DeepONet Surrogate for Accelerating Distributed Hydrological Model Simulations

Distributed hydrological models are the mainstream paradigm for watershed hydrological simulation, integrating heterogeneous factors through spatial discretization and demonstrating significant advantages in revealing the spatial differentiation patterns of hydrological processes. However, the high-dimensional parameter space leads to high computational costs and low robustness in parameter calibration in traditional distributed hydrological models. Taking Weihe River Basin and Water Allocation and Cycle Model (WACM), a traditional distributed hydrological model, as the study area and base model, this study proposed a surrogate Deep Neural Operator (DeepONet) model to enhance the calibration efficiency. The surrogate DeepONet uses a branch network to project the high-dimensional model parameters into a compact latent space and a trunk network to encode the spatiotemporal coordinates of runoff outputs, jointly learning a nonlinear mapping from parameters to runoff that replaces direct calibration in the original parameter space and thus greatly reduces both the effective parameter dimensionality and the computational cost of calibration. The results show that the median Kling–Gupta Efficiency (KGE) coefficient across all gauging stations exceeds 0.85, whereas the parameter calibration time is reduced to less than 10% of that required by traditional genetic algorithms. In addition, the surrogate model achieved high accuracy in runoff prediction, with KGE values above 0.80 at these ungauged stations. This study demonstrates that the deep integration of physical mechanisms and data-driven approaches can effectively enhance the trade-off in the efficiency-accuracy dilemma in hydrological simulations and presents a sound solution for high-dimensional parameter calibration in distributed hydrological models.