Error modeling of DEMs from topographic surveys of rivers using fuzzy inference systems

Abstract

Digital elevation models (DEMs) have become common place in the earth sciences as a tool to characterize surface topography and set modeling boundary conditions. All DEMs have a degree of inherent error that is propagated to subsequent models and analyses. While previous research has shown that DEM error is spatially variable it is often represented as spatially uniform for analytical simplicity. Fuzzy inference systems (FIS) offer a tractable approach for modeling spatially variable DEM error, including flexibility in the number of inputs and calibration of outputs based on survey technique and modeling environment. We compare three FIS error models for DEMs derived from TS surveys of wadeable streams and test them at 34 sites in the Columbia River basin. The models differ in complexity regarding the number/type of inputs and degree of site-specific parameterization. A 2-input FIS uses inputs derived from the topographic point cloud (slope, point density). A 4-input FIS adds interpolation error and 3-D point quality. The 5-input FIS adds bed-surface roughness estimates. Both the 4 and 5-input FIS model output were parameterized to site-specific values. In the wetted channel we found (i) the 5-input FIS resulted in lower mean δz due to including roughness, and (ii) the 4 and 5-input FIS resulted in a higher standard deviation and maximum δz due to the inclusion of site-specific bank heights. All three FIS gave plausible estimates of DEM error, with the two more complicated models offering an improvement in the ability to detect spatially localized areas of DEM uncertainty.