Hawth's Analysis Tools for ArcGIS

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 Summary

BATCH FIXED KERNEL DENSITY ESTIMATOR
Input: a point layer, containing an integer field representing unique ID's, and optionally containing a numerical field in the attribute table representing weights for each of the points
Output: one kernel density estimate raster for each unique ID, and optionally a set of percent volume contours
Features:

  • this tool calculates a fixed kernel density estimate using the quartic approximation of a true Gaussian kernel function
  • one raster layer is produced for each unique ID
  • this tool uses one of two automatic naming conventions for output rasters (see the Help section)
  • 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 many point features
  • see also the 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-D. In this example we use a set of points representing animal telemetry data from four different animals (each colour in Figure A represents a set of points with a different unique ID number). The kernel is calculated using the full extent option in B (you can therefore only see the kernel from one of the unique ID's becuase the others are covered up). In C, the smallest extent option is used and the four kernels have been assigned different colour schemes. Finally, in D, the 50% (red) and 95% (blue) by volume contours are shown for three of the four unique ID's (one set of contours was omited for clarity).

 Help

Getting started and unique ID numbers A point layer must be loaded into ArcMap in order to use this tool. The point attribute table must contain an integer field that represents unique ID numbers for groups of points. This number forms the basis for the batch processing. For instance, if your points represent telemetry locations then the unique ID number would represent different animals, or different animals in different seasons (depending on how you want to partition your data). Each kernel is calculated using only the points corresponding to that unique ID number. Kernels can be calculated with as few as 1 point, so you need not be concerned that a low sample size will cause this tool to fail. 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.

Extent of output rasters The extent of the output raster is determined automatically (i.e. any Spatial Analyst options you may have set are ignored as this tool is independent of Spatial Analyst). However, there are two options that control the extent of the raster:

  • FULL EXTENT: all of the rasters have identical extents and the extent is calculated as: the extent of all the point data + the smoothing factor. This option is very useful if you wish to subsequently combine the rasters (because if the extents do not overlap, then the output of Raster Calculator expressions is limited to the area of overlap of all the input layers, and all other cells receive a NoData value in the output).
  • SMALLEST EXTENT: in this case, the extent of the output raster is minimized for each unique ID using this calculation: the extent of the points for only that unique ID + the smoothing factor. The benefit of this option is that there is the potential to create much smaller output files.

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.

Naming convention The first and preferred naming convention this tool will attempt to implement is: the prefix you specify + the unique ID. If the length of this name is greater than 14 characters, or a raster of that name already exists (for ANY of the output rasters) then the tool switches to an automated naming convention: the prefix you specify + an arbitrary number that results in a unique file name. This arbitrary number begins at 1, and increments until a unique file name results. Because it would be difficult to associate an arbitrarily named raster file with the corresponding unique ID, the tool also then creates a text file called rasternames.txt in the output folder that maps each arbitrary raster name to the input data file and the unique ID number. This is a much less convenient naming system to work with, so it is highly recommended that you define a short prefix name and use unique ID numbers that are less than 6 digits long. This will enable the first, more intuitive naming convention to engage.

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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