||The radiance produced by artificial light is a major source of nighttime over-illumination. It can, however, be treated experimentally using ground-based and satellite data. These two types of data complement each other and together have a high information content. For instance, the satellite data enable upward light emissions to be normalized, and this in turn allows skyglow levels at the ground to be modelled under cloudy or overcast conditions. Excessive night lighting imposes an unacceptable burden on nature, humans and professional astronomy. For this reason, there is a pressing need to determine the total amount of downwelling diffuse radiation. Undoubtedly, cloudy periods can cause a significant increase in skyglow as a result of amplification owing to diffuse reflection from clouds. While it is recognized that the amplification factor (AF) varies with cloud cover, the effects of different types of clouds, of atmospheric turbidity and of the geometrical relationships between the positions of an individual observer, the cloud layer, and the light source are in general poorly known. In this paper the AF is quantitatively analysed considering different aerosol optical depths (AODs), urban layout sizes and cloud types with specific albedos and altitudes. The computational results show that the AF peaks near the edges of a city rather than at its centre. In addition, the AF appears to be a decreasing function of AOD, which is particularly important when modelling the skyglow in regions with apparent temporal or seasonal variability of atmospheric turbidity. The findings in this paper will be useful to those designing engineering applications or modelling light pollution, as well as to astronomers and environmental scientists who aim to predict the amplification of skyglow caused by clouds. In addition, the semi-analytical formulae can be used to estimate the AF levels, especially in densely populated metropolitan regions for which detailed computations may be CPU-intensive. These new results are of theoretical and experimental significance as they will motivate experimentalists to collect data from various regions to build an overall picture of the AF, and will encourage modellers to test the consistency with theoretical predictions.