Flux-Profile Relationships in the Atmospheric Surface Layer
01 Mar 1971-Journal of the Atmospheric Sciences (American Meteorological Society)-Vol. 28, Iss: 2, pp 181-189
TL;DR: In this article, the free constants in several interpolation formulas can be adjusted to give excellent fits to the wind and temperature gradient data, and the behavior of the gradients under neutral conditions is unusual, however, and indicates that von Karman's constant is ∼0.35, rather than 0.40 as usually assumed, and that the ratio of eddy diffusivities for heat and momentum at neutrality is ∼1.0.
Abstract: Wind and temperature profiles for a wide range of stability conditions have been analyzed in the context of Monin-Obukhov similarity theory. Direct measurements of heat and momentum fluxes enabled determination of the Obukhov length L, a key independent variable in the steady-state, horizontally homogeneous, atmospheric surface layer. The free constants in several interpolation formulas can be adjusted to give excellent fits to the wind and temperature gradient data. The behavior of the gradients under neutral conditions is unusual, however, and indicates that von Karman's constant is ∼0.35, rather than 0.40 as usually assumed, and that the ratio of eddy diffusivities for heat and momentum at neutrality is ∼1.35, compared to the often-suggested value of 1.0. The gradient Richardson number, computed from the profiles, and the Obukhov stability parameter z/L, computed from the measured fluxes, are found to be related approximately linearly under unstable conditions. For stable conditions the Richar...
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TL;DR: The second-moment turbulent closure hypothesis has been applied to geophysical fluid problems since 1973, when genuine predictive skill in coping with the effects of stratification was demonstrated as discussed by the authors.
Abstract: Applications of second-moment turbulent closure hypotheses to geophysical fluid problems have developed rapidly since 1973, when genuine predictive skill in coping with the effects of stratification was demonstrated. The purpose here is to synthesize and organize material that has appeared in a number of articles and add new useful material so that a complete (and improved) description of a turbulence model from conception to application is condensed in a single article. It is hoped that this will be a useful reference to users of the model for application to either atmospheric or oceanic boundary layers.
6,488 citations
TL;DR: In this article, a new parameterization of oceanic boundary layer mixing is developed to accommodate some of this physics, including a scheme for determining the boundary layer depth h, where the turbulent contribution to the vertical shear of a bulk Richardson number is parameterized.
Abstract: If model parameterizations of unresolved physics, such as the variety of upper ocean mixing processes, are to hold over the large range of time and space scales of importance to climate, they must be strongly physically based. Observations, theories, and models of oceanic vertical mixing are surveyed. Two distinct regimes are identified: ocean mixing in the boundary layer near the surface under a variety of surface forcing conditions (stabilizing, destabilizing, and wind driven), and mixing in the ocean interior due to internal waves, shear instability, and double diffusion (arising from the different molecular diffusion rates of heat and salt). Mixing schemes commonly applied to the upper ocean are shown not to contain some potentially important boundary layer physics. Therefore a new parameterization of oceanic boundary layer mixing is developed to accommodate some of this physics. It includes a scheme for determining the boundary layer depth h, where the turbulent contribution to the vertical shear of a bulk Richardson number is parameterized. Expressions for diffusivity and nonlocal transport throughout the boundary layer are given. The diffusivity is formulated to agree with similarity theory of turbulence in the surface layer and is subject to the conditions that both it and its vertical gradient match the interior values at h. This nonlocal “K profile parameterization” (KPP) is then verified and compared to alternatives, including its atmospheric counterparts. Its most important feature is shown to be the capability of the boundary layer to penetrate well into a stable thermocline in both convective and wind-driven situations. The diffusivities of the aforementioned three interior mixing processes are modeled as constants, functions of a gradient Richardson number (a measure of the relative importance of stratification to destabilizing shear), and functions of the double-diffusion density ratio, Rρ. Oceanic simulations of convective penetration, wind deepening, and diurnal cycling are used to determine appropriate values for various model parameters as weak functions of vertical resolution. Annual cycle simulations at ocean weather station Papa for 1961 and 1969–1974 are used to test the complete suite of parameterizations. Model and observed temperatures at all depths are shown to agree very well into September, after which systematic advective cooling in the ocean produces expected differences. It is argued that this cooling and a steady salt advection into the model are needed to balance the net annual surface heating and freshwater input. With these advections, good multiyear simulations of temperature and salinity can be achieved. These results and KPP simulations of the diurnal cycle at the Long-Term Upper Ocean Study (LOTUS) site are compared with the results of other models. It is demonstrated that the KPP model exchanges properties between the mixed layer and thermocline in a manner consistent with observations, and at least as well or better than alternatives.
