Ground albedo impacts on higher-order scattering spectral radiances of night sky
Introduction
Due to its high variability and dependence on a number of factors, the night sky brightness (NSB) is difficult to predict without a proper understanding of the fundamentals of light interaction with ambient environment. NSB became a subject to systematic investigation over the past decade, while providing a set of novel but non-trivial theoretical treatments and experimental findings [3], [4], [5], [13], [17], [20]. The need for a significant research effort is specifically driven by a constant increase of night light emissions from many sources distributed all over the world [6], [24] and potential negative effects of artificial light on living organisms and environment [10], [15]. We know that the artificial light can propagate deeply into nocturnal environment [2], [12], thus resulting in an increased background veiling luminance and consequent disruptions to the night sky darkness. This could be even critical to astronomical observatories that are normally situated outside lit urban areas and human settlements. NSB levels exceeding a certain threshold is definitely an adverse factor not only for professional astronomy, but also for nature.
Among other causes such as intensified light emissions upwards, the ground albedo (α) is one of core factors making night sky brighter. The more photons is reflected from the ground upwards, the more light resides in the atmosphere. This increases the chance of the photons to contribute to the NSB through an increased number of scattering events. The live of photons and their optical paths are prolonged, while generating secondary from a primary wave with a higher efficiency. For elevated values of α the reflection phenomena may become important and if appeared repeatedly the higher-order scattering radiance components can also be impacted. It is expected that the NSBs in higher-order scattering regime are somehow controlled by ground albedo, so highly reflective urban materials more than dark surfaces support the change of weighting coefficients in favor of higher scattering orders. Whatever of this sounds surprising, the reason for a shift towards higher-order scattering is that a) the generating function for the first-order radiance is due to superposition of direct emissions upwards and reflected light, and, in the same time, b) the reflected-component is controlled by α. The relative contribution of n-th scattering to the NSB is the superposition of radiance field and reflected light both for (n-1)-th scattering order (i.e. all higher-order scattering radiances are determined by the lower-order radiance field). Therefore, NSB is expected to partly deviate from linear relationship with α. The same applies to the ground reaching diffuse irradiance.
It is the purpose of this paper to verify the above hypotheses, while addressing the principal questions: a) does the relative contribution of higher-order scattering radiances change as the ground albedo approaches that of snow cover? I.e., do the higher-order scattering radiances increase to the same extent as those of the lower-order scattering radiances? b) Is single scattering still an appropriate approximation to the NSB under elevated ground reflectance? c) What are the factors that initiate the crossover from single- to multiple-scattering dominance of the skyglow? d) What effect altitude has on NSB distribution at both edges of visible spectrum? In most instances throughout the text 'altitude' refers to the altitude of an observer or an elementary atmospheric volume above sea level.
Section snippets
A framework for understanding NSB in multiple scattering regime
The fundamentals of night sky brightness modeling date back to Garstang [14], while the range of improvements to the single scattering approximation have been introduced later by Cinzano [8], Joseph et al. [18], Kocifaj [19]. However, multiple scattering effects are still poorly described and understood. Radiative transfer in multiple scattering night atmosphere illuminated from below by a number of isolated light sources is a 3D problem that is difficult to solve. Cinzano and Falchi [9]
Modeling results
Due to atmospheric optics the amplitude and angular pattern of NSB undergo large changes when transitioning from blue wavelengths to the red edge of the visible spectrum. The blue light is scattered intensively, but it has difficulty to propagate at large distances. The red light shows an opposite behavior. This is why we have made the computations for these two distinct conditions to demonstrate the range of sky glow changes we can expect at night. The modeling results presented in arbitrary
Conclusions
The ground albedo impacts on sky glow become increasingly important for light pollution research, mainly because a use of street lighting improperly orientating and focusing the luminous flux is gradually restricted, while the new modern systems with significantly lowered upward light output ratio are replacing them. Due to seasonal changes of urban albedo and large variability of land surface covers the ground reflected light can have various influence on night sky brightness and this can be
Declaration of Competing Interest
I wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.
Acknowledgments
This work was supported by the Slovak Research and Development Agency under Project No. APVV-18-0014.
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