Precipitation data collected from sparse monitoring stations in numerous karst basins pose a challenge for hydrologic models to accurately capture spatial and temporal correlation between precipitation and karst spring discharge, hindering the development of robust simulation models. To address this data scarcity issue, this study employes a coupled deep learning model that integrates a variation autoencoder (VAE) for augmenting precipitation data and a long short-term memory (LSTM) network for karst spring discharge prediction. The VAE contributes by generating synthetic precipitation data through an encoding-decoding process. This process generalizes the observed precipitation data by deriving joint latent distributions with improved preservation of temporal and spatial correlations in the data. The combined VAE-generated precipitation and observation data are used to train and test the LSTM for predicting the spring discharge. Applied to Niangziguan spring catchment in northern China, our coupled VAE/LSTM model demonstrated significantly higher predictive accuracy compared to a LSTM model using only field observations. We also explored temporal and spatial correlations in the observed data and the impact of different ratios of VAE-generated precipitation data to actual data on model performances. Additionally, our study evaluated the effectiveness of VAE-augmented data on various deep learning models and compared VAE with other data augmentation techniques. Our study demonstrates that the VAE offers a novel approach to address data scarcity and uncertainty, improving learning generalization and predictive capability of various hydrological models.

The hydraulic properties of coastal aquifer systems are relevant to various hydrogeological, hydro-ecological and engineering problems. This study presents an analytical solution for predicting groundwater head fluctuations induced by dual-tide in multilayered island aquifer systems, consisting of an unconfined aquifer on the top and any number of leaky aquifers below. The solution was derived via the methods of matrix differential calculus and separation of variables. It is more general than any existing analytical solutions for the tidal pressure propagation since the new solution can consider multilayered aquifer systems along with the effects of leakage and aquifer length. Using this solution, we illustrated potential errors that may occur due to neglecting one or more vital factors affecting groundwater fluctuations. Besides, we articulated the groundwater response to the dual-tide in complex coastal aquifers. Considering that some thin semipermeable layers may be ignored in practical field investigation, we also demonstrated the effects due to simplification of aquifer layers. The results showed that with the increase in the number of overlapped leaky layers, the tidal propagation in the bottom part of multilayered aquifer system approaches that in a single confined aquifer with the same transmissivity and storage.

Internal erosion is one of the most common causes of failure in hydraulic engineering structures, such as embankments and levees. It also plays a vital role in the geohazards (such as landslides and sinkhole developments) and more importantly, the earth landscape evolution, which has a broad environmental and ecosystem impacts. The groundwater seepage is multi-directional, and its multi-dimensional nature could affect the initiation and the progression of internal erosion. With a newly developed apparatus, we carry out nine internal erosion experiments under five different seepage directions. The results reveal that the critical hydraulic gradient increases as the seepage direction varies from the horizontal to the vertical. After a global erosion is triggered, preferential erosion paths distribute randomly from the bottom to the top of the specimen. If the seepage direction is not vertical, small preferential erosion paths merge into a large erosion corridor, in which the loss of fine particles is significant but negligible outside. Results of experiments manifest that the erosion is heterogeneous and three-dimensional, even in the unidirectional seepage flow. The particles are rapidly eroded at the early stage of the erosion, indicating a high erosion rate. With the erosion time increasing, the particle loss slows down and even ceases if the time is long enough. The erosion rate increases if the seepage direction approaches a vertical direction. Overall, the erosion rate approximately decreases with erosion time exponentially. We proposed exponential equations to illustrate the variation of the erosion rate in the erosion process.