A Revised Surface Flux Similarity Theory for Land–Atmosphere Interactions

A key challenge in boundary-layer meteorology and related disciplines is the accurate prediction of turbulent fluxes of momentum, heat, water vapor, and trace gases. For over 60 years, Monin-Obukhov similarity theory (MOST), which relates turbulent fluxes to mean gradients in the atmospheric surface layer, has served as a cornerstone of atmospheric boundary layer studies. Despite its widespread success, deviations from MOST have been observed by many investigators, and the potential for generalizations is broadly accepted. One key assumption in MOST is that the characteristic length scale of turbulent motions is characterized by the distance from the ground z. However, recent studies in both laboratory and atmospheric flows have revealed that large- and very-large-scale motions (LSMs, VLSMs), which occur on the scale of the boundary layer depth z_i or greater, modulate the amplitude and frequency of turbulent fluctuations in the atmospheric surface layer.

Using atmospheric surface layer data from the Advection Horizontal Array Turbulence Study (AHATS) and a suite of large eddy simulations spanning weakly to highly convective conditions, we propose a revised similarity theory that accounts for the effects of LSMs on the dimensionless mean wind shear φ_m. Deviations of φ_m from MOST are found to increase systematically with the large-scale velocity fluctuations for a given value of the MO stability parameter ζ. The results suggest a revised functional form of MO, φ_m = φ_m(ζ,α), where α is an additional dimensionless parameter that accounts for the effects of LSMs on turbulent flux-gradient relationships. Theoretical support for the proposed similarity theory is provided by a revised form of the O’KEYPS equation, an interpolation formula that captures the scaling behavior of φ_m in the weakly and highly unstable limits.