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Abstract Sparse precipitation data in karst catchments challenge hydrologic models to accurately capture the spatial and temporal relationships between precipitation and karst spring discharge, hindering robust predictions. This study addresses this issue by employing a coupled deep learning model that integrates a variation autoencoder (VAE) for augmenting precipitation 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 of the data. The combined VAE‐generated precipitation and observation data are used to train and test the LSTM to predict spring discharge. Applied to the Niangziguan spring catchment in northern China, the average performance of NSE, root mean square error, mean absolute error, mean absolute percentage error, and log NSE of our coupled VAE/LSTM model reached 0.93, 0.26, 0.15, 1.8, and 0.92, respectively, yielding 145%, 52%, 63%, 70% and 149% higher than an LSTM model using only 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. This study also evaluated the effectiveness of VAE‐augmented data on various deep‐learning models and compared VAE with other data augmentation techniques. We demonstrate that the VAE offers a novel approach to address data scarcity and uncertainty, improving learning generalization and predictive capability of various hydrological models. However, we recognize that innovations to address hydrologic problems at different scales remain to be explored. 

Abstract 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 non‐sinkhole depressions. In this study, we explored deep learning to directly identify sinkholes from DEM data and aerial imagery. A key contribution of our study is an evaluation of various ways of integrating these two types of raster data. We used an image segmentation model, U‐Net, 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. 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 the images of elevation data. In particular, DEM gradient data provided the best input for U‐net 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%.