Raster based density calculations represent a type of interpolation.The ArcGIS manual overview of the Density toolset states, "calculating density, you are in a sense spreading the values (of the input) out over a surface". The section of the ArcGIS manual on Understanding Density Analysis states, "[t]he Density tool distributes a measured quantity of an input point layer throughout a landscape to produce a continuous surface." Calculating density is not the same as generating topography from point elevations, but both density and topographic rasters represent an array of discrete points as a field of values. Thus, in a very general sense one can think of Density as a type of spatial interpolation.
ArcGIS provides three Density tools: Kernel, Line, and Point. Kernel densities produce tapered surfaces. Line and Point densities produce magnitude per unit area within the radius of each cell. The two figures below illustrate Point Density and Kernel Density surfaces generated from the same feature classes, that are in this case archaeological sites. Densities can be generated on just about any kind of point or line feature.
There are three important variables to consider when generating a density raster.
- Density type: Should the density raster have tapering values (kernel) or constant values (point density)?
- Output raster cell size: What is the size of the cells in the output raster. It is often useful to set the spatial resolution of the output density raster to the same as the digital elevation model (DEM) as this facilitates raster math.
- Search radius: This determines the size of the search neighborhood. In the literature, it is often referred to as "r". To avoid having densities of one entity, consider determining the distance of the minimum nearest feature and setting "r" slightly higher. When considering use areas around a site, a reasonable search radius might be the distance an individual walks in half a day.
- Population field: Should each input point from the feature class be weighted equally or is there a population field that can give greater weight to features that are larger. In the context of archaeological sites, area might make a useful population field. When mapping small objects like flakes, population fields may not be particularly useful. Whether or not a population field is useful depends on the analytical problem.
By default, density will use the extent of the input feature class. This means that points on the edges of the distribution will have truncated densities.
In most cases it is better to use a study area or some other larger bounding polygon to set the limits of the density operation. This is achieved by selecting the appropriate extent under the Environments button and selecting the Processing Extent option. Under Processing Extent, indicate the appropriate feature to employ and click OK.
Beware, that altering the Processing Extent can cause changes in the Output cell size and Search radius. Be sure that these values are correct or the density computation may not be useful. The same cell size as the input DEM is probably a prudent choice. The search radius is best defined by the structure of the data set or research question. For a set of sites on relatively flat terrain, search radius related to walking times can produce interesting results.
- For the qocha shapefile run the tool Convert feature to point.
- Be sure that the attributes transfer to the new point shapefile. Think about whether or not to constrain the points inside the feature or not. In this case, it is probably recommendable to place the point inside the feature.
- Once the features are converted to points, determine the location of the nearest feature.
- This can be done using the Generate Near Table tool, with ET GeoWizards, and probably some other tools (please report if you find another solution).
- If using the Generate Near Table tool, it is advisable to use the Find Only Closest Feature option as this will cut down on the creation of unnecessary information.
- Both the Input and the Near features should be the point shapefile.
- Open the resulting table of inter-feature distances and sort the entries by the near distance. What is the closest and what is the greatest inter-feature distance? The units are in meters. Is the distribution normal? Is it possible that some outliers could be identified and eliminated?
- After considering the results from calculating the nearest feature, run the density analysis tool. As we will be running the tool at least twice, it may be worth using the model builder to run the tool.
- For the first run of this tool, do not set any population field. We will do this in the next version.
- Set a logical location for the output raster.
- Set the output cell size to 90m.
- Set the search radius.
- Now it is time to go back to the results from the nearest feature calculation. In any density calculation, the "R" term is a critical variable. The "R" term sets the size of the search radius.
- The larger the search radius the coarser the densities while the smaller the search radius the finder the densities. In other words, more subtle patterning is detectable with a smaller search radius. In all cases the densities that result are an artifact or function of the size of the search radius.
- There is no hard and fast rule for determining the appropriate search radius and the value may be different depending on the analysis. At some level, it makes little sense to generate densities that are composed of a single entity (that is unless a population field is employed). Here we will use the nearest feature results to set the search radius. Set the search radius to the largest inter-feature distance.
- Were some outliers eliminated? If so, use the largest inter-feature distance that was retained in the set. Hint: this may well be the mean plus two standard deviations (right?).
- Set the area units to square meters, write down all of the parameters used and run the tool.
- Look at the results. Are there any especially notable densities? Are there notable voids?
- Run the density tool again and keep all parameters the same except for the area of the qocha (shape_area). How is the result different?
- Multiply the first density (no population value) by 1000 to move the decimal place. Then subtract this calculation from the second density (with a population value). Are there new patterns that emerge, and what might these mean or indicate? The flickr technique is a visual method to consider when comparing the two densities.
- Now calculate the same two densities using the kernel density tool. What differences are there between the point density and the kernel density when no population is used? What differences are there between point density and kernel density when a population field is used?