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Relationships between the Monin–Obukhov stability parameter and the bulk Richardson number are useful for explicit calculation of fluxes through the air–sea interface. The most straightforward method assumes simple proportionality and is supported well by experimental evidence in a recent work by Grachev and Fairall. On the other hand, the reference iterative method is regarded as more accurate. To recognize possible differences, calculated values of the proportionality factor as a function of wind speed and air–sea virtual potential temperature difference are shown. The calculation is based on commonly used sea roughness specifications and the Mellor–Yamada turbulence-closure model, which has been shown in previous studies to reproduce the three-sublayer structure of the atmospheric surface layer under convective conditions and to predict mean flow profiles that are consistent with empirical data. The results show that the proportionality factor varies with the wind speed and virtual potential t...

Because of the importance of the convective boundary layer depth (CBLD) in determining pollutant concentrations near the surface, a study of the morning evolution of the convective boundary layer was carried out at the Central Nuclear de Almaraz, Almaraz, Spain, from 25 to 29 September 1995, with a tethersonde and a meteorological mast equipped with a sonic anemometer. The CBLD was estimated from the potential temperature and wind profile obtained with the tethersonde using a 0.5 critical bulk Richardson number criterion. Also, the evolution of the CBLD was studied using three different theoretical zero-order jump models. The results given by the models show that, even with far from homogeneous surfaces, the models fit the observed CBLD very well by tuning the parameters conveniently. The entrainment coefficient that relates the heat flux at the top of the CBL with the heat flux at the surface was almost entirely responsible for the goodness of the fit. The encroachment model works best during situations in which the rate of entrainment is relatively small.

The morning transition between the stable nocturnal situation and the daytime convective boundary layer (CBL) is of interest both for basic understanding and for initializing prognostic models. While the morning growth phase of the CBL has been studied in detail, relatively little has been published on the transition itself. In this paper, conventional observations of surface temperature, humidity, and turbulent fluxes,and data from a meteorological tower, are combined with measurements of the onset of convection by boundary-layer wind profilers to explore the timing and behaviour of the transition period. The transition is defined here as the period between sunrise and the time at which the depth ofconvection reaches about 200 m AGL. Diagnostic relationships based on surface heat flux, the temperature difference between 2 m and 200 m, and bulk Richardson number are explored. The transition is foundto be enabled by surface heating relaxing the surface stability, while the warming of the layerbetween 2 m and 200 m is in large part due to shear-driven entrainment.

Simple and efficient formulas for calculating surface fluxes are presented for the nondimensional profile functional forms of wind and temperature in the atmospheric surface layer. Four formulations representing nondimensional profile functional forms are examined. New approximate solutions for the relationship between z/L and the bulk Richardson number are proposed. These new solutions are an improvement over the existing approximate solutions and give much better agreement with the numerical solutions obtained by iteration. The approach can be extended to other similar nondimensional profile functional forms.

On the basis of hourly measurements of wind and air and sea surface temperatures for at least 6 yr at three buoy stations in the eastern Gulf of Mexico, the onset of the free convection regime, which coincides with the commencement of stability class C (for slightly unstable conditions in the Pasquill stability classification) at approximately Rb = −0.03, −Z/L = 0.4, and −Zi/L = 5, is verified over the ocean, where Rb is the bulk Richardson number, Z (= 10 m) is the height above the sea, L is the Monin–Obukhov stability length, and Zi is the height of the convective boundary layer (CBL). Datasets for the CBL are analyzed in the context of the boundary layer physics of Garratt. It is found that Zi is linearly proportional to the surface buoyancy flux—that is, (w′θ′υ)0, where w is the vertical velocity and θυ is the virtual potential temperature. For operational diffusion applications, a statistical formula is proposed—that is, Zi = 369 + 6004(w′θ′υ)0. A method to compute this buoyancy flux from ro...

Recent measurements made onboard the R/P FLIP in the San Clemente Ocean Probing Experiment in September 1993 and onboard the R/V Moana Wave during Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment are used to evaluate the direct dependence between the Monin–Obukhov stability parameter (ratio of height to Obukhov length) ζ and the bulk Richardson number Rib derived from standard meteorological mean observations of water surface temperature, wind speed, air temperature, and humidity. It is found that in the unstable marine surface layer, ζ = C Rib(1 + Rib/Ribc)−1, where the numerical coefficient C and the saturation Richardson number Ribc are analytical functions of the standard bulk exchange coefficients. For measurements at a height of 10–15 m, C is about 10 and Ribc is about −4.5. Their values are insensitive to variations of Rib and ζ over three decades. Thus, a simple dependence between ζ and Rib has a much wider range of applicability than previously believed. The ...

Analytical solutions Of surface layer similarity equations are presented for the nondimensional profile functional forms suggested by Businger et al. For stable atmospheric conditions, exact analytical solutions of the Monin-Obukhoy stability parameters ζ=z/L, in terms of gradient Richardson number (Ri) and bulk Richardson number (Rib), respectively, are obtained. For unstable atmospheric conditions, an exact solution of the same in terms of Ri is found. An approximate relationship between ζ and Rib, for an unstable surface layer, based on the solution of ζ in terms of Ri, is suggested. The proposed analytical solutions can replace costly numerical iterative methods as well as some of the ad hoc parameterizations used for estimating surface fluxes and related turbulence characteristics.

Analytical relations are developed that relate the Monin-Obukhov parameter to a modified bulk Richardson number expressed in terms of measured wind speed and vertical temperature difference. Measured Monin-Obukhov parameters and Richardson numbers are compared with those calculated using these relations as well as those using the conversion schemes developed earlier by Golder. Measured surface heat and momentum fluxes under unstable conditions are also compared with those predicted using the present simple estimating scheme. Effects of different choices of parameters in the flux-profile relationship with respect to the predicted stability parameters and to the plume dispersion parameters are discussed.

Wangara data is used to examine the depth of the nocturnal boundary layer (NBL) and the height to which surface-linked turbulence extends. It is noted that a linearity of virtual temperature profiles has been found to extend up to a significant portion of the NBL, and then diverge where the wind shear rides over the surface-induced turbulence. A series of Richardson numbers are examined for varying degrees of turbulence and the significant cooling region is observed to have greater depth than the depth of the linear relationship layer. A three-layer parameterization of the thermodynamic structure of the NBL is developed so that a system of five equations must be solved when the wind velocity profile and the temperature at the surface are known. A correlation between the bulk Richardson number and the depth of the linear layer was found to be 0.89.

A criterion for the instability of shearing gravitational waves on the discontinuous interface between a two-isothermal-layer is derived from the result of Bjerkness et al. Comparison of this criterion with the Richardson number gives the results that in the present model the critical Richardson number is ½ and the vertical extent of the turbulent layer is estimated to reach 1/2(π) of the wavelength. Various observed data in actual clear air turbulence are used to evaluate these two constants.

Due to a lack of observational data, little information exists in the literature concerning quantitative relationships between turbulent gust intensity in the free atmosphere and commonly measured meteorological quantities. Measurements of turbulence, wind, and temperature made by a B-47 research aircraft are used to investigate such relationships in order to satisfy several practical needs. It is found that a quantity that is the product of wind speed and turning of the wind with height is more closely related to turbulent gust intensity than vertical wind shear or Richardson's number. Variations in the frequency of occurrence of turbulence are determined as the quantities mentioned above increase in magnitude. Moderate or severe turbulence has a frequency of occurrence greater than 50 per cent when the product of wind speed and vertical change of direction exceeds 0.8 deg sec−1, when vertical shear exceeds 0.027 sec−1, or when Richardson's number is less than 0.4 (for calculations made over 200...