Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation

Previous results of non-dimensional wind and temperature profiles as functions of ( = z/L) show systematic deviations between different experiments. These discrepancies are generally believed not to reflect real differences but rather instrumental shortcomings. In particular, it is clear that flow distortion has not been adequately treated in most previous experiments. In the present paper, results are presented from a surface-layer field experiment where great care was taken to remove any effects from this kind of error and also to minimize other measuring errors. Data from about 90 30-min runs with turbulence measurements at three levels (3, 6, and 14 m) and simultaneous profile data have been analysed to yield information on flux-gradient relationships for wind and temperature.The flux measurements themselves show that the fluxes of momentum and sensible heat are constant within ± 7% on average for the entire 14 m layer in daytime conditions and when the stratification is slightly stable. For more stable conditions, the flux starts to decrease systematically somewhere in the layer 6 to 14 m. From a large body of data for near-neutral conditions (¦¦ 0.1), values are derived for von Kármán's constant: 0.40 ± 0.01 and for _h at neutrally, 0.95 ± 0.04. The range of uncertainty indicated here is meant to include statistical uncertainty as well as the effect of possible systematic errors.Data for _m and _h for an extended stability range (1 > > – 3) are presented. Several formulas for _m and _h appearing in the literature have been used in a comparative study. But first all the formulas have been modified in accordance with the following assumptions: = 0.40 and ( _h ) _{= 0} = 0.95; deviations from this result in the various studies are due to incomplete correction for flow distortion. After new corrections are introduced, the various formulas were compared with the present measurements and with each other. It is found that after this modification, the most generally used formulas for _m and _h for unstable conditions, i.e., those of Businger et al. (1971) and Dyer (1974) agree with each other to within ± 10% and with the present data. For stable conditions, the various formulas still disagree to some extent. The conclusion in relation to the present data is not as clear as for the unstable runs, because of increased scatter. It is, however, found that the modified curve of Businger et al. (1971) for _h fits the data well, whereas for _m , Dyer's (1974) curve appears to give slightly better agreement.     

Stability functions correct at the free convection limit and consistent for for both the surface and Ekman layers

For the thermal stability function _h used to calculate heat and moisture fluxes in the surface layer, we choose a formulation which has the theoretically correct free convection limit % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeikaiabgk% HiTGqaciaa-PhacaqGVaGaamitaiaabMcadaahaaWcbeqaaiabgkHi% TiaaigdacaGGVaGaaG4maaaaaaa!3DFE!\[{\rm{(}} - z{\rm{/}}L{\rm{)}}^{ - 1/3} \]. We then use the experimental result that z/L Ri to deduce a formulation with an exponent -1/6 for the momentum stability function _m. This formulation also resolves the matching problem at the interface between the surface and Ekman layers. The proposed functions are found to remain reasonably close to another formulation that is well supported by observations and has exponents -1/2 for _h and -1/4 for _m. The intent of the proposals is mainly to clarify and simplify the parameterization of the convective boundary layer in present day atmospheric models, without significantly altering the results.     

Similarity of atmospheric Reynolds shear stress and heat flux fluctuations over a rough surface

Horizontal u and vertical w velocity fluctuations have been measured together with temperature fluctuations in the atmospheric surface layer, at a small height above a wheat crop canopy. Marginal probability density functions are presented for both individual fluctuations u, w, and for the instantaneous Reynolds stress uw, and heat fluxes w and u. Probability density functions of the velocity fluctuations deviate less significantly from the Gaussian form than the probability density of temperature. There appears to be closer similarity between statistics of the instantaneous heat fluxes than between the momentum flux and either of the heat fluxes investigated. The mean momentum flux receives equal contributions from the events referred to as ejections and sweeps in laboratory boundary layers. Sweeps provide the largest contribution to the heat fluxes.     

Local Similarity Relationships In The Urban Boundary Layer

To investigate turbulent structures in an urban boundary layer (UBL) with many tallbuildings, a number of non-dimensional variable groups based on turbulent observationsfrom a 325-m meteorological tower in the urban area of Beijing, China, are analyzedin the framework of local similarity. The extension of surface-layer similarity to localsimilarity in the stable and unstable boundary layer is also discussed. According to localsimilarity, dimensionless quantities of variables: e.g., velocity and temperature standarddeviations _i/u_*l (i=u,v,w) and_T/T_*l,correlation coefficients of uw and wT covariance, gradients of wind and temperature_m and _h, and dissipation rates of turbulent kinetic energy (TKE) andtemperature variance and _N can be represented as a functiononly of a local stability parameter z/, where is the local Obukhovlength and z is the height above ground. The average dissipation rates of TKE andtemperature variance are computed by using the u spectrum, and the uw and wTcospectra in the inertial subrange. The functions above were found to be in a goodagreement with observational behaviour of turbulence under unstable conditions, butthere were obvious differences in the stable air.     

