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.

Sinkholes are the most abundant surface features in karst areas worldwide. Understanding sinkhole occurrences and characteristics is critical for studying karst aquifers and mitigating sinkhole-related hazards. Most sinkholes appear on the land surface as depressions or cover-collapses and are commonly mapped from elevation data, such as digital elevation models (DEMs). Existing methods for identifying sinkholes from DEMs often require two steps: locating surface depressions and separating sinkholes from nonsinkhole depressions. In this study, we explored deep learning to directly identify sinkholes from images of DEMs and DEM derivatives. We used an image segmentation model, U-Net (a type of convolutional neural networks (CNNs)), to locate sinkholes. We trained separate U-Net models based on four input images of elevation data: a DEM image, a slope image, a DEM gradient image, and a DEM shaded relief image. We also explored an aerial image as a model input. Three normalization techniques (Global, Gaussian, and Instance) were applied to improve the model performance. Model results suggest that deep learning is a viable method to identify sinkholes directly from images of elevation data. In particular, DEM gradient data provided the best input for CNN-based image segmentation models to locate sinkholes. The model using the DEM gradient image with Gaussian normalization achieved the best performance with a sinkhole intersection over union (IoU) of 45.38% on the unseen test set. Aerial images, however, were not useful in training deep learning models for sinkholes as the models using an aerial image as input achieved sinkhole IoUs below 3 %.