EGU2020-10141, updated on 12 Jun 2020
EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Automatic estimation of parameter transfer functions for distributed hydrological models - a case study with the mHM model

Moritz Feigl1, Stephan Thober2, Mathew Herrnegger1, Luis Samaniego2, and Karsten Schulz1
Moritz Feigl et al.
  • 1Institute for Hydrology and Water Management, University of Natural Resources and Life Sciences (BOKU), Vienna, Austria (
  • 2Department of Computational Hydrosystems, UFZ-Helmholtz Centre for Environmental Research, Leipzig, Germany

The estimation of parameters for spatially distributed rainfall runoff models is a long-studied, complex and ill-posed problem. Relating parameters of distributed hydrological models to geophysical properties of catchments could potentially solve some of the major difficulties connected to it.

One way to define this relationship is by the use of explicit equations called parameter transfer functions, which relate geophysical catchment properties to the model parameters. Computing parameter fields using transfer functions would result in spatially consistent parameter fields and the potential to extrapolate to other catchments. A further advantage is that the dimensionality of the parameter space is reduced because the transfer function parameters are applied to all computational units (i.e., grid cells). However, the structure and parameterization of transfer functions is often only implicitly assumed or needs to be derived by a laborious literature guided trial and error process.

For this reason we use Function Space Optimization (FSO), a symbolic regression approach which automatically estimates the structure and parameterization of transfer functions from catchment data. FSO transfers the search of the optimal function to a searchable continuous vector space. To create this space, a text generating neural network with a variational autoencoder (VAE) architecture is used. It is trained to map possible transfer functions and their distributions to a 6-dimensional space. After training, a continuous optimization is applied to search for the optimal transfer function in this function space. FSO was already tested in a virtual experiment using a parsimonious hydrological model, where its ability to solve the problem of transfer function estimation was shown.

Here, we further test FSO by applying it in a real world setting to the mesoscale hydrological model (mHM). mHM is a widely applied distributed hydological model, which uses transfer functions for all its parameters. For this study, we estimate transfer functions for the parameters porosity and field capacity, which both influence a range of hydrologic processes, e.g. infiltration and evapotranspiration. We compare the FSO estimated transfer functions with the already existing mHM transfer functions and examine their influence on the model performance.

In summary, we show the general applicability of FSO for distributed hydrological models and the advantages and capabilities of automatically defining parameter transfer functions.

How to cite: Feigl, M., Thober, S., Herrnegger, M., Samaniego, L., and Schulz, K.: Automatic estimation of parameter transfer functions for distributed hydrological models - a case study with the mHM model, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10141,, 2020

Display materials

Display file

Comments on the display material

AC: Author Comment | CC: Community Comment | Report abuse

Display material version 1 – uploaded on 30 Apr 2020
  • CC1: Comment on EGU2020-10141, Flavio Alexander Asurza Véliz, 04 May 2020

    Could you say me the minimum computer requirements that you needed to perform FSO  if I would want to perform a study like yours?

    • AC1: Reply to CC1, Moritz Feigl, 04 May 2020

      Thank you for your question. It really depends on the hydrological model that you are using, since it usually is the most computational demanding part of the optimization. All the FSO preprocessing steps can potentially be run on a normal PC. Nevertheless, training the autoencoder without a GPU will be slow, but still possible. To give you an idea of the run time: training the autoencoder on a Nvidia GTX 1080 Ti takes about 20 min for an epoch with 8 million sampled transfer functions. It usually converges fast and produces good results after about 20 epochs.

  • CC2: Comment on EGU2020-10141, Erik Nixdorf, 05 May 2020

    Very interesting presentation. Looking on slide 19/20, the two different transfer function approaches generate very different parameter fields. For field capacity resulting fields even seem to be the opposite of each other (red and green areas on the right subplot appear green and yellow on the left subplot and vice versa). Surprisingly, using these very different parameter fields, the time series of simulated discharge on slide 17 resemble each other. How sensitive is the mhm model on the two parameters field capacity and ksat?

    • CC3: Reply to CC2, Erik Nixdorf, 05 May 2020

      just as addition: of course I see that the new parameter field significantly improve the performance of simulated discharge under baseflow conditions, but still I am somehow suprised about the impact of  parameter fields which are so different to each other

    • AC2: Reply to CC2, Moritz Feigl, 05 May 2020

      Thank you for your question. There was a similar question by Simon Stisen during the chat discussion, which I will try to answer here as well.

       Simon Stisen (convener) (01:42) very interesting work: Slide 19-20: the resulting parameter distribution maps for Ksat and Fc are very different and almost display opposite patterns. Which ones correspond best to soil texture maps? E.g. a sandy soil should result in a lower Fc compared to a clay soil. The identification of an optimal transfer function should not be limited to KGE performance, but also remain physically sound. 

       We deliberately chose those two parameters due to their sensitivity. Höllering et al. (2018) ( analyzed the sensitivity of mHM and showed that those two belong to the most sensitive parameters.

      The resulting field capacity fields are not necessarily physically sound, but we also did not yet run a full optimization. So far, the optimization does not include information on what "physical sound" values are. The points you are raising are very important. We will, as you have suggested, check the plausibility of the resulting parameter fields and are also considering to use additional information to regularize the optimization in such a way that physically sound parameter fields are enforced. In our manuscript which is currently under review ( we could show that additional information of hydrological fluxes increases FSO ability to find useful transfer functions.