Mass transfer to bean leaves

A vapour of radio-lead (²¹²Pb) has been used to measure the Sherwood number, Sh, of model leaves at various angles of incidence,, to the airstream in a wind tunnel. The results for=0 are compared with Pohlhausen's formula and the results for 0, with Powell's experiments. The local values of Sh on the upwind and downwind sides of discs have been obtained. For leaves in the canopy, Sh was found to be about 25% greater than would be predicted by applying Pohlhausen's equation without correction for orientation.     

Flux–Profile Relationships Over a Fetch Limited Beech Forest

The influence of an internal boundary layer and a roughness sublayer on flux–profile relationships for momentum and sensible heat have been investigated for a closed beech forest canopy with limited fetch conditions. The influence was quantified by derivation of local scaling functions for sensible heat flux and momentum (_h and _m) and analysed as a function of atmospheric stability and fetch. For heat, the influences of the roughness sublayer and the internal boundary layer were in agreement with previous studies. For momentum, the strong vertical gradient of the flow just above the canopy top for some wind sectors led to an increase in _m, a feature that has not previously been observed. For a fetch of 500 m over the beech forest during neutral atmospheric conditions, there is no height range at the site where profiles can be expected to be logarithmic with respect to the local surface. The different influence of the roughness sublayer on _h and _m is reflected in the aerodynamic resistance for the site. The aerodynamic resistance for sensible heat is considerably smaller than the corresponding value for momentum.     

Observed variations of σθ and σΦ in the nocturnal drainage flow in a deep valley

The variations of and in the drainage flow in the Brush Creek valley of western Colorado are investigated using data from Doppler acoustic sodars and instrumented towers. The data were obtained on two experimental nights during the 1984 ASCOT field study. There is good agreement between the variations derived from low-level observations of the sodars and those derived from the towers located throughout the valley. The observed hourly average and in the nocturnal drainage flow are about 20 ° to 25 ° and 5 °, respectively; these values are much larger than those generally observed over flat terrain during nighttime stable conditions. After sunrise (about 0600 MST), as the valley warms and the flow direction changes to up-valley, these parameters increase sharply to their peak values at about 0800 MST and then decrease to their normal daytime values after about two hours.In the drainage flow, the hourly average varies inversely with wind speed according to the relation u 0.7ms^-1. The vertical standard deviation is much less enhanced by complex terrain than the horizontal standard deviation. The observed values are predicted fairly well by the local similarity theory.Oak Ridge Associated Universities (ORAU) Summer Research Participant at ATDD in 1987 andOak Ridge Associated Universities (ORAU) Summer Research Participant at ATDD in 1987 and     

La conversion du rayonnement sphérique en rayonnement global

Résumé Une étude théorique permet d'estimer les sommes journalières soit du rayonnement global tombant sur un récepteur plan et horizontal, soit du rayonnement sphérique ou circumglobal tombant sur une sphère. Ces deux sommes dépendent fortement des conditions atmosphèriques: atmosphère pure, brume, humidité et nébulosité, ainsi que de la latitude géographique, de la déclinaison du soleil et de l'albédo du sol. On montre qu'il est quand-même possible de trouver une relation du deuxième ou troisième degré entre les deux types de mesures où les coefficients ne dépendent que de la différence – entre latitude et déclinaison et de l'albédo du sol. Cette relation est valable dans les basses latitudes <30° avec une faible dispersion des valeurs journalières; dans les latitudes plus élevées sa validité semble limitée au semestre estival.

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Summary The daily totals of radiation falling on a horizontal receiver as well as on a spherical one are calculated by theoretical approach. Both types of values change very much with atmospherical conditions, such as pure atmosphere, haze and humidity of the atmosphere and cloudiness and furthermore with the geographical latitude, the declination of sun and finally with the albedo of the ground. It is demonstrated that it is nevertheless possible to establish a relation of second or third order between both these types of values. The coefficients are function only of –, the difference between latitude and declination and of the albedo . This relation is valid in low latitudes <30° for daily totals; in higher latitudes its validity is limited to days of the summer period.

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Zusammenfassung Auf theoretischem Wege werden die Tagessummen sowohl der auf einen horizontalen Empfänger fallenden Globalstrahlung von Sonne und Himmel als auch der auf eine Kugel fallenden Zirkumglobalstrahlung ermittelt. Beide Werte hängen sehr stark von den atmosphärischen Verhältnissen, wie Reinheit der Atmosphäre, Dunst, Feuchtigkeit und Bewölkung, sowie von der geographischen Breite, der Deklination der Sonne und der Albedo der Bodenoberfläche ab. Es wird nun gezeigt, daß es trotzdem möglich ist, eine Beziehung zweiten oder dritten Grades zwischen den beiden Arten von Tagessummen herzuleiten, in der die Koeffizienten nur von der Differenz – zwischen geographischer Breite und Deklination der Sonne einerseits und der Albedo andererseits abhängen. Diese Beziehung gilt in niederen Breiten <30° für alle Einzelwerte, in höheren Breiten nur im Sommerhalbjahr.

