Geoscience Reference
In-Depth Information
way in which the different variations of a station's value is modeled, and the way in
which weighting factors are allocated. Weighting factors are used to allocate values
to pixels that originally have no value [MER 01]. A brief overview of these three
methods will be given in the next part of the chapter and examples that refer to the
spatial variation of sunshine in France for the month of July will be used.
2.3.1.1.
Inverse distance weighted interpolation
Newton's theory of gravitation is applied to the technique of IDW interpolation.
The principle states that the influence of a measurement that is taken from any site
in space decreases inversely with distance [LAN 94; LAN 96]: this means that a site
that is located near a weather station, from which a measurement has been taken,
will have a value similar to the values measured in the station and the inverse is true
for sites that are located further away from such climatological stations. The
weighting factor is provided by the taking the inverse of the distance or possibly by
taking the inverse of its square or log.
2.3.1.2.
Spline Interpolation
Different spline methods exist [ECK 89; MIT 99]. A spline interpolates a
continuous area from a local sample of sites by using a minimum curve, which
means that this continuous area will include the sample sites. The most common
spline method used is the one in which local values are adjusted by cubic
polynomials. The model seen in Figure 2.3b was created with the help of the
standardized function provided by the software ArcGIS. There are 12 sample sites
and the weight allocated to each of the sites is 0.1.
2.3.1.3.
Kriging
Kriging is a stochastic interpolation method that can also be referred to as an
optimal method or as a method of objective analysis, depending on the field it is
used in. Just like the previous interpolation methods mentioned, the kriging
approach takes full advantage of spatial autocorrelation. The aim of the kriging
method is to identify the autocorrelation area which is limited by an optimal
distance. This distance, which corresponds to the vertex of a variogram, acts as the
boundary between the following two samples:
- the first sample is located within the boundary and groups together all of the
sites that possess similar spatial organization characteristics;
- the other sample, located outside this range, is made up of stations that are
characterized by random variations.
Kriging is quite a complicated process and demands a good understanding of
spatial statistics [BUR 86; OLI 90]. Kriging is based on the theory of regional
variables. This theory states that the spatial representation of any variable, which
can be represented by quantitative values, is homogenous for any given surface.
This means that the same spatial distribution model must be observed in the whole
studied area. Local spatial variation is modeled by the semi-variogram, which
describes how data functions in relation to space.
