Non-dimensional Wind and Temperature Gradients in the Atmospheric Boundary Layer

We propose a single non-dimensional expression for the wind and temperature vertical profiles in the atmospheric boundary layer (ABL). Two major reformulations are implemented from the generalized function for dimensionless wind and temperature gradients, so that the theory from previous studies may be extended above the surface layer. First, the thermal part of the wind shear is modified based on a surface temperature scale θ * and a thermal-characteristic height z h instead of the Obukhov length. Second, we introduce two new terms in the total Reynolds stress associated with the nonlinear parts of the thermal-mechanical stress, where coefficients α and β maybe describe wind profiles of the low-level jets. The proposed wind and temperature profiles are compared with the universal function in the surface layer and validated with Wangara's wind and temperature profiles up to a height of 2 km, and their measurements of surface turbulent fluxes of heat and momentum. One case of unstable and four cases of stable conditions are selected from the Wangara dataset, representing cases of convective, stratified, nocturnal jet and transition between the stratified and jet profiles. The proposed function has a good correlation in the five cases of temperature and wind profiles with RMSE better than 0.7 K and 0.7 m s -1 respectively. The coefficients z h and b associated with the linear part of Reynolds stress, and the coefficients α and β associated with the nonlinear part of Reynolds stress are analized, and their possible physical meanings are discussed.