The effect of correcting the projection error in Digital Terrain Models on Earth surface processes

Hiking up a steep mountain, in comparison to walking on a flat beach, is unarguably different. But the horizontal distance made, estimated using a Digital Terrain Model (DTM), might be the same. The projection of 3D landscapes onto 2D grids in DTMs leads to a slope-dependent, inhomogeneous sampling of the surfaces, and a first-order error in topographic metrics. Using the slope dependency of this error, we can quantify and revert it. Foremost, correcting the projection error allows for more accurate estimates of area and volume, e.g., to quantify natural hazards; and enables the use of the full slope distribution to define the physical space of surface processes at any scale.

We quantify the projection error using synthetic landscapes for which analytical solutions of slope angles and surface area are known. In applying the correction to DTM data of a real landscapes, we can address geomorphological processes in physically more meaningful ways. The corrected extracted topographic proxies, here exemplary, the erosional response to uplift in the Mendocino Triple Junction (MTJ) area, California, USA, provide two aspects for interpretation of geomorphic processes. First, as all slope angles are now represented equally, the variations in slope distribution by region of uplift rate is more pronounced. Second, the erosional response causes not only a steepening but narrow slope distribution in the regions of high uplift. The transient response is visible in a broadening of the distribution towards the lower slope angles, as deposition becomes more prevalent. In this example, we also find that the surface area ratio, enables determining the effectiveness of Earth surface processes, by increasing or decreasing the differential between the standard-planform and the surface area. Earth surface processes, that involve transport and volume along the surfaces, if not referenced in time, the ratio between the planform and surface area can provide a spatial reference and could be explored further. Correcting topographic metrics also allows addressing additional questions, like, which slope angles characterize which process domains, which processes create steepening, which lowering of slopes, where, and to what extent? Or, which parts of landscapes, maybe not the steepest, correlate to the highest potential to erode?