Geography Reference
In-Depth Information
(at a simple level) the rest of the material presented in the topic will have been developed.
h e key components of the chapter can be summarized as follows:
•
Measuring distances.
•
Measuring lengths and perimeters.
•
Buf ers—measuring zones of i xed distances around objects.
•
Moving windows—mapping how values change from place to place. Moving
windows are used in many contexts, including ascertaining the gradient or
aspect of the terrain locally.
Geographical weighting—for a given location, giving more inl uence to
•
close-by values (e.g. estimating the mean at a given location, but giving greater
weight to close-by values than to values further away).
Spatial dependence and spatial autocorrelation—measuring the degree of
•
similarity in neighbouring values (or values separated by a particular distance).
h e ecological fallacy and the modii able areal unit problem—making inferences
•
from aggregated data (e.g. numbers of people aged over 65 in an area) and
considering changes in results due to changes in the size and shape of zones
(e.g. using large administrative zones or smaller zones that i t within them).
Merging polygons—joining subregions to form new larger regions.
•
Distances
4.2
Much of spatial data analysis relies on measuring straight line (Euclidean) distances
between dif erent locations. h e distance,
d
, between point
i
and point
j
is calculated
using Pythagoras' theorem:
2
2
(4.1)
d
=
(
x
-
x
)
+
(
y
-
y
)
ij
i
j
i
j
where location
i
has the coordinates
x
i
,
y
i
and location
j
has the coordinates
x
j
,
y
j
.
In words, the squared dif erence between the two
x
coordinates and the squared dif-
ference between the two
y
coordinates are calculated and added together, and the
square root of the product is taken. As an example, take a location with an
x
coordinate
of 10 and a
y
coordinate of 15, and a second location with an
x
coordinate of 22 and
a
y
coordinate of 19. h e distance between these two locations is obtained from:
(10
-+-= += =
22)
2
(15
19)
2
144
16
160
12.649
In some cases, straight line distances may not be meaningful. As well as Euclidean
distances, Manhattan distances (also referred to as taxicab distances) are also widely
used. h ese refer to distances along grids and the name derives from the grid-like
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