Uncertainty Analysis of Digital Elevation Models by Spatial Inference From Stable Terrain

Abstract

The monitoring of Earth’s and planetary surface elevations at larger and finer scales is rapidly progressing through the increasing availability and resolution of digital elevation models (DEMs). Surface elevation observations are being used across an expanding range of fields to study topographical attributes and their changes over time, notably in glaciology, hydrology, volcanology, seismology, forestry and geomorphology. However, DEMs frequently contain large-scale instrument noise and varying vertical precision that lead to complex patterns of errors. Here, we present a validated statistical workflow to estimate, model, and propagate uncertainties in DEMs. We review the state-of-the-art of DEM accuracy and precision analyses, and define a conceptual framework to consistently address those. We show how to characterize DEM precision by quantifying the heteroscedasticity of elevation measurements, i.e. varying vertical precision with terrain- or sensor-dependent variables, and the spatial correlation of errors that can occur across multiple spatial scales. With the increasing availability of high-precision observations, our workflow based on independent elevation data acquired on stable terrain can be applied almost anywhere on Earth. We illustrate how to propagate uncertainties for both pixel-scale and spatial elevation derivatives, using terrain slope and glacier volume changes as examples. We find that uncertainties in DEMs are largely underestimated in the literature, and advocate that new metrics of DEM precision are essential to ensure the reliability of future Earth and planetary surface elevation assessments.