Revisit Monin-Obukhov Similarity Theory and the Bulk Formula for Turbulence Parameterization

The observations from the Cooperative Atmosphere-Surface Exchange Study in 1999 (CASES-99) field experiment suggests that the turbulent momentum mixing under moderate to strong winds is proportional to the bulk shear (wind speed over observation height), not local wind shear (du/dz, where u and z are wind speed and height) as in Monin-Obukhov similarity theory (MOST). The new relationship, which is demonstrated in Sun et al. (2012, J. Atmos. Sci., 69, 338-351), is due to the fact that if the mixing length at a given point in the atmospheric boundary layer is large enough to reach the ground, which happens under near neutral conditions or moderate to strong winds, the effect of the ground on the turbulent mixing serves as a boundary condition to the point. However, if the mixing length is smaller than the observation height, such as under stable conditions, i.e., the ground cannot significantly impact turbulent mixing at the point, the local shear becomes more relevant in the turbulent strength at the point. In other words, the relevant shear for generating turbulence at a point is closely related to the mixing length there. Parameterizations of the turbulent momentum flux using the traditional bulk formula derived from MOST and a new formula based on the above understanding are compared.