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 z_im (eq.(13)), we assume that the plume can not be vertically mixed above z_im and the plume is reflected back into  the mixed layer. When the edge of the stabilized plume reaches the level of z_im , 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, z_im, 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 z_im , 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 h_es ; not as an effective parameter. It is important to note that z_ieff 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 z_r z_ieff then z_ieff is set equal to . This approach is also implemented for the penetrated source. For the penetrated and injected sources z_ieff is calculated using eq. (78) with _zs and h_es replaced by _zp and h_ep 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 plume’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 x_r0 as (a limit where the random or meander component should have minimum weight), F_yR does not approach , we do not allow F_yR to grow larger than F_yC . That is:

Having defined the two limits (eq. (79) and eq. (81) ), we can now interpolate between them by  assuming that the total horizontal “energy” is distributed between the wind’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 “energy” can be written as

if we assume that_u = _v . The random energy component is initially 2_v² 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 plume’s position. We can represent this evolution of the random component of the horizontal wind energy through the equation

T_r 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 (T_r = 24 hours), a "randomized" state of the plume transport would r be realized. From eq. (83) we can see that at small travel times, ²_r = 2_v²,while at large travel times (distances) _r² = 2_v² + 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 z_r replaced by z_p . 

6 The AMS/EPA Regulatory Model AERMOD

6.1 General Structure of AERMOD Including Terrain
6.2 AERMOD Concentration Predictions in the CBL
      6.2.1 DIRECT SOURCE CONTRIBUTION TO CONCENTRATION  
              CALCULATIONS IN THE CBL
      6.2.2 INDIRECT SOURCE CONTRIBUTION TO CONCENTRATION  
              CALCULATIONS IN THE CBL
      6.2.3 PENETRATED SOURCE CONTRIBUTION TO CONCENTRATION 
              CALCULATIONS IN THE CBL
6.3 Concentrations in the SBL Calculated by AERMOD 
6.4 Estimation of Dispersion Coefficients 
      6.4.1 AMBIENT TURBULENCE FOR USE IN CALCULATING DISPERSION
      6.4.2 BUOYANCY INDUCED DISPERSION (BID) COMPONENT OF _ AND _
              y z
      6.4.3 COMPONENT OF DISPERSION COEFFICIENTS DUE TO 
              DOWNWASH
6.5 Plume Rise Calculations in AERMOD
      6.5.1 PLUME RISE IN THE CBL 
      6.5.2 PLUME RISE IN THE SBL
6.6 Source Characterization 
6.7 Adjustments for the Urban Boundary Layer

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