PLUME RISE IN THE SBL

Plume rise in the SBL is taken from Weil (1990), which is modified by using an iterative approach which is similar to that found in Perry, et al. (1989). When a plume rises in an atmosphere with a positive potential temperature gradient, plume buoyancy decreases because the ambient potential temperature increases as the plume rises; thus, plume buoyancy with respect to the surroundings decreases. The plume rise equations have to be modified to account for this. This modification (the reader should refer to Weil (1988b) for details) produces the following plume rise formula which is used by AERMOD.. 

The velocity, u_P , and N are evaluated initially at stack height . Once plume rise has been p computed from these stack top values, subsequent plume rise estimates are made, iteratively, by averaging the u_P and N values at stack top with these at . Equation (120) applies only when the plume is still rising. The distance at which the stable plume reaches its maximum rise is given by the following expression:

Upon substituting eq. (121) for x in eq. (120) the maximum final rise of the stable plume

h_s{ x_f } reduces to: 

As with eq. (120), the velocity, u_p , and N in eqs. (122) are evaluated initially at stack height and P then iteratively.

When the atmosphere is close to neutral, the Brunt Vaisala frequency, N, is close to zero, and eq.(120) can predict an unrealistically large plume rise. Under, these circumstances, we assume that plume rise is limited by atmospheric turbulence. This happens when the rate of plume rise under neutral conditions is comparable to _w . Under these conditions (neutral limit) the plume rise can be calculated from:

L_n is calculated as:  

Also, when the wind speed in near zero (calm conditions) unrealistically large plume rise estimates would result from applying eq. (120). Under calm, stable atmospheric conditions we calculate plume rise from: 

By applying each of the above limits the final plume rise equation under stable conditions becomes:

i.e., the minimum value from eqs. (120), (122), (123) or (125); see for example Hanna and Paine (1989) . In addition AERMOD prevents the stable plume rise from exceeding the rise expected during neutral or convective conditions (i.e. h_s eq. (126) is not to exceed the rise calculated s from eq. (116)). Note, for situations when F_b = 0 no rise is calculated in stable conditions. 

Therefore, the distance dependent height of the plume in the SBL is given by the following expression:

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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