Scaling of the urban heat island intensity using time-dependent energy balance

The urban heat island intensity (UHI) can be scaled with the urban length scale and the wind speed, through the time-dependent energy balance. The heating of the urban surfaces during the daytime sets the initial temperature, and this overheating is dissipated during the night-time through mean convection motion over the urban surface. The energy balance shows that this cooling effect can be quantified in an exponential decay in time. The minimum temperature reached at the end of this cooling period corresponds to the UHI, which increases with increasing urban length scale and decreasing wind speed. The temporal data for Phoenix, Arizona are reasonably accurately traced by this model, for the time period, from 1983 to 2010 during which Phoenix has undergone substantial expansion and therefore an increase in the urban length scale. Comparisons with the data in several cities around the world also yield quantitatively correct results for the effect of the wind speed. This model does require one correction factor to account for different urban topology in different cities. Thus, using a small number of readily available data for the urban length scale and the wind speed, the UHI intensity can be described with possible predictions for future trends.