AERMOD Tech Guide
3.1.2 Friction Velocity(u) & Monin Obukhov Length(L) in the CBL 15*
In the CBL, AERMET computes the surface friction velocity, u*, and the Monin-Obukhov length, L, using the value of H estimated from eq. (1). Since the friction velocity and the Monin Obukhov length depend on each other, an iterative method, similar to that used in CTDMPLUS (Perry, 1992) is used. AERMOD initializes u* assuming neutral conditions, calculates L, then proceeds with subsequent estimates of u* and L until convergence is reached (i.e., there is less than a 1% change between successive iterations). The expression for u* (e.g., Panofsky and * Dutton, 1984) is.
The initial step in the iteration solves eq.(6) for u assuming that m = 0 (neutral limit) and *m setting u = u . Having an initial estimate of u , L is calculated from the following definition for ref * L (eg. see Wyngaard, 1988):
u* is recalculated with eqs. (6) and (7) and with L for eq. (8). This procedure is continued until * the values of u and L changes by less than 1%.
The reference heights for wind speed and temperature to be used in the determination of friction velocity and Monin-Obukhov length are optimally chosen to be representative of the surface layer in which the similarity theory has been formulated and tested with experimental data. Typically, a 10-m height for winds and a temperature within the range of 2 to 10 meters is chosen. However, for excessively rough sites (such as urban areas with z0 in excess of 1 meter), AERMET has a safeguard to accept wind speed reference data in the vertical height range between 7 zo and 100 meters. Below 7 zo (roughly, the height of obstacles or vegetation), measurements are unlikely to be representative of the general area. A similar restriction for temperature measurements is imposed, except that temperature measurements as low as zo are permitted. Above 100 meters, the wind and temperature measurements are likely to be above the surface layer, especially during stable conditions. Therefore, AERMET imposes an upper limit of 100 meters for reference wind speed and temperature measurements for the purpose of computing the similarity theory friction velocity and Monin-Obukhov length each hour. Of course, other US EPA guidance for acceptable meteorological siting should be consulted in addition to keeping the AERMET restrictions in mind.