# AERMOD Tech Guide

## 6.3 Concentrations in the SBL Calculated by AERMOD

The form of the AERMOD concentration expression, for stable conditions (L > 0), is similar to that used in ISC3

Although in stable conditions there is no analogous (to that in the CBL) lid to the mechanically mixed layer, AERMOD retards the plume material from unrealistically spreading into the region above the mixed layer height where the turbulence level is expected to be too small to support such plume mixing. When the final effective plume height is well below zim (eq.(13)), we assume that the plume can not be vertically mixed above zim and the plume is reflected back into the mixed layer. When the edge of the stabilized plume reaches the level of zim , the height at which vertical mixing is assumed to cease is allowed to rise up with the spreading plume to remain at a level near the upper edge of the plume. In this way, plume reflection is allowed, consistent with the lack of vertical turbulence aloft, but there is no strong concentration doubling effect as occurs with reflections off of an assumed hard lid. With this quasi-lid approach, AERMOD allows the plume to disperse downwards, but where the turbulence above is low, vertical plume growth is limited by a reflecting surface that is defined by eq. (78). The downward dispersion is determined by w averaged from the receptor to the effective plume height. This means that if the effective plume height is above the mixed layer height, zim, the calculation of the average w will include regions in which w is small. This will result in a decrease in both the average w and downward plume spread as the effective height increases.

When the plume buoyancy carries the rising plume into the relatively non-turbulent layer above zim , the reflecting surface is still placed at 2.15 zs above the effective plume height because there will be plume spread due to plume buoyancy and downward mixing is still important. Therefore, in the SBL plume material is assumed to reflect off an elevated surface which is defined as

where zs in eq. (78) is determined from eq. (87) with wm and u evaluated at hes ; not as an effective parameter. It is important to note that zieff depends on downwind distance since zs distance dependent. In fact, as eq. (78) suggests, this effective reflecting surface is only folding back the extreme tail of the upward distribution. Also, if zr zieff then zieff is set equal to . This approach is also implemented for the penetrated source. For the penetrated and injected sources zieff is calculated using eq. (78) with zs and hes replaced by zp and hep respectively.

In AERMOD we include the effect that lower-frequency, non-diffusing eddies (i.e., meander) have on plume concentration. We include the effects of meander only in the SBL since it not expected to have a significant effect in the CBL.

Meander (or the slow lateral plume shift due to wind direction shifting during the modeling period) decreases the likelihood of seeing a coherent plume at long travel times from sources. This effect on plume concentration could best be modeled with a particle trajectory model, since these models estimate the concentration at a receptor by counting the number of times a particle is seen in the receptor volume. However, as a simple steady state model, AERMOD is not capable of producing such information. AERMOD accounts for meander by interpolating between two limits of the horizontal distribution function: the coherent plume limit and the random plume limit. For the coherent plume, the horizontal distribution function has the familiar Gaussian form:

When the plumeâ€™s spread is assumed to be totally random, plume material will be uniformly distributed through an angle of 2. Therefore, for the random plume limit, the horizontal distribution function can be written as follows:.

To insure that xr0 as (a limit where the random or meander component should have minimum weight), FyR does not approach , we do not allow FyR to grow larger than FyC . That is:

Having defined the two limits (eq. **(79)** and eq. **(81)**), we can now interpolate between them by assuming that the total horizontal â€śenergyâ€ť is distributed between the windâ€™s mean and turbulent component. Noticing that close to the source, we can think of the horizontal wind as being composed of a mean component , and random components u and v . Then the total horizontal wind â€śenergyâ€ť can be written as

if we assume thatu = v . The random energy component is initially 2v2 and becomes equal to at large travel times from the source when information on the mean wind at the source h2 becomes irrelevant to the predictions of the plumeâ€™s position. We can represent this evolution of the random component of the horizontal wind energy through the equation

Tr is a time scale at which mean wind information at the source is no longer correlated with the location of plume material at a downwind receptor. Analyses involving autocorrelation of wind statistics, such as Brett and Tuller (1991), as well as physical intuition, suggest that after a period of one complete diurnal cycle (Tr = 24 hours), a "randomized" state of the plume transport would r be realized. From eq. **(83)** we can see that at small travel times, 2r = 2v2,while at large travel times (distances) r2 = 2v2 + 2, which is the total horizontal kinetic energy (i.e. h2 ) of the fluid. Based on the percentage of random energy contained in the system (i.e.r2 / h2, ) we can effectively weight the relative contributions of the coherent and random horizontal distribution functions to obtain a composite distribution function as follows:

The total concentration for the terrain responding state has the form of eq. **(77)** with zr replaced by zp .