The Cost Weighted Distance function

Distance and direction surfaces created with the Cost Weighted Distance function are used in a least-cost path analysis. With the exception of the cost weighted allocation surfaces, cost weighted surfaces are normally not used directly in analysis; whereas straight line distance surfaces often are.

Cost weighted surfaces are generally not used directly in analysis because cell values in a cost weighted distance surface are not distance values, but accumulated costs.

To calculate the cell values in a cost weighted surface, the Cost Weighted Distance function evaluates the neighbors of each cell, beginning with the source, multiplies the average cost between each pair by the distance between them, and assigns each of the neighboring cells a cost weighted value. The process moves to the cell with the lowest value, evaluates its neighbors with unknown values, and so on.

This graphic illustrates the iterative process behind the Cost Weighted Distance function.

Instead of a compass direction, each cell value in a cost weighted direction surface is given a code number that indicates the direction of the next least-cost cell. The decoder diagram below shows the direction each number code points.

If a cell has the code value of 5, the next least cost cell back to the source is to the left. If the code value is 8, the next least cost cell back to the source is to the upper right.

In an allocation surface created with the Cost Weighted Distance function, the shape and size of its compartments are determined by the cost of travel from the cells within it to the nearest source. This type of analysis would be useful if you had to consider the size of service areas based on the cost of travel over land.