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Dasymetric Mapping and Areal Interpolation

 

Details of the Technique

 

(Mennis, J. and Hultgren, T., 2006. Intelligent dasymetric mapping and its application to areal interpolation. Cartography and Geographic Information Science, 33(3): 179-194.)

IDM takes as input count data mapped to a set of source zones and a categorical ancillary data set, and redistributes the data to a set of target zones formed from the intersection of the source and ancillary zones.  Data are redistributed based on a combination of areal weighting and the relative densities of ancillary classes.  Consider a source zone s and an ancillary zone z where z is associated with ancillary class c.  Target zone t is defined as an area of overlap of s and z.  The estimated count for a given target zone is calculated as

(1)

where  is the estimated density of ancillary class c.

The value of  may be set by the analyst, if the analyst has a priori knowledge of the density value for that class.  Or, the analyst may choose to derive the data density for any ancillary class by sampling a subset of the total source zones that may be associated with that ancillary class.  The analyst has three options for the sampling method employed.  The ‘containment’ method selects those source zones that are wholly contained within an individual ancillary class.  The ‘centroid’ method selects those source zones that have their centroids contained within an individual ancillary class.  The ‘percent cover’ method allows the user to set a threshold percentage value and then selects those source zones whose area of occupation by a single ancillary class is equal to or exceeds that threshold.  Once a sample of source zones has been selected as representative of a particular ancillary class, may be calculated as

(2)

where m is the number of sampled source zones associated with ancillary class c

Note that even when an analyst chooses to derive the density of most of the ancillary classes by sampling, there may be one or two ancillary classes to which the analyst knows that no data should be distributed.  In the case where one or more ancillary classes are assigned a data density of zero by the analyst, the term  in Equation 1 refers only to the areas of target zones associated with ancillary classes that are inhabited, i.e. for which a data density of zero has not been enforced by the analyst.  Likewise, the term  in Equation 2 refers only to the densities of ancillary classes that are inhabited.  In addition, the term  in Equation 2 is replaced by the area of the source zone occupied by inhabited ancillary classes. 

To account for spatial variation in the relationship between data density and ancillary class, IDM can incorporate an additional data set of region zones, where the data density for each ancillary class is calculated separately for each individual region.  There is also the possibility that a particular ancillary class may go unsampled, which can occur using both the containment and percent cover sampling methods.  In this case, the unsampled class’s density is estimated using ‘refined’ areal weighting.  First, the count assigned to each target zone associated with an unsampled class is estimated based on the previously estimated densities of the other ancillary classes that occupy that target zone’s host source zone.  For instance, consider a source zone that overlaps multiple ancillary zones.  Some ancillary zones are associated with an ancillary class that has gone unsampled, denoted ancillary class u, whose density estimate is therefore unknown.  The other ancillary zones are associated with an ancillary class whose density estimate is known, denoted ancillary class k, because it was derived from sampling or assigned a preset density value by the analyst. The count of a target zone associated with u is calculated as

(3)

where  is the estimated count of the target zone associated with u,  is the estimated density of k,  is the area of the target zone associated with k, and  is the area of the target zone associated with u.  Note that  is a temporary estimate, used only to estimate the density of the ancillary class whose density estimate is unknown, and is not the ‘final’ estimated count for that target zone.  Once the value of  is found, the estimated density of ancillary class u can be calculated using the formula

(4)

where  is the estimated density of u and p is the number of target zones in the entire data set associated with u.