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Abstract Snow dominated mountainous karst watersheds are the primary source of water supply in many areas in the western U.S. and worldwide. These watersheds are typically characterized by complex terrain, spatiotemporally varying snow accumulation and melt processes, and duality of flow and storage dynamics because of the juxtaposition of matrix (micropores and small fissures) and karst conduits. As a result, predicting streamflow from meteorological inputs has been challenging due to the inability of physically based or conceptual hydrologic models to represent these unique characteristics. We present a hybrid modeling approach that integrates a physically based, spatially distributed, snow model with a deep learning karst model. More specifically, the high‐resolution snow model captures spatiotemporal variability in snowmelt, and the deep learning model simulates the corresponding response of streamflow as influenced by complex surface and subsurface properties. The deep learning model is based on the Convolutional Long Short‐Term Memory (ConvLSTM) architecture capable of handling spatiotemporal recharge patterns and watershed storage dynamics. The hybrid modeling approach is tested on a watershed in northern Utah with seasonal snow cover and variably karstified carbonate bedrock. The hybrid models were able to simulate streamflow at the watershed outlet with high accuracy. The spatial and temporal recharge and discharge patterns learned by the ConvLSTM model were then examined and compared with known hydrogeologic information. Results suggest that ConvLSTM simulates streamflow with higher accuracy than reference models for the study area and provides insight into spatially influenced hydrologic responses that are unavailable within lumped modeling approaches.