Geoscience Reference
In-Depth Information
All of these information layers are stored in a GIS and will be used in analysis as
explanatory variables. All of these information layers are not necessarily required
for the interpolation process to take place. The variables that are available will
influence any decision on the interpolation method that is to be used.
2.3. The main interpolation methods
The climatological data are located in what is known as 2D space (a third
dimension can be added if altitude is taken into consideration; however, in a GIS
altitude is considered more as an attribute than as a dimension). The theory
associated with spatial analysis involves providing an explanation about the
localization of the geographic objects that exist in space [ARN 00]. There are two
major stances that can be adopted as far as interpolation is concerned [CAR 03]:
- the first stance bases interpolation on spatial autocorrelation; the techniques of
interpolation that are used rely only on the location of the measurement sites;
- the second stance introduces geographic information in a different way, by
making explicit reference to space but in a different context. What is important here
is not the location of a measurement station in relation to its neighbors, but rather
the environment that surrounds the measurement station. In this way, it is the
geographic objects that are continually distributed in space and which can be
distinguished thanks to the shape and form of localized characteristics (exogenous
independent variables such as latitude, longitude, altitude, slope, etc). These
geographic objects will then be used as a support for the interpolation process.
2.3.1.
Interpolation based on spatial autocorrelation
The fundamental issue here relates to spatial correlation techniques, which are
based on distance and are well suited to the interpolation of localized data. The fact
that autocorrelation exists makes it possible to carry out analyses such as the
techniques of interpolation. This means that a particular piece of data is similar to its
neighboring data, and the similarity is inversely proportional to the distance that
seperates them. This inverse proportion, which can take many forms, leads to the
creation of gradients, which is another geographic concept. In all cases,
autocorrelation characterizes measurement stations, or neighboring regions whose
measurement values are similar [FLA 01; PHI 01]. If the measurements for a
particular given space were distributed randomly in terms of the distance that
separates the measurement sites, then it would not be possible to carry out spatial
analysis based on the process of autocorrelation.
It is possible to use three main methods of interpolation when only its
x
and
y
co-
ordinates (longitude and latitude) are known: inverse distance weighted (IDW),
kriging, and cubic spline. Each interpolation method has its own advantages and
disadvantages. The three methods rely on the idea that the value of any localized
measurement site depends on the values of the surrounding measuring stations
[GRA 02]. The main differences between these three interpolation methods are the
