Spatial interpolation - Spatial Data Analysis: An Introduction for GIS Users - page 150

9.7.3 Cokriging

h ere are several other forms of kriging; cokriging, for example, allows the integration
of information about secondary variables. In cases where we have a secondary variable
(or variables) that is cross-correlated with the primary variable, both (or all) variables
may be used simultaneously to make predictions using cokriging. With cokriging, the
variograms (which can be termed 'autovariograms') of both (or all) variables and the
cross-variogram (describing the spatial dependence between the two variables) must
be estimated and models i tted to all of these. Cokriging is based on the linear model
of coregionalization (see Webster and Oliver, 2007). For cokriging to be benei cial, the
secondary variable should be cheaper to obtain or more readily available than the
primary variable (i.e. the variable that will be mapped). If the variables are strongly
related linearly then cokriging may provide more accurate predictions than OK.

Other approaches and issues

9.8

h ere are many other widely used spatial interpolation approaches in addition to vari-
ants of TPS and kriging. Several approaches are summarized by Mitás and Mitásová
(1999). Specialist routines have been written for some applications. For example, the
routine of Hutchinson (1989) is used specii cally for generating DEMs. Clearly, the
selection of an interpolation method impacts on the i nal results, and researchers have
assessed variations in results following application of dif erent interpolation methods
(see Chapter 10 of Burrough and McDonnell (1998) for a review of related topics). h e
performance of dif erent spatial interpolation procedures will vary as a function of
sampling density and spatial variation. For example, if the sampling density is low
(there are large distances between samples) and there is short-range spatial variation
(values dif er a great deal over short distances), then we would expect there to be larger
dif erences between results obtained using dif erent procedures than in cases where
the sampling density is high and there is long-range spatial variation. Lloyd and
Atkinson (2002) show how dif erences in predictions (in terms of their accuracy)
increase as the sampling density decreases, and the benei ts of more sophisticated
approaches are shown to be more apparent where the sampling density is low.

Areal interpolation

9.9

h e focus so far in this section has been on point interpolation—that is, prediction
from a point sample to a regular grid. Ot en, there is a need to transfer between dif erent
sets of zones or transfer, for example, counts from zones (such as census reporting areas)
to grids (Martin et al. , 2002). Many techniques exist for solving such problems. In
the case of transferring values between dif erent sets of zones, overlay procedures (as
detailed in Chapter 5) provide a partial solution. Counts could be reassigned to new zones