Rossby Number Similarity Theory Research Articles

Wind turning in the atmospheric boundary layer over land

A climatology of the boundary‐layer wind‐turning angle over land is presented based on radiosonde observations from 800 stations in the Integrated Global Radiosonde Archive (IGRA). The dependence of the wind turning on a suite of parameters is analyzed. Results from previous studies indicating the importance of the planetary boundary layer (PBL) stratification for the angle of wind turning are confirmed here. A clear increase in the wind‐turning angle with wind speed, particularly for stratified conditions, is also evident. According to Rossby number similarity theory, the cross‐isobaric angle for a neutral and barotropic boundary layer decreases with increasing surface Rossby number, Ro. The IGRA observations indicate that this dependence on Ro might partly be linked to the dependence of the stratification on the wind speed, a dependence that seems to prevail even for the high wind speeds, a criterion that traditionally is used to approximate a neutral PBL. The vertical distribution of the turning of the wind is analyzed using the high‐resolution Stratospheric Processes And their Role in Climate (SPARC) data. For unstable cases, there is a maximum in the directional wind shear around the PBL top, whereas for the most stable class of cases there is a maximum near the surface. The wind‐turning angles from observations are also compared with values obtained from ERA‐Interim reanalysis fields, also presented over ocean. ERA‐Interim underestimates the magnitude of the wind‐turning angles as well as the range. Furthermore, the midlatitude cross‐isobaric mass transport is estimated using the IGRA data. This transport is generally underestimated by ERA‐Interim, likely related to the too small wind‐turning angles.

The Neutral, Barotropic Planetary Boundary Layer, Capped by a Low-Level Inversion

The presence of a low-level, capping inversion layer will affect the height and structure of the planetary boundary layer (PBL). Results from models of varying levels of sophistication, including analytical, turbulent kinetic energy (TKE), second-order closure (SOC), large-eddy simulation (LES) and direct numerical simulation (DNS) models, are used to investigate this influence for the neutral, barotropic PBL. Predicted and observed profiles of stress and geostrophic departure components, and integral measures, such as the parameters of Rossby-number similarity theory, are compared for the KONTUR, Marine Stratocumulus, JASIN, Leipzig, Pre-Wangara and Upavon field experiments.

Evaluating Models of The Neutral, Barotropic Planetary Boundary Layer using Integral Measures: Part I. Overview

Data for the cross-isobaric angle α0, the geostrophic drag coefficient Cg, and the functions A and B of Rossby number similarity theory, obtained from meteorological field experiments, are used to evaluate a range of models of the neutral, barotropic planetary boundary layer. The data give well-defined relationships for α0, Cg, and the integrated dissipation rate over the boundary layer, as a function of the surface Rossby number. Lettau's first-order closure mixing-length model gives an excellent fit to the data; other simple models give reasonable agreement. However more sophisticated models, e.g., higher-order closure, large-eddy simulation, direct numerical simulation and laboratory models, give poor fits to the data. The simplemodels have (at least) one free parameter in their turbulence closure that is matched toatmospheric observations; the more sophisticated models either base their closure onmore general flows or have no free closure parameters. It is suggested that all of theatmospheric experiments that we could locate violate the strict simplifying assumptionsof steady, homogeneous, neutral, barotropic flow required by the sophisticated models.The angle α0 is more sensitive to violations of the assumptions than is Cg.

On Integral Measures Of The Neutral Barotropic Planetary Boundary Layer

Two types of neutral planetary boundary layer (PBL) are distinguished:truly neutral – developed against a neutrally stratified free flow, and conventionally neutral – developed against a background stable stratification. Atmospheric PBLs treated asneutral are almost always conventionally neutral. Theoretical reasoning and results from large-eddy simulation (LES) show that A and B coefficients of the Rossby-number similarity theory are not constants. The same is true for thecoefficient Ch in the Rossby–Montgomery formula for the neutral boundary-layer depth h = Chu*/|f|, where u* is the friction velocity. Contrary to classical ideas, A, B and Ch depend on the ratio μN≡ N/|f| of the free-flow Brunt–V*auml;isal a frequency N to the absolute value of the Coriolis parameter |f|. This new development can explain why atmospheric and LES estimates of A, B and Ch appear inconsistent. It results from neglecting the fact that atmospheric data for μN ∼ 102 were compared with LES data for μN = 0, violating an obvious requirement of similarity with respect to μN.

