Mapping Distance and Density

Distance functions allow you to determine the nearest location of something or the least-cost path to a particular destination. Density functions, on the other hand, allow you to see the highest and the lowest concentrations of features in your data.

Distance functions may be directly or indirectly used in an analysis. The Straight Line Distance function, for example, computes the straight-line distance to a particular location, and is often the whole of an analysis (e.g., locating the nearest hospital). The value of each cell in a surface generated with the Straight Line Distance function equals the measured distance of a straight line from the cell's closest source.

The Cost Weighted Distance function, however, calculates the least-cost path to a particular location, a process that usually represents one part of a larger analysis (e.g., finding the least-cost path for constructing a pipeline). The cell values in a surface created with the Cost Weighted Distance function represent the accumulated cost of travel from the closest source. Distance is measured from each cell to the closest source, such as from a campsite to a store location.

In density surfaces, however, the cell values always indicate the number of features per unit of area, such as the number of people per square mile. Density surfaces are great for visualizing patterns in the data that otherwise might not be apparent.

Distance surfaces

You may have heard the expression "as the crow flies" used to describe distance or direction, for example, "The campsite is located 8 miles due south of town, as the crow flies." Since a crow can easily fly above obstacles such as forests, rivers, and gated communities, this expression implies a straight line path, or the shortest distance between two points.

For those of us who can't fly, forests, rivers, and gated communities are obstacles that will impede travel to the campsite, so we must decide the best way to navigate around or through them. You may even choose a campsite that is farther away because getting to it requires less effort. So, as the crow flies, the nearest campsite might in fact be 8 miles due south, but for you it could be a 20-mile hike.

With that in mind, consider two types of raster surfaces: one that measures distance as the crow flies, and the other that measures distance based on the cost of travel. These types of surfaces will help you find the nearest location of something or the least-cost way of getting there.

All distance surfaces are calculated based on a source, which is the location of some object of interest, such as your home. If there is more than one source, as in the case of city fire stations, the calculation is based on the nearest one.

Density surfaces

Density surfaces are good for illustrating concentrations of point or line locations. For example, if on an annual basis lightning strikes a hilltop more often than the valley below, then the density of lightning strikes will be concentrated near the hilltop.

Density is a calculation of the quantity of something per unit of area, such as the number of annual lightning strikes per acre. You can calculate the density of countable things: discrete objects or events (e.g., businesses, trees, car thefts, earthquake epicenters) and their attributes (e.g., employees of businesses, types of trees, property value of car thefts, magnitude of earthquakes).

The Density function has two methods for calculating density: simple and kernel. Both methods employ a circular neighborhood or search area to make the density calculation.