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Avec 8 Figures     

Exponential-linear stability correction functions for weak to moderate instability near the ground

Stability correction functions which combine the exponent of z/L, and a linear term in z/L, are proposed for the unstable case. The functions provide a reasonably close fit to the _m and _h results of Dyer and Hicks (1970) for 0 < –z/L 1, but they cannot be extended to cases of strong instability. Attractive features are the ability to integrate the expressions directly in terms of z/L, and a particularly close fit of the integrated result to experimentally derived _m values.     

The spectral velocity tensor for homogeneous boundary-layer turbulence

We have postulated a simple model for the spectral tensor _ij (k) of an anisotropic, but homogeneous turbulent velocity field. It is a simple generalization of the spectral tensor _inf ^{ij piso}(k) for isotropic turbulence and we show how in the limit of isotropy, _ij (k) becomes equal to _inf ^{ij piso}(k). Whereas _inf ^{ij piso}(k) is determined entirely by one scalar function of k = ¦k¦, namely the energy spectrum, we need three independent scalar functions of k to specify _ij (k). We show how it is possible by means of the three stream-wise velocity component spectra to determine the three scalar functions in _ij (k) by solving two uncoupled, ordinary linear differential equations of first and second order. The analytic form of the component spectra each has a set of three parameters: the variance and the integral length scale of the velocity component and a dimensionless parameter, which governs the curvature of the spectrum in the transition domain from the inertial subrange towards lower wave numbers. When the three sets of parameters are the same, the three spectra correspond to isotropic turbulence and they are all interrelated and related to the energy spectrum. We show how it is possible to obtain these spectral forms in the neutral surface layer and in the convective boundary layer from data reported in the literature. The spectral tensor is used to predict the lateral coherences for all three velocity components and these predictions are compared with coherences obtained in two experiments, one using three masts at a horizontally homogeneous site in Denmark and one employing two aircraft flying in formation over eastern Colorado. Comparison shows reasonable agreement although with considerable experimental scatter.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

An alternative analysis of flux-gradient relationships at the 1976 ITCE

An extensive micrometeorological data set from the 1976 International Turbulence Comparison Experiment (ITCE) is analysed to determine flux-gradient relationships in an unstable atmosphere for momentum, sensible heat and water vapour transfers. The data are first analysed for internal consistency, resulting in the rejection of some data. Following a least-square fit to the remaining data in the form /k = (1 – z/L)^-/k, rounded-off values of k, , and are selected for each form of transfer consistent with the statistical accuracy of the measurements. The equations finally adopted are _M = (1 – 28z/L)^-1/4 and _{H, W} = (1 – 14z/L)^-1/2 with k _M = k_H = k_W = 0.40.These expressions fit the averaged observations to within a few per cent in the stability range of the experiment (-4 < z/L < -0.004).     

Effects of heat and water vapor transport on eddy covariance measurement of CO2 fluxes

Flux densities of carbon dioxide were measured over an arid, vegetation-free surface by eddy covariance techniques and by a heat budget-profile method, in which CO₂ concentration gradients were specified in terms of mixing ratios. This method showed negligible fluxes of CO₂, consistent with the bareness of the experimental site, whereas the eddy covariance measurements indicated large downward fluxes of CO₂. These apparently conflicting observations are in quantitative agreement with the results of a recent theory which predicts that whenever there are vertical fluxes of sensible or latent heat, a mean vertical velocity is developed. This velocity causes a mean vertical convective mass flux (= _cw for CO₂, in standard notation). The eddy covariance technique neglects this mean convective flux and measures only the turbulent flux _c w. Thus, when the net flux of CO₂ is zero, the eddy covariance method indicates an apparent flux which is equal and opposite to the mean convective flux, i.e., _c w = – _c w. Corrections for the mean convective flux are particularly significant for CO₂ because _cw and _c w are often of similar magnitude. The correct measurement of the net CO₂ flux by eddy covariance techniques requires that the fluxes of sensible and latent heat be measured as well.     

The Askervein Hill Project: Mean wind variations at fixed heights above ground

This is one of a series of papers on the Askervein Hill Project. It presents results on the variations in mean wind speed at fixed heights (z) above the ground from linear arrays of anemometer posts and towers. Most of the data are for z = 10 m but some are for z = 3 m. Selected and directionally grouped data from the 55 Mean Flow runs are presented together with mean flow data from Askervein '83 Turbulence runs. Comparisons are made between the data and guideline estimates of fractional speed-up ratio at hilltop locations and between the data and MS3DJH/3 model predictions along the tower lines. There is good agreement in most cases.     

