Author(s): Max Rudolph; Alireza Kavousi; Thomas Wohling; Pierre-Yves Jeannin; Thomas Reimann

Linked Author(s): Thomas Reimann

Keywords: Hydrology; Modelling; Dimension Reduction; Optimization; Karst

Abstract: The tasks of parameter identification and uncertainty quantification for inverse problems are ubiquitous in environmental and hydrological sciences. Problems of this kind often suffer from the curse of dimensionality which makes the problems ill-posed and can lead to ambiguity in parameter combinations during calibration. This effect is further aggravated if the respective model parameters are not fully physically interpretable or if they cannot be validated or restricted by field measurements. To fight the curse of dimensionality, to make more robust parameter estimates, and to get insight into the most important parameters and relationships of processes within a certain model, dimensionality reduction (DR) techniques can be used. The method of active subspaces (AS) – related to proper orthogonal decomposition – offers the possibility for linear dimension reduction and has been previously successfully applied to aid the calibration of hydrological models and to identify surrogates. AS is a gradient-based method and tries to find the directions in the parameter space, in which the scalar model output changes more, on average, than in other directions. These directions are given by linear combinations (eigenvectors) of model parameters and thus enable a new level of model interpretability by analyzing the contributions in the different eigenvectors. Transforming the original data to the lower-dimensional setting with a subset of the eigenvectors allows for the analysis of the model input-output relationship and for surrogate construction. We set up a lumped parameter model to simulate karst system spring discharge of the already well studied Milandre karst system in Switzerland, utilizing hourly precipitation and discharge data and daily evaporation data from one measurement station in the catchment. The model consists of a two-flow-component non-linear recharge model and an impulse response function. We explore the 13-dimensional parameter space with a Markov chain Monte Carlo (MCMC) approach with uniform priors to generate posterior parameter samples. Additionally, we use uniform distributions together with a Latin hypercube scheme (LHS) to obtain unconditioned samples. Gradients of the scalar model output (NSE criterion) with respect to the parameters are computed utilizing a finite forward difference (FFD) scheme. It has been shown that lower dimensional structure could be identified independently of the combination of methods used. The more global approach of the unconditioned LHS based method with FFD gradients showed distinct differences in terms of subspace quality and structure compared to the MCMC generated results. The more global view of LHS produced eigenvectors, in which directions the model changes drastically, while the MCMC eigenvectors give a more local representation around the optimal solution. We found that the MCMC and FFD based method provided results from which observed system properties were extractable.

DOI: https://doi.org/10.3850/IAHR-39WC2521711920221822

Year: 2022