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, C_D , as k/ln (z_ref / 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

u_cr 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).

3 Meteorological Preprocessor (AERMET)

3.1 Derived Parameters in the CBL 
      3.1.1 SENSIBLE HEAT FLUX (H) IN THE CBL
      3.1.2 FRICTION VELOCITY (u ) & MONIN OBUKHOV LENGTH (L) IN
              THE CBL 15 *
      3.1.3 CONVECTIVE MIXING HEIGHT (z )
      3.1.4 CONVECTIVE VELOCITY SCALE (w )
      3.1.5 MECHANICAL MIXING HEIGHT (z ) IN THE CBL
3.2 Derived Parameters in the SBL 
      3.2.1 FRICTION VELOCITY (u ) IN THE SBL
      3.2.2 SENSIBLE HEAT FLUX (H) IN THE SBL
      3.2.3 MONIN OBUKHOV LENGTH (L) IN THE SBL
      3.2.4 MECHANICAL MIXING HEIGHT (z ) IN THE SBL

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