Geoscience Reference
In-Depth Information
that the position of the boundary necessarily becomes an approximation.
4
However,
the general approach can be modified by examining conditions within a particular
sector of each region instead of the whole region. This is illustrated by considering
conditions in the vicinity of the inter-metropolitan axis
A
0
B
0
.
The density function for region
A
now refers to conditions within a sector
subtending a given angle, and extending from metropolitan area
A
0
toward metro-
politan area
B
0
. For region
B
the corresponding “sectoral density function” is based
on metropolitan area
B
0
, and extends in the direction of metropolitan area
A
0
. The
relevant part of the boundary between regions
A
and
B
now occurs at the inter-
section of the two sectoral density functions. This yields a more accurate estimate
of the boundary, which will inevitably become less regular than a boundary shown
in Fig.
6.3
.
Having estimated the location boundary (with or without the assumption of
radial symmetry), it is a relatively straightforward matter to move to the multi-
regional case. In this second modification, the density functions for the various
regions could be expected to have differing central densities and slopes. Here the
overall boundary of a given region would be derived by determining the boundary
between that region and each adjoining region, and disregarding the redundant parts
of these boundaries.
6.6
Closing Comments
The notion of a regional density function has support from various strands of
location theory. Here attention has been drawn to the possibility of using regional
density functions as a method of determining the boundary between adjacent
economic regions. The rationale for this approach is that at the boundary of two
adjacent regions the interaction with the respective metropolitan nodes is of a
comparable level, and also that population density is a proxy for this interaction.
It will be recognized that there is an interesting parallel between the boundary in the
urban density function and its regional counterpart considered here. When the
density function is applied at the metropolitan area level, the boundary occurs
where some minimum urban density is encountered. When, however, the density
function is employed at the regional level, the boundary of the region occurs where
the density function intersects a corresponding density function of an adjacent
region. In both settings, therefore, it is an aspect of density that defines the relevant
boundary.
The results of this density-function approach to regional boundaries are broadly
in line with observed conditions, and are not in major conflict with the predictions
of other theoretical models based on wholly different foundations. For example, the
boundary derived above is similar to the boundary for most cases of the Economic
4
The asymmetry at distance
x
may be due to the presence of one or more urban centers or to the
existence of physical features such as mountains, deserts or large expanses of water.
