HydroStartML: A combined machine learning and physics-based approach to reduce hydrological model spin-up time

TL;DR

This work tackles the heavy computational burden of spin-up in transient hydrological simulations by introducing HydroStartML, a CNN-based emulator trained on steady-state $DTWT$ configurations from ParFlow CONUS2. It predicts a near-steady initial $DTWT$ field from four terrain- and groundwater-features inputs ($k_z$, $R$, $S_x$, $S_y$) to seed spin-up computations, enabling faster convergence and reduced resource use. The model, built as a U‑Net–like architecture, achieves a patch-averaged RMSE around $28.7$ m on test data and demonstrates substantial spin-up time savings, particularly in regions with deep $DTWT$; it also shows robustness in many unseen terrains and atypical patches. While promising, the approach is validated within a 150 × 150 patch framework and calls for further work on generalization to other continents, larger basins, and improvements for deep-$DTWT$ predictions to maximize practical impact in hydrological forecasting and resource management.

Abstract

Finding the initial depth-to-water table (DTWT) configuration of a catchment is a critical challenge when simulating the hydrological cycle with integrated models, significantly impacting simulation outcomes. Traditionally, this involves iterative spin-up computations, where the model runs under constant atmospheric settings until steady-state is achieved. These so-called model spin-ups are computationally expensive, often requiring many years of simulated time, particularly when the initial DTWT configuration is far from steady state. To accelerate the model spin-up process we developed HydroStartML, a machine learning emulator trained on steady-state DTWT configurations across the contiguous United States. HydroStartML predicts, based on available data like conductivity and surface slopes, a DTWT configuration of the respective watershed, which can be used as an initial DTWT. Our results show that initializing spin-up computations with HydroStartML predictions leads to faster convergence than with other initial configurations like spatially constant DTWTs. The emulator accurately predicts configurations close to steady state, even for terrain configurations not seen in training, and allows especially significant reductions in computational spin-up effort 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.

Figures (14)

• Figure 1: Typically, spin-up computations rely on an initial condition for the depth-to-water table (DTWT), and provide an initial condition at steady-state for the subsequent hydrological simulations.
• Figure 2: Convergence behavior of the normalized storage change during SUCs, initialized with different initial DTWT configurations.
• Figure 3: All patches of size $150\times150$ grid cells on the CONUS2 domain that were included and later used as training, validation and testing dataset are marked in yellow. The outline of the full CONUS2 domain is marked Yang2023CONUS2. Excluded regions either do not belong to the CONUS, mainly consist of water or are in local proximity to the demo basins $1,2,3,4$. A patch with a particularly atypical DTWT (marked with an $A$) contains an atypical basin that we will use as additional demo basin.
• Figure 4: Ground truth steady-state DTWT configuration in a patch of $150 \times 150$ grid cells, in which demo basin $1$ is encapsulated.
• Figure 5: Architecture of the convolutional neural network HydroStartML with a U-Net structure, including the size of the input of each layer.