The impacts of climate change on hydrology underscore the urgency of understanding watershed hydrological patterns for sustainable water resource management. The conventional physics-based fully distributed hydrological models are limited due to computational demands, particularly in the case of large-scale watersheds. Deep learning (DL) offers a promising solution for handling large datasets and extracting intricate data relationships. Here, we propose a DL modeling framework, incorporating convolutional neural networks (CNNs) to efficiently replicate physics-based model outputs at high spatial resolution. The goal was to estimate groundwater head and surface water depth in the Sabgyo Stream Watershed, South Korea. The model datasets consisted of input variables, including elevation, land cover, soil type, evapotranspiration, rainfall, and initial hydrological conditions. The initial conditions and target data were obtained from the fully distributed hydrological model HydroGeoSphere (HGS), whereas the other inputs were actual measurements in the field. By optimizing the training sample size, input design, CNN structure, and hyperparameters, we found that CNNs with residual architectures (ResNets) yielded superior performance. The optimal DL model reduces computation time by 45 times compared to the HGS model for monthly hydrological estimations over five years (RMSE 2.35 and 0.29 m for groundwater and surface water, respectively). In addition, our DL framework explored the predictive capabilities of hydrological responses to future climate scenarios. Although the proposed model is cost-effective for hydrological simulations, further enhancements are needed to improve the accuracy of long-term predictions. Ultimately, the proposed DL framework has the potential to facilitate decision-making, particularly in large-scale and complex watersheds.