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 saturated hydraulic conductivity and field capacity. To avoid the influence of parameter equifinality, the remaining mHM parameter values are optimized simultaneously. The study domain consists of 229 basins, including 7 major basins for Training and 222 smaller basins for validation, distributed across Germany. 5 years of data are used for training und 35 years for validation. By validating the estimated transfer functions in a set of validation basins in a different time period, we can examine the FSO estimated transfer functions influence on model performance, scalability and transferability. We find that transfer functions estimated by FSO lead to a robust performance when being applied in an ungauged setting. The median KGE of the validation basins in the validation time period is 0.73, while the median KGE of the 7 training basins in training time is 0.8. These results look promising, especially since we are only using 5 years of training data, and show the general applicability of FSO for distributed hydrological models.

Parameter estimation is one of the most challenging tasks in large-scale distributed modeling, because of the high dimensionality of the parameter space. Relating model parameters to catchment/landscape characteristics reduces the number of parameters, enhances physical realism, and allows the transfer of hydrological model parameters in time and space. This study presents the first large-scale application of automatic parameter transfer function (TF) estimation for a complex hydrological model. The Function Space Optimization (FSO) method can automatically estimate TF structures and coefficients for distributed models. We apply FSO to the mesoscale Hydrologic Model (mHM, mhm-ufz.org), which is the only available distributed model that includes a priori defined TFs for all its parameters. FSO is used to estimate new TFs for the parameters “saturated hydraulic conductivity” and “field capacity”, which both influence a range of hydrological processes. The setup of mHM from a previous study serves as a benchmark. The estimated TFs resulted in predictions in 222 validation basins with a median NSE of 0.68, showing that even with 5 years of calibration data, high performance in ungauged basins can be achieved. The performance is similar to the benchmark results, showing that the automatic TFs can achieve comparable results to TFs that were developed over years using expert knowledge. In summary, the findings present a step towards automatic TF estimation of model parameters for distributed models.