Catchment to model space mapping – learning transfer functions from data by symbolic regression

The Function Space Optimization (FSO) method, recently developed by Feigl et al. (2020), automatically estimates the transfer function structure and coefficients to parameterize spatially distributed hydrological models. FSO is a symbolic regression method, searching for an optimal transfer function in a continuous optimization space, using a text generating neural network (variational autoencoder).

We apply our method to the distributed hydrological model mHM (www.ufz.de/mhm), which is based on a priori defined transfer functions. We estimate mHM transfer functions for the parameters “saturated hydraulic conductivity” and “field capacity”, which both influence a range of hydrologic processes, e.g. infiltration and evapotranspiration.

The FSO and standard mHM approach are compared using data from 229 basins, including 7 large training basins and 222 smaller validation basins, distributed across Germany. For training, 5 years of data of 7 gauging stations is used, while up to 35 years, with a median of 32 years, are used for validation. This setup is adopted from a previous study by Zink et al. (2017), testing mHM in the same basins and which is used as a benchmark. Maps of soil properties (sand/clay percentage, bulk density) and topographic properties (aspect, slope, elevation) are used as possible inputs for transfer functions.

FSO estimated transfer functions improved the mHM model performance in the validation catchments significantly when compared to the benchmark results, and only show a small decrease in performance compared to the training results. Results demonstrate that an automatic estimation of parameter transfer functions by FSO is beneficial for the parameterization of distributed hydrological models and allows for a robust parameter transfer to other locations.

 

Feigl, M., Herrnegger, M., Klotz, D., & Schulz, K. (2020). Function Space Optimization: A symbolic regression method for estimating parameter transfer functions for hydrological models. Water resources research, 56(10), e2020WR027385.

Zink, M., Kumar, R., Cuntz, M., & Samaniego, L. (2017). A high-resolution dataset of water fluxes and states for Germany accounting for parametric uncertainty. Hydrol. Earth Syst. Sci, 21, 1769-1790.