In ArcMap 9.3 I've used Kernel Density to map various incidents, but the resulting shapefile doesn't display any units of measurement. Is there a good, not-to-technical source that would explain in lay terminology the interpretation of the output values in terms of the input cell size and search radius?
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This is almost a duplicate of How to interpret GRASS v.kernel results?, but it differs slightly in asking for an interpretation in terms of the search radius. Let's talk about that.
A kernel density is a convolution. In nontechnical terms this means that the value of each cell in the input grid is spread around its vicinity. The "kernel" is a function that describes the shape of the spreading. Think of the value as recording the height of sand poured into a box based on the cell. If you were to remove the box, the sand would slump. The kernel says what shape it would acquire; the amount of sand determines how high that shape is. Independently repeat this process for each cell in the grid, allowing the piles of sand to accumulate vertically (without introducing any additional slumping from the overlap).
From this description we can deduce the answers to the two questions posed here:
These figures illustrate the effects of changing the radius (for a Gaussian kernel) on a sparse input grid having values of 0 or 1.
An image and some of its Gaussian kernel densities
Darkness depicts grid values (black = 1, white = 0). All images are 16 by 16.
The same figure shown as 3D plots of grid values
Height depicts grid values. All plots are on a common scale for comparison. This plotting method shows the original piles of "sand" as cones rather than as boxes.