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Monin-Obukhov similarity theory (MOST) is used in virtually every Earth System Model (ESM) to parameterize the near-surface turbulent exchanges, however there is high uncertainty in the literature about the appropriate parameterizations to be used. In addition, MOST has limitations in very stable and unstable regimes, over heterogeneous terrain and complex orography, and has been found to incorrectly represent the surface fluxes. A new approach including turbulence anisotropy as a scaling parameter has recently been developed, allowing to overcome these limitations and generalize the flux-variance relations to complex terrain. In this paper we analyze the flux-gradient relations for five well known datasets. The scaling relations show substantial scatter and highlight the uncertainty in the choice of parameterization 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 ($\phi_M$) in unstable conditions, and for temperature gradient ($\phi_H$) both in unstable and stable regime. This analysis shows that both $\phi_M$ and $\phi_H$ are strongly dependent on turbulence anisotropy and allows to finally settle the longly discussed free convection regime for $\phi_M$, which clearly exhibits a $-{1/3}$ 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., Comment: 27 ages, 8 figures

Recent works on wall-bounded flows have corroborated the coexistence of wall-attached eddies, whose statistical features are predicted through Townsend's attached eddy hypothesis (AEH), and very-large-scale motions (VLSMs), which are not encompassed in the AEH. Furthermore, it has been shown that the presence of wall-attached eddies within the logarithmic layer is linked to the appearance of an inverse-power-law region in the streamwise velocity energy spectra, upon significant separation between outer and viscous scales. In this work, a near-neutral atmospheric surface layer (ASL) is probed with a wind LiDAR to investigate the contributions to the streamwise velocity energy associated with wall-attached and VLSMs for a very-high Reynolds-number boundary layer. Energy and linear coherence spectra (LCS) of the streamwise velocity are interrogated to identify the spectral boundaries associated with eddies of different typologies and the maximum height attained by wall-attached eddies. Inspired by the AEH, an analytical model for the LCS associated with wall-attached eddies is formulated. The experimental results show that the identification of the wall-attached-eddy energy contribution through the analysis of the energy spectra leads to an underestimate of the associated spectral range, maximum height attained, and turbulence intensity. This feature is due to the overlap of the energy associated with VLSMs obscuring the inverse-power-law region. On the other hand, the Townsend-Perry constant for the turbulence intensity seems to be properly estimated through the spectral analysis. The LCS analysis estimates wall-attached eddies with a streamwise/wall-normal ratio of about 14.3 attaining a height of about 30% of the outer scale of turbulence.

Monin-Obukhov similarity theory (MOST) stands at the center of understanding of atmospheric surface-layer turbulence. Based on the hypothesis that a single length scale determined by surface fluxes governs the turbulent exchange of momentum, mass, and energy between the Earth's surface and the atmosphere, MOST has been widely used in parametrizations of turbulent processes in virtually all numerical models of atmospheric flows. However, its inherent limitations to flat and horizontally homogeneous terrain, the non-scaling of horizontal velocity variances, and stable turbulence have plagued the theory since its inception. 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. Here we present a first generalized extension of MOST encompassing a wide range of realistic surface and flow conditions. The novel theory incorporates information on the directionality of turbulence exchange (anisotropy of the Reynolds stress tensor) as a key missing variable. The constants in the standard empirical MOST relations are shown to be functions of anisotropy, thus allowing a seamless transition between traditional MOST and its novel generalization. The new scaling relations, based on measurements from 13 well-known datasets ranging from flat to highly complex mountainous terrain, show substantial improvements to scaling under all stratifications. The results also highlight the role of anisotropy in explaining general characteristics of complex terrain and stable turbulence, adding to the mounting evidence that anisotropy fully encodes the information on the complexity of the boundary conditions.

It was discovered several decades ago that eddy covariance measurements systematically underestimate sensible and latent heat fluxes, creating an imbalance in the surface energy budget. Since then, many studies have addressed this problem and proposed a variety of solutions to the problem, including improvements to instruments and correction methods applied during data postprocessing. However, none of these measures have led to the complete closure of the energy balance gap. The leading hypothesis is that not only surface-attached turbulent eddies but also sub-mesoscale atmospheric circulations contribute to the transport of energy in the atmospheric boundary layer, and the contribution from organized motions has been grossly neglected. The problem arises because the transport of energy through these secondary circulations cannot be captured by the standard eddy covariance method given the relatively short averaging periods of time (~30 minutes) used to compute statistics. There are various approaches to adjust the measured heat fluxes by attributing the missing energy to the sensible and latent heat flux in different proportions. However, few correction methods are based on the processes causing the energy balance gap. Several studies have shown that the magnitude of the energy balance gap depends on the atmospheric stability and the heterogeneity scale of the landscape around the measurement site. Based on this, the energy balance gap within the surface layer has already been modelled as a function of a nonlocal atmospheric stability parameter by performing a large-eddy simulation study with idealized homogeneous surfaces. We have further developed this approach by including thermal surface heterogeneity in addition to atmospheric stability in the parameterization.

While advances in computation are enabling finer grid resolutions in numerical weather prediction models, representing land-atmosphere exchange processes as a lower boundary condition remains a challenge. This partially results of the fact that land-surface heterogeneity exists at all spatial scales and its variability does not `average' out with decreasing scales. The work here presented uses large-eddy simulations and the concept of dispersive fluxes to quantify the effect of surface thermal heterogeneity with scales $\sim$ 1/10th the height of the atmospheric boundary layer and characterized by uniform roughness. Such near-canonical cases describe inhomogeneous scalar transport in an otherwise planar homogeneous flow when thermal stratification is weak or absent. Results illustrate a regime in which the flow is mostly driven by the surface thermal heterogeneities, in which the contribution of the dispersive fluxes can account for more than 40\% of the total sensible heat flux at about 0.1$z_i$, with a value of 5 to 10\% near the surface, regardless of the spatial distribution of the thermal heterogeneities, and with a weak dependence on time averaging. Results also illustrate an alternative regime in which the effect of the surface thermal heterogeneities is quickly blended, and the dispersive fluxes match those obtained over an equivalent thermally homogeneous surface. This character seems to be governed by a new non-dimensional parameter representing the ratio of the large-scale advection effects to the convective turbulence. We believe that results from this research are a first step in developing new parameterizations appropriate for non-canonical atmospheric surface layer conditions., Comment: Manuscript submitted to Boundary-Layer Meteorology