The role of topography in the scaling distribution of landslide areas: A cellular automata modeling approach

Abstract Power law scaling has been widely observed in the frequency distribution of landslide sizes. The exponent of the power-law characterizes the probability of landslide magnitudes and it thus represents an important parameter for hazard assessment. The reason for the universal scaling behavior of landslides is still debated and the role of topography has been explored in terms of possible explanation for this type of behavior. We built a simple cellular automata model to investigate this issue, as well as the relationships between the scaling properties of landslide areas and the changes suffered by the topographic surface affected by landslides. The dynamics of the model is controlled by a temporal rate of weakening, which drives the system to instability, and by topography, which defines both the quantity of the displaced mass and the direction of the movement. Results show that the model is capable of reproducing the scaling behavior of real landslide areas and suggest that topography is a good candidate to explain their scale-invariance. In the model, the values of the scaling exponents depend on how fast the system is driven to instability; they are less sensitive to the duration of the driving rate, thus suggesting that the probability of landslide areas could depend on the intensity of the triggering mechanism rather than on its duration, and on the topographic setting of the area. Topography preserves the information concerning the statistical distribution of areas of landslides caused by a driving mechanism of given intensity and duration.

[1]  Fawzi Doumaz,et al.  Release of a 10-m-resolution DEM for the Italian territory: Comparison with global-coverage DEMs and anaglyph-mode exploration via the web , 2012, Comput. Geosci..

[2]  Christensen,et al.  Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes. , 1992, Physical review letters.

[3]  Richard M. Iverson,et al.  Landslide triggering by rain infiltration , 2000 .

[4]  F. Guzzetti,et al.  Scaling properties of rainfall induced landslides predicted by a physically based model , 2013, 1306.1529.

[5]  C. Goltz,et al.  Multifractal and entropic properties of landslides in Japan , 1996 .

[6]  Steven J Franke,et al.  Critical level interaction of a gravity wave with background winds driven by a large-scale wave perturbation , 2009 .

[7]  M. Church,et al.  Sediment transfer by shallow landsliding in the Queen Charlotte Islands, British Columbia , 2002 .

[8]  M. Rossi,et al.  Rainfall thresholds for the initiation of landslides in central and southern Europe , 2007 .

[10]  S. Ouchi.  Effects of uplift on the development of experimental erosion landform generated by artificial rainfall , 2011 .

[11]  F. Guzzetti,et al.  Landslide rupture and the probability distribution of mobilized debris volumes , 2009 .

[12]  L. Melelli,et al.  Scale-Invariance in the Spatial Development of Landslides in the Umbria Region (Italy) , 2015, Pure and Applied Geophysics.

[13]  Jean-Louis Dessalles,et al.  Characterizing emergent phenomena (1): a critical review , 1995 .

[14]  L. Bjerrum.  PROGRESSIVE FAILURE IN SLOPES OF OVERCONSOLIDATED PLASTIC CLAY AND CLAY SHALES , 1967 .

[15]  David R. Montgomery,et al.  Topographic controls on erosion rates in tectonically active mountain ranges , 2002 .

[16]  Simone Tarquini,et al.  TINITALY/01: a new Triangular Irregular Network of Italy , 2007 .

[17]  O. Korup,et al.  The role of landslides in mountain range evolution. , 2010 .

[18]  Oded Katz,et al.  Controls on the size and geometry of landslides: Insights from discrete element numerical simulations , 2014 .

[19]  S. Wolfram,et al.  Two-dimensional cellular automata , 1985 .

[20]  S. Bonnet,et al.  Macroscale dynamics of experimental landscapes , 2006, Geological Society, London, Special Publications.

[21]  S. Pucci,et al.  Morphotectonics of the Upper Tiber Valley (Northern Apennines, Italy) through quantitative analysis of drainage and landforms , 2014, Rendiconti Lincei.

[22]  I. Moore,et al.  Digital terrain modelling: A review of hydrological, geomorphological, and biological applications , 1991 .

[23]  E. Aharonov,et al.  Landslides in vibrating sand box: What controls types of slope failure and frequency magnitude relations? , 2006 .

[24]  M. Eeckhaut,et al.  Characteristics of the size distribution of recent and historical landslides in a populated hilly region , 2007 .

