3.2.2 CONVECTIVE VELOCITY SCALE (w*)

AERMOD utilizes the convective velocity scale to characterize the convective portion of

the turbulence in the CBL. Field observations, laboratory experiments, and numerical modeling

studies show that the large turbulent eddies in the CBL have velocities proportional to the

convective velocity scale (w*) (Wyngaard 1988). Thus in order to estimate turbulence in the

CBL, an estimate of w* is needed. AERMET calculates the convective velocity scale from its

definition as:

 

3.3 Derived Parameters in the SBL

In this section the parameters used to characterize the SBL are discussed along with their

estimation methods. During stable conditions the energy budget term associated with the ground

heating component is highly site-specific. During the day, this component is only about 10% of

the total net radiation, while at night, its value is comparable to that of the net radiation (Oke

1978). Therefore, errors in the ground heating term can generally be tolerated during the

daytime, but not at night. To avoid using a nocturnal energy balance approach that relies upon

an accurate estimate of ground heating, AERMIC has adopted a much simpler semi-empirical

approach for computing u* and L.

3.3.1 FRICTION VELOCITY (u*) IN THE SBL

The computation of u* depends on the empirical observation that the temperature scale, 2

* ,

defined as

varies little during the night. Following the logic of Venkatram (1980) we combine the

definition of L eq. (8) with eq. (10) to express the Monin-Obukhov length in the SBL as

From (Panofsky and Dutton 1984) the wind speed profile in stable conditions takes the form

where $m = 5 and zref is the wind speed reference measurement height. Substituting eq. (11) into

eq. (12) and defining the drag coefficient, CD, as k (z z ) (Garratt 1992), results in ref o ln

Multiplying eq. (13) by CD u*

2 and rearranging yields a quadratic of the form

where u z g T . As is used in HPDM (Hanna and Chang 1993) and CTDMPLUS o m ref ref

2 =β θ*

(Perry 1992) this quadratic has a solution of the form

 

 

 

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