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Ninety years of historical landslide records were used as input to the Poisson and binomial probability models. Results from these models show that, for precipitation-triggered landslides, approximately 9 percent of the area of Seattle has annual exceedance probabilities of 1 percent or greater. Application of the Poisson model for estimating the future occurrence of individual landslides results in a worst-case scenario map, with a maximum annual exceedance probability of 25 percent on a hillslope near Duwamish Head in West Seattle. Application of the binomial model for estimating the future occurrence of a year with one or more landslides results in a map with a maximum annual exceedance probability of 17 percent (also near Duwamish Head). Slope and geology both play a role in localizing the occurrence of landslides in Seattle. A positive correlation exists between slope and mean exceedance probability, with probability tending to increase as slope increases. Sixty-four percent of all historical landslide locations are within 150 m (500 ft, horizontal distance) of the Esperance Sand/Lawton Clay contact, but within this zone, no positive or negative correlation exists between exceedance probability and distance to the contact.

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.