Outdoor Lighting and Crime - Amper

Terrain
Reflectance RT
Upward
Fraction UF
UF / UF0.1
TABLE 4. Upward Light Loss as a Function of Terrain Reflectance
0.05 0.1 0.2 0.3 0.6 0.7 0.8 0.9
0.26 0.299 0.377 0.455 0.688 0.766 0.844 0.922
0.86 1 1.26 1.52 2.30 2.56 2.82 3.08
The values of the Upward Fraction are fairly insensitive to the assumptions made, within
ranges that might be expected in practice.
A fresh snowfall covering all upwardly facing surfaces and viewed from directly overhead
could be expected to have RT = 0.9 approximately, thereby increasing the apparent light flux
from a city by about 3.08 times. It would be less than this if seen from appreciable zenith
distances because of the area of building walls visible and not covered by snow. Other factors
could also reduce the effective average terrain reflectance, such as cleared roads and paths,
and dirty, thin, patchy, consolidating or melting snow. All of these effects can be taken
account of by using an appropriately lower value for the reflectance.
Accordingly, the net effect of complete fresh snow cover is estimated as an increase of about
three times in upward light energy loss, although a factor of four has been used by others in
discussions of city lights and satellite measurements. Using a factor of three or even four still
leaves substantial discrepancies between the claim about Las Vegas and the data for the first
three cities in Table 3.
It might be thought that suburban lights seen from space would appear to extend further into
the countryside when snow cover increases the Upward Fraction. This would be true if the
light sources on the ground gradually became more spread out with distance from the city
centre. However, lit features typically tend to be sharply delimited according to Elvidge et al.
(1997). The thresholding process for city light limits is described in NASA (2000). Planning
controls on land use would appear to be a factor in the relatively well defined edges observed.
Natural boundaries such as waterways and steep changes in terrain level could also contribute.
The point here is that overestimation of city area does not seem to be an important effect
resulting from snow cover and therefore does not help to explain why Las Vegas is not at the
top of the list in Table 3.
If there are problems with the internal consistency of the satellite data, the effect would be to
increase the unexplained variance in lighting and crime correlations such as those described
below. For the present, the anomaly has to be left unresolved. This does not prevent further
use being made of the data.
Unfortunately, crime data for many of the 153 cities listed by Isobe and Hamamura are either
incomplete or apparently not available or not readily comparable with those of cities in other
countries because of differing criminal justice systems (eg the Scottish system compared with
that of England and Wales, or the New Zealand system in comparison with Australia’s). Both
crime and light loss data are required for several cities from any particular country as a
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