3,756 citations
TL;DR: In this paper, the authors described the behavior of spectra and cospectra of turbulence in the surface layer using wind and temperature fluctuation data obtained in the 1968 AFCRL Kansas experiments.
Abstract: The behaviour of spectra and cospectra of turbulence in the surface layer is described within the framework of similarity theory using wind and temperature fluctuation data obtained in the 1968 AFCRL Kansas experiments. With appropriate normalization, the spectra and cospectra are each reduced to a family of curves which spread out according to z/L at low frequencies but converge to a single universal curve in the inertial subrange. The paper compares these results with data obtained by other investigators over both land and water.
Spectral constants for velocity and temperature are determined and the variability in the recent estimates of the constants is discussed. The high-frequency behaviour is consistent with local isotropy. In the inertial subrange, where the spectra fall as n−5/3, the cospectra fall faster: uω and ωθ as n−7/3, and uθ, on the average, as n−5/2. The 4/3 ratio between the transverse and longitudinal spectral levels is observed at wavelengths of the order of the height above ground under unstable conditions and at wavelengths of the order of L/10 under stable conditions. This lower isotropic limit is shown to be governed by the combined effects of shear and buoyancy on small-scale eddies.
2,408 citations
TL;DR: In this paper, a model for the representation of vertical eddy fluxes of heat, momentum and water vapour in a forecast model is presented, and two tests are presented, using the scheme in a one-dimensional model: the simulation of the diurnal cycle and the transformation of a polar air mass moving over the warm sea.
Abstract: A scheme for the representation of the vertical eddy fluxes of heat, momentum and water vapour in a forecast model is presented. An important feature of the scheme is the dependence of the diffusion coefficients on the static stability of the atmosphere. Two tests are presented, using the scheme in a one-dimensional model: the simulation of the diurnal cycle, and the transformation of a polar air mass moving over the warm sea.
2,357 citations
TL;DR: The Coupled Ocean-Atmosphere Response Experiment (COARE) bulk algorithm was published in 1996, and it has become one of the most frequently used algorithms in the air-sea interaction community.
Abstract: In 1996, version 2.5 of the Coupled Ocean–Atmosphere Response Experiment (COARE) bulk algorithm was published, and it has become one of the most frequently used algorithms in the air–sea interaction community. This paper describes steps taken to improve the algorithm in several ways. The number of iterations to solve for stability has been shortened from 20 to 3, and adjustments have been made to the basic profile stability functions. The scalar transfer coefficients have been redefined in terms of the mixing ratio, which is the fundamentally conserved quantity, rather than the measured water vapor mass concentration. Both the velocity and scalar roughness lengths have been changed. For the velocity roughness, the original fixed value of the Charnock parameter has been replaced by one that increases with wind speeds of between 10 and 18 m s−1. The scalar roughness length parameterization has been simplified to fit both an early set of NOAA/Environmental Technology Laboratory (ETL) experiments and...
2,097 citations
Cites background or methods from "Flux-Profile Relationships in the A..."
...0 Kansas (Businger et al. 1971): unstable Holtslag (1990): stable Kader and Yaglom (1990) Smith (1988) a 5 0....
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...They adopt the standard Kansas stability profile functions across the entire unstable range from near-neutral to free convection, and Eq....
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...2) The Kansas stable profile functions (Businger et al. 1971) have been replaced by those from Beljaars and Holtslag (1991) which, based on new profile data taken over the Arctic ice cap (Persson et al....
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...As with COARE 2.5, ZZD use the Kansas profile functions for near-neutral atmospheric stability, with the convective forms of Kader and Yaglom (1990) and the relations of Holtslag et al. (1990) in very stable conditions....
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...Substituting (11) into (9) and ignoring the small difference in velocity and temperature transfer coefficients in the stability terms, then 21z 5 C R (1 2 BR ) ,b ib ib (12) which becomes singular when 21R $ B ø 0.2.ib (13) This result is consistent with the original Kansas analysis that suggested a critical gradient Richardson number on the order of 0.2....
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