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82 S. Siedentop and S. Fina
as defined by the Federal Office for Building and Regional Planning (‘Bundesamt für
Bauwesen und Raumordnung’).
The actual implementation followed in a number of working tasks:
(1) First, we developed methods to calculate and visualise indicator values for the area
of Germany, using the formulas given in Annex 1. Because the scale of available
databases varied (area units, urban areas), and because some of the indicators are
area-dependent, we needed to establish a uniform spatial baseline configuration for
these calculations. For this purpose, all indicator values have been transformed to an
area-wide grid of cells. The initial size of this grid (10 · 10 km) was selected as a
compromise between the intention to provide sufficient detail to detect regional
patterns from nationwide maps and the limitations of data accuracy. Sensitivity tests
with alternative grid sizes revealed that larger grids caused indicator results to be
highly generalised as a result of data aggregations (20 · 20 km). At the same time,
smaller grid sizes (5 · 5 km) did not produce much more spatial differentiation,
because most of the areas that this data was sourced from were actually larger than
5 · 5 km (municipalities).
(2) Second, all outputs for indicator calculations were then scaled to this grid, using GIS
transformation routines. For surface and density indicators, this task relied on the
processing of area statistics for municipalities, using polygon-in-polygon arithmetic
to aggregate statistics data to 10 · 10 km cells in the GIS. In other words, the
indicator values for a cell represent the average of the corresponding values in the
underlying municipalities, weighted by the area proportion of a polygon that the cell
actually covers. Pattern indicators are different in nature, as they require polygon
processing in the GIS to calculate values for urban areas, rather than simply
aggregating and transforming area statistics. The indicator description worksheets
explain these calculations in detail. The translation of the final values on the polygon
scale to 10 · 10 km cells is then similar as with surface and density indicators: the
transformation method calculates an area-weighted mean value for all polygons and
polygon portions that lie within a cell.
(3) The resulting information was then mapped out in comparable layouts. For consistent
visualisation we used a greyscale colour scheme with a quantile classification method
as the default. Apart from rounding, we made some adjustments to the classification
where the default method did not produce conclusive classes. In the maps (Figures
3–5), brighter colours mean less sprawl-like characteristics, and darker colours show
where sprawl-like impacts are higher according to the indictor values.
(4) In the final step, we analysed the results statistically to determine areas that are
potentially affected by high sprawl levels. For this purpose, we conducted a factor
analysis with the calculated indicator values. To test different configurations in this
analysis, we used the three spatial variations mentioned above, with the full indicator
set for 14,800 cells in the 5 · 5 km grid, 3585 cells in the 10 · 10 km grid and
1026 cells in the 20 · 20 km grid. The analysis of the results showed that the pattern
indicators formed a distinct principal component at the 10 · 10 km scale. The same
effect was not as pronounced at the other scales. We interpreted this result to be an
effect of the resolution of the data, reacting at an optimum at the 10 · 10 km scale.
For this reason we chose the 10 · 10 km scale as the representative input for the
subsequent cluster analysis. With this method we summarised the results of the
factor analysis in a spatial sense and produced a final map for Germany’s ‘sprawl
geography’. The detailed results will be discussed in Section 4.