Development of a Combined Machine Learning and Physics-based Approach to Reduce Hydrologic Model Spin-up Time

Finding the initial state groundwater configuration of a catchment is one of the major challenges when simulating the hydrological cycle with an integrated hydrological model. The choice of this initial condition has a large impact on the results of the subsequent simulation, and it is often found by repeatedly running the hydrological model with constant atmospheric settings until the system equilibrates. These spin-up computations are computationally expensive and often require many years of simulated time, especially if the initial groundwater configuration before the spin-up computations is far from this steady state.

We hypothesize that existing large-scale groundwater simulations at steady state can be used to machine learn how steady-state depth-to-water tables (DTWTs) for groundwater depend on readily available data sources like large-scale conductivity and surface slopes. But how well can steady-state DTWTs be estimated by such ideas? How much computing speed can be gained with improved initializations of spin-up simulation? And how well does the estimation of improved initializations generalize across different geological settings and climate?

To answer these questions, we developed the machine learning emulator HydroStartML to accelerate the spin-up computation. HydroStartML is trained on converged steady-state DTWT distribution, and it generates a configuration of the DTWT of the respective watershed. This configuration is used as the starting configuration for spin-up computations. Doing so reduces the overall computational effort compared to the typical approach of initiating spin-up computations with a uniform DTWT across the whole catchment. HydroStartML is trained on the entire contiguous United States on spatially distributed patches with a fixed set of parameters.

Spin-up computations with these DTWT configurations as starting configurations converge faster and with a reduced computational effort compared to spin-up computations with other initial configurations. We found that HydroStartML is indeed able to generate DTWT configurations that are close to the steady state, even on unseen terrain. Although the generation of shallow DTWTs is possible with especially small errors, the strongest reductions in spin-up effort occurs in regions with deep DTWTs. This work opens the door for hybrid approaches that blend machine learning and traditional simulation, enhancing predictive accuracy and efficiency in hydrology for improving water resource management and understanding complex environmental interactions.