@article{FischerKowalskiPudasainietal.2009,
  author    = {Fischer, Jan-Thomas and Kowalski, Julia and Pudasaini, Shiva P. and Miller, S. A.},
  title     = {Dynamic Avalanche Modeling in Natural Terrain},
  series = {International Snow Science Workshop, Davos 2009, Proceedings ; Proc. ISSW 2009},
  journal   = {International Snow Science Workshop, Davos 2009, Proceedings ; Proc. ISSW 2009},
  pages     = {448 -- 452},
  year      = {2009},
  abstract  = {The powerful avalanche simulation toolbox RAMMS (Rapid Mass Movements) is based on a depth-averaged hydrodynamic system of equations with a Voellmy-Salm friction relation. The two empirical friction parameters μ and � correspond to a dry Coulomb friction and a viscous resistance, respectively. Although μ and � lack a proper physical explanation, 60 years of acquired avalanche data in the Swiss Alps made a systematic calibration possible. RAMMS can therefore successfully model avalanche flow depth, velocities, impact pressure and run out distances. Pudasaini and Hutter (2003) have proposed extended, rigorously derived model equations that account for local curvature and twist. A coordinate transformation into a reference system, applied to the actual mountain topography of the natural avalanche path, is performed. The local curvature and the twist of the avalanche path induce an additional term in the overburden pressure. This leads to a modification of the Coulomb friction, the free-surface pressure gradient, the pressure induced by the channel, and the gravity components along and normal to the curved and twisted reference surface. This eventually guides the flow dynamics and deposits of avalanches. In the present study, we investigate the influence of curvature on avalanche flow in real mountain terrain. Simulations of real avalanche paths are performed and compared for the different models approaches. An algorithm to calculate curvature in real terrain is introduced in RAMMS. This leads to a curvature dependent friction relation in an extended version of the Voellmy-Salm model equations. Our analysis provides yet another step in interpreting the physical meaning and significance of the friction parameters used in the RAMMS computational environment.},
  language  = {en}
}
@article{FischerKowalskiPudasaini2012,
  author    = {Fischer, Jan-Thomas and Kowalski, Julia and Pudasaini, Shiva P.},
  title     = {Topographic curvature effects in applied avalanche modelling},
  series = {Cold Regions Science and Technology},
  volume    = {74-75},
  journal   = {Cold Regions Science and Technology},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {1872-7441},
  doi       = {10.1016/j.coldregions.2012.01.005},
  pages     = {21 -- 30},
  year      = {2012},
  abstract  = {This paper describes the implementation of topographic curvature effects within the RApid Mass MovementS (RAMMS) snow avalanche simulation toolbox. RAMMS is based on a model similar to shallow water equations with a Coulomb friction relation and the velocity dependent Voellmy drag. It is used for snow avalanche risk assessment in Switzerland. The snow avalanche simulation relies on back calculation of observed avalanches. The calibration of the friction parameters depends on characteristics of the avalanche track. The topographic curvature terms are not yet included in the above mentioned classical model. Here, we fundamentally improve this model by mathematically and physically including the topographic curvature effects. By decomposing the velocity dependent friction into a topography dependent term that accounts for a curvature enhancement in the Coulomb friction, and a topography independent contribution similar to the classical Voellmy drag, we construct a general curvature dependent frictional resistance, and thus propose new extended model equations. With three site-specific examples, we compare the apparent frictional resistance of the new approach, which includes topographic curvature effects, to the classical one. Our simulation results demonstrate substantial effects of the curvature on the flow dynamics e.g., the dynamic pressure distribution along the slope. The comparison of resistance coefficients between the two models demonstrates that the physically based extension presents an improvement to the classical approach. Furthermore a practical example highlights its influence on the pressure outline in the run out zone of the avalanche. Snow avalanche dynamics modeling natural terrain curvature centrifugal force friction coefficients.},
  language  = {en}
}