Flux-gradient relations and their dependence on turbulence anisotropy

Abstract

Monin–Obukhov similarity theory (MOST) is used in virtually all Earth System Models to parametrize the near-surface turbulent exchanges and mean variable profiles. Despite its widespread use, there is high uncertainty in the literature about the appropriate parametrizations to use. In addition, MOST has limitations in very stable and unstable regimes, over heterogeneous terrain and complex orography, and has been found to represent the surface fluxes incorrectly. A new approach including turbulence anisotropy as a non-dimensional scaling parameter has recently been developed and has been shown to overcome these limitations and generalize the flux-variance relations to complex terrain. In this article, we analyze the flux-gradient relations for five well-known datasets, ranging from flat and homogeneous to slightly complex terrain. The scaling relations show substantial scatter and highlight the uncertainty in the choice of parametrization even over canonical conditions. We show that, by including information on turbulence anisotropy as an additional scaling parameter, the original scatter becomes well bounded and new formulations can be developed that drastically improve the accuracy of the flux-gradient relations for wind shear ((Formula presented.)) in unstable conditions and for temperature gradient ((Formula presented.)) in both unstable and stable regimes. This analysis shows that both (Formula presented.) and (Formula presented.) are strongly dependent on turbulence anisotropy and allows us finally to settle the extensively discussed free convection regime for (Formula presented.), which clearly exhibits a (Formula presented.) power law when anisotropy is accounted for. Furthermore, we show that the eddy diffusivities for momentum and heat and the turbulent Prandtl number are strongly dependent on anisotropy and that the latter goes to zero in the free convection limit. These results highlight the necessity to include anisotropy in the study of near-surface atmospheric turbulence and lead the way for theoretically more robust simulations of the boundary layer over complex terrain.