Is Turbulence Anisotropy the missig ingredient in classical atmospheric surface layer turbulence theory?

Traditionally, land-atmosphere turbulent exchanges of momentum, energy, and mass, are interpreted through Monin-Obukhov similarity theory (MOST). Based on dimensional analysis, MOST states that for high Reynolds number flows, in the absence of mean downward vertical flow, steady-state conditions, and horizontal homogeneity, turbulence is dictated by the balance between shear and buoyancy production/destruction, represented by a single non-dimensional length scale, ζ. Thus, based on MOST, any mean quantity θ representing the land-atmosphere turbulent exchanges, when properly non-dimensionalized with the respective turbulent scaling variable θ_*, can be expressed as a universal function φ of the scaling parameter ζ, such that θ/θ_* ∼ φ(ζ). The specific functional forms of the scaling relations φ have been obtained experimentally by curve fitting through years of experimental campaigns. These relations are widely used in atmospheric surface layer parametrizations for most Earth System Models of different scales.

​​​​​​​However MOST suffers from significant failures that limit its applicability like the lack of scaling of horizontal velocity variances under unstable thermal stratification, the non-scaling of surface-normal velocity and temperature variances in stable stratification, as well as the general breakdown of scaling for intermittent turbulence. Furthermore, MOST also fails in representing land-atmosphere turbulent exchanges over perturbed surfaces (e.g. heterogeneous landscapes, complex terrain, etc.), where the original MOST assumptions breakdown. It has now been long hypothesized the need for an additional non-dimensional parameter that is able to encapsulate the missing information. In this work, we suggest using the metric of turbulence anisotropy as a remedy for generalizing the representation of near surface turbulent exchanges over perturbed surface conditions. To demonstrate its potential, we use an unprecedented set of atmospheric datasets representative of a wide range of different surface and flow conditions. The resulting novel scaling relations not only offer a path-forward in addressing a 70-year old problem in ABL meteorology, but also provide a deeper understanding of turbulence, and its role in the surface-atmosphere exchange over realistic terrain.