Methodology¶

Kernel Creation¶

All of SET’s methods for applying its light propagation model are in the file Itest.py, which executes the main function. In this function, SET first checks if a kernel is already created and, if no kernel is supplied, creates a kernel. A kernel is essentially a matrix with numerical coefficients representing the weight of light scattering from the source to the line of sight of the observer. Each pixel in the kernel thus contains a unitless value that compares the amount of light emitted from the ground to the amount of light scattered.

The kernel creation process is executed in main in lines 30-38:

if os.path.isfile(kerneltiffpath) is False:
    # Estimate the 2d propagation function
    # bottom bottom_lat = 40.8797
    # top lat= 46.755666
    propkernel, totaltime = fsum_2d(regionlat_arg, k_am_arg, zen_arg, azimuth_arg)
    logger.debug('propagation array: %s', propkernel)
    kerneltiffpath = 'kernel_' + str(regionlat_arg) + '_' +  str(k_am_arg) + '_' + str(zen_arg) + '_' + str(azimuth_arg)
    array_to_geotiff(propkernel, kerneltiffpath, filein)
    logger.info("time for prop function ubreak 10: %s", totaltime)

The block calls fsum_2d, which goes from line 109-230 and produces the array that serves as the light propagation kernel. fsum_2d begins by gathering several inputs: regional latitude, Earth radius, and the array of beta angles. By applying the haversine formula, the program then creates an array of the distances from the observation site to the light sources along an ellipsoid surface, \(D\), from the latitude and Earth radius. Additionally, an array of beta angles, \(\beta\), is created that corresponds with the array of great circle distances.

Diagram of the light propagation model created by Cinzano. Shows the relationships between the observation site and the light source. Taken and modified from REF 2, Fig. 6, p.648.

Geodesic Constants

Radius of the Earth at the equator, \(R_{equator}\), assuming an ellipsoidal surface:

Radius of the Earth at the poles, \(R_{polar}\), assuming an ellipsoidal surface:

Atmospheric Constants

\(N_{m,0}\), molecular density at sea level (Cinzano et al., 2000, p.645)

\(c_{isa}\), the inverse scale altitude of aerosols. For each kilometer above sea level, the molecular density of aerosols is assumed to be reduced by a factor of 0.104 (Cinzano et al., 2000, p.645).

For the general case, the ratio \(K\) of aerosol scattering to gas molecule scattering is assumed to be 1:1. A higher number indicates greater optical thickness, a lower number clearer skies (Falchi et al., 2016, p.10). For the western United States, a lower setting like 0.5 might be more representative of typical conditions.

\(a_{sha}\), the scale height of aerosols (Cinzano et al., 2000, p.646)

Coefficient \(\sigma_m\) of Rayleigh scattering of visual light through a vertical cross-section of the atmosphere (Cinzano et al., 2000, p.646).

References:

1. Falchi, F., P. Cinzano, D. Duriscoe, C.C.M. Kyba, C.D. Elvidge, K. Baugh, B.A. Portnov, N.A. Rybnikova and R. Furgoni, 2016. The new workd atlas of artificial night sky brightness. Sci. Adv. 2.
2. Cinzano, P., F. Falchi, C.D. Elvidge and K.E. Baugh, 2000. The artificial night sky brightness mapped from DMSP satellite Operational Linescan System measurements. Mon. Not. R. Astron. Soc. 318.
3. Garstang, R.H., 1989. Night-sky brightness at observatories and sites. Pub. Astron. Soc. Pac. 101.

Literature¶

Foundational Papers

Cinzano, P., Falchi, F., & Elvidge, C. D. (2001). The first world atlas of the artificial night sky brightness. Monthly Notices of the Royal Astronomical Society, 328(3), 689–707. Retrieved from http://mnras.oxfordjournals.org/content/328/3/689.short

Falchi, F., Cinzano, P., Duriscoe, D., Kyba, C. C. M., Elvidge, C. D., Baugh, K., Furgoni, R. (2016). The new world atlas of artificial night sky brightness. Science Advances, 2(6), e1600377. doi:10.1126/sciadv.1600377

Garstang, R. H. (1989). Night sky brightness at observatories and sites. Publications of the Astronomical Society of the Pacific, 101(637), 306. Retrieved from http://iopscience.iop.org/article/10.1086/132436/meta

Jing, X., Shao, X., Cao, C., Fu, X., & Yan, L. (2015). Comparison between the Suomi-NPP Day-Night Band and DMSP-OLS for Correlating Socio-Economic Variables at the Provincial Level in China. Remote Sensing, 8(1), 17. https://doi.org/10.3390/rs8010017

Other Methodology Papers

Cinzano, P., Falchi, F., Elvidge, C. D., & Baugh, K. E. (2000). The artificial night sky brightness mapped from DMSP satellite Operational Linescan System measurements. Monthly Notices of the Royal Astronomical Society, 318(3), 641–657. Retrieved from http://mnras.oxfordjournals.org/content/318/3/641.short

Cinzano, P., Falchi, F., & Elvidge, C. D. (2001). Naked-eye star visibility and limiting magnitude mapped from DMSP-OLS satellite data. Monthly Notices of the Royal Astronomical Society, 323(1), 34–46. Retrieved from http://mnras.oxfordjournals.org/content/323/1/34.short

Duriscoe, D. M. (2013). Measuring anthropogenic sky glow using a natural sky brightness model. Publications of the Astronomical Society of the Pacific, 125(933), 1370. Retrieved from http://iopscience.iop.org/article/10.1086/673888/meta

Cinzano, P., & Falchi, F. (2012). The propagation of light pollution in the atmosphere. Monthly Notices of the Royal Astronomical Society, 427(4), 3337–3357. https://doi.org/10.1111/j.1365-2966.2012.21884.x

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