The orientation of terrain surface (aspect) can have dramatic effects on landscape-scale variation in soil temperature and moisture. Summarizing aspect angle is complicated by the fact that sampled values are measured on a circular scale. The circular package for R can be used to summarize, model, and visualize this type of data.

An example function is presented below that demonstrates several components of the circular package: special data structures, summary functions, plotting functions and their application to circular data derived from measurements collected by compass. Spread and central tendency are depicted with a combination of circular histogram and kernel density estimate. The circular mean, and relative confidence in that mean are depicted with an arrow: longer arrow lengths correspond to greater confidence in the mean.

Circular Histogram

Recently I was re-reading a paper on predictive soil mapping (Park et al, 2001), and considered testing one of their proposed terrain attributes in GRASS. The attribute, originally described by Blaszczynski (1997), is the distance-weighted mean difference in elevation applied to an n-by-n window of cells:

Equation 4 from (Park et al, 2001)

 
where n is the number of cells within an (odd-number dimension) square window excluding the central cell, z is the elevation at the central cell, z_{i} is the elevation at one of the surrounding cells i, d_{i} is the horizontal distance between the central cell and surrounding cell i. I wasn't able to get a quick answer using r.neighbors or r.mfilter, so I cooked up a simple R function to produce a solution using r.mapcalc. The results are compared with the source DEM below; concave regions are blue-ish, convex regions are red-ish. The magnitude and range are almost identical to mean curvature derived from v.surf.rst, with a Pearson's correlation coefficient of 0.99. I think that it would be of general interest to add functionality to r.neighbors so that it could perform distance-weighted versions of commonly used focal functions.

Elevation surface (left) and resulting mean curvature estimate (right)

linear regression with RCS

regression tree

• Soil Survey in National Parks
• Upscaling and Downscaling Soil Survey