International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
southern states). For all cases, correlations using the total
(summed) radiance figures perform better than the lit-area
figures.
US Census Divisions US States
Lit-area 0.499 / 0.328 0.699 / 0.563
Log lit-area 0.641/ 0.373 0.729 / 0.467
Total Radiance 0.652 / 0.49 0.844 / 0.75
Log radiance 0.784 / 0.55 0.900 / 0.79
Table 1. Correlation of energy consumption / GRP and night-
time lights at state and aggregated US Census Division level.
3.2 Regional aggregations
The variation in the correlation of parameters at a given scale
depends on how regions are aggregated. In having data at two
hierarchical sub-national scales, it is possible to test the
national correlation at the smaller scale (regions), by using
different aggregations of larger scale units (states). Economic
data from the BEA were also presented using their regional
classification. Their grouping of states is similar to that of the
US Census using traditional aggregations based on states'
locations with respect to the various geographical regions (e.g.
Plains, Great Lakes, Mountain Division, South Atlantic). In
addition to these two classical aggregations, three others were
devised. One was a geographical aggregation, which
established five regions according to their latitudinal position.
The other two consisted of a random aggregation based on
seven alphabetical divisions and one, which divided the states
after they had been ranked by GSP. The five aggregations are
shown in (Figure 1).
US BEA (8)
Ranked by Gross State Product (7)
Figure l. Aggregation of US states into larger zones according
to 5 different criteria.
Two of the aggregation methods produce ‘regions’ which are
composed of non-contiguous states. Examining how different
aggregations affect the correlation of total radiance with the
GRP, it appears that a wide range of results can be obtained
depending on how one assembles the regions.
In addition to comparing the r-squared value at this scale, the
intra-regional correlation was also computed to see if any
discernable patterns were present. The intra-regional
correlation here refers to the average correlation of states
within a given zone. Figure 2 shows firstly that a regional
correlation of different strengths (0.4 —0.95) can be obtained
depending on how regions are arranged. Secondly, that the
intra-regional correlation (i.e. those states which when
summed form one point on the regional level scatter plot)
declines as the regional level correlation increases.
14 A m | EB Regional
09 @ Intra-regional
0.8
0.7
R-Squared
e Ce 0.0. OO .o
MN) CO in
C) —
US Census BEA Alphabetical Latitudinal Rank
Aggregation method
Figure 2. Comparison of regional and (mean) intra-regional
correlation coefficients (of total radiance vs. GDP by state) for
different aggregation methods.
These results suggest that the US Census divisions seem to be
unsuitable for building a national scale correlation, but more
appropriate for intra-regional analysis. By shifting one or two
states here and there to build the BEA regions, the correlations
improve in both measures, though these geographical divisions
are generally unsuitable. Even something as random as an
alphabetical classification provides a better regional
correlation result than the two traditional geographically
regional zones. By using a geographical criterion to aggregate
states, the latitudinal divisions provide a regional and intra-
regional correlation that is most similar to each other.
However, ranking states based on their GSP gives the best
regional correlation, but the worst intra-regional correlation,
despite the component states being of roughly equal economic
magnitude to each other. The same pattern of results was also
observed for the power consumption data.
4. DERIVED RELATIONSHIPS AND OUTLYING
POINTS
One further point to examine is what effect different
aggregations have on the magnitude of relationships associated
with these correlations. Figure 3 shows the trajectory of the
relationship for each aggregation method. Also plotted (bold in
red) is the relationship derived from state level radiance-GRP
plot. Two points on the plot are of particular interest. Firstly,
there is a point around 1E+07 radiance units (point A), where
the all-state relationship intersects that of the US Census and
BEA relationships. Secondly, further along around 1.75E+07
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