Automatic Estimation of Parameter Transfer Functions for Distributed Hydrological Models - Function Space Optimization Applied on the mHM Model

Abstract:

Relating parameters of distributed hydrological models to geophysical properties of catchments (i.e. transfer functions) is a state-of-the-art approach for efficient estimation of spatially distributed parameters. This study investigates the performance of an algorithm for automatic parameter transfer function optimization in a real world setting. We use the Function Space Optimization (FSO) algorithm to estimate transfer functions for two parameters of the mesoscale Hydrological Model (mHM).

FSO is a symbolic regression method that allows for automatic estimation of the structure and parameterization of transfer functions from catchment data. The FSO method transforms the search for an optimal transfer function into a continuous optimization problem using a text generating neural network (variational autoencoder).
mHM is a widely applied distributed hydrological model, which uses transfer functions for all its parameters. For this study, we estimate transfer functions for the parameters porosity and field capacity. To avoid the influence of parameter equifinality, the remaining mHM parameter values are optimized simultaneously.
The study domain consist of 229 basins, including 7 major basins and 222 smaller basins, distributed across Germany. Training and calibration splits for time series and basins were defined based on a previous study (Zink et al., 2017, doi.org/10.5194/hess-21-1769-2017), which applied mHM to the same set of basins. This allows us to compare the FSO estimated transfer functions with the default mHM transfer functions and examine their influence on the model performance, scalability and transferability.
We find that transfer functions estimated by FSO lead to a significantly better prediction compared to the default transfer function across all basins. In detail, the FSO transfer functions jointly estimated across a selection of basins outperforms the single-site calibration using the default transfer function at most basins. The new transfer functions lead to an improved prediction at ungauged locations and scalability of the model from 4 to 16 km.