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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
radiance units (point B) is a point where all the relationships
converge except the all-state relationship. Despite their
divergence at high radiance values, all models would produce
similar results if the input values were between these points.
The results show that the US Census and BEA relationships
are markedly different from those of the other three
aggregation schemes. More importantly, it also shows that the
overall state-level relationship is most similar to these
simulated aggregation schemes and not to those of the
conventional US regions. This has important implications for
extending this technique to areas that have only one level of
sub-national data.
4000000 = ; Imc
$8 3500000
p
= 30000 ec
= 3000000 E.
= 2500000 T
= "ms A
$ 2000000 A e oz US census
x 1500000 4 BEA
S 1000000 Alphabet
a A
a 500000 + latitude
2 ; Rank
o 0+
a —— AIl States
-500000 T T T T 1
0 1E+07 2E+07 3E+07 4E+07 5E+07
Radiance (W.cm^-2.um^-1.sr^-1)
Figure 3. Comparison of different relationships derived from
the five aggregation schemes displayed in Figure 1.
Taking these points into consideration it is suggested that the
US has a number of regional sub-economies, hence the high
intra-regional correlation coefficients of the US Census and
BEA divisions. However, the regions themselves vary greatly
and bear little relationship to each other. This is not to say that
there is no general nationwide correlation. The reason why the
intra-regional correlation is so poor for the ranked states may
relate back to the nature of the individual regional economies.
Assembling regions by ranking states puts the most
economically productive states (California, Texas, Florida,
Illinois, Ohio, Pennsylvania, and New York) together.
However, they apparently bear little resemblance to each other.
This trend continues for each group of states. BEA (and US
Census) regions by contrast usually consist of one dominant
state and a number of less economically productive satellite
states. Working down the list of states, each BEA region
generally has a good mix of members from each group of
(ranked) states. The exceptions are the Plains and Mideast
regions which contain Ohio and Illinois, and New York and
Pennsylvania respectively, and conversely the Rocky Mountain
region, which has no member from the most economically
active group of states. However, when viewed in totality their
component states fit a single nationwide model albeit with two
outliers (New York and California). Many countries anlaysed
also exhibited one or two regions which did not fit the general
model for the rest of the country.
Spain provides an interesting example of how an outlying point
can affect its parent regions. The relationships derived at each
NUTS level were found to vary more than any other country.
The gradient becomes progressively shallower as larger areas
are considered in the analysis ranging through y = 0.069%,
0.059x and 0.056x for NUTS levels-3, 2 and 1 respectively.
793
These values are for relationships constrained to run through
the origin and include the outlying points, whose effect
becomes less influential as the spatial units become larger in
size. The generally good correlation in Figure 4 masks much of
the detail. Despite the standard deviation of the GRP/radiance
quotients being relatively low compared to other countries
analysed the individual NUTS-3 zones have been combined in
such a way as to result in vastly different relationships at
different NUTS levels and confuse the base-level correlation.
x
Radiance
(C10^- 10 WW /cm^2/um/sr)
* xit Madrid +
; ME. à p
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y =0.0539x
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2 150000 : [Este E
= NUTS-2 :
E a
= 100000 4 Catalunya + NUT
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Barcelona &
m e uat
50000 x
o4 | : A
a 1000000 2000000 3000000 4000000 5000000
Radiance (W.cm^-2.um^-1.sr^-1)
Figure 4. Night-time lights of Spain with its NUTS-3
boundaries and total radiance — GRP scatterplot. The
relationship is based on NUTS-3 points only, excluding
Barcelona and Madrid. The NUTS-1 regions of Madrid and
Este are outlined in black on the map. Catalufia lies within the
region of Este and is outlined in brown (n=40).
The NUTS-3 area of Barcelona is far more radiant than other
NUTS-3 regions and is observed to be an outlier. The capital,
Madrid is a NUTS-1 region and is about one third brighter
than Barcelona. Barcelona is part of Cataluña, which is itself
part of the Este NUTS-1 region. The other regions of Este have
anomalously low GRP for the total radiance in the region.
Barcelona dominates this region to such an extent that not only
does it pull its NUTS-2 point away from the trendline but it
has also pulled its NUTS-1 point towards it. In fact, it is only
due to the presence of Barcelona in the region that its NUTS-1
point is anywhere near the regression line. Its position without
Barcelona's contribution is also shown in Figure 4. In this
case, due to the magnitude of these modifiable areal unit
effects, it is most prudent to just use the original NUTS-3
relationship and treat Barcelona and Madrid as separate
outliers. This is the relationship displayed on the graph in
