Interpolating Nominal and Ordinal Data

In interpolating nominal or ordinal data, no direct single value can be calculated for the target polygons. Rather, for each target polygon, each unique data value from the intersecting source polygons must be recorded, along with the proportion of the target zone that each value occupies. This routine creates a separate data table related to the target polygons, which contains for each intersecting source polygon, the target polygon id, the nominal/ordinal value from the source polygon, and the percentage that source polygon occupies within the target polygon.

Formula

The percentage occurrence of each unique nominal/ordinal value within the target polygon is calculated as the area of each target/source intersection summed for each unique value, as a percentage of the whole target polygon.

Thus, for each Vs there is a corresponding Vt with

V% = Σ Ats / At * 100 

where:

Vs = value of the source polygon

Vt = value of the target polygon

V% = percentage of the target polygon occupied by a unique value

Ats = area of the intersection of the target and source polygons

At = area of the target polygon

Non-areal proportions require special treatment.

Example

Consider the following coverages:

Source polygons

Plygons A and B
Target polygons

Plygons 1 and 2

Target-Source intersections

Target-Source intersections 1A, 1B, 2A and 2B

Assuming Vs Ats and At shown below, PARS calculates V% as follows:

Source values (Vs)

Source values low and high
Target values (Vt)

Target values 80% low and 20% high versus 68% high 32% low

target polygon portion Vs Ats
area (ha)
At
area (ha)
V%
Polygon 1 1A low 600 750 80 %
1B high 150 20 %
Polygon 2 2A low 400 1250 32 %
2B high 850 68 %

Source: modified from Ballard and Schut, 1995