Beyond Monin-Obukhov Similarity Theory and the Implications for Turbulence over Complex Terrain

Turbulent exchange of mass, momentum and heat at the Earth’s surface is the crucial component of the climate system. Correctly representing this interaction is therefore of fundamental importance in weather, climate and air pollution models. Parametrizations of turbulent exchange between the Earth's surface and the atmosphere in virtually all numerical models of atmospheric flows are based on Monin-Obukhov Similarity Theory (MOST). MOST identifies surface fluxes of momentum and heat, and height above the surface, as key parameters fully describing all turbulence exchange. MOST is, however, strongly limited by its assumptions of horizontally homogeneous and flat terrain, not representative of the majority of the Earth’s surface. In addition, MOST does not recognize the anisotropic nature of turbulence forcing, nor does it cover the strongly stable and unstable stratification, often encountered in real world applications. Thus, the limitations of MOST, and its use beyond its intended range of validity contribute to large uncertainty in weather, climate, and air-pollution models, particularly in polar regions and over complex terrain, both experiencing unprecedented warming.

Here we explore why the directionality of turbulence exchange (anisotropy of the Reynolds stress tensor) is fundamental in understanding surface-layer atmospheric turbulence, and present how its inclusion into MOST can provide a first generalized extension of MOST encompassing a wide range of realistic surface and flow conditions. The novel theory shows that the constants in the classical MOST, are actually functions of anisotropy, allowing a seamless transition between classical MOST and the novel generalization. The new scaling relations, based on a large ensemble of measurement datasets ranging from flat to highly complex mountainous terrain, show substantial improvements in scaling under all stratifications. The results also highlight the role of anisotropy in explaining general characteristics of complex terrain and strongly unstable and stable turbulence, adding to the mounting evidence that anisotropy fully encodes the information on the complexity of the boundary conditions.