EFFECTS OF DIGITAL ELEVATION MODEL ERRORS ON SLOPE ANGLE, STATIC FACTOR OF SAFETY, AND NEWMARK ACCELERATION UNCERTAINTY IN GIS-STYLE LANDSLIDE HAZARD MODELING

Spatially distributed models of shallow landslides triggered by earthquakes or rainstorms depend upon grids of slope angles that are often calculated without considering digital elevation model (DEM) errors and their effects on derivative values such as the static factor of safety and Newmark critical acceleration. Preliminary analysis of nearly 1700 GPS measurements from an 18 km² portion of Seattle shows that elevation errors in a USGS 10 m DEM have a multi-scale spatial correlation structure that may be partly controlled by topography over distances of hundreds to thousands of meters. The spatial correlation structure of elevation error over distances relevant to the calculation of slope angles from DEMs, however, appears to be independent of topography. The short-range component of elevation error relevant to slope angle calculations has a variogram range of about 50 m and a sill of about 2 m², with a value of about 1.6 m² for points located 20 m apart. Monte Carlo simulations of slope angle calculations using this amount of elevation error show that a DEM-derived slope angle of 20° calculated by assuming no elevation error may in fact represent a normally distributed population of possible slope angles ranging over 8 ≤ β ≤ 32° (mean=20.4° and s.d.=±4.4°). Further assuming that the slope is dry and cohesionless with φ=30°, simulated static factors of safety range over 0.92 ≤ FS ≤ 4.25 (compared to an error-free estimate of 1.58) with a nearly lognormal distribution. Newmark accelerations are nearly normally distributed and range over 0 ≤ a_c ≤ 0.44 g (compared to an error-free estimate of 0.2 g). A first-order analytical approximation shows that the effect of elevation errors on calculated slope angles is inversely proportional to slope if elevation errors are not strongly correlated with slope angles. Failure to consider elevation errors can therefore lead to considerable uncertainty in GIS-style slope stability assessments based on DEM-derived slope angles, which may be amplified by the common practice of calibrating models by adjusting geotechnical variables while ignoring slope angle estimates.

This research was supported by USGS NEHRP FY 2004 award 04HQGR0035.