density - How to interpret GRASS v.kernel results?

GRASS manual reads:

v.kernel - Generates a raster density map from vector points data using a moving 2D isotropic Gaussian kernel ...

Ok, but how do I interpret the results? I understand that v.kernel is the more advanced than v.neighbor function but I'm unsure as to which advantages it has.

Answer

The results estimate points per unit area. As a check, you should multiply the density values by the area of a cell and add up these values over the grid: the total should equal the sum of the original data. (These two values often differ for two reasons, boundary effects and numerical imprecision. The boundary effects occur because the density map can spread data off the edge of the map and those values don't get recovered from the density grid. But the differences ought to be small.)

One image I have used in classes asks students to imagine the kernel as a bucket of sand: you upend the bucket at a point, allowing the sand to slump. The slumping barely occurs for short half-widths but is extensive for large band-widths (maybe the sand is wetter ;-). Regardless, it's always the same amount of sand left, no matter how slumping occurs. Now go dump one bucket at the location of each point (or, more generally, if there is a positive value x associated with each data point, first put an amount of sand in the bucket proportional to x and then dump it). The sand slumps. It piles up in areas where there are lots of buckets. The density grid gives you the height of the piled sand at the center of each grid cell. Multiplying this by a cell's area estimates the volume of sand occupying each cell. Summing this cell volume over any region (such as a Census block) estimates the total volume of sand in that region, which represents the total amount of quantity x you think is in the region.