The Allometric Scaling of Thermal Emissions from Temperate and Tropical Cities

ABSTRACT

Cities around the world develop energy balances that are different to their surroundings. This study examines the application of allometric scaling to the thermal emission of cities in temperate and tropical regions. Overpasses of UK and Nigeria of the Moderate Resolution Imaging Spectroradiometer (MODIS), covering the period between 2000 and 2017 were sampled to examine the seasonal variability in night-time clear-sky upwelling long-wave energy for selected cities of the two countries. Total (area-integrated) emitted energy was calculated per city and interpreted by looking for ‘allometric’ (power law) scaling against the total population of the urban areas. Both sets of cities produce strong correlations (R²≥ 0.8 and R²≥0.7) of log (total emission) against log (population). Total night-time emitted energy is found to scale sub-linearly (i.e. with power law index < 1) with population on both countries. However, the slope derived from UK allometry (0.85 ± 0.03) is quite different from that derived for cities in Nigeria (0.4 ± 0.05). When scaled against log (city area), both sets of cities produce linear scalings, demonstrating that the total area of built surface is a more general predictor of thermal emissions than total population, a surprising result given the differences in built form in the two sets of cities. These results are robust to the method chosen to delineate the city boundary. We further investigate the factors underlying these allometric relationships using Local Climate Zone (LCZ) classifications.