All-sky night brightness maps (calibrated images of the night sky with hemispherical field-of-view (FOV) taken at standard photometric bands) provide useful data to assess the light pollution levels at any ground site. We show that these maps can be efficiently described and analyzed using Zernike circle polynomials. The relevant image information can be compressed into a low-dimensional coefficients vector, giving an analytical expression for the sky brightness and alleviating the effects of noise. Moreover, the Zernike expansions allow us to quantify in a straightforward way the average and zenithal sky brightness and its variation across the FOV, providing a convenient framework to study the time course of these magnitudes. We apply this framework to analyze the results of a one-year campaign of night sky brightness measurements made at the UCM observatory in Madrid.