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Kocifaj, M. (2014). Modeling the night-sky radiances and inversion of multi-angle and multi-spectral radiance data. Journal of Quantitative Spectroscopy and Radiative Transfer, 139, 35–42.
Abstract: Information on a city's emission pattern is crucial for any reasonable predictions of night sky radiances. Unfortunately, the bulk radiant intensity distribution as a function of zenith angle is scarcely available for any city throughout the world. Even if the spatial arrangements of urban light fixtures and lamp specifications are known, the cumulative effect on upwardly directed beams is difficult to determine; due to heterogeneity of the ambient environment, reflectance from ground surfaces, arbitrarily scattered obstacles, orography of terrain and many other site specific factors.
The present paper develops a theoretical model and a numerical technique applicable to the retrieval of a City Emission Function (CEF) from the spectral sky radiances measured under clear sky conditions. Mathematically it is an inverse problem that is solved using a regularization algorithm in which the minimization routines penalize non-smooth solutions and the radiant intensity pattern is found subject to regularizing constraints.
When spectral sky radiances are measured at a set of discrete wavelengths or at a set of discrete distances from the monitored light source, both the aerosol optical properties and the CEF can be determined concurrently. One great advantage of this approach is that no a-priori assumptions need to be made concerning aerosol properties, such as aerosol optical depth.
The numerical experiment on synthetically generated city emissions' patterns has proven the functionality of the method presented.
Kocifaj, M. (2014). Night sky luminance under clear sky conditions: Theory vs. experiment. Journal of Quantitative Spectroscopy and Radiative Transfer, 139, 43–51.
Abstract: Sky glow is caused by both natural phenomena and factors of anthropogenic origin, and of the latter ground-based light sources are the most important contributors for they emit the spatially linked spectral radiant intensity distribution of artificial light sources, which are further modulated by local atmospheric optics and perceived as the diffuse light of a night sky. In other words, sky glow is closely related to a city's shape and pattern of luminaire distribution, in practical effect an almost arbitrary deployment of random orientation of heterogeneous electrical light sources. Thus the luminance gradation function measured in a suburban zone or near the edges of a city is linked to the City Pattern or vice versa.
It is shown that clear sky luminance/radiance data recorded in an urban area can be used to retrieve the bulk luminous/radiant intensity distribution if some a-priori information on atmospheric aerosols is available. For instance, the single scattering albedo of aerosol particles is required under low turbidity conditions, as demonstrated on a targeted experiment in the city of FrÃ½dek-Mistek. One of the main advantages of the retrieval method presented in this paper is that the single scattering approximation is satisfactorily accurate in characterizing the light field near the ground because the dominant contribution to the sky glow has originated from beams propagated along short optical paths.