Allometric scaling of thermal infrared emitted from UK cities and its relation to urban form City and Environment Interactions

As a result of differences in heat absorption and release between urban and rural landscapes, cities develop a climate different from their surroundings. The rise in global average surface temperature and high rates of urbanization, make it important to understand the energy balance of cities, including whether any energy-balance-related patterns emerge as a function of city size. In this study, images from the Moderate Resolution Imaging Spectro-radiometer (MODIS) satellite instrument, covering the period between 2000 and 2017, were sampled to examine the seasonal (winter and summer) night-time clear-sky upwelling long-wave energy for 35 UK cities. Total (area-summed) emitted energy per overpass per city is shown to correlate closely (R2 ≥ 0.79) with population on a log-log ‘allometry’ plot. The production of emitted energy from the larger cities is smaller than would be produced from a constellation of smaller cities housing the same population. The mean allometry slope over all overpasses sampled is 0.84 ± 0.06, implying an ‘economy (or parsimony) of scale’ (i.e., a less-than-proportional increase) of about 21% (i.e. 100(2–100.84log(2))) for each doubling of city population. City area shows a very similar economy of scale, so that the scaling of night-time emitted energy with urban area is close to linear (1.0 ± 0.05). This linearity with area indicates that the urban forms used in UK cities to accommodate people more efficiently per unit area as the urban population grows, do not have a large effect on the thermal output per unit area in each city. Although often appearing superficially very different, UK cities appear to be similar in terms of the components of urban form that dictate thermal properties. The difference between the scaling of the heat source and literature reports of the scaling of urban-rural air (or surface) temperature difference is very marked, suggesting that the other factors affecting the temperature difference act to decrease strongly its scaling with population.