allowing a region’s sum light for each year during the period
to be calculated. Additionally, an administrative region’s
(e.g., a country or province/state) total CO
2
emission can be
taken from a statistics bureau or an energy organization (e.g.,
United Nations Statistics Division, US Energy Information
Administration, or International Energy Agency). Conse-
quently, the amount of CO
2
emissions represented by one
unit of sum light can be computed producing the slope of the
linear function. Since all such linear functions’ intercepts are
0, any one year’s linear function can be developed. Although
directly using the linear functions to map CO
2
emissions will
generate relatively large errors, the approach is still valuable,
especially to map multi-year high-resolution CO
2
emissions at
large scales when considering on the ground situations where
many countries or regions do not have high-quality statistical
systems and/or sufficiently detailed socioeconomic or envi-
ronmental
GIS
data (Chen and Nordhaus, 2010).
Some characteristics of nighttime lights make nighttime
light imagery data become a good proxy for CO
2
emissions. In
modern society population and affluence both greatly influ-
ence the amount of fossil fuel usage and consequently the
amount of CO
2
emissions (Rayner
et al.
, 2010). A region’s
brightness of nighttime lights reflects not only the region’s
population but also the region’s affluence (Bharti
et al.
, 2011;
Chen and Nordhaus, 2010; Sutton
et al.
, 2001; Sutton
et al.
,
2003; Zhao and Samson, 2012). Hence, nighttime light data
can more accurately reflect CO
2
emissions than population
or economy data (Oda and Maksyutov, 2011; Rayner
et al.
,
2010). However, some limitations of stable light annual image
products will lead to a certain number of errors when stable
light image products are used to disaggregate CO
2
emissions
regardless of a selection of the linear, exponential, or piece-
wise functions.
First, regions with relatively bright nighttime lights do not
necessarily have the relatively large amounts of CO
2
emis-
sions. Through checking with Google
™
Map’s high-resolution
images, we found that a considerable number of regions
with over-distribution of CO
2
emissions in urban and subur-
ban areas are compact residential districts. In daytime most
residents go to urban core areas to work and there are no
large-CO
2
-emissions resources in the residential districts. So
the amounts of CO
2
emissions in such regions are not very
large. Yet, at nighttime when most residents return home the
residential areas have relatively bright lights. Hence, CO
2
emission in such residential areas is likely to be over-distrib-
uted. More importantly, a region not represented as lit area in
nighttime light images may still have a certain amount of CO
2
emissions. Regions without any nighttime lights are likely
to have socioeconomic activities and CO
2
emissions during
the day. For example, a small factory emits a certain amount
of CO
2
in daytime but stops its production and turns off all
lights at night. Moreover, capability of the
DMSP-OLS
to detect
nighttime lights is limited. The
DMSP-OLS
cannot record a vis-
ible band light source if radiance of the light source is smaller
than 10
-9
Watts/cm
2
/sr (Doll, 2008). In daytime a certain num-
ber of vehicles travel on secondary highways in rural areas
and consequently emit a certain amount of CO
2
. Yet, at night-
time the number of vehicles traveling on secondary highways
reduces markedly. Light derived from sporadically passing
cars is too weak to be observed by the
DMSP-OLS
. Thus, a con-
siderable number of areas indicated by the
DN
value of 0 in
nighttime light images actually have certain amounts of CO
2
emissions but are not distributed in any significant amounts.
In 2002 about 7.08 percent of CO
2
(63,564,614 tonnes) was
emitted in unlit regions.
Second, in stable light image products radiance of night-
time lights is converted into 6-bit
DN
values (i.e.,
DN
values
of 0 to 63). In the stable light image products, regions with
the same
DN
values are very likely to have small differences
in radiance of nighttime lights and small differences in CO
2
emissions. However, when only stable light image products
are used such regions will be distributed the same amounts of
CO
2
emissions.
Finally, during the day a large number of people and
socioeconomic activities intensively migrate to urban core
areas. At nighttime the urban core areas have many lights,
but brightness of the lights is still not large enough to reflect
the actual amounts of CO
2
emissions mainly resulting from
the daytime activities. Particularly, existence of a saturation
problem results in large under-distributions in urban core
areas. Although the radiance calibrated lights product does
not contain any saturated pixels, at present only eight radi-
ance calibrated lights products for eight years are available.
Moreover, no more radiance calibrated lights products will
be produced in the future due to no fixed-gain imagery after
2011. Thus, uses of the radiance calibrated lights product
are greatly limited. By contrast, stable lights annual image
composites have covered 22 years from1992 to 2013. Night-
time-light-imagery users have recognized that the saturated
pixels in stable lights annual image composites may reduce
the quality of quantitative application of stable lights annual
image composites for estimating socioeconomic parameters
(Oda and Maksyutov, 2011; Zhao
et al.
, 2012). Letu
et al.
(2010) corrected this saturated pixel problem but additional
GIS
data of built-up area rates were needed. In the present
study we focused on examining mapping accuracy when only
stable light image products were used, so saturated pixels in
the piecewise function were simply revalued from 63 to 71.61
dependent on the averaged amount of CO
2
emissions corre-
sponding to the saturated pixels and the exponential correla-
tion between brightness of nighttime lights and the amounts
of CO
2
emissions. The saturated pixels should have had dif-
ferent
DN
values; revaluing the saturated pixels to 71.61 is just
an expedience without involvement of any third-party data.
Whereas, 71.61 is a mean value for the saturated pixels’ actual
DN
values in this particular study, we can assume some num-
ber of the saturated pixels’
DN
values should be larger than
71.61. Consequently, the amounts of CO
2
emissions in certain
areas of urban core regions were still under-estimated even
after the revaluation. We caution that 71.61 as a mean value
of the saturated pixels is case specific only and a limitation
of our methodology. We do not suggest using 71.61 to revalue
saturated pixels in the other applications of nighttime light
imagery. When the nighttime light image data are used to dis-
aggregate other socioeconomic factors (e.g.,
GDP
and electric
power consumption), coefficients of the regression functions
and average amounts of the socioeconomic factors corre-
sponding to the saturated pixels will be evidently changed.
Thus, the mean value should be adjusted accordingly.
Therefore, whichever function is selected, the following
three major cases of limitations exist when only stable light
image products are used to map CO
2
emissions: (a) CO
2
fails
to be mapped in the unlit regions, (b) Regions with the same
DN
values of nighttime light images are valued at the same
amount of CO
2
emissions, and (c) Amounts of CO
2
emissions
in urban core regions, particularly in regions with the
DN
value
of 63 in nighttime light images, are greatly under-estimated.
It can be expected that a sound way to overcome the above
limitations is to employ additional socioeconomic or physical
geographic data. The additional data should have the fol-
lowing characteristics: (a) non-zero values in unlit areas, (b)
acceptable differing values in areas with the same
DN
values
of nighttime light imagery, and (c) relatively large values
in areas with saturated pixels of nighttime light imagery to
compensate under-estimation generated by the under-valued
nighttime light image data. Therefore, with nighttime light
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