Characterizing the zenithal night sky brightness in large territories: How many samples per square kilometer are needed?

A recurring question arises when trying to characterize, by means of measurements or theoretical calculations, the zenithal night sky brightness throughout a large territory: how many samples per square kilometer are needed? The optimum sampling distance should allow reconstructing, with sufficient accuracy, the continuous zenithal brightness map across the whole region, whilst at the same time avoiding unnecessary and redundant oversampling. This paper attempts to provide some tentative answers to this issue, using two complementary tools: the luminance structure function and the Nyquist-Shannon spatial sampling theorem. The anaysis of several regions of the world, based on the data from the New world atlas of artificial night sky brightness (Falchi et al 2016, Sci. Adv. 2, e1600377) suggests that, as a rule of thumb, about one measurement per square kilometer could be sufficient for determining the zenithal night sky brightness of artificial origin at any point in a region to within 0.1 magV/arcsec2 (in the root-mean-square sense) of its true value in the Johnson-Cousins V band. The exact reconstruction of the zenithal night sky brightness maps from samples taken at the Nyquist rate seems to be considerably more demanding.