where Pij is the population for land cover patch j in land cover class i, Aij is the area of
the land cover patch j in land cover class i and Di the population density for land
cover class i derived from the inland sample cities.
The probabilistic modelling approach was then applied, as before, to disaggregate
the population to the 25 25 m grid level.
2.3.3. Spatial analysis approach
A spatial analysis approach was used to model distributary roads. These were
identified in the statistical description of the sample cities as being situated between
main roads and minor roads in the road hierarchy. To allow for their predominance
in areas of high population densities they were modelled using a cost-distance algorithm
(Longley and Batty, 1996). Within the ArcINFO GRID environment least-cost
paths between specified origins and destinations were calculated on the basis of a
defined cost attribute. Origins and destinations were randomly selected 25 25 m
gridded points located close to feeder and ring roads within areas of high population
densities (population density > 0.005 pop/m2). The SIENA population was used as
the cost attribute. A cost-weighted distance function was then calculated which
modified the Euclidian distance between origins and destinations by equating distance
with the cost of travel (ESRI, 2001). This identified the shortest route between
the specified start and end points which maximised the population density. This was
repeated 20 times for each set of distributary roads to obtain an array of possible
least-cost paths. The distributary roads for SIENA were then digitised as the mean of
the 20 possible paths.
2.4. Internal validation
An internal validation approach was chosen to evaluate the degree to which
structures and inter-dependencies observed in SIENA matched those of the sample
cities. This provided an indication whether SIENA was a realistic, acceptable representation
of a typical urban area.
The same urban metrics used to describe the inland cities (see Table 1) were
applied to SIENA. The results were compared to the mean of the inland cities using
one-sample t-tests. For the urban metrics describing land cover patches the nonparametric
ManneWhitney U and KolmogoroveSmirnov statistics were used
because these metrics were not normally distributed.