temporary and spurious lights are removed.<sup>26</sup> The result is the v.4 DMSP stable lights data set with between 20 and 100 observations per year per pixel depending upon circumstances (Baugh et al. 2009). Archives currently exist for 30 satellite-years of raw and processed data covering the years 1992 to 2012.<sup>27</sup> Elvidge et al (2013) then used an inter-calibration technique to reduce sensor inaccuracies (more on this below) over time and across over-lapping satellite observations. They also eliminated observations with _DN_ <6 in order to ensure the removal of background noise from areas known to be free of detectable lighting. As noted earlier, in most years, there were estimates from two satellites. Following Elvidge et al (2013), we averaged these overlapping estimates to produce one data series per country per year for _AoL_ , _R_ and _SoL_ . The sample is nationally summarized night-time lights data for 69 countries between 1992 and 2011. The sample excludes could have been larger and could have included 2012 except that some of the dependent variables were missing.

The annual growth rates appear to be rather noisy. The properties of the growth rates are summarized in Table 2 below. The average growth rate for radiance, _R_ , is -1.1 with a symmetrical distribution across countries and a standard deviation of ±8.7 percent. The properties for _AoL_ are quite different. These data are much noisier. The average growth rate is 4.0 percent, with a large standard deviation of ±18.4 percent and a distribution that is highly peaked and skewed towards positive values. The noisiness bears further investigation. Inspection of the data reveals that _AoL_ appears to shrink and expand by large percentages from year to year. For example, in France, the observed _AoL_ shrank by 2 percent in 2002, increased by 6 percent in 2003, and shrank again by 9 percent in 2004. It seems unlikely that this is an accurate depiction of what really happened, especially since the growth rates for real GDP and electricity consumption did not display similar trends. The properties for _SoL_ are similar to those for _AoL_ . The average growth rate is 2.9 percent with a standard deviation of ±14.7 percent, and a highly peaked distribution skewed towards positive values.

|**Table 2: Growth Rates of Night-Lights Variables, Full Sample, 1992-2011 Period Averages 1/**|
|---|

||**Radiance (****_R)_**|**Area of Lights (****_AoL)_**|**Sum of Lights (****_SoL)_**|
|---|---|---|---|
|Median|-0.4|2.0|2.3|
|Average|-1.1|4.0|2.9|
|Standard Deviation|8.7|18.4|14.7|
|Skewness|-0.7|1.8|1.8|
|Kurtosis|8.0|16.3|22.5|

1. Sample includes only those pixels with _DN_ >=6. _Sources:_ NGDC v4 and author’s calculations.

The three night-time lights measures react differently to growth. Consider a scenario in which the region depicted in Figure 2 above shows growth in the illuminated area and growth in the radiance of individual pixels, producing the numbers shown in Figure 5 below. The interesting result is that the area of light, AoL, increases by 150 percent, the sum of lights, SoL, increases by 44 percent while the average radiance, R, decreases by 43 percent. This divergence occurred because the growth of AoL outpaced growth in SoL. Positive growth in R is possible only with much faster growth of radiance within pixels, as depicted in Figure 6.

> 26 Observations contaminated by bright moon light, sunlight at high latitudes, the aurora, forest fires, gas flaring, reflections from snow cover and reflections from cloud cover are omitted.  Observations outside 65 degrees south and 75 degrees north latitude are excluded due to insufficient observations due to high snow cover, long days, heavy cloud cover and the aurora.  The remaining data from all orbits of a given satellite in a given year are averaged to filter out noise and non-permanent light sources.

> 27 <u>http://ngdc.noaa.gov/eog/dmsp/download_national_trend.html.</u>