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Natural Hazards and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 15, issue 3 | Copyright
Nat. Hazards Earth Syst. Sci., 15, 671-685, 2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 30 Mar 2015

Research article | 30 Mar 2015

Modelling rapid mass movements using the shallow water equations in Cartesian coordinates

S. Hergarten1 and J. Robl2 S. Hergarten and J. Robl
  • 1Universität Freiburg i. Br., Institut für Geo- und Umweltnaturwissenschaften, Freiburg, Germany
  • 2Universität Salzburg, Fachbereich Geographie und Geologie, Salzburg, Austria

Abstract. We propose a new method to model rapid mass movements on complex topography using the shallow water equations in Cartesian coordinates. These equations are the widely used standard approximation for the flow of water in rivers and shallow lakes, but the main prerequisite for their application – an almost horizontal fluid table – is in general not satisfied for avalanches and debris flows in steep terrain. Therefore, we have developed appropriate correction terms for large topographic gradients. In this study we present the mathematical formulation of these correction terms and their implementation in the open-source flow solver GERRIS. This novel approach is evaluated by simulating avalanches on synthetic and finally natural topographies and the widely used Voellmy flow resistance law. Testing the results against analytical solutions and the proprietary avalanche model RAMMS, we found a very good agreement. As the GERRIS flow solver is freely available and open source, it can be easily extended by additional fluid models or source areas, making this model suitable for simulating several types of rapid mass movements. It therefore provides a valuable tool for assisting regional-scale natural hazard studies.

Publications Copernicus
Short summary
Snow avalanches and debris flows are abundant natural hazards in mountainous regions. Numerical models describing rapid mass movements are essential for hazard studies and mitigation strategies, but only a few software tools are available for this purpose. This paper presents a new method using the shallow water equations widely applied to lakes and oceans. It introduces appropriate correction terms for steep terrain and can be implemented in a variety of fluid-dynamics software packages.
Snow avalanches and debris flows are abundant natural hazards in mountainous regions. Numerical...