prediction. Results and conclusions ML-4DVar substantially improved predictive skill relative to benchmark methods, achieving a Spearman's correlation coefficient of 0.92, an RMSE of 369.29 kg/ha, and an R 2 of 0.86. The results demonstrate that incorporating machine learning into 4DVar provides a more flexible representation of uncertainties and improves the fusion of remote sensing and model information for yield estimation. Significance The proposed ML-4DVar framework offers a promising pathway for advancing data–model fusion in agricultural monitoring. Future research may extend this approach across regions, crop types, and higher-resolution data streams to support scalable, policy-relevant agricultural forecasting under global change.