The urban surface is warmer than the rural surface because the urban surface cools at a slower rate than the rural surface when the sun sets. Two reasons for the slower cooling are that buildings in the urban area trap the outgoing thermal radiation and the larger thermal capacity of the urban subsurface. The convective contribution is a function of the convective velocity scale, which in turn, depends on the surface heat flux and the mixed layer height. The upward heat flux is a function of the urban-rural temperature difference. Oke presents observed urban-rural temperature differences for a number of Canadian cities of size varying from a population of about 1000 up to 2,000,000.
P o is the city population associated with the maximum temperature difference.
Since the ambient nighttime temperature of an urban area is higher than its surrounding rural areas, an upward surface heat flux must exist in the urban area. We chose to ensure that the upward heat flux is consistent with a maximum measured values of the order of 0.1 ms-1C . The second relation implicitly assumes that population densities do not vary substantially from city to city. The assumptions that underlie the above equations are open for discussion. However, in the absence of better information, they represent our best estimate of the governing phenomena.