An Interpretable Hybrid TCN-BiLSTM Model for Reference Evapotranspiration Prediction

Accurate reference evapotranspiration (ET0) prediction is crucial for hydrologic processes and irrigation water management. Different from the Penman Monteith Equation for ET0 calculation, the current popular machine learning based models can predict ET0 using limited meteorological factors. However, this makes interpretation difficult and leads to low user trust in such prediction techniques. In this regard, this paper explores the study of the interpretability of ET0 prediction model. This paper proposes an ET0 prediction model that combines temporal convolutional network (TCN) and bi-directional long short-term memory (BiLSTM). The Huber loss is designed as the loss function to enhance the performance of the proposed model. The local interpretable model-agnostic explanations (LIME) model is adopted to provide explicit interpretability for the ET0 prediction model. The daily meteorological data from three weather stations in Donglei Yellow River irrigation area are collected for ET0 prediction. The effectiveness and superiority of the proposed model are validated in comparison with TCN-LSTM, BiLSTM and TCN based ET0 prediction models. The prediction results illustrate that the proposed TCN-BiLSTM model using Huber loss can obtain more accurate prediction and stronger robustness, with its testing MSE and testing MAE being 75% and 90% of those using MSE loss. The proposed enhanced TCN-BiLSTM shows the best performance across all the weather station datasets. The order of the prediction accuracy is the proposed enhanced TCN-BiLSTM > TCN-LSTM > BiLSTM > TCN. Based on the interpretable model of LIME, the proposed model can predict ET0 accurately up to 10 days in advance and the meteorological factors $$\left\{{R}_{s}, n, {T}_{max}, {T}_{mean}, {T}_{min}\right\}$$ show significant impact on the ET0 prediction.