The major part of the data, images and maps seen here has been created
with IDL (Research Systems Inc.), a powerful programming language for manipulating
and visualizing large amounts of scientific data.
IDL is an offspring of NASA's Mariner Mars program and nowadays is used by NASA,
ESA and DLR (the American, European and German aerospace agencies, resp.) to
process data from all major astronomical satellites (such as the Hubble Space Telescope). IDL is
particularly suited for working with large data matrices (images) - IDL code working
with matrices is typically 50 % to 80% shorter than code written in FORTRAN
or VB and considerably faster. In addition visualisation of data is an integrated feature requiring
only some additional lines of code. Combined with a large library of mathematical
and statistical routines IDL is a perfect tool for geoinformatical research.
REGEOTOP can be seen as a typical example for the need of integrated use of
research tools from image processing, GIS, multivariate statistics and geostatistics.
Interpolation of discrete point data obtained from measurements of meteorological
stations to obtain climate data fileds is still a major problem. The influence
of topography is mostly dealt with simple descriptors such as absolute altitude
or exposition and slope angle. In order to provide with a more objective method
to account for the influence of topography Benichou and Lebreton (1987) have
proposed to parameterise topography with the help of a principal component analysis
(PCA).
For each element of the DEM a relative topography is obtained by subtracting
its elevation from the elevation values of a square window (e.g. 5 by 5 or 11
by 11 elements) centred on that element. In the statistical context each element
of the window is seen as a variable and each DEM element is seen as a case or
object. After rearranging the results of each window as input data for the PCA
each row of the input matrix represents one case and each column represents
one variable.
The input matrix is subjected to a R-mode PCA (Richman, 1986). The relative
topography in the domain can then be described as a linear combination of the
resulting eigenvectors of the minor product of the input matrix weighted by
their corresponding principal components (PC). Each eigenvector is interpreted
as a 'basic topography' ('paysage du base', Benichou and Lebreton, 1987) representing
different basic morphological elements such as domes or depressions, slopes,
saddles or parallel ridges of different exposition or different orientation.
With decreasing variance PCs explain increasingly complex topographic features
that defy easy descriptions. This approach allows to decompose the topography
around a station into the PCs of its relative landscape and the absolute altitude
of the station itself. As PCs are not correlated with each other they offer
an added advantage as predictors for a regression analysis.
Stepwise multiple linear regression is then used
to select significant predictors for the observed climatic values (such as a
monthly or annual mean value) from relative topographies decomposed into basic
topographic components (PCs) and absolute altitude. Application of the regression
equation to each element of the DEM then results in a predicted climate data
field. The residuals between observed and predicted values are interpolated
via a geostatistical method ('kriging') and added to the regression field to
account for any remaining spatial variation.
The resulting data fields contain both the influence of small-scale (continentality,
monsoon dynamics) and large-scale (topography) forcing factors on climate. Typical
topography related effects such as orographically enhanced rain on windward
slopes and 'rain-shadow' areas are modelled.
A detailed description of the method and results is to appear in the International Journal of Climatology