Under stable atmospheric conditions the brightness of the urban sky varies throughout the night following the time course of the anthropogenic emissions of light. Different types of artificial light sources (e.g. streetlights, residential, and vehicle lights) have specific time signatures, and this feature makes it possible to estimate the amount of brightness contributed by each of them. Our approach is based on transforming the time representation of the zenithal night sky brightness into a modal expansion in terms of the time signatures of the different sources of light. The modal coefficients, and hence the absolute and relative contributions of each type of source, can be estimated by means of a linear least squares fit. A practical method for determining the time signatures of different contributing sources is also described, based on wide-field time-lapse photometry of the urban nightscape. Our preliminary results suggest that, besides the dominant streetlight contribution, artificial light leaking out of the windows of residential buildings may account for a significant share of the time-varying part of the zenithal night sky brightness at the measurement locations, whilst the contribution of the vehicle lights seems to be significantly smaller.