Zernike power spectra of clear and cloudy light-polluted urban night skies

Abstract

Received Month X, XXXX; revised Month X, XXXX; accepted Month X, XXXX; posted Month X, XXXX (Doc. ID XXXXX); published Month X, XXXX The Zernike power spectra of the all-sky night brightness distributions of clear and cloudy nights are computed using a modal projection approach. The results obtained in the B, V and R Johnson-Cousins' photometric bands during a one-year campaign of observations at a light-polluted urban site show that these spectra can be described by simple power laws with exponents close to −3 for clear nights and −2 for cloudy ones. The second-moment matrices of the Zernike coefficients show relevant correlations between modes. The multiplicative role of the cloud cover, that contributes to a significant increase of the brightness of the urban night sky in comparison with the values obtained in clear nights, is described in the Zernike space. 1.IntroductionThe constant increase of the sky glow produced by the anthropogenic emissions of light is one unwanted side-effect of the continuous spread of public and private lighting systems. A considerable amount of research is being devoted to the measurement and characterization of this phenomenon, in order to get reliable data for modeling accurately its propagation [1−6], to understand better its consequences in diverse fields [7−14], and to devise practicable strategies to keep it within acceptable limits [15−16].The multiplicative role of the cloud cover is also a matter of concern. Clouds greatly enhance the night sky brightness by reflecting (scattering) the upward radiation of the city lights. Urban overcast skies may reach radiances an order of magnitude higher than the corresponding clear skies, and four times bigger than rural clear moonlit nights [17−19]. Overall, the present levels of light pollution in many places across the world amount to a substantial change in the natural conditions of the nighttime environment.A widespread technique for monitoring the night sky brightness is based on the use of all-sky cameras with hemispheric field-of-view [20−23] that record with good spatial resolution the sky radiance in standard astronomical photometric bands like the B, V, and R Johnson-Cousins' set [24]. In a previous work [25] we have shown that the all-sky night brightness maps obtained in clear and moonless nights can be efficiently described in terms of Zernike polynomials [26−27]. Using this approach the information content of each map is condensed into an equivalent small-sized vector whose elements (the Zernike coefficients) have a definite physical meaning.Besides achieving a significant level of essentially lossless data compression, the study of the hemispherical night sky brightness may benefit that way from the conceptual and computational tools associated with modal analysis.As an example of application we described in that work the modal composition of clear and moonless urban night skies in the range of low to mid Zernike frequencies (radial orders 10 ≤ n ). While an expansion up to this order is generally enough for a succes...

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