Abstract
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. Slope and aspect estimates on a DEM contain errors and uncertainties inherited 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 m−2 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 1 m 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 4 m 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 4 m 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.
Highlights
Continuous surfaces are often projected onto an evenly sampled grid – digital elevation models (DEMs) are a common example
This study presents a detailed account of uncertainties and errors in the calculation of terrain slope and aspect derived from both truncation errors and uncertainty in the underlying source DEM
We extend our methodology onto a high point-density lidar dataset, which allows us to compare the relative impacts of gridding truncation errors and propagated elevation uncertainty on the calculation of topographic metrics
Summary
Continuous surfaces are often projected onto an evenly sampled grid – digital elevation models (DEMs) are a common example. The methods D-8 and Dinfinity are optimized towards hydrologic flow-routing problems, on DEMs of low spatial resolution (Tarboton, 1997), and the methods of Evans (1980) and Zevenbergen and Thorne (1987) include some smoothing of the underlying DEM to minimize the impacts of DEM noise All of these methods contain some intrinsic error due to truncation error (TE) – the deviation of the gridded sample from the continuous original surface (Fig. 1). We first use synthetic data with known properties as a control to define generalized functions applicable to any DEM and to develop a quality metric for slope and aspect calculations Following this analysis, we turn to a high-resolution lidar dataset covering complex terrain to study the spatial structure of uncertainty in topographic metrics propagating from both TE and DEM uncertainty. Error bounds from the combination of TE and PEU, and to analyze the implications of using suboptimal DEM resolutions for calculating slope and aspect
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