A novel transformer-based neural network under model interpretability for improving wheat yield estimation using remotely sensed multi-variables

Timely and accurate yield prediction before wheat harvest is of great significance for food policy formulation and national economic development. Deep learning method gains importance on crop yield estimation and growth monitoring with the rapid development of deep learning models combined with remotely sensed data. However, the problems of nonlinear parameter optimization and long-term dependence in time series data have restricted the improvement of yield estimation accuracy. Transformer model completely abandons the traditional deep learning architecture and is gradually applied to time series tasks due to the advantage in modeling long-term dependence. This study introduced a novel transformer-based deep learning framework to estimate winter wheat yield in the Guanzhong Plain utilizing remotely sensed multi-variables, namely leaf area index (LAI), fraction of photosynthetically active radiation (FPAR) and vegetation temperature condition index (VTCI). The proposed model, called SSA-LSTM-transformer (SLTF), was developed for dealing with above problems under the automatic optimization capability of the sparrow search algorithm (SSA) and the long-term memory advantage of the long short-term memory (LSTM) structure. The findings demonstrated that the SLTF model achieved better estimation accuracy at the county level (R2 = 0.72, RMSE = 488.68 kg/ha) compared with the single transformer model (R2 = 0.61, RMSE = 573.99 kg/ha). The analysis on SLTF model's performance at sampling sites over different disasters suggested that the model can effectively learn the effects of diseases, lodge and pests on crop yield estimation, which had good generalization ability at all sampling sites (R2 = 0.45, RMSE = 738.63 kg/ha). The Shapley Additive exPlanations (SHAP) approach was employed to evaluate the relative importance of remotely sensed multi-variables to yield and to understand how each input variable influences the estimated yield for global interpretability and local interpretability of the SLTF model. It was found that FPAR played the largest roles in yield estimation with the highest importance value, and FPAR and LAI from late April to late May and VTCI from late March to mid-April were regarded as important features for the estimated yield with high importance value. In conclusion, our findings indicated the potential of SLTF model for winter wheat yield estimation, which contributes to promoting further application of remotely sensed technology for agricultural production.