# AERMOD Tech Guide

## 6.4.1 Ambient Turbulence for Use in Calculating Dispersion

*Lateral Dispersion from Ambient Turbulence*

For the direct and Indirect sources int ehCBL the ambient component of the lateral dispersion is determined as follows:

The direct source plume height hed is calculated using eq (116)

The form of eq (88), with a=78 and p=0.3, follows frim an anlysisofthe lateral spread measured in the Prairie Grass experiment (Barad, 1985)

To account for the variations in release height from that at Prairie Grass we set

The value of hs , when applied in eq. **(89)** is limited to a minimum of zPG .

For sources in the SBL, the ambient component of the lateral dispersion is determined from

The Lagrangian time scale, in eq. **(90)** has been inferred from analysis of ground level concentrations in the Prairie Grass (Barad, 1958) experiments (see eqs. **(88)** and **(89)**) and extrapolated to more elevated sources and/or plume heights. This analysis resulted in a TLys given by

and z, zPG are the pollutant release heights. The appearance of zmax in the above accounts for plume heights greater than the Prairie Grass source height, zPG , (note that TLys increases with release height). Furthermore, vm in the above is limited by eq. **(44)**.

Substituting eq. **(91)** into eq. **(90)** yields a form for the lateral dispersion in the SBL that is similar to that for the CBL (eq. **(88)**).

The ambient component of the lateral dispersion for the penetrated source (yap ), which has been released below zi, but penetrates above, is calculated using eqs. **(90)** with hes set equal to hep (the height of the penetrated source). However, for the injected source, i.e. our released above zi, no substitution is needed since these sources are modeled as a stable source. I

*Vertical Dispersion from Ambient Turbulence*

For sources in the SBL, and for injected sources, the ambient portion of the vertical dispersion is composed of an elevated and surface portion. To produce a smooth transition between the expressions the following interpolation formula is used:

The expression for calculating hes is found in eq. **(127)**.

The elevated portion of the vertical dispersion for the stable source in AERMOD follows the form of the familiar equation:

The vertical Lagrangian time scale (TLz) used in eq. **(93)** is taken from Venkatram ,et al. (1982)as

This form for TLzs is also used in CTDMPLUS. The length scale, l, interpolates between the neutral length scale, ln , and the stable length scale, ls , as

Under very stable conditions or at large heights, the composite length scale, l, approaches the stable value, ls . When conditions are near neutral, N is very small, and l approaches ln .

Substituting eq. **(95)** into eq. **(94)** and eq. **(93)** results in the following expression that is used by AERMOD to compute the elevated portion of the vertical dispersion for the stable source:

Now, the surface portion of vertical dispersion for the stable source is given by (following from Venkatram, 1992)

In the CBL, the ambient portion of the vertical dispersion, for the Direct and Indirect sources, is also composed of an elevated and surface portion. The penetrated source is assumed unaffected by the underlying surface since this source is assumed to be decoupled from the ground surface by its location above zi . The total ambient components of the vertical dispersion for the Direct

and Indirect sources is:

The elevated portion of vertical dispersion for the Direct & Indirect Source is given by the following expression

The bj â€™s in eq. **(99)** result from the assumed bi-Gaussian p.d.f. (see Weil et al., 1997) and are given by

with R = 2 and the aj â€™s given by eq. **(72)**.

The first constant (0.6) on the right-hand side of the b expression is included to maintain consistency in the neutral-limit forms of z for a surface source in the CBL and the SBL. In this limit, zs for the CBL (eq. **(103)**) is zero, and from eq. **(97)** for the SBL, we have TS ~ 0.8u*x/u

To avoid this near-surface, near-neutral discontinuity, the elevated form for z (eq. (99)) remains non-zero even for HP = 0. That is, the b (for HP = 0) in combination with eqs. **(98)** and **(99)** and the neutral limit for w (= 1.3 u* from eq. **(38)**) yields surface z = 0.8u*x/u in the CBL (consistent with the neutral limit).

For the Direct & Indirect Sources (CBL), the surface portion of the vertical dispersion is calculated from

where: bc= 0.5

The parameterization of eq. **(103)** is based on Venkatramâ€™s (1992) results for z due to a surface z source in the unstable surface layer; i.e., . The parameterization is designed to: 1) agree with Venkatramâ€™s result in the limit of a surface release (i.e., HP = 0), 2) provide good agreement between the modeled and observed concentrations from the Prairie Grass experiment , and 3) decrease with source height in the surface layer (HP < 0.1 zi ) and ultimately vanish for HP > 0.1 zi . The constant bc was chosen to satisfy the second requirement above.

As indicated above the vertical dispersion for the penetrated source should be unaffected by the ground surface. Therefore, the vertical dispersion for the penetrated source is computed as the elevated portion of a stable source (eq. **(96)**) with N = 0 and with no contribution from the surface component. The Brunt-Vaisala frequency, H, assumes the neutral limit of zero because the penetrated plume passes through the well mixed layer prior to penetration and back through that layer in dispersing to receptors within the mixed layer.

As always, the injected source is modeled as any source in a stable layer.