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Quantifying Earth’s topography: steeper and larger than projected in Digital Terrain Models
  • Anne Voigtländer,
  • Aljoscha Rheinwalt,
  • Stefanie Tofelde
Anne Voigtländer
GFZ German Research Centre for Geosciences

Corresponding Author:[email protected]

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Aljoscha Rheinwalt
University of Potsdam
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Stefanie Tofelde
University of Potsdam
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Abstract

Grid- or pixel-based models, used across all sciences, scales, and spatial resolution, carry projection errors. Taking Digital Elevation Models (DTMs), where 3D landscapes are sampled slope-dependent and inhomogenously and then projected onto 2D grids, create first-order errors on topographic metrics, such as surface area or slope angles. We quantify this error by comparing topographic metrics calculated on gridded DTMs of synthetic landscapes with their analytical solution. Because the error in surface area is proportional to the cosine of its slope angle, we can correct the models. Application to real-world landscapes in California, USA, reveal systematic underestimation of surface area by up to a third, and mean slope angles by up to 10$^{\circ}$ in steep topography in current DTMs. Correcting the projection error allows for more accurate estimates of surface area and volume and the use of slope distribution to define the physical space of surface processes at any scale.