Reconstruct karst spring discharge data with hybrid deep learning models and ensemble empirical mode decomposition method

Having a continuous and complete karst discharge data record is necessary to understand hydrological behaviors of the karst aquifer and manage karst water resources. However, caused by many problems such as equipment errors and failure of observation, lots of hydrological and research dataset contains missing spring discharge values, which becomes a main barrier for further environmental and hydrological modeling and studies. In this work, a novel approach that integrates deep learning algorithms and ensemble empirical mode decomposition (EEMD) is developed to reconstruct missing karst spring discharge values with the local precipitation. EEMD is firstly employed to decompose the precipitation data, extract useful features, and remove noises. The decomposed precipitation components are then fed as input data to various deep learning models for performance comparison, including convolutional neural network (CNN), long short-term memory (LSTM), and hybrid CNN-LSTM models to reconstruct the missing discharge values. Root mean squared error (RMSE) and Nash–Sutcliffe efficiency coefficient (NSE), are calculated to evaluate the reconstruction performance as metrics. The models are validated with the spring discharge and precipitation data collected at Barton Spring in Texas. The reconstruction performance of various deep learning models with and without EEMD are compared and evaluated. The main conclusions can be summarized as: 1) by using EEMD, the integrated deep models significantly improve reconstruction performance and outperform the simple deep models; 2) among three integrated models, the LSTM-EEMD model obtains the best reconstruction results among three deep learning algorithms; 3) For models with monthly data, the reconstruction performance decreases greatly with the increase of missing rate: the best reconstruction results are obtained when the missing rate is low. If the missing rate was 50%, the reconstruction results become notably poorer. For models with daily data, the reconstruction performance is less impacted by the missing rate and the models can obtain satisfactory reconstruction results when missing rates range from 10% to 50%.