An Experiment Using a Circular Neighborhood to Calculate Slope Gradient from a DEM

Abstract

The traditional 3 ϫ 3 cell neighborhood used in a focal operation on a raster layer has a square shape that results in a dimensional neighborhood of which the orientation is eventually arbitrary to the physical features represented. This paper presents an experiment using a circular neighborhood IntroductionThe traditional 3 ϫ 3 cell neighborhood used in a focal operation on a raster layer has two characteristics: its size is determined by the resolution of the input layer, and its shape is usually square. The resolution-determined size causes inconsistency in the terrain attribute values computed from gridded DEMs with different resolutions. This problem has been studied by many researchers (e.g., Chang and Tsai, 1991;Hodgson, 1995;Gao, 1997;Kienzle, 2004;Zhou and Liu, 2004). Conclusions drawn by these researchers do not totally agree with each other (mainly due to the different benchmarks or "true values" they used), but there is a consensus that the DEM resolution (eventually the size of the neighborhood determined by this resolution) has a strong effect on the accuracy of the terrain attributes derived from the DEM, and in turn on the outcome from the erosion or hydrological models based on these attributes. The resolution-determined neighborhood size also leads to the problem of mismatch between human-perceived and computer-calculated values of terrain attributes, people doing fieldwork (e.g., soil surveyors) always have their own measuring scales. This mismatch has become an important source of error in knowledge-based digital soil mapping. Ironically, this is becoming a more An Experiment Using a Circular Neighborhood to Calculate Slope Gradient from a DEM Xun Shi, A-Xing Zhu, James Burt, Wes Choi, Rongxun Wang, Tao Pei, Baolin Li, and Chengzhi Qin serious problem since high-resolution DEMs are becoming more readily available. Burt and Zhu (2002) solved this mismatch problem by employing a user-defined neighborhood to replace the resolution-determined neighborhood. In this method, the user specifies the size of the neighborhood, and the computer selects the eight cells (not necessarily contiguous) that make up the square with the specified size to calculate the terrain attributes for the cell at the center of the neighborhood. This method allows the user to specify a neighborhood size that matches the scale in their mind, regardless of the resolution of the input DEM.On the other hand, the square shape results in a dimensional neighborhood: the values in the diagonal directions are farther from the center of the neighborhood than the values in the cardinal directions. This dimensional property has a significant effect on derived terrain attributes (Zhou and Liu, 2004) while from a physical standpoint, the orientation of a DEM grid is arbitrary. To reduce this effect, some algorithms (e.g., Horn, 1981) assign different weights to the cells in different directions. The square shape, after all, is merely a convenient setting for the nine contiguous cells that define the neighborhood. Ideally, the ...

A comparison of LiDAR-based DEMs and USGS-sourced DEMs in terrain analysis for knowledge-based digital soil mapping

“…In this study, we tested three algorithms, including the Evans-Young algorithm (Evans, 1979;1980;Pennock et al, 1987;Young, 1978), Horn's algorithm (Horn, 1981), and a modified Zevenbergen-Thorne algorithm (Shi et al, 2007;Zevenbergen and Thorne, 1987). The Evans-Young algorithm was chosen, because it has been argued to be the most optimal method under certain conditions (Florinsky, 1998;Jones, 1998a;1998b).…”

“…Major justifications for using the USGS-sourced DEM include their complete national coverage and low cost. On the other hand, the inherent error in these DEM resulting from the data source and the creation process has been well studied (e.g., Guth, 1999;Holmes et al, 2000;USGS, 2000), and the impact of the coarse resolutions of these DEM on environmental modeling has drawn considerable and continuous attention, particularly from the soil science area (e.g., Erskine, et al, 2007;Pike, et al, 2006;Shi, et al, 2007;Smith et al 2006; Thompson et al, 2001;Venteris and Slater, 2005).…”

“…The value of, e.g., slope gradient, is fractal and also method-or model-based. As Florinsky (1998) points out, the "accuracy" is reference-dependent and people have used widely different references in the "accuracy" evaluation, including hand measurements from topographic maps (Evans, 1980;Skidmore 1989), calculated values from a high-resolution DEM (Chang and Tsai, 1991), calculated values from a mathematically created smooth (derivable) surface (Hodgson, 1995;Jones, 1998a;1998b;Zhou and Liu, 2004), and field measurements (Bolstad and Stowe, 1994;Giles and Franklin 1996;Shi, et al 2007). Apparently, the "accuracy" evaluated using these different references do not mean the same thing.…”

Airborne LiDAR and Aerial Imagery to Assess Potential Burrow Locations for the Desert Tortoise (Gopherus agassizii)

“…The Zevenbergen-Thorne method was applied separately to the four cardinal cells and four diagonal cells (eight surrounding cells); the average of the results from the two operations was used as the final result. We used a radius of 10 neighborhood cells in all cases [39].…”

Modeling Rare Endemic Shrub Habitat in the Uinta Basin Using Soil, Spectral, and Topographic Data

“…An area solar radiation map was generated in ArcMap, using the spring equinox layer as a reasonable average representation of total annual incoming solar radiation. The pit-filled DEM was used to calculate several common surface derivatives using the Soil Inference Engine add-in for ArcGIS (ArcSIE; Shi, 2013) using a 10-m square neighborhood with the Shi algorithm (Shi et al, 2007). A slope map in gradient percentage was calculated along with the overall curvature, the general shape of the landscape (Curvature); profile curvature or vertical landscape shape (ProfCurvature); planform curvature or horizontal landscape shape (PlanCurvature), and tangential curvature, the shape of the landscape in the direction that is perpendicular to the surface at the given location (TanCurvature).…”