A similarity theory of convective planetary bounary layer

A higher order closure model is employed to derive the form of the similarity functions for the convective planetary boundary layer (PBL). The PBL is divided into a surface gradient, well mixed, and turbulent inversion layers. The Monin-Obukhov similarity is assumed to by valid up to the interface of the surface and well-mixed layers so long as the stability parameter is at least five. Similarity properties for the entire convective PBL are formulated, along with wind veering angle change with height. Momentum and thermodynamic equations are included in order to close the system describing the turbulent inversion layer, resulting in six parameters which are necessary to represent the state of a general convective PBL. A third similarity function for the relationship between the bulk potential temperature difference through the PBL and the surface sensible heat flux is defined. Implications for the wind speeds and directions in the three levels of the PBL are explored.