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represent municipalities (M1). Thus, the A i values in the M3 model are signi
cantly
higher than in the M1 model.
The differences between models are a consequence of taking the densely pop-
ulated peripheral districts of Warsaw into consideration, which do not in
uence the
grid-based models (M2 and M3), but do have an impact on the central-location
oriented municipal model (M1). Furthermore, the population is more concentrated
in the municipalities which are located along the main transport networks or those
where urbanised land constitutes a relatively low percentage of the area (e.g.
woodlands, river valleys). In consequence the total travel time between the average
(population-weighted) origin-destination grid nodes is shorter than calculated at the
municipal level. For that reason the potential accessibility values are higher in both
grid-based models.
Second, in case of almost all administrative units, the self-potentials produced by
the municipal model are higher than in both of the grid-based models. This effect
can either be caused by excessive internal speed impedance or by too short internal
distances. However, the internal speed of 20 km/h at the municipal level seems, in
general, to even be too low when compared with other accessibility studies that
include self-potential values [ 8 ]. This speed is also lower than that observed in the
Warsaw metropolitan area [ 30 ]. Therefore, we conclude that the internal distance
used to calculate the self-potential should be increased beyond the length of 0.5
radius proposed by Rich [ 33 ] (for detailed discussion concerning the approximation
of travel impedance please consult: Frost and Spence [ 38 ]).
Third, the differences in accessibility values between municipal and grid-based
models are not caused by the distinct method of calculating the self-potential val-
ues. Therefore, our hypothesis is that the main cause of the differences of A i values
observed is the complexity of transportation and land use relations between
neighbouring municipalities. Nevertheless, the issue of the impact of disaggregation
of population data (or even more generally: the mass applied for the potential
accessibility model) should be further investigated. Although our analysis provides
some empirical results presenting the consequences of the use of different types of
spatial data (i.e. administrative units vs. raster cells), the role of the MAUP in
accessibility studies is still an open question.
fl
References
1. Openshaw S, Taylor PJ (1981) The modi able areal unit problem. In: Wrigley N, Bennett RJ
(eds) Quantitative geography: a British view. Routledge, London, pp 60 - 70
2. Fotheringham AS (1989) Scale-independent spatial analysis. In: Goodchild M, Gopa S (eds)
The accuracy of spatial databases. Taylor & Francis, London, pp 221
228
3. Fotheringham SA, Brunsdon C, Charlton M (2000) Quantitative geography: perspectives on
spatial data analysis. Sage Publications, London
4. Sheppard E, McMaster R (2004) Scale and geographical inquiry: nature, society, and method.
Blackwell, Boston
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