Simulating debris flows through a hexagonal cellular automata model: SCIDDICA S<sub>3–hex</sub>

Abstract

Abstract. Cellular Automata (CA) represent a formal frame for dynamical systems, which evolve on the base of local interactions. Some types of landslide, such as debris flows, match well this requirement.The latest hexagonal release (S 3−hex ) of the deterministic model SCIDDICA, specifically developed for simulating debris flows, is described. For CA simulation purposes, landslides can be viewed as a dynamical system, subdivided into elementary parts, whose state evolves exclusively as a consequence of local interactions within a spatial and temporal discretum. Space is the world of the CA, here constituted by hexagonal cells. The attributes of each cell ("substates") describe physical characteristics. For computational reasons, the natural phenomenon is "decomposed" into a number of elementary processes, whose proper composition makes up the "transition function" of the CA. By simultaneously applying this function to all the cells, the evolution of the phenomenon can be simulated in terms of modifications of the substates.SCIDDICA S 3−hex exhibits a great flexibility in modelling debris flows. With respect to the previous releases of the model, the mechanism of progressive erosion of the soil cover has been added to the transition function. Considered substates are: altitude; thickness and energy of landslide debris; depth of erodable soil cover; debris outflows. Considered elementary processes are: mobilisation triggering and effect (T 1 ), debris outflows (I 1 ), update of landslide debris thickness and energy (I 2 ), and energy loss (T 2 ).Simulations of real debris flows, occurred in Campania (Southern Italy) in May 1998 (Sarno) and December 1999 (San Martino V.C. and Cervinara), have been performed for model calibration purposes; some examples of analysis are briefly described. Possible applications of the method are: risk mapping, also based on a statistical approach; evaluating the effects of mitigation actions (e.g. stream deviations, topographic alterations, channelling, embankments, bridges, etc.) on flow development.

The importance of entrainment and bulking on debris flow runout modeling: examples from the Swiss Alps

“…Debris flow entrainment modeling has been introduced into runout models using algorithms considering the properties of the debris flow (Crosta et al, 2003;D'Ambrosio et al, 2003;Medina et al, 2008). Another approach relies on user-specified erosion layer properties (Beguería et al, 2009;Hungr and McDougall, 2009;Hussin et al, 2012) where the user predefines the volume or depth of eroded sediment.…”

“…Physically based numerical models were developed to investigate runout distance and inundation patterns as well as flow heights and flow velocities (Crosta et al, 2003;D'Ambrosio et al, 2003;Medina et al, 2008;Hungr and McDougall, 2009;Christen et al, 2012). Only recently have researchers focused on better understanding the process by which debris flows entrain sediment from the bed of a torrent channel as part of the erosion process (e.g., Hungr et al, 2005;Mangeney et al, 2007;Berger et al, 2011;McCoy et al, 2010McCoy et al, , 2012McCoy et al, , 2013.…”

Debris-flow modeling at Meretschibach and Bondasca catchments, Switzerland: sensitivity testing of field-data-based entrainment model

“…Computational debris-flow runout models, which usually neglect entrainment, are often used to assess runout distance and pattern (Crosta et al, 2003;D'Ambrosio et al, 2003;Medina et al, 2008;Hungr and McDougall, 2009; and are therefore useful for hazard analysis where predictions of flow intensity (e.g., the spatial distribution of flow depth and velocity) are required (e.g., Scheuner et al, 2011). Because the debris-flow process has often been observed to cause significant entrainment of sediment, which can strongly influence the flow (e.g., Dietrich and Dunne, 1978;Suwa and Okuda, 1980;Gallino and Pierson, 1984;Hungr et al, 1984;Benda, 1990;Pierson et al, 1990;Meyer and Wells, 1997;Vallance and Scott, 1997;Berti et al, 1999;Cannon and Reneau, 2000;Fannin and Wise, 2001;May, 2002;Wang et al, 2003;Revellino et al, 2004;Scott et al, 2005;Godt and Coe, 2007;Breien et al, 2008;Gartner et al, 2008;Pastor et al, 2009;Guthrie et al, 2010;Procter et al, 2010;Berger et al, 2010aBerger et al, , b, 2011Schürch et al, 2011;Iverson et al, 2011;McCoy et al, 2012;Cascini et al, 2014;Tobler et al, 2014;Frank et al, 2015), including entrainment and bulking debris-flow runout modeling would be appropriate.…”

“…Because the debris-flow process has often been observed to cause significant entrainment of sediment, which can strongly influence the flow (e.g., Dietrich and Dunne, 1978;Suwa and Okuda, 1980;Gallino and Pierson, 1984;Hungr et al, 1984;Benda, 1990;Pierson et al, 1990;Meyer and Wells, 1997;Vallance and Scott, 1997;Berti et al, 1999;Cannon and Reneau, 2000;Fannin and Wise, 2001;May, 2002;Wang et al, 2003;Revellino et al, 2004;Scott et al, 2005;Godt and Coe, 2007;Breien et al, 2008;Gartner et al, 2008;Pastor et al, 2009;Guthrie et al, 2010;Procter et al, 2010;Berger et al, 2010aBerger et al, , b, 2011Schürch et al, 2011;Iverson et al, 2011;McCoy et al, 2012;Cascini et al, 2014;Tobler et al, 2014;Frank et al, 2015), including entrainment and bulking debris-flow runout modeling would be appropriate. Processed-based entrainment rates using algorithms which consider the material properties of the debrisflow bulk (Crosta et al, 2003;D'Ambrosio et al, 2003;Medina et al, 2008; as well as pre-specified entrainment rates which pre-define the absolute volume of eroded material (Beguería et al, 2009;Hungr and McDougall, 2009;Hussin et al, 2012) have been introduced in numerical runout models.…”

2-Dimensional Reversible Hexagonal Cellular Automata with Periodic Boundary

“…A remarkable application of the family of these CAs is presented by Truno [2] where a model is presented to simulate the evolution of forest res and Hernández Encinas et al [3] where they introduce a new mathematical model for predicting the spread of a re front in homogeneous and inhomogeneous environments. Also, in [4], debris ows are simulated and modeled by two-dimensional hexagonal cellular automata. These families of cellular automata are also applied to design discrete models of chemical reaction-diusion systems [5].…”