AERMOD Tech Guide
3.2.1 Friction Velocity(u) in the SBL
The computation of u* depends on the empirical observation that the temperature scale, * , defined as
varies little during the night. Following the logic of Venkatram (1980) we combine the definition of L eq. (8) with eq. (17) 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.
Substituting eq. (18) into eq. (19) and defining the drag coefficient, CD , as k/ln (zref / z0) (Garratt, 1992), results in
Multiplying eq. (20) by u*2 and rearranging yields a quadratic of the form
This quadratic has a solution, as is used in HPDM (Hanna and Chang, 1993) and CTDMPLUS (Perry, 1992), of the form
ucr is the minimum wind speed for which eq. (22) produces real-valued solutions. The temperature scale, * , is taken from the empirical expression of van Ulden and Holtslag (1985) as:
For the wind speed less than the critical value which results from eq. (23), we assume that u* and * can be parameterized by the following linear expression:
These expressions approximate the u* verses * dependence found by van Ulden and Holtslag (1983).