LSTM-FKAN coupled with feature extraction technique for Precipitation–Runoff modeling

Abstract

Precipitation-runoff modeling is an essential non-engineering measure for assessing water resources and ensuring their sustainable use. For the complex hydrological cycle, Long Short-Term Memory (LSTM) networks have proven effective in handling hydrological time series data. However, LSTM’s compatibility with various data forms and its accuracy still require further improvement. This study aims to propose a high-accuracy modeling method that directly processes time series data and raster data. A Long Short-Term Memory-Fourier Kolmogorov-Arnold Networks coupled with feature extraction technique (CNN-LSTM-FKAN) was developed based on traditional LSTM. By incorporating feature extraction techniques, the model enhances its ability to capture spatial information, while the coupling of Fourier Kolmogorov-Arnold Networks (FKAN) improves simulation accuracy. The model was applied to three basins located in the water source region of the middle route of the South-to-North Water Transfer Project in China, using meteorological data from stations and raster data to simulate runoff processes. The results indicate that the CNN-LSTM-FKAN model consistently outperforms the LSTM model across all study areas, with improvements in the Nash Sutcliffe Efficiency (NSE) during the test period ranging from 0.04 to 0.17. The model generally achieved optimal results at a 60-day time step, with NSE values exceeding 0.89. The optimal hyperparameter combinations varied significantly depending on the time step. The model demonstrated strong applicability across different basins, with the best simulation results yielding NSE values of 0.902, 0.926, and 0.895 in the respective basins. The CNN-LSTM-FKAN model’s capability to extract spatial information further enhanced its performance, with NSE improvements of up to 0.121 compared to the LSTM-FKAN model. In the Hanzhong basin and Xun River basin, the NSE of CNN-LSTM-FKAN improved by more than 0.1 compared to Random Forest. Additionally, the NSE of CNN-LSTM-FKAN increased by up to 0.11 compared to Informer at longer time steps. Furthermore, CNN-LSTM-FKAN demonstrated significantly higher accuracy in capturing flood peaks than both Random Forest and Informer. The CNN-LSTM-FKAN model performed well in simulating runoff during both high-flow and low-flow periods, showcasing significant potential for precipitation-runoff modeling.