A stochastic framework for estimating changes in storage from repeat DEMs

Many strategies for quantifying uncertainty in estimates of geomorphic change involve establishing a threshold, or minimum level of detection (minLoD), below which any topographic changes are discarded from the analysis. The general premise is that when there is a greater difference between two topographic surfaces one has greater confidence that the change observed reflects real geomorphic change, and is not just an artifact of survey techniques or grid interpolation. However, approaches that establish binary change detection thresholds can be problematic in landscapes where much of the topographic change is subtle, as is the case in many fluvial environments. Additionally, a necessary assumption of strategies that rely on establishing a minLoD is that erosion and deposition are normally distributed. Yet, deposition in rivers is often more diffuse than erosion, thus a relatively greater proportion of the total deposition may be excluded from the analysis. Here, we present an alternative approach for estimating change in storage volumes in light of quantified uncertainty estimates. Our strategy relies on a stochastic modeling framework to generate probability distribution functions of erosion and deposition for each cell in a DEM of difference. We demonstrate an application of our technique using a multi-year data set from a restored reach of the Provo River in northern Utah. We illustrate the advantages this technique provides in a setting where the topographic changes of interest are relatively subtle and accurately identifying these changes has significant management implications. Additionally, we demonstrate how the probabilistic approach provides a framework for more fully describing channel morphodynamics and may improve insights gained from morphologic sediment budgets.