# AERMOD Tech Guide

## 6.7 Adjustments for the Urban Boundary Layer

AERMODâ€™s urban formulation applies only to the nighttime boundary layer; there is no distinction made between urban and rural boundary layers during the day. The urban convective boundary layer forms in the night when stable rural air flows onto a warmer urban surface. 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.

In order to account for the unique characteristics of the nighttime urban boundary layer, AERMOD enhances the turbulence of the rural stable boundary layer. This enhancement consists of a convective urban contribution to the total turbulence in the urban SBL. 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.

The urban-rural temperature difference depends on a large number of factors that cannot easily be accounted for in applied models, such as AERMOD. For simplicity, we chose to use the data presented in Oke (1973, 1982) to construct an empirical model. 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. An empirical fit to the data yields the following relationship

Po 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 assume that this upward surface heat flux is related to this urban-rural temperature difference through the following relationship:

where is an empirical constant. We chose to ensure that the upward heat flux is consistent with a maximum measured values of the order of 0.1 ms-1C . Because Tu-r has a maximum u-r value on the order of 10Â° C, and u* on the order of 0.1 m/s, should have a maximum value on o * the order of 0.1. Although we assume that a 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. The variation of a from 0 at the edge of the urban area to about 0.1 at the center of the urban area is unknown, but a linear variation with distance from the edge of the urban area would result in an areal average equal to one-third 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 a equal to 0.03 against the Indianapolis data. This choice for a (i.e. a = 0.03) is consistent with measured values of the upward heat flux in certain Canadian cities reported by Oke (1973, 1982). The results of the developmental testing indicated that this choice for a resulted in an adequate fit between observations and AERMOD-predicted concentrations.

The mixing height in the nighttime urban boundary layer, ziu is based on empirical evidence presented in Oke (1973, 1982), which suggests the following relationships:

.where R is a measure of the size of a city and P is the population of the city. The first relationship is based on observed growth of the internal convective boundary layer next to shorelines (See Venkatram, 1978 for example). 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.

Eq. **(131)** leads to the following equation for z ,

where ziuo is the boundary layer height corresponding to Po .

Hanna and Chang (1991) report lidar measurements from the Indianapolis tracer study program for nocturnal conditions. While the mixing heights at night range from 100 to 500 meters, they approach 400 meters during clear, calm conditions. Using eq. **(132)** and an Indianapolis population of 700,000, the value of ziuo is computed to be 500 meters. This is fairly consistent with the estimate for ziuo on the order of 400 meters mentioned by Bornstein (1968).

In addition, since effects from urban heating should not cause ziu to be less than the mechanical mixing height, ziu is restricted from being less than zim . Therefore, from eq. **(132)** the mixed layer height for the nighttime urban boundary layer is written as:

Once the urban mixing height has been estimated the enhancement to turbulence can be calculated. To calculate the enhanced turbulence in the nighttime urban boundary layer we first calculate a w* (appropriate for the magnitude of convective turbulence present) by substituting z* and Hu into eq. **(10)**; i.e.,

Then the total vertical and lateral turbulence used in the concentration calculations are calculated from wc (eq.**(36)** is the convective portion of wT ) and vc (eq. **(45)** is the convective portion of vT ) with the convective portion of the turbulence computed by setting zic equal to ziu and by using w* as calculated from eq. **(134)**. This in essence enhances turbulence at night in the urban * boundary layer. Vertical dispersion due to ambient turbulence (za ), in the urban boundary layer, is calculated from eq. **(96)** (the SBL formulation for za ) with the urban PBL assumed to be neutral (i.e., N = 0). Similarly, for the lateral dispersion in the urban boundary layer, ya is calculated using the SBL formulation given by eq. **(90)**

The potential temperature gradient in the night-time urban boundary layer is set equal to the upwind rural profile (i.e., as measured or calculated from eq. **(31)**) for all heights above ziu , and is assumed to be equal to a small positive value below ziu ; i.e.,

For plumes below ziu , the effective reflection surface is set equal to the height of the urban boundary layer (i.e., zieff = ziu; this effective reflection surface in analogous to that calculated in eq. **(78)** for rural stable sources). Plumes that â€śpenetrateâ€ť above ziu are modeled in a manner iu similar to penetrated sources in the CBL. Plume rise in the urban stable boundary layer is calculated from eq. **(126)** with an assumed near-neutral potential temperature gradient (i.e., ). Use of this value for provides an appropriate near-neutral plume rise formulation that is expected within the nocturnal urban boundary layer. However, plume height in these conditions is not allowed to exceed 1.25 ziu

Finally, in the nighttime urban boundary layer, plume meander is not modeled since this modified stable layer has many of the turbulent characteristics of a weak convective layer. Use of this urban boundary layer formulation has yielded satisfactory performance of AERMOD for the Indianapolis data. For daytime conditions (L < 0) in urban areas, AERMOD uses the same formulations as in rural areas (i.e., no adjustments to boundary layer characteristics).