Articles | Volume 17, issue 2
https://doi.org/10.5194/gmd-17-781-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-17-781-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
MinVoellmy v1: a lightweight model for simulating rapid mass movements based on a modified Voellmy rheology
Stefan Hergarten
CORRESPONDING AUTHOR
Institut für Geo- und Umweltnaturwissenschaften, Albert-Ludwigs-Universität Freiburg, Albertstr. 23B, 79104 Freiburg, Germany
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The Bohemian Massif is one of several low mountain ranges in Europe that rises more than 1 km above the surrounding lowlands. Landscape characteristics indicate relief rejuvenation due to recent surface uplift. To constrain the pace of relief formation, we determined erosion rates of 20 catchments that range from 22 to 51 m Myr-1. Correlating these rates with topographic properties reveals that contrasts in bedrock erodibility represent a critical control of landscape evolution.
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Numerical glacier and ice-sheet models have been widely used in the context of climate change and landform evolution. While simulations of ice flow were numerically expensive for a long time, their performance has recently been boosted to an unprecedented level by machine learning techniques. This paper aims at keeping classical numerics competitive by introducing a novel numerical scheme, which allows for simulations at spatial resolutions of 25 m or even finer on standard desktop PCs.
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Faceted topographies are impressive footprints of active tectonics in geomorphology. This paper investigates the evolution of faceted topographies at normal faults and their interaction with a river network theoretically and numerically. As a main result beyond several relations for the geometry of facets, the horizontal displacement associated with normal faults is crucial for the dissection of initially polygonal facets into triangular facets bounded by almost parallel rivers.
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Toma hills are relatively isolated hills found in the deposits of rock avalanches, and their origin is still enigmatic. This paper presents the results of numerical simulations based on a modified version of a friction law that was originally introduced for snow avalanches. The model produces more or less isolated hills (which look much like toma hills) on the valley floor. The results provide, perhaps, the first explanation of the occurrence of toma hills based on a numerical model.
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Large landslides turn into an avalanche-like mode of flow at high velocities, which allows for a much longer runout than predicted for a sliding solid body. In this study, the Voellmy rheology widely used in models for hazard assessment is reinterpreted and extended. The new approach predicts the increase in runout length with volume observed in nature quite well and may thus be a major step towards a more consistent modeling of rock avalanches and improved hazard assessment.
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Rockslides are a major hazard in mountainous regions. In formerly glaciated regions, the disposition mainly arises from oversteepened topography and decreases through time. However, little is known about this decrease and thus about the present-day hazard of huge, potentially catastrophic rockslides. This paper presents a new theoretical framework that explains the decrease in maximum rockslide size through time and predicts the present-day frequency of large rockslides for the European Alps.
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This study uses dendritic flow patterns to analyze the recession behavior of aquifer springs. The results show that the long-term recession becomes slower for large catchments. After a short recharge event, however, the short-term behavior differs strongly from the exponential recession that would be expected from a linear reservoir. The exponential component still accounts for more than 80 % of the total discharge, much more than typically assumed for karst aquifers.
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The transition from hillslopes to channelized flow is typically attributed to a threshold catchment size in landform evolution models. Here we propose an alternative concept directly based on topography. Using this concept, channels and hillslopes self-organize, whereby the catchment size of the channel heads varies over some range. Our numerical results suggest that this concept works better than the established idea of a strict threshold catchment size.
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In this study, we benchmark a topography-based model for glacier erosion (OpenLEM) with a well-established process-based model (iSOSIA). Our experiments show that large-scale erosion patterns and particularly the transformation of valley length geometry from fluvial to glacial conditions are very similar in both models. This finding enables the application of OpenLEM to study the influence of climate and tectonics on glaciated mountains with reasonable computational effort on standard PCs.
