Estimating Slope From Raster Data – A Test of Eight Algorithms at Different Resolutions in Flat and Steep Terrain

Abstract

Different slope algorithms can result in totally different estimates. In the worst case, this may lead to inappropriate and useless modelling estimates. A frequent lack of awareness when choosing algorithms justifies a thorough comparison of their characteristics, making it possible for researchers to select an algorithm which is optimal for their purpose. In this study, eight frequently used slope algorithms applied to Digital Elevation Models (DEMs) are compared. The influences of the resolution of the DEM (0.5, 1, 2, and 5 metres), as well as the terrain form (flat and steep terrain), are considered. It should be noted that the focus of the study is not to compare estimates with ‘ground truth’ data, but on the comparisons between the algorithms, and the ways in which they might differ depending on resolution and terrain. Descriptive statistics are calculated in order to characterize the general characteristics of the eight tested algorithms. Eight combinations of DEM resolution and terrain form are analysed. The results show that the Maximum and Simple Difference algorithms always yield higher mean slope values than the other algorithms, while the Constrained Quadratic Surface algorithm produces the lowest values compared to the others. It is concluded that the estimated slope values are heavily dependent on the number of neighbouring cells included in the estimation. An Analysis of Variance (ANOVA) of estimated slope values strongly indicates (at the significance level of 0.01) that the tested algorithms yield statistically different results. The eight algorithms produce different estimates for all tested resolutions and terrain forms but one. The differences are more pronounced in steep terrain and at a higher resolution. More detailed pairwise comparisons between estimated slope values are also carried out. It is concluded that the smoothing effects associated with the Constrained Quadratic Surface algorithm are greater in steeper terrain, showing significantly lower estimates than other algorithms. On the other hand, the Maximum and Simple Difference algorithms show significantly higher estimates in almost all cases, except the combination of steep terrain and low resolution. With an increase in grid cell size, the loss of information contents in DEMs leads to lower estimated slope values as well as smaller relative differences between algorithms. Based on the results of this study it is concluded that the choice of algorithm results in different estimated slope values, and that resolution and terrain influences these differences significantly.

Indigenous communities of Peru: Level of accessibility to health facilities

“…25 , 26 The calculation of the slope of the land was generated from a digital elevation model (DEM) that allows for the calculation of the specific slope of territory. 27 , 28 …”

A High-Precision Sub-Grid Parameterization Scheme for Clear-Sky Direct Solar Radiation in Complex Terrain in the Atmospheric Model

“…In addition, the slope algorithms may also affect the accuracy of the CSHDSI calculation. Tang et al (2013) found statistical differences in slope results across 8 algorithms. Four scholars believe that the slope accuracy of the third-order finite difference algorithm (3FDA) is higher than that of the second-order finite difference algorithm (2FDA), while three scholars have reached the opposite conclusion (Liu et al, 2004).…”

“…The differences of CSHDSI between using 2FDA (3FDA) and 2TPA-AHS show there are more significant negative deviations (Figures 5e-5l). Tang et al (2013) pointed out that the more points involved in the calculation for slope, the stronger the smoothing effect of the finite difference.…”

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“…Алгоритм расчета уклона и экспозиции элементарной поверхности. Из восьми существующих в настоящее время алгоритмов расчета уклона в разрабатываемой системе применяется наиболее устойчивый из них [Tang et al, 2013].…”