PE&RS December 2015 - page 940

Results and Discussion
Figures 3, 4, 5, and 6 show that functional relationships
between brightness of nighttime lights and the amount of CO2
emissions that are invariant across the state and the national
levels: (a) overall correlations are exponential rather than lin-
ear; (b) in regions where DN values of nighttime light imagery
are equal to or smaller than 50, the relationship form is linear;
and (c) in regions where DN values of nighttime light imagery
are larger than 50, the relationship form is exponential but not
linear. Figure 7 shows differences between the actual aver-
aged amounts of CO2 emissions corresponding to pixels with
the same DN values of stable lights imagery and those estimat-
ed by the linear, the exponential, and the piecewise functions.
The averaged amounts of CO2 emissions predicted by the lin-
ear function have the largest differences while those predicted
by the piecewise function have the smallest differences to the
actual averaged amounts of CO2 emissions. Specifically, when
the linear function is used, CO2 emission is first over-esti-
mated (from DN value of 3 to DN value of 60). Moreover, with
the increase in the DN value of nighttime light imagery, the
over-estimation becomes larger and larger until the DN value
of nighttime light imagery increases to 50. After such increase
in the DN value CO2 emission is still over-estimated, but the
over-estimation becomes increasingly smaller until the DN
value of stable lights imagery increases to 60. After a DN value
larger than 60, CO2 emission is greatly under-estimated with
linear function. When the exponential function is used, CO2
emission in the beginning is over-estimated until the DN value
of stable lights imagery increases to 40. In regions where the
DN values are larger than 40 and smaller than 50, CO2 emis-
sion is over-estimated again but the over-estimations are
smaller than those predicted by the linear function. When
the DN value is larger than 60, CO2 emission is still greatly
under-estimated but the under-estimations are smaller than
those predicted by the linear function. When the piecewise
function is applied errors of CO2 emissions estimation are not
notable until the DN value of nighttime light imagery is larger
than 50. In regions where the DN values are larger than 50 and
smaller than 60, CO2 emission is first under-estimated and
then over-estimated with the piecewise function. After the DN
value is larger than 60, CO2 emission is under-estimated but
the under-estimations are smaller than those predicted by the
linear or exponential functions.
Plate 1a, 1b, and 1c show spatial distribution of the differ-
ences between the actual CO2 emissions and CO2 emissions
estimated by the linear, the exponential, and the piecewise
functions. In this study we defined regions with DN values
of 61 to 63 of the nighttime light image as urban core areas,
those with DN values of 3 to 60 as urban and suburban areas,
and those with DN value of 0 of the nighttime light image
as rural areas. Then, common features of Plate 1a, 1b, and
1c are: (a) under-estimation in most urban core regions, (b)
over-estimation in most urban and suburban regions, (c) small
under-estimation (>-50 tonnes C/km2/year and < 0 tonnes C/
km2/year) in rural areas, and (d) medium under-estimation (>-
300 tonnes C/km2/year and <-50 tonnes C/km2/year) in areas
along main highways. Apparent differences are that when the
linear function is used, the amount of CO2 emissions in large
areas of urban core regions (45.64 percent to total urban core
regions) are extremely under-estimated (<-600 tonnes C/km2/
year) and that 47.27 percent of urban and suburban regions
are largely (>100 tonnes C/km2/year and <300 tonnes C/km2/
year) or moderately (>50 tonnes C/km2/year and <100 tonnes
C/km2/year) over-estimated. When the piecewise function is
used the area of urban core regions with the extremely large
under-estimation in the CO2 emission (28.31 percent in total
urban core regions) apparently decreases. Additionally, 9.35
percent of urban and suburban regions no longer experience
large or medium over-estimation using the piecewise func-
tion. Instead, the CO2 emission in such urban and suburban
regions is slightly over (>0 tonnes C/km2/year and <50 tonnes
C/km2/year) or under-estimated (>-50 tonnes C/km2/year and
<0 tonnes C/km2/year). Therefore, compared to the use of the
linear function, the use of the piecewise function reduces
over-estimation in suburban and urban regions and under-
estimation in urban core regions.
RMSEs of the three CO2 emissions maps (Figure 2a, 2b, and
2c) produced by the linear, the exponential, and the piecewise
functions are 777.64, 771.76, and 742.78 respectively. There-
fore, compared to the use of the linear function, the use of the
piecewise function apparently reduces overall errors of map-
ping CO2 emissions. Dividing lit areas into two parts (3 to 50
and 51 to 63 of DN values of nighttime light imagery) avoids
relatively large over-estimation of CO2 emissions in low
and medium brightness regions and relatively large under-
estimation of CO2 emissions in high brightness regions except
regions with saturated pixels of nighttime light imagery.
Compared to the piecewise function, the linear function
produces larger errors in mapping CO2 emissions. However,
the linear function has distinct advantages for mapping CO2
emissions. It is highly improbable that sum light and the total
amount of CO2 emissions always change with the same pro-
portion across different years, so coefficients of the piecewise
functions are evidently variant in different years. Since the
coefficients are obtained by regression, assorted CO2 emis-
sions data for the regression are needed and that greatly limits
practical application of the piecewise functions. Yet, there is
no such limitation when the linear function is used to map
CO2 emissions. The stable lights annual image products from
1992 to 2010 can be obtained freely from the NOAA ’s NGDC
Figure 7. Differences between actual averaged amounts of CO2 emissions corresponding to pixels with the same DN values of nighttime
imagery and those estimated by linear, exponential, and piecewise functions. (The DN value of saturated pixels is not re-valued. Differ-
ences = Estimated CO2 - Vulcan CO2)
940 December 2015 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING