Accounting for uncertainty in DEMs from repeat topographic surveys: improved sediment budgets

Abstract Repeat topographic surveys are increasingly becoming more affordable, and possible at higher spatial resolutions and over greater spatial extents. Digital elevation models (DEMs) built from such surveys can be used to produce DEM of Difference (DoD) maps and estimate the net change in storage terms for morphological sediment budgets. While these products are extremely useful for monitoring and geomorphic interpretation, data and model uncertainties render them prone to misinterpretation. Two new methods are presented, which allow for more robust and spatially variable estimation of DEM uncertainties and propagate these forward to evaluate the consequences for estimates of geomorphic change. The first relies on a fuzzy inference system to estimate the spatial variability of elevation uncertainty in individual DEMs while the second approach modifies this estimate on the basis of the spatial coherence of erosion and deposition units. Both techniques allow for probabilistic representation of uncertainty on a cell‐by‐cell basis and thresholding of the sediment budget at a user‐specified confidence interval. The application of these new techniques is illustrated with 5 years of high resolution survey data from a 1 km long braided reach of the River Feshie in the Highlands of Scotland. The reach was found to be consistently degradational, with between 570 and 1970 m 3 of net erosion per annum, despite the fact that spatially, deposition covered more surface area than erosion. In the two wetter periods with extensive braid‐plain inundation, the uncertainty analysis thresholded at a 95% confidence interval resulted in a larger percentage (57% for 2004–2005 and 59% for 2006–2007) of volumetric change being excluded from the budget than the drier years (24% for 2003–2004 and 31% for 2005–2006). For these data, the new uncertainty analysis is generally more conservative volumetrically than a standard spatially‐uniform minimum level of detection analysis, but also produces more plausible and physically meaningful results. The tools are packaged in a wizard‐driven Matlab software application available for download with this paper, and can be calibrated and extended for application to any topographic point cloud (x,y,z). Copyright © 2009 John Wiley & Sons, Ltd.