Quantifying Earth's Topography: Steeper and Larger Than Projected in Digital Terrain Models

Abstract

Grid- or pixel-based models, used across various scientific disciplines from microscopic to planetary scales, contain an unquantified error that bias our interpretation of the data. The error is produced by projecting 3D data onto a 2D grid. For Digital Terrain Models (DTMs) the projection error affects all slope-dependent topographic metrics, like surface area or slope angle. Due to the proportionality of the error to the cosine of the slope, we can correct for it. We quantify the error and test the correction using synthetic landscapes for which we have analytical solutions of their metrics. Application to real-world landscapes in California, reveal the systematic underestimation of surface area by up to a third, and mean slope angles by up to 10° in steep topography in current DTMs. Correcting projection errors allow for true estimates of surface areas and slope distributions enabling physics-based models of surface processes at any spatial scale.