Sensitivity of Arctic climate simulations to different boundary-layer parameterizations in a regional climate model

Arctic climate simulations with the high resolution regional climate model HIRHAM showsome deviations from station data in the planetary boundary layer (PBL) during winter, whichindicates the necessity of improvements in the atmospheric PBL parameterization for a betterdescription of the vertical stratification and atmosphere–surface energy exchange. A1-dimensional single column model scheme has been used to investigate the influence of twodifferent PBL parameterizations in monthly integrations for January 1991 and July 1990. Thefirst scheme uses the boundary layer parameterization of the atmospheric circulation modelECHAM3, including the Monin–Obukhov similarity theory in the surface layer and a mixinglength approach above. The second scheme applies the Rossby-number similarity theory forthe whole PBL, connecting external parameters with turbulent fluxes and with universal functionsdetermined on the basis of Arctic data. For both schemes the heat and humidity advectionhas been determined as residual term of the PBL balance equations. Diabatic sources havebeen computed from the current model solution and local temperature and humidity changesare estimated from radiosonde data. The simulated vertical structure and the atmosphere–surface energy exchange during January strongly depends on the used PBL parameterizationscheme. These different PBL parameterization schemes were then applied for simulations of theArctic climate in the 3-dimensional regional atmospheric climate model HIRHAM, usingECHAM3 with Monin–Obukhov similarity theory, ECHAM3 with Rossby-number similaritytheory and ECHAM4 parameterizations with a turbulent kinetic energy closure. The nearsurface temperature, the large-scale fields of geopotential and horizontal wind are simulatedsatisfactorily by all three schemes, but strong regional differences occur. The results show asensitivity to the type of turbulence exchange scheme used. The comparison with ECMWFanalyses and with radiosonde data reveals that during January ECHAM3 with Rossby numbersimilarity theory more succesfully simulates the cold and stable PBL over land surfaces, whereasover the open ocean ECHAM3 with Monin Obukhov similarity works better. ECHAM3 withRossby-number similarity theory delivers a better adapted vertical heat exchange under stableArctic conditions and reduces the cold bias at the surface. The monthly mean surface turbulentheat flux distribution strongly depends on the use of different PBL parameterizations and leadsto different Arctic climate structures throughout the atmosphere with the strongest changes atthe ice edge for January.

Proposal for new PBL resistance laws for neutrally-stratified flow

The history of the development of Rossby-Number Similarity Theory for the neutral Planetary Boundary Layer (PBL) is reviewed. It is shown that the logarithmic profile derived by asymptotic matching is only valid in the matched layer and not in the surface layer proper. Derivation of the traditional PBL Resistance Laws from the theory is outlined. A best-fit polynomial through observations of geostrophic drag coefficients suggests that the traditional form of the Resistance Laws is inadequate. A new formulation is derived from a generalization of the theory that allows the logarithmic form of the wind profile in the matched layer to differ from that in the surface layer. This new formulation is evaluated against observations made during the 1967 Wangara Experiment. Finally, it is demonstrated how wind speed and wind shear profiles that are consistent with the new Resistance Laws may be obtained.

Resistance law, effective roughness length, and deviation angle over hilly terrain

In this note, we derive from the resistance law of Rossby number similarity theory the expressions for the drag coefficient and the deviation angle for strongly unstable and strongly stable stratifications. The extension of the applicability of the resistance laws to inhomogeneous terrain is discussed. A determination of the deviation angle over inhomogeneous terrain from a numerical experiment is presented.

