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Earth Surface Dynamics An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/esurf-2018-96
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esurf-2018-96
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 02 Jan 2019

Research article | 02 Jan 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Earth Surface Dynamics (ESurf).

Determining the Optimal Grid Resolution for Topographic Analysis on an Airborne Lidar Dataset

Taylor Smith, Aljoscha Rheinwalt, and Bodo Bookhagen Taylor Smith et al.
  • Institute of Earth and Environmental Sciences, Universität Potsdam, Germany

Abstract. Digital Elevation Models (DEMs) are a gridded representation of the surface of the earth and typically contain uncertainties due to data collection and processing. The topographic metrics slope and aspect contain errors and uncertainties inherited both from the representation of a continuous surface as a grid (referred to as truncation error, TE), and from any DEM uncertainty. We analyze in detail the impacts of TE and propagated elevation uncertainty (PEU) on slope and aspect.

Using synthetic data as a control, we define functions to quantify both TE and PEU for arbitrary grids. We then develop a quality metric which captures the combined impact of both TE and PEU on the calculation of topographic metrics. Our quality metric allows us to examine the spatial patterns of error and uncertainty in topographic metrics, and to compare calculations on DEMs of different sizes and accuracies.

Using lidar data with point density of ~ 10 pts/m2 covering Santa Cruz Island in southern California, we are able to generate DEMs and uncertainty estimates at several grid resolutions. Slope (aspect) errors on the one-meter dataset are on average 0.3° (0.9°) from TE, and 5.5° (14.5°) from PEU. We calculate an optimal DEM resolution for our SCI lidar dataset of four meters that minimizes the error bounds on topographic metric calculations due to the combined influence of TE and PEU for both slope and aspect calculations over the entire SCI. Average slope (aspect) errors from the four meter DEM are 0.25° (0.75°) from TE and 5° (12.5°) from PEU. While the smallest grid resolution possible from the high-density SCI lidar is not necessarily optimal for calculating topographic metrics, high point-density data are essential for measuring DEM uncertainty across a range of resolutions.

Taylor Smith et al.
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Taylor Smith et al.
Taylor Smith et al.
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Latest update: 20 Mar 2019
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Short summary
Representing the surface of the earth on an equally spaced grid leads to errors and uncertainties in derived slope and aspect. Using synthetic data, we develop a quality metric that can be used to compare the uncertainties in different datasets. We then apply this method to a real-world lidar dataset, and find that one-meter data has larger error bounds than lower resolution data. The highest data resolution is not always the best choice – it is important to consider the quality of the data.
Representing the surface of the earth on an equally spaced grid leads to errors and...
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