Scaling properties of rainfall induced landslides predicted by a physically based model

Abstract Natural landslides exhibit scaling properties revealed by power law relationships. These relationships include the frequency of the size (e.g., area, volume) of the landslides, and the rainfall conditions responsible for slope failures in a region. Reasons for the scaling behavior of landslides are poorly known. We investigate the possibility of using the Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability analysis code (TRIGRS), a consolidated, physically-based, numerical model that describes the stability/instability conditions of natural slopes forced by rainfall, to determine the frequency statistics of the area of the unstable slopes and the rainfall intensity ( I )–duration ( D ) conditions that result in landslides in a region. We apply TRIGRS in a portion of the Upper Tiber River Basin, Central Italy. The spatially distributed model predicts the stability/instability conditions of individual grid cells, given the local terrain and rainfall conditions. We run TRIGRS using multiple, synthetic rainfall histories, and we compare the modeling results with empirical evidences of the area of landslides and of the rainfall conditions that have caused landslides in the study area. Our findings revealed that TRIGRS is capable of reproducing the frequency of the size of the patches of terrain predicted as unstable by the model, which match the frequency size statistics of landslides in the study area, and the mean rainfall D ,  I conditions that result in unstable slopes in the study area, which match rainfall I  −  D thresholds for possible landslide occurrence. Our results are a step towards understanding the mechanisms that give rise to landslide scaling properties.

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

[2]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[3]  Rex L. Baum,et al.  Rainfall characteristics for shallow landsliding in Seattle, Washington, USA , 2006 .

[4]  Pietro Aleotti,et al.  A warning system for rainfall-induced shallow failures , 2004 .

[5]  Constantino Tsallis,et al.  Nonextensive statistical mechanics: Applications to high energy physics , 2011 .

[6]  F. Guzzetti,et al.  Improving predictive power of physically based rainfall-induced shallow landslide models: a probabilistic approach , 2013, 1305.4803.

[7]  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..

[8]  P. Reichenbach,et al.  GIS techniques and statistical models in evaluating landslide hazard , 1991 .

[9]  James C. Bathurst,et al.  Physically based modelling of shallow landslide sediment yield at a catchment scale , 1998 .

[10]  M. Rossi,et al.  Landslide volumes and landslide mobilization rates in Umbria, central Italy , 2009 .

[11]  W. Z. Savage,et al.  TRIGRS - A Fortran Program for Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability Analysis, Version 2.0 , 2002 .

[12]  Olivier Maquaire,et al.  Forecasting the behaviour of complex landslides with a spatially distributed hydrological model , 2003 .

[13]  D. Benson,et al.  Particle tracking and the diffusion‐reaction equation , 2013 .

[14]  Peter Lehmann,et al.  Rainfall‐triggered shallow landslides at catchment scale: Threshold mechanics‐based modeling for abruptness and localization , 2013 .

[15]  R. Rigon,et al.  GEOtop: A Distributed Hydrological Model with Coupled Water and Energy Budgets , 2006 .

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

[17]  L. Telesca,et al.  Statistical physics of landslides: New paradigm , 2011 .

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

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

[21]  A. F. Chleborad,et al.  Preliminary evaluation of a precipitation threshold for anticipating the occurrence of landslides in the Seattle, Washington, area , 2003 .

[22]  Numerical modeling of rainfall thresholds for shallow landsliding in the Seattle, Washington, area , 2008 .

[23]  Negative correlation between frequency-magnitude power-law exponent and Hurst coefficient in the Long-Range Connective Sandpile model for earthquakes and for real seismicity , 2012 .

[24]  N. Caine,et al.  The Rainfall Intensity - Duration Control of Shallow Landslides and Debris Flows , 1980 .

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

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

[27]  Characteristic scales in landslide modelling , 2009 .

[28]  Rex L. Baum,et al.  Modeling rainfall conditions for shallow landsliding in Seattle, Washington , 2008 .

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

[30]  Fausto Guzzetti,et al.  Rainfall induced landslides in December 2004 in south-western Umbria, central Italy: types, extent, damage and risk assessment , 2006 .

[31]  M. Rossi,et al.  The rainfall intensity–duration control of shallow landslides and debris flows: an update , 2008 .

[32]  D. Montgomery,et al.  Landslide erosion controlled by hillslope material , 2010 .

[33]  Giovanni B. Crosta,et al.  Distributed modelling of shallow landslides triggered by intense rainfall , 2003 .

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

[35]  M. Newman.  Power laws, Pareto distributions and Zipf's law , 2005 .

[36]  Tang,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

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

[38]  P. Reichenbach,et al.  Landslide hazard evaluation: a review of current techniques and their application in a multi-scale study, Central Italy , 1999 .

[39]  Fausto Guzzetti,et al.  Improving predictive power of physically based rainfall-induced shallow landslide models: a probabilistic approach , 2014 .

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

[41]  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.

[42]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

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

[44]  L. Milano,et al.  Finite driving rate and anisotropy effects in landslide modeling. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  John L. Innes,et al.  Debris flows , 1983 .

[46]  S. Hergarten.  Self-Organized Criticality in Earth Systems , 2002 .

[47]  P. Reichenbach,et al.  Distribution of landslides in the Upper Tiber River basin, central Italy , 2008 .

[48]  Fausto Guzzetti,et al.  Rainfall thresholds for the possible occurrence of landslides in Italy , 2010 .

[49]  Yang Hong,et al.  Advances in landslide nowcasting: evaluation of a global and regional modeling approach , 2012, Environmental Earth Sciences.

[50]  L. A. Richards.  Capillary conduction of liquids through porous mediums , 1931 .

[51]  A prototype system to forecast rainfall induced landslides in Italy , 2009 .

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

[53]  Giovanni B. Crosta,et al.  A methodology for physically based rockfall hazard assessment , 2003 .

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

[55]  H. J. Neugebauer,et al.  Self‐organized criticality in a landslide model , 1998 .

[56]  G. Wieczorek,et al.  Effect of rainfall intensity and duration on debris flows in central Santa Cruz Mountains, California , 1987 .

[57]  Giacomo Bertoldi,et al.  Modelling the probability of occurrence of shallow landslides and channelized debris flows using GEOtop‐FS , 2008 .

[58]  D. Montgomery,et al.  A physically based model for the topographic control on shallow landsliding , 1994 .

[59]  M. Moser,et al.  Geotechnical aspects of soil slips in Alpine regions , 1983 .

[60]  C. Tsallis.  Nonextensive statistics: theoretical, experimental and computational evidences and connections , 1999, cond-mat/9903356.

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

[62]  S. Hergarten.  Topography‐based modeling of large rockfalls and application to hazard assessment , 2012 .

[63]  David G. Tarboton,et al.  The SINMAP Approach to Terrain Stability Mapping , 1998 .

[64]  A. Klar,et al.  Analytical and observational relations between landslide volume and surface area , 2011 .