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This study relies on topography to simulate the origin and displacement of potentially river-blocking landslides. It highlights a continuous range of simulated landslide dams that go unnoticed in the field due to their small scale. The computation results show that landslide-dammed lake volume can be estimated from upstream drainage area and landslide volume, thus enabling an efficient hazard assessment of possible landslide-dammed lake volume – and flooding magnitude in case of dam failure.
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Many contemporary models of large-scale fluvial erosion focus on the detachment-limited regime where all material entrained by the river is immediately excavated. This limitation facilitates the comparison with real river profiles and strongly reduces the numerical complexity. Here a simple formulation for the opposite case, transport-limited erosion, and a new numerical scheme that achieves almost the same numerical efficiency as detachment-limited models are presented.
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The Bohemian Massif is one of several low mountain ranges in Europe that rises more than 1 km above the surrounding lowlands. Landscape characteristics indicate relief rejuvenation due to recent surface uplift. To constrain the pace of relief formation, we determined erosion rates of 20 catchments that range from 22 to 51 m Myr-1. Correlating these rates with topographic properties reveals that contrasts in bedrock erodibility represent a critical control of landscape evolution.
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This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
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Numerical glacier and ice-sheet models have been widely used in the context of climate change and landform evolution. While simulations of ice flow were numerically expensive for a long time, their performance has recently been boosted to an unprecedented level by machine learning techniques. This paper aims at keeping classical numerics competitive by introducing a novel numerical scheme, which allows for simulations at spatial resolutions of 25 m or even finer on standard desktop PCs.
Stefan Hergarten
Earth Surf. Dynam., 12, 1315–1327, https://doi.org/10.5194/esurf-12-1315-2024, https://doi.org/10.5194/esurf-12-1315-2024, 2024
Short summary
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Faceted topographies are impressive footprints of active tectonics in geomorphology. This paper investigates the evolution of faceted topographies at normal faults and their interaction with a river network theoretically and numerically. As a main result beyond several relations for the geometry of facets, the horizontal displacement associated with normal faults is crucial for the dissection of initially polygonal facets into triangular facets bounded by almost parallel rivers.
Stefan Hergarten
Earth Surf. Dynam., 12, 1193–1203, https://doi.org/10.5194/esurf-12-1193-2024, https://doi.org/10.5194/esurf-12-1193-2024, 2024
Short summary
Short summary
Toma hills are relatively isolated hills found in the deposits of rock avalanches, and their origin is still enigmatic. This paper presents the results of numerical simulations based on a modified version of a friction law that was originally introduced for snow avalanches. The model produces more or less isolated hills (which look much like toma hills) on the valley floor. The results provide, perhaps, the first explanation of the occurrence of toma hills based on a numerical model.
Stefan Hergarten
Earth Surf. Dynam., 12, 219–229, https://doi.org/10.5194/esurf-12-219-2024, https://doi.org/10.5194/esurf-12-219-2024, 2024
Short summary
Short summary
Large landslides turn into an avalanche-like mode of flow at high velocities, which allows for a much longer runout than predicted for a sliding solid body. In this study, the Voellmy rheology widely used in models for hazard assessment is reinterpreted and extended. The new approach predicts the increase in runout length with volume observed in nature quite well and may thus be a major step towards a more consistent modeling of rock avalanches and improved hazard assessment.
Stefan Hergarten
Nat. Hazards Earth Syst. Sci., 23, 3051–3063, https://doi.org/10.5194/nhess-23-3051-2023, https://doi.org/10.5194/nhess-23-3051-2023, 2023
Short summary
Short summary
Rockslides are a major hazard in mountainous regions. In formerly glaciated regions, the disposition mainly arises from oversteepened topography and decreases through time. However, little is known about this decrease and thus about the present-day hazard of huge, potentially catastrophic rockslides. This paper presents a new theoretical framework that explains the decrease in maximum rockslide size through time and predicts the present-day frequency of large rockslides for the European Alps.
