Geoscience Reference
In-Depth Information
P
b
t
ab
M
b
P
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ð
Þ
P
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P
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M
a
A
i
¼
M
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exp
ð
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Þ
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P
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ð
t
ac
M
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Þ
P
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M
c
M
a
X
þ
j
M
j
exp
ð
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P
a
M
a
Þ
P
k
P
a
ð
t
ak
M
k
Þ
P
k
M
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M
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P
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k
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exp
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ð
6
Þ
The indirect consequence of the application of these three potential accessibility
models is that they each include self-potential in a different way. The
'
municipal
model
estimates the self-potential using the radius of a circle equalling the area of
the municipality in order to approximate the travel impedance, according to for-
mula
3
. In the case of the
'
, the potential of municipality i resulting from
the interconnections between all grid-cell-nodes located inside i is calculated as a
population-weighted average of values of potential accessibility indicator obtained
for these nodes. The last model uses the population-weighted average travel times
between all pairs of grid-cell-nodes located inside a municipality i
'
grid model
'
to estimate the
internal
travel
time (t
ii
). The difference in the self-potentials of municipality
i between the
first and the third model is then related to the different methods of
receiving the internal
travel
time (the area originated vs. population-weighted
average travel time).
In the next section the empirical results of potential accessibility analyses are
presented. We concentrate on two main issues: the differences in the results
obtained from the three different models, and the impact of different methods of
calculation of self-potential on these differences.
4 Results
The application of three different models produces some visible differences in
potential accessibility values. In general, the grid model (M2) provides higher A
i
values
the population weighted average amounts to 1,623 comparing to 1,368 in
the case of the municipal model (M1), thus the A
i
values are multiplied by 1.19 on
average, while the difference between M1 and M3 is slightly lower (on average
1.12). Application of model M1 results leads to the largest amplitude of outliers.
Nevertheless, when standardising the results with the use of the population-
weighted regional average (Fig.
1
) the accessibility patterns are rather similar. In all
variants the dominating position of Warsaw is clearly visible. The dominance of the
Polish capital mainly results from its self-potential, although an important role of
the densely populated metropolitan area, as well as the relatively good connections to
the motorway and express road network in a south-westerly direction, are also
—
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