Flux-gradient relations: insights from anisotropy analysis

Almost all Earth System Models (ESM) use Monin-Obukhov similarity theory (MOST) to parameterize near surface turbulence. Despite its popularity, MOST has limited applicability and creates high uncertainties in very stable and unstable regimes, over heterogeneous and complex terrain, and is known to incorrectly represent the fluxes at the surface. Including turbulence anisotropy as a non-dimensional scaling parameter has recently proved successful in extending MOST to complex terrain for the scaling of variances and other near surface statistical properties.

Here we extend this approach to the scaling of surface gradients of mean wind and temperature, using data from five datasets ranging from flat and homogeneous to slightly complex terrain. The flux-gradient scaling relations exhibit large scatter, especially in unstable conditions where the data’s behavior is unclear. We show that adding turbulence anisotropy into the scaling of gradients allows to drastically reduce the scatter in the relations and develop new and more accurate parametrizations. This is especially true for the flux-gradient relations for wind shear (φ_m) in unstable conditions, and for temperature gradient (φ_h) both in unstable and stable regime.

The strong dependence of scaled wind speed gradient (φ_m), on turbulence anisotropy also allows us to finally settle the debate on the free convective regime, which clearly exhibits a -1/3 power law when anisotropy is considered. Whereas the strong dependence of scaled temperature gradients (φ_h) might explain a poorer performance of that scaling relation in predicting the surface sensible heat flux. Furthermore, the eddy diffusivities for momentum and heat and the turbulent Prandtl number are heavily modulated by anisotropy and the latter vanishes in free convective conditions.

These results further accentuate the need to incorporate turbulence anisotropy in boundary layer studies and parametrizations, paving the way for reliable surface parametrizations in ESMs.