Jannick Strüven and Stefan Hergarten
Hydrol. Earth Syst. Sci., 27, 3041–3058, https://doi.org/10.5194/hess-27-3041-2023, https://doi.org/10.5194/hess-27-3041-2023, 2023
Short summary
Short summary
This study uses dendritic flow patterns to analyze the recession behavior of aquifer springs. The results show that the long-term recession becomes slower for large catchments. After a short recharge event, however, the short-term behavior differs strongly from the exponential recession that would be expected from a linear reservoir. The exponential component still accounts for more than 80 % of the total discharge, much more than typically assumed for karst aquifers.
Stefan Hergarten and Alexa Pietrek
Earth Surf. Dynam., 11, 741–755, https://doi.org/10.5194/esurf-11-741-2023, https://doi.org/10.5194/esurf-11-741-2023, 2023
Short summary
Short summary
The transition from hillslopes to channelized flow is typically attributed to a threshold catchment size in landform evolution models. Here we propose an alternative concept directly based on topography. Using this concept, channels and hillslopes self-organize, whereby the catchment size of the channel heads varies over some range. Our numerical results suggest that this concept works better than the established idea of a strict threshold catchment size.
Moritz Liebl, Jörg Robl, Stefan Hergarten, David Lundbek Egholm, and Kurt Stüwe
Geosci. Model Dev., 16, 1315–1343, https://doi.org/10.5194/gmd-16-1315-2023, https://doi.org/10.5194/gmd-16-1315-2023, 2023
Short summary
Short summary
In this study, we benchmark a topography-based model for glacier erosion (OpenLEM) with a well-established process-based model (iSOSIA). Our experiments show that large-scale erosion patterns and particularly the transformation of valley length geometry from fluvial to glacial conditions are very similar in both models. This finding enables the application of OpenLEM to study the influence of climate and tectonics on glaciated mountains with reasonable computational effort on standard PCs.
Stefan Hergarten
Earth Surf. Dynam., 10, 671–686, https://doi.org/10.5194/esurf-10-671-2022, https://doi.org/10.5194/esurf-10-671-2022, 2022
Short summary
Short summary
Many studies on modeling landform evolution have focused on mountain ranges, while large parts of Earth's surface are quite flat and alluvial plains have been preferred locations for human settlements. Conducting large-scale simulations of fluvial erosion and sediment transport, this study reveals that rivers in a tectonically inactive foreland are much more dynamic than rivers in a mountain range; the local redistribution of deposits in the foreland is the main driver of the dynamics.
Stefan Hergarten and Jörg Robl
Geosci. Model Dev., 15, 2063–2084, https://doi.org/10.5194/gmd-15-2063-2022, https://doi.org/10.5194/gmd-15-2063-2022, 2022
Short summary
Short summary
The influence of climate on landform evolution has attracted great interest over the past decades. This paper presents a simple model for simulating the influence of topography on precipitation and the decrease in precipitation over large continental areas. The approach can be included in numerical models of large-scale landform evolution and causes only a moderate increase in the numerical complexity. It opens a door to investigating feedbacks between climate and landform evolution.
Stefan Hergarten
Earth Surf. Dynam., 9, 937–952, https://doi.org/10.5194/esurf-9-937-2021, https://doi.org/10.5194/esurf-9-937-2021, 2021
Short summary
Short summary
This paper presents a new approach to modeling glacial erosion on large scales. The formalism is similar to large-scale models of fluvial erosion, so glacial and fluvial processes can be easily combined. The model is simpler and numerically less demanding than established models based on a more detailed description of the ice flux. The numerical implementation almost achieves the efficiency of purely fluvial models, so that simulations over millions of years can be performed on standard PCs.
