An experiment using a circular neighborhood to calculate slope gradient from a DEM

The traditional 3 x 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 to calculate slope gradient. Comparisons of the results from a circular neighborhood with the results from some traditional methods show that (a) for a smooth surface, the result from a circular neighborhood is more accurate than that from a square neighborhood, (b) a circular neighborhood is generally more sensitive to noise in the input DEM than a square neighborhood, and (c) in a validation using field measurements, the circular neighborhood performs better than the square neighborhood when the ratio of user-specified neighborhood size to cell size is high.