A hybrid self-adaptive DWT-WaveNet-LSTM deep learning architecture for karst spring forecasting

Abstract

Karst spring discharge plays a vital role in understanding karst systems and managing karst groundwater resources. Due to its inherent heterogeneity and complexity, hydrological factors in the karst system often exhibit highly nonlinear and nonstationary characteristics. To overcome this challenge, a novel self-adaptive deep learning architecture is proposed to forecast daily karst spring runoff with precipitation in this study. The newly proposed model effectively integrates discrete wavelet transform (DWT), WaveNet, and long short-term memory (LSTM), enhanced by the attention mechanism and residual connections to learn underlying patterns, mitigate the overfitting risk, focus on the most relevant time steps, and improve the prediction accuracy. The framework is structured into two parts: one part is dedicated to predicting the karst spring discharge, whereas another part primarily predicts the residuals arising from the main predictions. By intergrading the two-part approach, the innovative model can adaptively correct the systematic errors and refine its understanding of some aspects that it might initially struggle with. The newly proposed model and three existing deep learning models including LSTM, GRU and simple RNN models are applied to predict karst spring discharge at Barton Springs, Texas, USA. The results imply that the newly developed DWT-WaveNet-LSTM model can leverage the advantages of various models, adapt to various aspects of the hydrometeorological data, and better capture intrinsic patterns from nonlinear and nonstationary input features. It outperforms other models at all time steps, evidenced by lower RMSE and higher NSE values. The residual analysis is conducted by comparing the predicted and observed spring discharge values. The self-adaptive DWT-WaveNet-LSTM model exhibits residuals that are closely centered around zero with a symmetrical, bell-shaped distribution, indicating superior performance and robust predictions in the karst system due to its effective capture of complex and nonlinear patterns.