Anne-Laure Argentin, Jörg Robl, Günther Prasicek, Stefan Hergarten, Daniel Hölbling, Lorena Abad, and Zahra Dabiri
Nat. Hazards Earth Syst. Sci., 21, 1615–1637, https://doi.org/10.5194/nhess-21-1615-2021, https://doi.org/10.5194/nhess-21-1615-2021, 2021
Short summary
Short summary
This study relies on topography to simulate the origin and displacement of potentially river-blocking landslides. It highlights a continuous range of simulated landslide dams that go unnoticed in the field due to their small scale. The computation results show that landslide-dammed lake volume can be estimated from upstream drainage area and landslide volume, thus enabling an efficient hazard assessment of possible landslide-dammed lake volume – and flooding magnitude in case of dam failure.
Stefan Hergarten
Earth Surf. Dynam., 8, 841–854, https://doi.org/10.5194/esurf-8-841-2020, https://doi.org/10.5194/esurf-8-841-2020, 2020
Short summary
Short summary
Many contemporary models of large-scale fluvial erosion focus on the detachment-limited regime where all material entrained by the river is immediately excavated. This limitation facilitates the comparison with real river profiles and strongly reduces the numerical complexity. Here a simple formulation for the opposite case, transport-limited erosion, and a new numerical scheme that achieves almost the same numerical efficiency as detachment-limited models are presented.
Cited articles
Aaron, J. and Hungr, O.: Dynamic simulation of the motion of partially-coherent landslides, Engin. Geol., 205, 1–11, https://doi.org/10.1016/j.enggeo.2016.02.006, 2016. a
Bartelt, P. and Buser, O.: Frictional relaxation in avalanches, Ann. Glaciol., 51, 98–104, https://doi.org/10.3189/172756410791386607, 2010. a
Bouchut, F. and Westdickenberg, M.: Gravity driven shallow water models for arbitrary topography, Commun. Math. Sci., 2, 359–389, https://doi.org/10.4310/CMS.2004.v2.n3.a2, 2004. a, b
Buser, O. and Bartelt, P.: Production and decay of random kinetic energy in granular snow avalanches, J. Glaciol., 55, 3–12, https://doi.org/10.3189/002214309788608859, 2009. a
Christen, M., Kowalski, J., and Bartelt, P.: RAMMS: Numerical simulation of dense snow avalanches in three-dimensional terrain, Cold Reg. Sci. Technol., 63, 1–14, https://doi.org/10.1016/j.coldregions.2010.04.005, 2010. a
Denlinger, R. P. and Iverson, R. M.: Granular avalanches across irregular three-dimensional terrain: 1. Theory and computation, J. Geophys. Res.-Earth, 109, F01014, https://doi.org/10.1029/2003JF000085, 2004. a
Dufresne, A., Bösmeier, A., and Prager, C.: Sedimentology of rock avalanche deposits – Case study and review, Earth Sci. Rev., 163, 234–259, https://doi.org/10.1016/j.earscirev.2016.10.002, 2016. a
Fischer, J.-T., Kowalski, J., and Pudasaini, S. P.: Topographic curvature effects in applied avalanche modeling, Cold Reg. Sci. Technol., 74–75, 21–30, https://doi.org/10.1016/j.coldregions.2012.01.005, 2012. a, b
Hergarten, S.: MinVoellmy [software], http://hergarten.at/minvoellmy, last access: 8 December 2023a. a
Hergarten, S.: MinVoellmy v1: a lightweight model for simulating rapid mass movements, Zenodo [code and data set], https://doi.org/10.5281/zenodo.10304665, 2023b. a
Hergarten, S. and Robl, J.: Modelling rapid mass movements using the shallow water equations in Cartesian coordinates, Nat. Hazards Earth Syst. Sci., 15, 671–685, https://doi.org/10.5194/nhess-15-671-2015, 2015. a, b
Hutter, K., Wang, Y., and Pudasaini, S. P.: The Savage–Hutter avalanche model: how far can it be pushed?, Philos. T. Roy. Soc. A, 363, 1507–1528, https://doi.org/10.1098/rsta.2005.1594, 2005. a
