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 ...
