Scaling of the urban heat island effect based on the energy balance: Nighttime minimum temperature increase vs. urban area length scale

One of the adverse results of urbanization is the urban heat island (UHI) effect, wherein a combination of various factors renders the temperatures in an urban region higher than in the surroundings. We examined the UHI effect in 2 cities: Phoenix and Tucson (Arizona, USA), with disparate length scales but similar meteorological conditions. Based on analyses of both the urbanized land surface areal growth and thermal energy balance, a correlation appears wherein the nighttime minimum temperature (an indicator of the UHI effect) is seen to follow the square-root of the area, or the length scale of the urbanized land area. Using thermal energy transport for the air mass above the urbanized area, this scaling can be explained by a time-dependent energy balance, which shows that the rate of decrease in temperature also scales linearly with the length scale of the urban area. Viewed in this perspective, the length scale of an urbanized area is an important parameter in determining the severity of the UHI effects, as the advection rate is diminished when the length scale of the urban area is increased. Based on this scaling, the UHI effect, as indicated by nighttime temperature deviations from undisturbed levels, will tend to increase as the square-root of the urbanized area due to the advection rate effect.