reflecting from cloud cover at night.<sup>28</sup> This means that a particular radiance value might be assigned different digital numbers by the same satellite on different nights or by each of two satellites on the same night. The averaging of multiple images per year by the NGDC tends to reduce the problem, as does averaging across satellites. The inter-calibration technique documented by Elvidge et al (2009) reduce but do not eliminate measurement errors. These methods rely on the identification of geographic areas with night-time lights that are presumed to have extremely stable radiance levels across the full range of _DN_ =1 through _DN_ =63.<sup>29</sup> Another problem referred to as “blooming.” Croft (1979) noted that light tended to spread out beyond the edges of urban areas to include empty, unlit spaces. Blooming has been a source of frustration for those using night-time lights as an aid to mapping the extent of urban areas. For example, the illuminated shares recorded in Table 1 above are likely to be over-stated. It also creates problems when light from one region is incorrectly attributed to an adjacent region: light from the periphery of one country or region often spills over into another country or region – or into the ocean. According to Small et al (2005), blooming is the result of the relatively coarse spatial resolution of the OLS sensor, the large overlap in the footprints of adjacent OLS pixels, and the accumulation of geolocation errors in the compositing process. Abrahams et al (2015) provides a detailed analysis and proposes a correction.

Blooming creates problems for those interested in data in levels or in changes over time. For data in levels, blooming increases the observed area of lights, _AoL_ , and decreases the observed average radiance, _R_ . This occurs because the sum of observed light, _SoL_ , does not change, e.g. the amount of energy reaching the sensors should be the same, even if it is incorrectly attributed to a larger area than the actual radiating region. As regards growth rates data, when _actual_ growth in _AoL_ is _positive_ , the growth rate of the _observed_ area of light, _AoL_ , becomes _less positive_ than actual while the growth rate of observed average radiance, _R_ , becomes more positive than actual. Conversely, when actual growth in _AoL_ is negative, the observed growth rate of _AoL_ will be more positive than actual while the observed growth rate of _R_ will be less positive than actual. The discrepancy between actual and observed growth rates will tend to be smaller for large initial values of _AoL_ since the blooming will account for a smaller share of total observed area.<sup>30</sup> The effect of blooming on observed positive growth is illustrated below. Figure 11 shows an example of how Figure 9 might look if some of the light from each pixel were attributed to all eight adjacent pixels, while preserving the value of _SoL_ . Figure 12 shows how Figure 10 (period 2) would look after the same kind of blooming. Table 6 shows that the observed growth rate for _AoL_ is reduced by 20 percentage points to 9 percent from the true growth rate of 29 percent because almost all of the observed pixels already appeared to be illuminated in period 1. With the growth rate of _SoL_ unchanged, the observed growth rate of _R_ (7 percent) is 20 percentage points more positive than the actual rate of -13 percent.

Note that blooming can lead to some quite misleading results. For example, an actual _AoL_ pixel count of 32 can look like a count of 60 or even a count of 95, depending upon whether the actual pixels are concentrated in one area (urban) or dispersed (suburban). Thus, a change from a disbursed, suburban distribution to a concentrated urban distribution within a fixed location would show almost no change in observed _AoL_ .

> 28 The US Air Force does not keep records of the changes in gain.  The sensors also gradually degrade over time, a problem reduced somewhat by periodically launching replacement satellites.

> 29 Li _et al_ (2013) offer a competing methodology based on regression techniques.

> 30 This assertion is built on the assumption that the degree of blooming is not a function of radiance.  This may be incorrect.  Abrahams et al (2015) argues that blooming extends no more than 4km from low radiance sources and up to 77km for high radiance sources.  This distinction is likely to be very relevant for specific cities but perhaps less so at national and sub-national scales where a wide variety of radiance distributions are summed together.