Larsen, I. J., Montgomery, D. R., and Korup, O.: Landslide erosion controlled by hillslope material, Nat. Geosci., 3, 247–251, https://doi.org/10.1038/ngeo776, 2010. a
Legros, F.: The mobility of long-runout landslides, Engin. Geol., 63, 301–331, https://doi.org/10.1016/S0013-7952(01)00090-4, 2002. a, b, c
McDougall, S.: A new continuum dynamic model for the analysis of extremely rapid landslide motion across complex 3D terrain, PhD thesis, University of British Columbia, https://doi.org/10.14288/1.0052928, 2006. a
McDougall, S.: 2014 Canadian Geotechnical Colloquium: landslide runout analysis – current practice and challenges, Can. Geotech. J., 54, 605–620, https://doi.org/10.1139/cgj-2016-0104, 2017. a
Mergili, M., Fischer, J.-T., Krenn, J., and Pudasaini, S. P.: r.avaflow v1, an advanced open-source computational framework for the propagation and interaction of two-phase mass flows, Geosci. Model Dev., 10, 553–569, https://doi.org/10.5194/gmd-10-553-2017, 2017. a, b
Nessyahu, H. and Tadmor, E.: Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys., 87, 408–463, https://doi.org/10.1016/0021-9991(90)90260-8, 1990. a
Pietrek, A., Hergarten, S., and Kenkmann, T.: Morphometric characterization of longitudinal striae on Martian landslides and impact ejecta blankets and implications for the formation mechanism, J. Geophys. Res.-Planet., 125, e2019JE006255, https://doi.org/10.1029/2019JE006255, 2020. a
Pudasaini, S. P. and Mergili, M.: A multi-phase mass flow model, J. Geophys. Res.-Earth, 124, 2920–2942, https://doi.org/10.1029/2019JF005204, 2019. a
Rauter, M. and Tuković, Ž.: A finite area scheme for shallow granular flows on three-dimensional surfaces, Comput. Fluids, 166, 184–199, https://doi.org/10.1016/j.compfluid.2018.02.017, 2018. a, b
Salm, B.: Flow, flow transition and runout distances of flowing avalanches, Ann. Glaciol., 18, 221–226, https://doi.org/10.3189/S0260305500011551, 1993. a
Savage, S. B. and Hutter, K.: The motion of a finite mass of granular material down a rough incline, J. Fluid Mech., 199, 177–215, https://doi.org/10.1017/S0022112089000340, 1989. a, b, c, d
Scheidegger, A. E.: On the prediction of the reach and velocity of catastrophic landslides, Rock Mech., 5, 231–236, https://doi.org/10.1007/BF01301796, 1973. a
Shreve, R. L.: Sherman Landslide, Alaska, Science, 154, 1639–1642, https://doi.org/10.1126/science.154.3757.1639, 1966. a
Tonnel, M., Wirbel, A., Oesterle, F., and Fischer, J.-T.: AvaFrame com1DFA (v1.3): a thickness-integrated computational avalanche module – theory, numerics, and testing, Geosci. Model Dev., 16, 7013–7035, https://doi.org/10.5194/gmd-16-7013-2023, 2023. a
Voellmy, A.: Über die Zerstörungskraft von Lawinen, Schweiz. Bauzeitung, 73, 212–217, https://doi.org/10.5169/seals-61891, 1955. a
Vreugdenhil, C. B.: Numerical Methods for Shallow-Water Flow, Springer, Berlin, Heidelberg, New York, https://doi.org/10.1007/978-94-015-8354-1, 1994. a, b
Short summary
The Voellmy rheology has been widely used for simulating snow and rock avalanches. Recently, a modified version of this rheology was proposed, which turned out to be able to predict the observed long runout of large rock avalanches theoretically. The software MinVoellmy presented here is the first numerical implementation of the modified rheology. It consists of MATLAB and Python classes, where simplicity and parsimony were the design goals.
The Voellmy rheology has been widely used for simulating snow and rock avalanches. Recently, a...