Hawth's Analysis Tools for ArcGIS

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 Summary

KERNEL DENSITY ESTIMATOR
Input: a point layer, optionally containing a numerical field in the attribute table representing weights for each of the points
Output: a raster kernel density estimate
Features:

  • this tool calculates a fixed kernel density estimate using the quartic approximation of a true Gaussian kernel function
  • the user can optionally specify a field that assigns weights to the input points in the density estimate
  • the user can optionally create contour lines representing the x% by volume contour (e.g. the 95% by volume contour)
  • this is a processing intensive process, so can take a considerable time to run for layers containing manypoint features
  • see also the Batch Fixed Kernel Density Estimator tool
  • this tool only requires an ESRI 3D or Spatial Analyst extension license if you are generating the optional percent volume contours.

Limitations:

  • the point layer MUST be in a projected coordinate system (this tool will not produce logical results if a geographic coordinate system is used)
  • if a weight field is specified, under no circumstances should negative numbers be used to represent NoData in that field; if a weight cannot be assigned to a point the user should either give it no weight at all (weight=1), or eliminate it from the analysis
  • this tool is designed to work with shapefiles, other vector formats have not been tested


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 Example

Figures A-C. In this example we use a set of points representing animal telemetry data (Figure A). The resulting kernel is shown in B, and the 50% (red) and 95% (blue) by volume contours are shown in C.

 Help

Getting started A point layer must be loaded into ArcMap in order to use this tool. If you wish to use point weights in the kernel density estimate, ensure that the attribute table contains a numerical field with a weight for each point. Note that a weight of 1 is neutral, and a weight of 0 effectively eliminates the point from the dataset (the point contributes nothing to the density estimate). Negative weights will result in nonsensical results or errors during processing.

Output folder As this tool can generate many different output layers, the user is asked to specify an output folder (preferably a new, empty folder). An empty folder will ensure that the program does not encounter naming conflicts with pre-existing data layers.

Output raster The extent of the output raster is determined automatically as: the extent of point data + the smoothing factor. This tool completely ignores any Spatial Analyst options you may have set (this tool is independent from Spatial Analyst). The output raster name should be 14 characters or less, and not contain any special characters. The output is a floating point Grid. It is highly recommended that you apply a scaling factor to preserve the precision of the density estimate (see below).

Smoothing factor The smoothing factor (also referred to as the bandwidth or h statistic) is what controls how smoothed the kernel density estimate is. There are a number of ways of determining what the smoothing factor should be. Two objective approaches include the href estimate, and least-squares cross validation (LSCV). The appropriateness of these estimates depends to a large degree on the nature of your data. There is some evidence that neither of these estimates perform particularly well. In most of the applications I deal with, an estimate of the smoothing factor based on expert biological knowledge and careful inspection of the resulting kernel density estimate is often the best approach.

Scaling factor Kernel density estimates often produce very small numbers, e.g. 0.000000147. The scaling factor simply multiplies these small values by a constant (e.g. 1000000). It is usually very wise to use a scaling factor, especially because Grids only permit the storage of single precision floating point numbers. If you do not use a scaling factor, you are likely to lose a great deal of precision in the kernel density estimate as a result of the density values being truncated. The important thing to note about the scaling factor is that the relative values in the output cells are the same, it is simply the units of the density estimate that change. There is therefore no down-side to using a scaling factor and it is highly recommended that you do so. (The scaling factor will not affect the percent volume contours either).

Percent volume contours Note that a percent volume contour is not the same as the simple contours that are typically produced in tools like Spatial Analyst. A percent volume contour represents the boundary of the area that contains x% of the volume of a probability density distribution. A simple contour (like the ones that are produced in Spatial Analyst) represent only the boundary of a specific value of the raster data, and does not in any way relate to probability. For applications like animal home range delineation it is the percent volume contour that is required. The 95% volume contour would therefore on average contain 95% of the points that were used to generate the kernel density estimate.

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