## Abstract

In the middle of the convective atmospheric boundary layer is often a deep layer of vertically uniform wind speed (*M*_{UL}), wind direction, and potential temperature (*θ*_{UL}). A radix layer is identified as the whole region below this uniform layer, which includes the classic surface layer as a shallower subdomain. An empirical wind speed (*M*) equation with an apparently universal shape exponent (*A*) is shown to cause observations from the 1973 Minnesota field experiment to collapse into a single similarity profile, with a correlation coefficient of roughly 0.99. This relationship is *M*/*M*_{UL} = *F*(*z*/*z*_{R}), where *F* is the profile function, *z* is height above ground, and *z*_{R} is depth of the radix layer. The profile function is *F* = (*z*/*z*_{R})^{A} exp[*A*(1 − *z*/*z*_{R})] in the radix layer (*z*/*z*_{R} ⩽ 1), and *F* = 1 in the uniform layer (*z*_{R} < *z* < 0.7*z*_{i}). The radix-layer equations might be of value for calculation of wind power generation, wind loading on buildings and bridges, and air pollutant transport.

The same similarity function *F* with a different radix-layer depth and shape exponent is shown to describe the potential temperature (*θ*) profile: (*θ* − *θ*_{UL})/(*θ*_{0} − *θ*_{UL}) = 1 − *F*(*z*/*z*_{R}), where *θ*_{0} is the potential temperature of the air near the surface. These profile equations are applicable from 1 m above ground level to the midmixed layer and include the little-studied region above the surface layer but below the uniform layer. It is recommended that similarity profiles be formulated as mean wind or potential temperature versus height, rather than as shears or gradients versus height because shear expressions disguise errors that are revealed when the shear is integrated to get the speed profile.

*Corresponding author address:* Dr. Roland Stull, Atmospheric Science Programme, Dept. of Geography, University of British Columbia, 1984 West Mall, Vancouver, BC, V6T 1Z2, Canada.