Assessment of New Alternative Scaling Properties of the Convective Boundary Layer: Application to Velocity and Temperature Spectra

Abstract

There are two models for the surface layer in the convective boundary layer (CBL). First is the standard Monin–Obukhov similarity theory, and second is the McNaughton–Laubach model (Laubach and McNaughton 2009, Boundary-Layer Meteorology 133:219–252; hereafter MNL model) developed based on the complex dynamical system approach to address characteristics of the unstable surface layer. The fundamental difference between the Monin–Obukhov similarity theory and the MNL model is the use of local and non-local parameters for analyzing surface-layer spectra in the CBL. However, there is a need to check applicability of this new model at various flow conditions before the model could be extensively used. Subsequently, applicability of the MNL model is tested in comparison to the standard model using CBL observations from three different regions with increasing terrain complexity (i.e. over flat-terrain, onslope, and ridge-top sites). The MNL model is tested by estimating and using the non-local scaling parameters to collapse the power spectra of velocity and temperature on the frequency–amplitude scale under the generalized hypothesis that convective surface layer depends on non-local outer variables. We find that the u and v spectra for all sites indicate run-to-run similarity of each spectra with MNL scaling irrespective of the height limiting role of local buoyancy on the shape of the spectra. Similarly, w spectra from all sites indicate transitions between the surface friction layer and the outer layer are governed by flow in the entire CBL. The temperature spectra collapse using $(z \epsilon _o)^{2/3} H_0^{-2}$ as amplitude scaling and $kz_i^{1/2}z^{1/2}$ as wavenumber scaling, is a new observation within the surface friction layer, where the streamwise wavenumber is k, measurement height is z, CBL height is $z_i$, the dissipation rate of turbulence energy in the outer CBL is $\epsilon _o$, and the surface heat flux is $H_0$. These observations corroborate well with the MNL model conjecture that the convective temperature spectra do not depend only on local stability, and CBL parameters affect spectra when a subset of local factors remains constant.