Probability models for estimation of number and costs of landslides

Abstract

The objective of this report is to describe the development of probability models for estimation of the number and costs of landslides during a specified time. Important philosophical ideas about natural processes and probability models are presented first. Then two probability models for the number of landslides that occur during a specified time are investigated: a continuous-time model (Poisson model) and a discrete-time model (binomial model). Estimation theory is developed for the estimation of the parameters of both of the models. The exceedance probability of one or more landslides during a specified time is formulated for both models. The estimation theory and probability formulation of the Poisson model are applied to the future occurrence of landslides in Seattle, Washington, using historical data from 1909 to 1997. Theoretical and numerical comparisons between the Poisson and binomial models are conducted that show the binomial model is an approximation to the Poisson model. An economic probability model is developed as an addition to the Poisson model for the estimation of the total damage from future landslides in terms of economic loss as costs in dollars. For illustrative purposes the economic probability model is applied to damaging landslides caused by El Nino rainstorms within the winter season 1997-98 in the San Francisco Bay region, California. Philosophy of Probability Models Natural Processes Important philosophical ideas about natural processes: Determinism or the law of cause and effect is the doctrine that all events in the universe are deterministic: every event has a cause. At the scale of geologic and atmospheric hazards (e.g., landslides, earthquakes, floods, tsunamis, volcanoes, and storms), nature is deterministic: every hazardous event has a cause.

Analysis of a landslide multi-date inventory in a complex mountain landscape: the Ubaye valley case study

“…A simple approach is therefore used to estimate the temporal probability of landslide reactivation by calculating how many times a portion of the territory is affected by landslides for a given period of time. The exceedance probability of having one or more landslides in each grid-cell (250 × 250 m) is computed by (i) ascertaining the mean recurrence interval of landslides in each mapping unit (from 1956 to 2009), (ii) assuming that the rate of slope failures remains the same for the future, and (iii) using a Poisson probability model (Crovelli, 2000;Guzzetti et al, 2003Guzzetti et al, , 2005. The landslide recurrence is calculated per grid-cell on the basis of the observed rate of landslide occurrence for the period 1956-2009, knowing the interval of (re)-activations (e.g.…”

Epistemic uncertainties and natural hazard risk assessment. 1. A review of different natural hazard areas

“…The epistemic uncertainty is convolved into a question of what statistical distribution should be used and how uncertainty in the tail behaviour is estimated. Probabilistic models such as binomial model, Poisson model (Crovelli, 2000) and the power-law distribution (Hungr et al, 1999;Dussauge-Peisser et al, 2002) 25 have been suggested in the literature to estimate the frequency (or return period) of landslides of a given size.…”

Risk-based analysis of monitoring time intervals for landslide prevention

“…There have been studies using the temporal probability of landslide occurrence to generate hazard maps not only considering spatial probability that means the potential of slope terrain 25 failure (Lopez Saez et al, 2012;Tien Bui et al, 2013;Guzzetti et al, 2005). To present the probability of landslide occurrence, Crovelli (2000) used a Poisson distribution model as below, which is frequently adopted to demonstrate random events in continuous time in natural environments. The probability of n landslides occurring during time t is:…”

“…To denote the probability of landslide occurrence, the concept of reliability is used to derive the formula for the probability 30 of landslide occurrence in this study, and its outcome is the same as the equation expressed by (Crovelli, 2000) based on a Poisson distribution model that is frequently employed to demonstrate the random events of natural hazards on a continuous timeline. The monitoring time interval is calculated quantitatively to reduce the landslide risk by adopting the concept of timeNat.…”