Interpretable multi-step hybrid deep learning model for karst spring discharge prediction: Integrating temporal fusion transformers with ensemble empirical mode decomposition

Karst groundwater is a critical freshwater resource for numerous regions worldwide. Monitoring and predicting karst spring discharge is essential for effective groundwater management and the preservation of karst ecosystems. However, the high heterogeneity and karstification pose significant challenges to physics-based models in providing robust predictions of karst spring discharge. In this study, an interpretable multi-step hybrid deep learning model called selective EEMD-TFT is proposed, which adaptively integrates temporal fusion transformers (TFT) with ensemble empirical mode decomposition (EEMD) for predicting karst spring discharge. The selective EEMD-TFT hybrid model leverages the strengths of both EEMD and TFT techniques to learn inherent patterns and temporal dynamics from nonlinear and nonstationary signals, eliminate redundant components, and emphasize useful characteristics of input variables, leading to the improvement of prediction performance and efficiency. It consists of two stages: in the first stage, the daily precipitation data is decomposed into multiple intrinsic mode functions using EEMD to extract valuable information from nonlinear and nonstationary signals. All decomposed components, temperature and categorical date features are then fed into the TFT model, which is an attention-based deep learning model that combines high-performance multi-horizon prediction and interpretable insights into temporal dynamics. The importance of input variables will be quantified and ranked. In the second stage, the decomposed precipitation components with high importance are selected to serve as the TFT model’s input features along with temperature and categorical date variables for the final prediction. Results indicate that the selective EEMD-TFT model outperforms other sequence-to-sequence deep learning models, such as LSTM and single TFT models, delivering reliable and robust prediction performance. Notably, it maintains more consistent prediction performance at longer forecast horizons compared to other sequence-to-sequence models, highlighting its capacity to learn complex patterns from the input data and efficiently extract valuable information for karst spring prediction. An interpretable analysis of the selective EEMD-TFT model is conducted to gain insights into relationships among various hydrological processes and analyze temporal patterns.