[25]  S. Dadson,et al.  Effects of earthquake and cyclone sequencing on landsliding and fluvial sediment transfer in a mountain catchment , 2008 .

[26]  R. Guthrie,et al.  Magnitude and frequency of landslides triggered by a storm event, Loughborough Inlet, British Columbia , 2004 .

[27]  R. Guthrie,et al.  Exploring the magnitude–frequency distribution: a cellular automata model for landslides , 2008 .

[28]  D. Or,et al.  Hydromechanical triggering of landslides: From progressive local failures to mass release , 2012 .

[29]  D. Lague,et al.  Laboratory experiments simulating the geomorphic response to tectonic uplift , 2003 .

[30]  John J. Clague,et al.  Giant landslides, topography, and erosion , 2007 .

[31]  Efi Foufoula-Georgiou,et al.  Landscape reorganization under changing climatic forcing: Results from an experimental landscape , 2015 .

[32]  J. Pelletier.  Scale-invariance of soil moisture variability and its implications for the frequency-size distribution of landslides , 1997, physics/9705035.

[33]  Saro Lee,et al.  Statistical analysis of landslide susceptibility at Yongin, Korea , 2001 .

[34]  Andrea Taramelli,et al.  Detecting Alluvial Fans Using Quantitative Roughness Characterization and Fuzzy Logic Analysis , 2008, ICCSA.

[35]  Self-organized criticality in two-variable models , 2000 .

[36]  L. Ayalew,et al.  The application of GIS-based logistic regression for landslide susceptibility mapping in the Kakuda-Yahiko Mountains, Central Japan , 2005 .

[37]  P. Bak,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[38]  Fausto Guzzetti,et al.  Probability distributions of landslide volumes , 2009 .

[39]  Stéphane Bonnet,et al.  Landscape response to climate change: Insights from experimental modeling and implications for tectonic versus climatic uplift of topography , 2003 .

[40]  S. Pucci,et al.  Interaction between regional and local tectonic forcing along a complex Quaternary extensional basin: Upper Tiber Valley, Northern Apennines, Italy , 2014 .

[41]  M. Ellis,et al.  The emergence of topographic steady state in a perpetually dynamic self‐organized critical landscape , 2015 .

[42]  S. Ouchi.  Experimental landform development by rainfall erosion with uplift at various rates. , 2015 .

[43]  D. Turcotte,et al.  Landslide inventories and their statistical properties , 2004 .

[44]  Diana Salciarini,et al.  Spatially distributed rainfall thresholds for the initiation of shallow landslides , 2012, Natural Hazards.

[45]  Characteristic scales in landslide modelling , 2009 .

[46]  N. Hovius,et al.  The characterization of landslide size distributions , 2001 .

[47]  P. Reichenbach,et al.  Probabilistic landslide hazard assessment at the basin scale , 2005 .

[48]  O. Korup.  Effects of large deep-seated landslides on hillslope morphology, western Southern Alps, New Zealand , 2006 .

[49]  Oliver Korup,et al.  Distribution of landslides in southwest New Zealand , 2005 .

[50]  T. Oguchi,et al.  Rainfall conditions, typhoon frequency, and contemporary landslide erosion in Japan , 2014 .

[51]  S. Hergarten,et al.  Landslides, sandpiles, and self-organized criticality , 2003 .

[52]  W. Dietrich,et al.  A multidimensional stability model for predicting shallow landslide size and shape across landscapes , 2014, Journal of geophysical research. Earth surface.

[53]  Bruce D. Malamud,et al.  Power-law correlations of landslide areas in central Italy , 2001 .

[54]  P. Frattini,et al.  The role of material properties and landscape morphology on landslide size distributions , 2013 .

[55]  J. Morel,et al.  Landscape evolution models: A review of their fundamental equations , 2014 .

[56]  Fausto Guzzetti,et al.  Lithological and seasonal control on rainfall thresholds for the possible initiation of landslides in central Italy , 2012 .

[57]  Bruce D. Malamud,et al.  Self-Organized Criticality Applied to Natural Hazards , 1999 .

[58]  M. Church,et al.  Representing the landslide magnitude–frequency relation: Capilano River basin, British Columbia , 2004 .

[59]  Fausto Guzzetti,et al.  Self-organization, the cascade model, and natural hazards , 2002, Proceedings of the National Academy of Sciences of the United States of America.