Pressure Drag of Obstacles in the Atmospheric Boundary Layer

Pressure drag of obstacles in the atmospheric boundary layer is computed with a mesoscale numerical model of the troposphere. Different parts of the drag can be separated from the numerical results: total pressure drag is determined from the surface pressure distribution, hydrostatic drag from the temperature distribution in the atmosphere, and form drag as a residual. The dependence of the different parts of the drag on the main influencing parameters, such as geometric parameters, dynamical and thermal parameters, and the surface roughness, is given. The influencing parameters are deduced from a scale analysis of the equation of motion. Wave drag due to gravity waves and flow separation will not be considered in this paper. The study shows among other points that there is a surface Rossby number similarity for form drag on smooth obstacles, that there may be wave drag due to inertial waves even for neutral or unstable stratification due to inertial waves, and that there is Reynolds number similarity for form drag only with respect to molecular viscosity and not with respect to turbulent viscosity of the air. The results suggest the separation of form drag into two parts: a viscous form drag due to turbulent viscosity of the air, and a turbulent form drag due to additional production of turbulence in the vicinity (mainly in the Ice) of the obstacle. The distinction of different drag producing mechanisms will help in the task of parameterization. Parameterization using similarity theories is meaningful only for ensembles of obstacles. Here, isolated obstacles are considered for simplicity, therefore, only the prerequisites for the parameterization are discussed in this paper. The main result is that parameterization of pressure drag in terms of an effective roughness length using Rossby number similarity theory will be possible only for the two parts of the form drag. All other parts of the drag have no corresponding mechanisms in the homogenous boundary layer.

A Statistical Comparison of Methods for Determining Ocean Surface Winds

Abstract The performance of various techniques which determine ocean surface winds using information from large-scale analyses and forecast models is discussed. The techniques evaluated are the geostrophic relation, a simple empirical law, National Meteorological Center (NMC) 1000-mb winds, a two-region analytically matched boundary layer, a two-region boundary layer based on Rossby number similarity theory, and the Fleet Numerical Oceanography Center (FNOC) marine winds. Statistical comparisons of the model winds were made with observed buoy and ship winds for wind speed, wind direction, and the vector wind. This study is based on analyses and 24-h forecasts made once a day at 0000 UTC from 3 December 1985 through 6 January 1986 on a 2.5 × 2.5 degree latitude, longitude, grid. The statistical results indicate that no one Model was clearly the best. The absolute wind speed difference between all the models and observations is, on the average, about 3 m s−1, and the RMS difference is about 4.O m s−1. Howev...

Pressure drag and effective roughness length with neutral stratification

A two-dimensional numerical mesoscale model is used to determine the pressure drag of sinoidal mountains and valleys in a neutral atmosphere. In the first part, pressure distributions and flow patterns for isolated obstacles are considered. For large aspect ratios, the pressure drag exerted by valleys becomes small compared to that of mountains. In the second part, interactions between several obstacles are investigated. For mountains, the drag on downstream obstacles is reduced considerably by the first obstacle when the obstacles are close together. For valleys there is a slight increase of the average drag exerted by each obstacle. In the limit for a large number of obstacles, average drag exerted by one mountain is equal to average drag for one valley. For smaller aspect ratios, this average drag can be entered into the resistence law from the Rossby number similarity theory to yield an ‘effective roughness length’.

Aerodynamic roughness over an inhomogeneous ground surface

The aerodynamic roughness parameter z 0 over inhomogeneous ground surfaces, such as cities, rural towns and so on, is determined by analyzing the wind data at AMeDAS observatories in the Tohoku and Kanto districts of Japan, by making use of Rossby number similarity theory. It is found that the aerodynamic roughness parameter is proportional to the average size of the roughness elements. A practical method of estimating the aerodynamic roughness parameter over an extensive area with various inhomogeneities is developed. In this method, the Digital National Land Information data bank is employed. As an example, the roughness parameter distribution around Tsukuba Academic City is presented.

A Model Study of the Stably Stratified Steady-State Atmospheric Boundary Layer over a Slightly Inclined Terrain

A simple, steady-state, numerical model is used to examine the Rossby-number similarity theory of the atmospheric boundary layer over a slightly inclined terrain. The model confirms the similarity predictions. The slope-influenced universal profiles of the wind velocity defects and the stress components are obtained by the model simulation.

Change of surface roughness and the planetary boundary layer

The ratio between upstream and far downstream surface friction velocities relative to a change in surface roughness is given on the basis of results from surface Rossby number similarity theory. By simple theories for the internal boundary layer, which are found here to compare quite well with recent numerical results from higher-order closure models, it is found that even at a downwind distance such that the internal boundary layer has grown to the full height of the planetary boundary layer, the surface stress still considerably exceeds the equilibrium value.

