AERMOD Tech Guide

Gaussian Plume Air Dispersion Model

3.1.5 Mechanical Mixing Height(z) in the CBL

In the early morning when the convective mixed layer is small, the full depth of the PBL may be controlled by mechanical turbulence. AERMET estimates the height of the PBL during convective conditions as the maximum of the estimated (or measured if available) convective boundary layer height (zic) and the estimated (or measured if available) mechanical mixing height (zim ). AERMET uses this procedure to insure that in the early morning, when zic is very small but considerable mechanical mixing may exist, the height of the PBL is not underestimated. When measurements of the mechanical mixed layer are not available, the mechanical boundary layer height is calculated by assuming that it approaches its equilibrium height given by Zilitinkevich (1972):

Equation (11)

Although eq. (11) was designed for application in the SBL, it is used in the CBL only for the short transitional period at the beginning of the day when mechanical turbulence dominates. The procedure, used by AERMET, guarantees the use of the convective mixing height once adequate convection has been established even though the mechanical mixing height is calculated during all convective conditions. Since AERMET used eq. (11) to estimate the height of the mixed layer in the SBL, discontinuities in zi from night to day are avoided.

Venkatram (1980) has shown that, in mid-latitudes, eq.

Equation (12)

(11) can be empirically epresented as where zie is in (m) and u* is in (m/s). zie calculated from Eq. (12) is the unsmoothed mechanical mixed layer height. When measurements of the mechanical mixed layer height are available they are used in lieu of zie .

We smooth the equilibrium height, whether measured or calculated from eq. (12), in order to avoid sudden and unrealistic drops in zim during hours that experience a large decrease in wind speed. This smoothing is accomplished by controlling the time evolution of zie.

The time evolution of the mechanical mixed layer height, zim , is taken to be

Equation (13)

where is the time scale at which the mechanical mixed layer height approaches its equilibrium value given by eq. (12). Notice that when zim < zie, the mechanical mixed layer height increases to catch up with its current equilibrium value; conversely, when zim > zie , the mechanical mixed layer height decreases towards its equilibrium value.

It is reasonable to assume that the time scale, , that governs the evolution of the stable boundary layer is governed by the boundary layer height and the surface friction velocity,

Equation (14)

so that where ß is an empirical constant, which, we have tentatively assigned the value of 2. As an example, with u* of order 0.2ms–1 , and zim of order 500 m, the time scale is of the order of 1250 seconds.

Because the friction velocity, u* , changes with time, we integrate eq. (13) numerically as follows:

Equation (15)

where the average time scale, , is given by:

Equation (16)

In eq. (15) zim {t} is the smoothed value at time t (previous hour) and zie {t +t } is the current hour’s unsmoothed value. Therefore eq. (15) produces a smoothed value for use in for the current hour.