Experimental image modeling light pollution in the continental United States. This is based on the location and population (1990 census) of significant U.S. cities and towns (over 50 population). As the program is made more efficient, I hope to be able to include more smaller towns and perhaps rural population. I may include 2000 census (and Canadian) info once it becomes available in a list of town lat, lon, & population.
The image is a plot of expected sky glow at the zenith. Light pollution from a city is assumed to be related linearly to the population and the inverse 2.5 power of the distance (as in Walker's law). The relation used here is I = 11300000 x population x r^-2.5, where I is in nanoLamberts and r is in meters. This is corrected for earth's curvature at large distances (this necessity was pointed out by Roy Garstang). This is currently done by calculating what fraction of the air molecules and other scatterers over the observer lie within the earth's shadow as seen from the city. The overall scale height for these scatterers (defined as the incremental height required to see a drop off by a factor of 2.718) is currently set to 4000m. This is less than the "clear air" value of 8000m to account for a modest amount of aerosols. A number of ideas and equations used come from publications by Roy Garstang.
The assumed radius of each city is a function of city population, ranging from 2.5 km to 24 km. Walker's law applies if we are outside the city radius. Inside the city radius, the sky glow increases linearly toward the center by another factor of 2.5.
A value for the natural sky glow is added onto the light pollution contribution. The natural sky glow is assumed to be equal to 60 nanoLamberts (V = 21.9 mag / sq sec) at solar minimum. The last step in arriving at a pixel value is scaling the brightness with respect to the logarithm of the sky glow. The brightest city has pixel values of (255,255,255), and the darkest country site has pixel values of (42,52,67). The calibration bar is intended to linearly represent the sky brightness in terms of magnitudes per square arcsec.
Fred Schaaf has provided much helpful discussion that has led to substantial improvements in this image. As part of the calibration process of the image, we are comparing the expected amount of light pollution for various locations with observations of limiting magnitude and sky quality according to the Schaaf Scale (Nov. '94 Sky and Telescope, p64-65).
If you'd like to help in the calibration of this image, please send along the lat/lon of your favorite observing site, expressed in decimal degrees, and accurate to .001 degree if possible. This should be within the continental United States. Please include a naked eye limiting magnitude and/or sky brightness measurement if you can obtain one. The year/month of the observation is needed to help correlate with the solar cycle. These measurements should be taken at the zenith under "perfect" observing conditions, free of haze, clouds, and moonlight.
Star magnitudes for limiting magnitude determination can be obtained from a good star catalog or you can try this star count method used by meteor observers. Visual observers should have good dark adaptation. Not shown here is how the variation of limiting magnitude depends on the observer's visual acuity. The calculated magnitudes can be adjusted along a sliding scale depending on how good your vision is. A large enough set of observations has value, by virtue of the scatter about the mean values, for calculating the limiting magnitude as seen by a "typical" observer at a given site.
Sky brightness measurements should be in units of either nanoLamberts or magnitudes per square arcsec. I'm not too familiar with the intrumentation for CCD or photo-electric observations. Any references or links about this would be appreciated.
You might wish to look at the latest calibration data that compares predicted and observed light pollution at various observing sites. These are valid for solar minimum and solar maximum . Two tables are necessary because the natural background airglow is noticeably (about 50%) brighter near solar maximum compared with solar minimum. The site marked "Background" represents the best possible site if there is no light pollution. Some of the columns in the tables are defined as follows:
IMAGE COORDS- I and J pixel location. Note these vary linearly with respect to latitude and longitude. Computed LP - Calculated light pollution in nanoLamberts above natural background Mag sq sec - Calculated Magnitudes per square arcsec Lim Mag - Calculated Zenithal Limiting Magnitude (typical naked eye acuity) Lim Mag - Observed Zenithal Limiting Magnitude (if non-zero) obsvd Measured LP - The measured light pollution value in nanolamberts. First the sky brightness is measured directly in nanolamberts, or is converted from magnitudes per square second to nanolamberts. The assumed natural background is then subtracted to yield the displayed result.
When using zenithal limiting magnitude to judge how good your observing site is, a couple of additional factors should be considered. Since the vast majority of celestial objects transit to the south of the zenith, the best place to locate an observing site is to the south of the nearest town instead of the north. This would confine the worst sky glow to the less observed northern sky. Other things being equal (like ZLM), a more distant town is better than a closer one as its increased light pollution, relative to the zenithal value, becomes more confined to the horizon (at least that's my impression).
For more information about sky glow and light pollution, check out the International Dark Sky Association (IDA). Their site includes a link using this image to find dark sky sites near you. I'd be interested to see if anyone has had any luck with overlaying a state map on this image. This can be done noting that the image is in a lat/lon projection.
Page produced by Steve Albers