Change of surface roughness and the planetary boundary layer

AbstractThe ratio between upstream and far downstream surface friction velocities relative to a change in surface roughness is given on the basis of results from surface Rossby number similarity theory. By simple theories for the internal boundary layer, which are found here to compare quite well with recent numerical results from higher‐order closure models, it is found that even at a downwind distance such that the internal boundary layer has grown to the full height of the planetary boundary layer, the surface stress still considerably exceeds the equilibrium value.

不安定成層で且つ地衡風に鉛直シアーがある場合の海上風と等圧線のなす角度及び海上風速と地衡風速の比

Wind fields in the baroclinic, unstably stratified planetary boundary layer above the ocean have been analysed for the data of the AMTEX experiments executed during winter in the East China Sea. For the so-called cold air advection, the angle between winds and isobars increases as the height decreases at the lower half of the planetary boundary layer, while at the upper half layer the angles have negative values. The typical angles in the lower and upper layers are 20-50 deg. and -10- -40deg., respectively, when the horizontal temperature gradient is about 1.5°C per 100km.An empiric formula for the Rossby-number similarity theory is obtained, of which form is a modification of the AryaWyngaard's theoretical expression for the baroclinic, convective boundary layer model. The present result with respect to the baroclinicity dependence of the numerical constants of Rossbynumber similarity theory is slightly different from the empirical result derived from the Wangara data by Clarke and Hess.

Observations of the barotropic Ekman layer over an urban terrain

Data from low-level soundings over Cambridge, U.S.A. were selected on the basis of an Ekman-like variation of the wind vector with altitude combined with evidence of a barotropic atmosphere. The method of geostrophic departure was used to determine the shear-stress distribution. The analysis yields the dimensionless properties of the barotropic Ekman layer under neutral and stable stratification. Some important results include: the geostrophic drag coefficient displays no dependence on the degree of static stability; the dimensionless height of the boundary layer decreases with increasing stability in agreement with the prediction of Zilitinkevich; the properties of the urban surface layer, where the roughness elements are multistory buildings, show no dependence on atmospheric stability under the moderate wind conditions which display the Ekman-like wind profile; and the directions of the horizontal shear stress and the vertical derivative of the velocity vector usually tend to be parallel only near the surface layer. Values of the two constants of the Rossby number similarity theory are found for the neutral barotropic Ekman layer at a surface Rossby number equal to 2 × 105. The implications of the work with respect to wind-tunnel simulation of the flow over models of urban areas are discussed.

On the relation between surface wind and pressure gradient, especially in lower latitudes

Observations show that the angle between surface wind and isobar increases equatorward in low latitudes while the ratio of surface to geostrophic wind speed decreases. With the use of Southern Hemisphere winter fields of surface pressure and temperature over the oceans, and Rossby number similarity theory (including the effects of baroclinicity) in several different forms, the expected latitudinal variation of the angle and ratio has been computed. A check has also been made of mean ATEX and BOMEX data. It appear that the variations with latitude are probably mainly due to baroclinicity. With this factor taken into account, similarity theory fairly adequately explains the observations.

Resistance Laws and Prediction Equations for the Depth of the Planetary Boundary Layer

Abstract A further discussion of the resistance laws for barotropic planetary boundary layers is presented. Concrete expressions are obtained for universal functions A(μ0), B(μ0) C(μ0)of Rossby number similarity theory for the Ekman boundary layer as well as of analogous functions for non-steady boundary layers. Prediction equations are proposed, which describe variations of the boundary layer depth for unstable and stable stratifications.

Geostrophic departure and the functions A and B of Rossby-number similarity theory

A new empirical assessment of the functions A and B of Rossby-number similarity theory is made based on the Wangara data. Variations of these functions with stability, baroclinicity and time of day are discussed. It is found that B is dependent on stability in agreement with older data but contradicting the prediction of Csanady (1972). Coefficients expressing the variation of A and B with the two components of baroclinicity have been derived from the data, and these are claimed to be correct in regard to sign and approximately in regard to magnitude. Longer period time changes, represented by the diurnal cycle, are shown to result in systematic differences in A and B between the case of increasing stability and that of decreasing stability, for the same value of the stability parameter. The first attempt, to our knowledge, to present the actual functional form of the wind departure components (based on field data) is made. As the surface layer is approached in near-neutral conditions, the departure component in the direction of the surface wind assumes the expected logarithmic form.

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