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How to interpret GRASS v.kernel results?

The attached image shows trees in a study area based on their actual height in the field. The trees are overlaying a raster that was produced in ArcGIS using the Kernel Density tool. A population field was used for the kernel density estimate which included the tree heights in meters. The following descriptive statistics are for the displayed trees in the image:

  • n = 117
  • Min height = 0.2 m
  • Max height = 8.68 m
  • Mean height = 0.76 m

How should I interpret the results of the kernel density estimate as displayed in the legend? You can see the largest KDE value is approximately half the average tree height. What am I missing here?

enter image description here

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    For various answers, search our site. A kernel density of tree heights is a strange thing to do, though: the units in the density map are height/area = 1/length. It's hard to see how that would be relevant to any property of the trees.
    – whuber
    Commented Jan 24, 2013 at 19:06
  • @whuber None of these answers address the KDE weighted by the population field. KDE results based off tree locations are different than those that include the height attribute for each tree.
    – Aaron ♦
    Commented Jan 24, 2013 at 19:23
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    Please explain that, Aaron: how does a height--which is just a number--differ at all from any other numeric attribute (such as the constant 1 used for unweighted KDEs)? For instance, my answer at gis.stackexchange.com/a/14376 uses a "sand pile" analogy in which the amount of sand corresponds to the "weight" or "population" field. (I freely admit there is a huge intellectual challenge in thinking of tree heights as amounts of sand or amounts of anything else--but that's exactly what you're doing when you use heights to weight a kernel density. Are you sure this is what you want?)
    – whuber
    Commented Jan 24, 2013 at 20:03
  • ESRI's documentation, states:"If a population field setting other than NONE is used, each item's value determines the number of times to count the point. For example, a value of 3 would cause the point to be counted as three points." I understand how search radius works in Arc (as described in your post), although I do not understand how weighting the KDE based on a population field changes the units of the output. That is clearly not addressed in any of the post.
    – Aaron ♦
    Commented Jan 24, 2013 at 20:48
  • In my answer (cited above) I wrote, "the output values give ... the amount per unit area. (This is what "density" means.)" I'm sorry if the ESRI docs are confusing--its kernel density definitely does not assume the weights are counts, nor does it compute a count of points--but I hope that the answers on our site are sufficiently clear! Applying my statement to your case, it says that the KDE output will be tree height per unit area. Also, because a density is an amount per unit area, there are no predetermined statistical relationships between the original heights and the KDE results.
    – whuber
    Commented Jan 24, 2013 at 23:05

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