1000 up to 2,000,000. These data represent the maximum urban effect for each city since they

were collected during ideal conditions of clear skies, low winds, and low humidities. An

empirical fit to the data yields the following relationship

where )Tmax = 12 °C, Po = 2,000,000 (the city population associated with the maximum

temperature difference in Oke’s data), and P is the population of the urban area being modeled.

Since the ambient nighttime temperature of an urban area is higher than its surrounding rural

area, an upward surface heat flux must exist in the urban area. It is assumed that this upward

surface heat flux is related to the urban-rural temperature difference through the following

relationship

where " is an empirical constant, D is the density of air, and cp is the specific heat at constant

pressure. This expression is analogous to the bulk transfer parameterization of heat flux over a

homogeneous surface (e.g., Businger (1973)),with " defined as the “bulk” transfer coefficient.

We chose " to ensure that the upward heat flux is consistent with maximum measured values of

the order of 0.1 m s-1 oC . Because )Tu-r has a maximum value on the order of 10 oC, and u* is on

the order of 0.1 m s-1, " should have a maximum value on the order of 0.1. Although we assume

that " has a maximum (city center) value of about 0.1, AERMOD uses an effective value of " a

that is averaged over the entire urban area. Assuming a linear variation of " from 0 at the edge of

the urban area to about 0.1 at the center of the urban area results in an areal average equal to onethird

of that at the center (since the volume of cone is one-third of that of a right circular cylinder

of the same height). Therefore, AERMIC tested an area-averaged value of " equal to 0.03 against

the Indianapolis data. This choice for " is consistent with measured values of the upward heat

flux in Canadian cities reported by Oke (1973; 1982). The results of the developmental testing

indicated that this choice for " resulted in an adequate fit between observations and AERMODpredicted

concentrations.

The mixing height in the nighttime urban boundary layer, ziu, is based on empirical evidence

presented in Oke (1973; 1982) that, in turn, suggests the following relationships:

where R is a measure of the city size and P is the population of the city. The first relationship is

based on the observed growth of the internal convective boundary layer next to shorelines

(Venkatram 1978). The second relationship implicitly assumes that population densities do not

vary substantially from city to city.

 

 

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