arXiv subjects

Daniel Bittner

Publications and source records attributed to Daniel Bittner.

3 recordsLinked to original sources

arXiv2019

Bayesian calibration and sensitivity analysis for a karst aquifer model using active subspaces

In this article, we perform a parameter study for a recently developed karst hydrological model. The study consists of a high-dimensional Bayesian inverse problem and a global sensitivity analysis. For the first time in karst hydrology, we use the active subspace method to find directions in the parameter space that dominate the Bayesian update from the prior to the posterior distribution in order to effectively reduce the dimension of the problem and for computational efficiency. Additionally, the calculated active subspace can be exploited to construct sensitivity metrics on each of the individual parameters and be used to construct a natural model surrogate. The model consists of 21 parameters to reproduce the hydrological behavior of spring discharge in a karst aquifer located in the Kerschbaum spring recharge area at Waidhofen a.d. Ybbs in Austria. The experimental spatial and time series data for the inference process were collected by the water works in Waidhofen. We show that this case study has implicit low-dimensionality, and we run an adjusted Markov chain Monte Carlo algorithm in a low-dimensional subspace to construct samples of the posterior distribution. The results are visualized and verified by plots of the posterior's push-forward distribution displaying the uncertainty in predicting discharge values due to the experimental noise in the data. Finally, a discussion provides hydrological interpretation of these results for the Kerschbaum area.

stat.CO↗

arXiv2018

On the relation between parameters and discharge data for a lumped karst aquifer model

Hydrological models of karst aquifers are often semi-distributed, and physical processes such as infiltration and spring discharge generation are described in a lumped way. Several works have previously addressed the problems associated with the calibration of such models, highlighting in particular the issue of model parameter estimation and model equifinality. In this work, we investigate the problem of model calibration using the active subspace (AS) method, a novel tool for model parameter dimension reduction. We apply the method to a newly proposed hydrological model for karst aquifers, LuKARS, to investigate if the AS framework identifies catchment-specific characteristics or if the results only depend on the chosen model structure. Therefore, we consider four different case studies, three synthetic and one real case (Kerschbaum springshed in Waidhofen a.d. Ybbs, Austria), with varying hydrotope distributions and properties. We find that both the hydrotope area coverage and the catchment characteristics have major impacts on parameter sensitivities. While model parameters are similarly informed in scenarios with less varying catchment characteristics, we find significant differences in parameter sensitivities when the applied hydrotopes were different from each other. Our results show that the AS method can be used to investigate the relation between the model structure, the area of a hydrotope, the physical properties of a catchment and the discharge data. Finally, we successfully effectively reduce the parameter dimensions of the LuKARS model for the Kerschbaum case study using the AS method. The model with reduced parameter dimensions is able to reproduce the observed impacts of land use changes in the Kerschbaum springshed, highlighting the robustness of the hydrotope-based modeling approach of LuKARS and its applicability for land use change impact studies in karstic systems.

physics.geo-ph↗

arXiv2014

New Approximations for the Area of the Mandelbrot Set

Due to its fractal nature, much about the area of the Mandelbrot set $M$ remains to be understood. While a series formula has been derived by Ewing and Schober to calculate the area of $M$ by considering its complement inside the Riemann sphere, to date the exact value of this area remains unknown. This paper presents new improved upper bounds for the area based on a parallel computing algorithm and for the 2-adic valuation of the series coefficients in terms of the sum-of-digits function.

math.DS↗