Advancing Flood Forecasting With Wavelet‐ <scp>LSTM</scp> : The Role of Nonlinearity in Discharge Prediction

ABSTRACT Discharge modeling utilizing novel deep learning techniques is highly recommended due to their high efficacy in modeling nonlinear time series. In this study, a hybrid discharge model is developed, termed wavelet‐based long short‐term memory (WLSTM), by integrating wavelet transform and Long Short‐Term Memory (LSTM). This technique focuses on improving discharge prediction by effectively denoising the input data and amplifying the most relevant temporal patterns for the model. However, since LSTM models depend on underlying data patterns, their performance can be significantly affected by the intensity of nonlinearity in hydrological time series. To address this, we introduce a novel method using ApEn (Approximate Entropy) to quantify nonlinearity intensity. Then, we applied Fuzzy Clustering to classify nonlinearity into weak, moderate, and high nonlinearity categories. The performance of both LSTM and WLSTM is evaluated using daily discharge data from 16 hydrometric stations in Hesse, Germany, for the period 2000–2017. The results notably show a remarkable reduction of 66.43% for Root Mean Squared Error (RMSE) and of 45.49% for Mean Absolute Percentage Error (MAPE) for WLSTM performance compared to LSTM. Furthermore, WLSTM increased R ‐squared ( R 2 ) by 2.06%. This research acknowledges that there is a direct correlation between the streamflow nonlinearity and WLSTM accuracy. With increasing nonlinearity intensity, WLSTM captures the complexity of streamflow patterns more effectively. RMSE is 0.1194, 0.0836, 0.0547 and R 2 is 0.9976, 0.9990, 0.9994 for weak, moderate, and high nonlinearity groups, respectively. This study highlights the importance of streamflow nonlinearity analysis in improving flood forecasting and risk management.