Similarity equations for wind and temperature profiles in the radix layer, at the bottom of the convective boundary layer

Abstract

In the middle of the convective boundary layer, also known as the mixed layer, is a relatively thick region where wind speed and potential temperature are nearly uniform with height. Below this uniform layer (UL), wind speed decreases to zero at the ground, and potential temperature increases to the surface skin value. This whole region below the UL is called the radix layer (RxL), and is of order hundreds of meters thick. Within the bottom of the RxL lies the classical surface layer (order of tens of meters thick) that obeys traditional Monin-Obukhov similarity theory. The RxL depth is shown to depend on friction velocity, Deardorff velocity, and boundary layer depth. The wind RxL is usually thicker than the temperature RxL. Using RxL depth, UL wind speed, and UL potential temperature as length, velocity, and temperature scales, respectively, one can form dimensionless heights, velocities, and temperatures. When observations obtained within the RxL are plotted in this dimensionless framework, the data collapse into similarity curves. This data collapse is tightly packed for data collected over single-location homogeneous surfaces, and shows more scatter for data collected along 72-km flight tracks over heterogenous surfaces. Empirical profile equations are proposed to describe this RxL similarity. When these profile equations are combined with the flux equations from convective transport theory, the results are new flux-profile equations for a deep region within the bottom of the convective boundary layer. These RxL profile similarity equations are calibrated using data from four sites with different roughnesses: Minnesota, BLX96-Lamont, BLX96-Meeker, and BLX96-Winfield. The empirical parameters are found to be invariant from site to site, except for the profile shape parameter for wind speed. This parameter is found to depend on standard deviation of terrain elevation, rather than on the aerodynamic roughness length. The resulting parameter values are compared with independent data from a forested fifth site, Koorin, and it is found that displacement height must be subtracted from all the heights in the RxL profile equations. The resulting profile equations could be useful for calculating wind loading on bridges, wind turbine power estimation, air pollutant transport, or other applications where wind speeds or temperatures are needed over the bottom hundreds of meters of the convective boundary layer.