A Probabilistic Approach to Spatially Distributed Landslide Hazard Modeling William C. Haneberg Copyright ©2003 William C. Haneberg All rights reserved

What is a probabilistic model? Probabilistic: Inexact cause- effect relationship described by laws of probability. (If X then probably Y) Rational: Based on underlying physics (process- based).

Why use probabilistic models? Any model is subject to:  Model uncertainty.  Parameter variability.  Parameter uncertainty. Probabilistic models:  Naturally incorporate parameter variability and uncertainty into their results.  Reduce or eliminate the need for multiple scenarios (e.g., wet vs. dry or best-case vs. worst- case).

The basic approach Probabilistic input yields probabilistic output

Some probabilistic results Two different methods:  Numerical Monte Carlo (USFS LISA)  Analytical first-order, second-moment approximation (FOSM) Probability of sliding  Prob[FS ≤ 1] Nonparametric slope reliability index  (Mean[FS] -1) / SD[FS].

DEM uncertainty A factor in spatially distributed models DEM elevation errors affect calculated slope angles and FS values. Use a FOSM approximation to calculate slope angle variance from published RMS elevation error. DEM elevation errors are likely to be spatially correlated.  Future research topic?

Wheeling, OH-WV quadrangle Ohio River valley 1 m/yr precipitation Deciduous hardwood forests 200 m relief Flat lying Pennsylvanian-Permian sedimentary rocks of the Appalachian Plateau  Monongahela, Dunkard Gr. Many colluvial landslides, especially late winter and spring.

Input for Wheeling example 11 ≤  ≤ 36° 19 ≤  m ≤ 20 kN/m 3 19 ≤  sat ≤ 20 kN/m 3 0 ≤ H w ≤ 1 c s = 0 (residual strength) c r = q T = 0 D unspecified Uniform distributions Slope angle means and variances from DEM  68 x 101 grid of elevations

Wheeling results DEM topography

Wheeling results DEM topography Mean slope angle

Wheeling results DEM topography Mean slope angle Slope variance

Wheeling results DEM topography Mean slope angle Slope variance Mean FS

Wheeling results DEM topography Mean slope angle Slope variance Mean FS Log variance FS

Wheeling results DEM topography Mean slope angle Slope variance Mean FS Log variance FS Reliability index

Wheeling results DEM topography Mean slope angle Slope variance Mean FS Log variance FS Reliability index Prob[FS ≤ 1]

Model vs. map correspondence Threshold Prob{FS ≤ 1} = 0.5 Dormant, Susceptible, and Cove assumed unstable

Do hazard map units have distinct probability distributions? No Slide and Active map units have distinct distributions. Results for other units are equivocal, but generally have lower probabilities than the Active unit. Why?

Is it possible to do better? Perhaps not if models are compared to maps made by humans. Correspondence at least as good as that reported for landslide maps prepared by different geologists.  21 to 65% between pairs of maps (Ardizzone et al., 2002; Wills and McCrink, 2002).  20% among three maps (Ardizzone et al., 2002).

Multi-component hazard assessment How can we use potentially conflicting yet valuable subjective information? Choice of hazard assessment methods is not an “either…or” proposition. Best approaches combine all available information into a useful format. A job for fuzzy logic?

Summary Probabilistic methods allow uncertainty and variability to be incorporated into model results.

Summary Probabilistic methods allow uncertainty and variability to be incorporated into model results. FOSM approximations are well suited for spatially distributed applications and produce good results for symmetric input distributions.

Summary Probabilistic methods allow uncertainty and variability to be incorporated into model results. FOSM approximations are well suited for spatially distributed applications and produce good results for symmetric input distributions. FOSM model accounts for high percentage of active and stable ground in Wheeling example.

Summary Probabilistic methods allow uncertainty and variability to be incorporated into model results. FOSM approximations are well suited for spatially distributed applications and produce good results for symmetric input distributions. FOSM model accounts for high percentage of active and stable ground in Wheeling example. “Dormant” and “susceptible” map units are ambiguous.

Summary Probabilistic methods allow uncertainty and variability to be incorporated into model results. FOSM approximations are well suited for spatially distributed applications and produce good results for symmetric input distributions. FOSM model accounts for high percentage of active and stable ground in Wheeling example. “Dormant” and “susceptible” map units are ambiguous. The best hazard assessments combine all available information into a useful format.