Comparative study of deep learning models for daily karst spring discharge forecasting:LSTM Versus Hybrid VMD-LSTM

YANG Yang; ZHAO Liangjie

doi:10.11932/karst20250502

Abstract：The discharge process of karst spring is controlled by complex hydrogeological structure and multi-scale dynamic mechanisms,exhibits characteristics of non-stationary and strongly nonlinearity,posing significant challenges for high-precision predictive modelings.Conventional physics-based models rely heavily on extensive hydrogeological parameters and often struggle to accurately capture non-stationary processes during extreme events.Consequently,integrating signal decomposition techniques with deep learning has emerged as a promising approach to enhance both prediction accuracy and physical interpretability.This study develops a hybrid model that combines Variational Mode Decomposition(VMD)with a Long-Short-Term Memory(LSTM)networks,referred to as VMD-LSTM,aiming to address non-stationarity and multi-scale coupling issues in daily karst spring discharge forecasting.Through a system comparison of the performance of the VMD-LSTM model and standard LSTM model during training,validation,and testing phases,the study evaluates improvements in prediction accuracy,extreme events characterization,and model stability,while elucidating the mechanisms by which VMD enhances the modeling performance of LSTM. This study utilized daily spring discharge and corresponding precipitation data from the Zhaidi karst system in Guilin,Guangxi,spanning from 2013 to 2023.The original spring discharge series was decomposed using VMD into ten Intrinsic Mode Functions(IMFs).Among them,six modes(Mode 5 to Mode10),which collectively represent the dominant karst hydrodynamic processes,were selected as inputs to a two-layer LSTM network for modeling.The model was trained using the Adam optimizer and the mean squared error loss function.The dataset was chrono-logically partitioned into a training set(80％),a validation set(10％),and a testing set(10％).Model performance was comprehensively evaluated using metrics including RMSE,MAE,NSE,KGE,and peak RMSE(caculated for the top 5％of high-flow events). Results demonstrated that the VMD-LSTM model consistently outperformed the standard LSTM across all three phases of the training,validation and testing.During the testing phase,the VMD-LSTM achieved an NSE of 0.951 and an RMSE of 0.524,representing improvements of 57.0％and 64.6％,respectively,compared to the LSTM model.Notably,the hybrid model exhibited substantially enhanced capability in predicting extreme discharges,reducing the peak RMSE from 6.208 to 1.542(a decrease of 75.2％).The VMD decomposition effectively mitigated non-stationarity and mode mixing present in the original series,enabling the LSTM network to more reliably identify and simulate the"rapid response-slow recession"characteristcs inherent in karst hydrological processes.This approach significantly syppressed the systematic underestimation and error dispersion during high-flow events.The VMD-LSTM hybrid model not only markedly enhanced the forecasting accuracy and extreme event modeling for karst spring discharge but also exhibited strong cross-phase consistency and physical interpretability,demonstrating high generalizability and robustness in practical forecasting scenarios.Future research could focus on incorporating hydrological physical constraints,conducting uncertainty quantification analysis,and extending the framework to higher spatiotemporal resolutions and multivariable coupling to further enhance model applicability and forcasting reliability across diverse karst systems.