# AERMOD Tech Guide

## 4.1.5 Vertical Turbulence Calculated by the Interface

In the CBL, the vertical velocity variance or turbulence (2wT ) is profiled using an expression that contains a mechanical and convective portion and is similar to one introduced earlier by Panofsky et al. (1977) and included in other dispersion models (e.g., Berkowicz at al., 1986, Hanna and Paine, 1989, Weil, 1988). It is

The above expression effectively interpolates between a mechanical or neutral stability limit (wT ~ wc ~u* ) and a strongly convective limit (wT ~ wc ~w* ).

The convective portion (2wT ) of the total variance is calculated as follows: 2

Wc where the expression for z 0.1 zic is the free convection limit (Panofsky et al, 1977), for 0.1zi < z zic is the mixed-layer value (Hicks,1985) and for z > zic is a parameterization to connect the mixed layer 2wc to the assumed near-zero value well above the CBL. The profile of convective vertical turbulence described in eq. **(36)** is also presented pictorially in **Figure 5**.

**Figure 5:**Convective portion of the vertical turbulence in the CBL.

In an earlier AERMOD formulation for mechanical (or shear induced) turbulence, values at the top of the mechanically mixed layer, i.e., v {zim } and w {zim }, were based on their values at the surface. Peer review comments suggested that since the surface is generally decoupled from higher layers, a formulation based either on measurements above zim or an assumed parameterized turbulent intensity at zim coupled with wind speed estimates would be more appropriate.

Therefore, the mechanical turbulence portion of 2wT is assumed to consist of a contribution from 2 wT the boundary layer and from a â€śresidual layerâ€ť above the boundary layer (z>zi ). This is done to: I 1) satisfy the assumed decoupling between the turbulence aloft (z>zi ) and at the surface in the I CBL shear layer, and 2) maintain a continuous variation of 2wt with z near z=zi . The mechanical turbulence is parameterized by:

The expression used to calculate _ is wml

where the wml =1.3u at z=0 is consistent with Panofsky et al. (1977).

For z > zi wmr is set equal to wmx , the maximum value of the mechanical turbulence in the residual layer. wmx is calculated as the average of all measured values above zi . If measurements are not available, then wmx is taken as the default value of 0.02u{zi}. The 0.02 is an assumed turbulence intensity iz ( = w / u) for the very stable conditions presumed to exist above zi . This value of turbulence intensity is similar to that assumed in Gifford (1975).

Within the mixed layer, i.e. z < zi , the residual turbulence is reduced from its value at zi to zero at the surface. Therefore, for all z the residual turbulence takes the form

**Figure 6** presents the profile of the mechanical portion of the vertical turbulence in the CBL. The effect of combining the residual and boundary layer mechanical turbulence (eq. **(37)**) can be seen in this figure. For the purposes of computing wmr in **Figure 6** we set L=.1zi and zo =.0001Zi

**Figure 6:**Mechanical portion of the vertical turbulence in the CBL

In the SBL the vertical turbulence contains only a mechanical portion and it is given by eq. **(37)** and eq. **(38)**. The use of the same wm expressions for the SBL and CBL is done to ensure 2 wm continuity of turbulence in the limit of neutral stability, i.e., as z 0 or | L | . That is, the turbulence should be the same as neutral stability is approached either from unstable or stable conditions. **Figure 7** is similar to **Figure 6** except for a notably increase in the value of wmr. Values for wmr are based on the magnitude of the wind speed at zi . Therefore the differences in the two figures stem from setting zo =.0001Zi in the CBL and zo =.001Zi in the SBL

**Figure 7:**Profile of vertical turbulence in the SBL