Reconstruction of missing spring discharge by using deep learning models with ensemble empirical mode decomposition of precipitation

A continuous and complete spring discharge record is critical in understanding the hydrodynamic behavior of karst aquifers and the variability of freshwater resources. However, due to equipment errors, failure of observation and other reasons, missing data is a common problem for spring discharge monitoring and further hydrological investigations and data analysis. In this study, a novel approach that integrates deep learning algorithms and ensemble empirical mode decomposition (EEMD) is proposed to reconstruct the missing spring discharge data with a given local precipitation record. Using EEMD, the local precipitation data is decomposed into several intrinsic mode functions (IMFs) from high to low frequencies and a residual function, which are served as the input of convolutional neural network (CNN), long short-term memory (LSTM), and hybrid CNN-LSTM models to reconstruct the missing discharge data. Evaluation metrics, including root mean squared error (RMSE), mean absolute error (MAE), and Nash-Sutcliffe efficiency coefficient (NSE), are calculated to evaluate the reconstruction performance. The monthly spring discharge and precipitation data from March 1978 to October 2021 collected at Barton Springs in Texas are used for the validation and evaluation of newly proposed deep learning models. The results indicate that deep learning models coupled with EEMD overperform the models without EEMD and significantly improve the reconstruction results. The LSTM-EEMD model obtains the best reconstruction results among three deep learning algorithms. For models with monthly data, the missing rate affects the reconstruction performance because of the number of data samples: the best reconstruction results are achieved when the missing rate was low. If the missing rate was 50%, the reconstruction results become notably poorer. However, when the daily precipitation and discharge data are used, the models can obtain satisfactory reconstruction results with missing rate ranged from 10 to 50%.