This tool can be used to calculate the circular variance (i.e. one minus the mean resultant length) of aspect for a digital elevation model (DEM). This is a measure of how variable slope aspect is within a local neighbourhood of a specified size (`filter`). circular_variance_of_aspect is therefore a measure of surface shape complexity, or texture. It will take a value of 0.0 for smooth sites and near 1.0 in areas of high surface roughness or complex topography.

The local neighbourhood size (`filter`) must be any odd integer equal to or greater than three. Grohmann et al. (2010) found that vector dispersion, a related measure of angular variance, increases monotonically with scale. This is the result of the angular dispersion measure integrating (accumulating) all of the surface variance of smaller scales up to the test scale. A more interesting scale relation can therefore be estimated by isolating the amount of surface complexity associated with specific scale ranges. That is, at large spatial scales, the metric should reflect the texture of large-scale landforms rather than the accumulated complexity at all smaller scales, including microtopographic roughness. As such, this tool normalizes the surface complexity of scales that are smaller than the filter size by applying Gaussian blur (with a standard deviation of one-third the filter size) to the DEM prior to calculating circular_variance_of_aspect. In this way, the resulting distribution is able to isolate and highlight the surface shape complexity associated with landscape features of a similar scale to that of the filter size.

This tool makes extensive use of integral images (i.e. summed-area tables) and parallel processing to ensure computational efficiency. It may, however, require substantial memory resources when applied to larger DEMs.

## References

Grohmann, C. H., Smith, M. J., & Riccomini, C. (2010). Multiscale analysis of topographic surface roughness in the Midland Valley, Scotland. IEEE Transactions on Geoscience and Remote Sensing, 49(4), 1200-1213.

## See Also

aspect, spherical_std_dev_of_normals, multiscale_roughness, edge_density, surface_area_ratio, ruggedness_index

## Function Signature

`def circular_variance_of_aspect(self, dem: Raster, filter_size: int = 11) -> Raster: ...`

## Project Links

WbW Homepage User Manual Support WbW