Equation (103) leads to the following equation for the nocturnal urban boundary layer height

due to convective effects alone:

68

where ziuo is the boundary layer height corresponding to Po. Based on lidar measurements taken

in Indianapolis (1991), and estimates of ziu found by Bornstein (1968) in a study conducted in

New York city, ziuo is set to 400 m in AERMOD.

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, the mixed layer

height for the nighttime urban boundary layer is computed as:

 

Once the urban mixing height has been estimated, a surrogate convective velocity scale

(appropriate for the magnitude of convective turbulence present) is computed by substituting ziu

and Hu into the definitional equation for w* (Deardorff 1970). That is,

where w*u is the urban nighttime convective velocity scale and T is the near-surface air

temperature.

Having estimated w*u the turbulence in the nighttime urban can be enhanced using the

expressions found in Section 4.1.5. However, since for low level sources FwT depends primarily

on u* (see eqs. (34) and (35)) it is not possible to directly enhance FwT for these sources using w*u.

Therefore, an effective friction velocity (u*eff) is developed as a surrogate for w*u in the lower

portion of urban PBL. We define u*eff as the friction velocity that is consistent with Fwm = Fwc at z

= 7zo. Assuming that z = 7zo is always less 0.1ziuc, u*eff is estimated by equating Fwc (eq. (35)) with

Fwm (eq. (37)) and solving for u*. Once u*eff is found, the urban friction velocity for nighttime

conditions (u*u) is calculated as the maximum of u*eff and u* (the rural and daytime urban friction

velocity).

Then using the enhanced velocity scales u*u and w*u, the nighttime convective portion of the

turbulence in the urban boundary layer is computed using the expressions turbulence found in

Section 4.1.5. That is, Fwc and Fwm are calculated from eqs. (35) and (37), respectively, with w*u

used in place of the daytime convective velocity scale (w*) and u*u substituted for the rural u*.

Furthermore, for consistency purposes, a urban nighttime Monin-Obukhov length is calculated

using eq. (8) with substitutions u*u for u* and Hu (eq. (102)) for H.

Finally, the total nighttime turbulence in the urban boundary layer is calculated as the sum (in

quadrature) of the convective and mechanical portions. With these enhanced levels, vertical

dispersion due to ambient turbulence (Fza) in the urban boundary layer is calculated from eq. (

 

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