Steve Albers Dan Duriscoe Modeling Light Pollution from Population Data and Implications for National Park Service Lands here are many factors that affect nighttime sky brightness, both natural and human-made. It is useful to think of what the main light sources are and how this light is scattered. The natural sources come from stars, the Milky Way, airglow, and moonlight. Human-made sources include streetlights and other outdoor Tlights, concentrated largely in towns and cities. Light is scattered by air mole- cules, natural and anthropogenic particulates, and haze (an enlargement of these particulates related to atmospheric moisture). The result of all these factors is what we see at night in terms of the sky brightness. To help clarify the further discussion, some simplifications will be helpful. We will assume no moonlight and relatively low levels of particulates and haze—in other words, that we are looking at the night sky under conditions that are among the best for a given location. We also neglect things such as surface albedo, which af- fects how much light is directed upward from city lights. The main remaining factor is city lights, whose effect is approximately related to population, and natural airglow (a continuous aurora-like glow) that actually varies during the course of the sunspot cycle. The darkest sites on earth have a brighter glow than those in outer space for two main reasons: the scattering of starlight by the atmosphere, and airglow. A number of people have mod- gram (DMSP; run by the U.S. Air eled light pollution in various ways. Force) to estimate skyglow in the As an example, Garstang (1986) has close vicinity of urban areas. This done detailed calculations for a has the advantage of considering ac- number of observatory sites, creating tual satellite data at high resolution, maps showing how the skyglow var- both spatially and in terms of inten- ies at different altitudes and azimuths sity. However, limited consideration from each site. Burton (2000) is is given to atmospheric scattering, analyzing satellite data from the De- especially over large distances. fense Meteorological Satellite Pro- DMSP data have been linked with 56 The George Wright FORUM a robust scattering model in Europe tance to the city in meters. This is by Cinzano et. al. (2000, 2001). corrected for earth’s curvature at When properly calibrated, this pro- large distances (this necessity was vides greater spatial information pointed out by Garstang). The cor- about the sources of light pollution rection is done by calculating the than population data alone. fraction f of the air molecules and other scatterers over the observer Assumptions and data source. that lie above the earth’s shadow that The present effort is unique in that it is formed from light traveling in a produces an areal map of zenithal sky straight line from the city. The over- brightness over the entire USA. It all scale height s for these scatterers works both within and at large dis- (defined as the altitude increase re- tances from urban centers. The quired to see a drop-off by a factor of model also employs assumptions e) is currently set to 4,000 m. This is about scattering embodied in less than the “clear air” value of Walker’s Law, with additional con- 8,000 m accounting for a typical sideration of the earth’s curvature. amount of aerosols. The scattering The model is based on the location from this mixture is more strongly and population (1990 census) of sig- concentrated at low altitudes than nificant U.S. cities and towns (over that from air molecules alone. 50 population). f = e-h/s (2) Mechanics of the model. The The height h is the amount of the air model creates a map of expected column above the observing location skyglow at the zenith. For each loca- that is not in a direct line of sight to tion in the map, the light pollution the light-polluting city due to the contribution from each city is as- curvature of the earth. Adding this sumed to be related linearly to the correction term f into equation 1 population and the inverse 2.5 yields a further modified form of power of the distance. This is similar Walker’s law as shown in equation 3. to the relation used in Walker’s law I = 11300000pr-2.5f (3) (Walker 1977), except that we are i estimating light pollution at the ze- Finally the light pollution from each nith instead of 45 degrees high in the city is summed to get the total artifi- azimuth of the brightest city. The cial skyglow I at a given location on relation used here for each city i is in the light pollution map as in equation equation 1, where 4. -2.5 Ii = 11,300,000pr (1) I = summation Ii (4) Ii is sky glow in nanoLamberts, p is A number of other ideas and the city population, and r is the dis- equations used come from publica- Volume 18 • Number 4 2001 57 tions by Garstang. The assumed ra- darkest country site has pixel values dius of each city is a function of city of (42,52,67). The calibration bar is population, ranging from 2.5 km to intended to linearly represent the sky 24 km. Walker’s law applies if we are brightness in terms of magnitudes outside the city radius. Inside the per square arcsec. The model result city radius, the sky glow increases is shown in Figures 1 and 2. linearly toward the center by another Schaaf Sky Quality Scale. Fred factor of 2.5. Schaaf has provided much helpful A value for the natural skyglow is discussion that has led to substantial added onto the light pollution con- improvements in this image. As part tribution. The natural skyglow is as- of the calibration process of the im- sumed to be equal to 60 nanoLam- age, we are comparing the expected berts (V = 21.9 mag / sq sec) at solar amount of light pollution for various minimum. The last step in arriving at locations with observations of limit- a pixel value is scaling the brightness ing magnitude and sky quality ac- with respect to the logarithm of the cording to the Schaaf scale (Table 1; skyglow. The brightest city has pixel Schaaf 1994). values of (255,255,255), and the 58 The George Wright FORUM Schaaf Zenithal Limiting Magnitude Class 1 <4.75 2 4.75-5.25 3 5.25-5.75 4 5.75-6.20 5 6.20-6.55 6 6.55-6.76 7 6.76-6.81 Volume 18 • Number 4 2001 59 Verification of the model with dicts. observations. Field data have been received from locations throughout A natural extension of this work the USA, primarily from the Interna- would be to incorporate DMSP data, tional Meteorological Organization. perhaps along with the population These data are in the form of zenith data, to gain a better idea of where limiting magnitude, and can be com- the light sources are in the USA. pared with values predicted by the This has been done for Europe and model for the same location. Figure 3 may be extended to other parts of the is a scatter plot of observations re- world by Cinzano et. al. (2001). The ceived near sunspot maximum com- use of population data from other pared with predicted limiting mag- census decades could provide a time nitude for the site. The graph shows series of light pollution in the USA that the predicted values are in rela- over many years. tively good agreement with those observed, especially between mag- nitudes 5 and 6. For very dark skies, observers typically do not see stars as The model may be used to evalu- faint as the model predicts, and for ate the effects of light pollution on brighter skies, observers consistently areas administered by the National see stars fainter than the model pre- Park Service (NPS) for the purpose 60 The George Wright FORUM of protecting night sky visibility. West were predicted to still possess When the image generated by the Schaaf class 7 (pristine ) skies, while model is imported into a geographic such sites were very rarely east of the information system such as ArcInfo, Mississippi River. Large areas of and the park boundaries superim- class 7 skies are seen in Nevada, posed, a simple intersection of the Montana, North Dakota, eastern two themes yields data on the relative Oregon, southeastern Utah, northern proportion of each park that falls Arizona, western Texas, and Wyo- within each of the Schaaf scale ming. These regions were far enough classes. Figures 4 through 8 show from large urban centers that the in- selected regions of the USA (in a fluence of light pollution was mini- negative image for clarity) with NPS mal. Several large and well-known areas superimposed upon the light national parks fall within these areas, pollution model. The state bounda- including Glacier, Yellowstone, ries are also added, and the maps are Canyonlands, Grand Canyon, and produced in Lambert’s Conformal Death Valley. Conic Projection. The GIS analysis produced a ta- Examination of these maps reveals ble of park areas showing what per- that, as of 1990, large areas of the centage of the area within each park Volume 18 • Number 4 2001 61 62 The George Wright FORUM fell within each of the Schaaf classes. authors apologize in advance if the Also, a mean Schaaf class was com- reader’s favorite park was left out. puted, and the total acreage of each The table is ordered first from dark- park was calculated (Table 2).