most appropriate to describe the relationship between the
DN
values of nighttime light imagery and the amounts of CO
2
emissions. To detect dim lights in suburban areas, relatively
large gain values are usually set for the OLS. Although such
settings provide more nighttime lights detected, they also
result in emergence of pixel saturation when very bright
lights in urban areas are observed (Doll, 2008). In the 6-bit
stable light image composites the maximal
DN
value of 63 is
assigned to the saturated pixels. The value of 63 is not scaled
to the other lower
DN
values and so was excluded from the
regression of the exponential function (Figure 3c). Through
overlaying the nighttime light image on the Vulcan CO
2
emis-
sions raster layer, we obtained 2,736.69 tonnes C as the aver-
aged amount of CO
2
emissions corresponding to pixels with
the
DN
value of 63. Since actual
DN
values of all the saturated
pixels are definitely larger than 50, a transition point between
linear and exponential functions, the quantitative correlation
between brightness of the saturated pixels and amounts of
CO
2
emissions should be more accurately described by the
exponential function (i.e., the equation in Figure 3c) than the
linear function (i.e., the equation in Figure 3b). Hence, after
the exponential function (i.e., the equation in Figure 3c) was
regressed, we put the value of 2,736.69 into the exponential
function and obtained the corresponding
DN
value of 71.61.
So we re-valued all the saturated pixels’
DN
as 71.61. It was
found that when 50 is selected as a transition point between
linear and exponential functions, accuracies of the two regres-
sion functions (i.e., R
2
of the regression functions) reach the
greatest extents simultaneously. Advancing our approach we
divided the whole regression into two segments (Figures 3b
and 3c) and revised the exponential function (i.e., the equa-
tion in Figure 3a) as a piecewise function:
CO
2
=
0,
DN
= 0
10.583×
DN
+ 24.944, 0 <
DN
≤
50
8.344
e
0.081×
DN
,
DN
> 50
(3)
Another CO
2
emissions map (Figure 2c) of the contiguous
US was produced based on Equation 3.
To compare accuracy of the maps generated by the above
three different functions (i.e., Equations 1, 2, and 3), we
produced another three maps (Plate 1a, 1b, and 1c) showing
differences between spatial distribution of CO
2
emissions
predicted by nighttime lights image data and actual spatial
distribution of CO
2
emissions by subtracting the Vulcan CO
2
emissions map from CO
2
emissions maps produced by the
linear, the exponential, and the piecewise functions, respec-
tively. We also computed root mean square errors (
RMSE
s) of
the three CO
2
emissions maps by
Plate 1. Differences between actual CO
2
emissions and CO
2
emissions estimated by (a) linear, (b) exponential, and (c) piecewise func-
tions. (Differences = Estimated CO
2
- Vulcan CO
2
).
Figure 4. Correlations between DN values of nighttime light imagery and amount of CO
2
emissions for California. The DN value of 63 was
excluded from the regression in Figure 4c due to its incompatibility with the other DN values in stable lights image products.
938
December 2015
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
