Effects of digital elevation model errors on spatially distributed seismic slope stability calculations; an example from Seattle, Washington

More than 1,600 centimeter-accurate differential GPS measurements show that elevation errors in a 10-m digital elevation model (DEM) covering an 18-km (super 2) portion of Seattle can have significant effects on calculated values of slope angle, static factor of safety, Newmark acceleration, and slope displacement. Declustered error data from the study area have a mean of -0.92 m and a standard deviation of + or -2.36 m, comparable to results reported by others. Conditional Gaussian simulation and normal score back-transformation were used to create 25 error realizations with the same statistical distribution and spatial correlation as the measured errors, and the error realizations were subsequently used to create elevation, slope angle, static factor of safety, Newmark acceleration, and displacement realizations. The maximum slope angle uncertainty magnitude decreases from more than 10 degrees to about 4 degrees as slope angle increases, but the minimum slope angle uncertainty varies between + or -1 degrees and + or -2 degrees regardless of slope angle. Typical slope angle standard deviations arising from DEM errors are in the range of + or -3 degrees to + or -4 degrees . The resulting uncertainties in calculated Newmark displacements as the consequence of a hypothetical large earthquake affecting the study area (Arias intensity of 4 m/s) are in most cases less than + or -3 cm, but some values are greater than + or -10 cm. If the acceptable maximum probability of misclassifying a potentially unstable area as stable is decreased from 50 to 5 percent, incorporation of displacement uncertainty into the calculus of hazard increases from 0.6 to 4.1 percent the portion of the study area that may be susceptible to landsliding as a result of the hypothetical earthquake.