LATERAL TURBULENCE CALCULATED BY THE INTERFACE

In the CBL the total lateral turbulence , ²_vT , is computed as a combination of a mechanical and convective portion (as was adopted for ²_vT ) such that 

In the SBL the total lateral turbulence contains only a mechanical portion.

Mechanical Portion of the Lateral Turbulence

The variation with height of the mechanical portion of the lateral turbulence is bounded by its value at the surface and an assumed residual value at the top of the mechanical mixed layer. The variation between these two limits is assumed to be linear. Based on observations from numerous field studies, Panofsky and Dutton (1984) report that, in purely mechanical turbulence, the lateral variance near the surface has the form

where the constant, C, ranges between 3 and 5 with an average value of approximately 3.6. Hicks (1985) supports the form of eq. (41) and the value of 3.6 for C.

Above the mechanically mixed layer, we expect the lateral turbulence to maintain a modest residual level. Hanna (1983) has analyzed ambient measurements of lateral turbulence in stable conditions. He has found that even in the lightest wind conditions, the measurements of _v were typically 0.5 m/sec, but were observed to be as low as 0.2 m/sec. AERMOD adopts the lower limit of 0.2 m/sec for _v for near-surface conditions (eq. (44)), but uses the more typical value of 0.5 m/sec for the residual _v above the mixed layer. Furthermore, we found that a value of the _v²= 0.25m²s^-2 order provided consistently good model performance (for plumes commonly above  z_im ) during the developmental evaluation thus supporting the presence of residual lateral turbulence in this layer. 

Between the near-surface and the top of the mechanically mixed layer, we assume the _v²  varies linearly as.

The linear variation of ²_vm with z is consistent with field observations (e.g., Brost et al 1982).

Figure 8: Family of lateral mechanical turbulence profiles over a range of mechanical mixing heights

Figure 8 shows how the vertical profile of lateral turbulence changes over a range of mechanical mixing heights. The values of u_* used to produce these curves are consistent with the relationship between z_im and u_* which is found in eq. (12). In the SBL Figure 8 represents the im * total lateral turbulence. In the CBL these curves depict only the mechanical portion of the total lateral variance. This in conjunction with the convective portion eq. (45) constitute the turbulence as expressed in eq. (40)

In very light wind conditions, u_* may also be quite small and _vo from eq. (43) may be unrealistically small. Based in part on model performance comparisons with data during the developmental evaluation, _vm is bounded (when used in calculations of _y and thus concentration) as follows

The wind speed u, in eq. (44) is evaluated at the same height as _vm . 

Convective Portion of the Lateral Turbulence

The convective portion of the lateral turbulence is calculated in AERMOD from:

This constant value of in the convective mixed layer is supported by the Minnesota data (Reading et al., 1974 and Kaimal et al., 1976) and by data collected at Ashchunch England (Canghey and Palmer, 1979).

 For z > z_i , the model linearly decreases _vc² from _vc² { z_ic } to 0.25 at 1.2 z_ic and holds constant above 1.2 z . However, if _vc² {z_ic } < .25 m²s^-2 , then _vc² {z_ic } is persisted upward from z_ic. 

If observations of _v are available below z_ic , then the value at the lowest level is assumed to v ic persist down to the surface and at the highest level up to z_ic . If the highest observed _v is above 1.2 z_ic then that value is persisted up. For observations which extend to a level between z_ic and 1.2 z_ic we linearly extrapolate the highest observed value to 1.2 z_ic , based on the slope of the reference profile. Above 1.2 z_ic we persist the value _v at 1.2 z_uc .

In the SBL the total lateral turbulence contains only a mechanical portion and it is given by eqs.(42) thru (44). Use, by AERMOD, of the same _vm expression in the CBL and SBL is done vm to maintain continuity of _vm in the limit of neutral stability. vm.40

4 AERMOD’s Meteorological Interface

4.1 General Profiling Equations
      4.1.1 WIND SPEED PROFILING IN THE INTERFACE
      4.1.2 WIND DIRECTION PROFILES IN INTERFACE 
      4.1.3 PROFILES OF THE POTENTIAL TEMPERATURE GRADIENT IN THE
              INTERFACE
      4.1.4 POTENTIAL TEMPERATURE PROFILING IN THE INTERFACE
      4.1.5 VERTICAL TURBULENCE CALCULATED BY THE INTERFACE
      4.1.6 LATERAL TURBULENCE CALCULATED BY THE INTERFACE
4.2 Vertical Inhomogeneity in the Boundary Layer as Treated by the INTERFACE

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