A model of turbulence spectra in the atmospheric surface layer

The spectral equations of turbulent kinetic energy and temperature variance have been solved by using Onsager's energy cascade model and by extending Onsager's model to closure of terms that embody the interaction of turbulent and mean flow.The spectral model yields the following results: In a stably stratified shear flow, the peak wave numbers of the spectra of energy and temperature variance shift toward larger wave numbers as stability increases. In an unstably stratified flow, the peak wave numbers of energy spectra move toward smaller wave numbers as instability increases, whereas the opposite trend is observed for the peak wave numbers of temperature variance spectra. Hence, the peak wave numbers of temperature spectra show a discontinuity at the transition from stable to unstable stratification. At near neutral stratification, both spectra reveal a bimodal structure.The universal functions of the Monin-Obukhov similarity theory are predicted to behave as _m ~ _H ~ (- Z/L)^-1/3 in an extremely unstable stratification and as _m ~ _H ~ z/L in an extremely stable stratification. For a stably stratified flow, a constant turbulent Prandtl number is expected.     

The behaviour of a mixed-layer model of the convective boundary layer coupled to a big leaf model of surface energy partitioning

Daily mean values of the Priestley-Taylor coefficient, ¯, are derived from a simple model of the daily growth of a convective boundary layer. For a particular control set of driving environmental variables, ¯ is related to the prescribed bulk surface resistance, r_S by 1/¯ = 1/₀ + mr_S for parameters ₀ and m. The dependence of the parameters ₀ and m on weather is explored and a potential use of this linear relation to provide information about regional values of r_S is indicated.     

The Kolmogorov constant for carbon dioxide in the atmospheric surface layer over a paddy field

From measurements in the atmospheric surface layer over a paddy field, the Kolmogorov constants for CO₂ and longitudinal wind velocity were obtained. In this study, the nondimensional dissipation rate _nc = (1–16 _v )^-1/2 for CO₂ variance and = (1–16 _v )^-1/4 – _v for turbulent energy were used, assuming the equality of the local production term and the local dissipation term, and neglecting the divergence flux term in the budget equation. The value of the constant for CO₂ was consistent with recent determinations for temperature and humidity. The constant for longitudinal wind velocity showed good agreement with other recent observations.     

Transport-Dissipation Analytical Solutions to the E-∈Turbulence Model and their Role in Predictions of the Neutral ABL

E- turbulence model predictions of the neutralatmospheric boundary layer (NABL) are reinvestigated to determine thecause for turbulence overpredictions found in previous applications. Analytical solutions to the coupled E and equations for the case of steady balance between transport and dissipation terms, the dominant balance just below the NABL top, are derived. It is found that analytical turbulence profiles laminarizeat a finite height only for values of closure parameter ratio c ₂ /_e equal toor slightly greater than one, with laminarization as z for greater . The point = 2 is additionally foundthat where analytical turbulent length scale (l) profilesmade a transition from ones ofdecreasing ( < 2) to increasing ( > 2)values with height. Numerically predicted profiles near the NABL topare consistent with analytical findings. The height-increasingvalues of l predicted throughout the NABL with standard values ofclosure parameters thus appear a consequence of 2.5(> 2), implied by these values (c ₂ = 1.92, _{= 1.3}, _{e = 1}). Comparison of numericalpredictions with DNS data shows that turbulence overpredictions obtained with standard-valued parameters are rectifiedby resetting and _e to 1.1 and 1.6, respectively, giving, with c ₂ = 1.92, 1.3, and laminarization of the NABL's cappingtransport-dissipation region at a finite height.     

Analysis of Astex-Stratocumulus Observational Data Using a Mass-Flux Approach

A mass-flux approach is applied to observational data obtained in a convective boundary layer topped with stratocumulus clouds. The observational data were obtained from aircraft measurements during the Atlantic Stratocumulus Transition Experiment (ASTEX). A conditional sampling method is used to calculate average updraft and downdraft values. The vertical fluxes calculated with the mass-flux approach are found to be proportional to the real (measured) fluxes, with a proportionality factor being about 0.6. This value is predicted by theory for two variables having a joint Gaussian distribution function; proportionality factor = 2^-1 0.637. The horizontal fractional entrainment and detrainment rates calculated from the data ( 1–2 × 10^-2 m^-1) are an order of magnitude higher than the rates obtained by large eddy simulations for cumulus convection ( 2–3 × 10^-3 m^-1) and two orders of magnitude higher than those used in modelling cumulus convection with a mass-flux scheme in an operational weather forecast model ( 3 × 10^-4 m^-1). A numerical mass-flux model for the thermodynamics was developed and showed that results are in good agreement when compared with measured profiles of the liquid water content.     

Analytical investigations of horizontal meso-scale momentum equations with Newtonian nudging

Summary This study presents an analytical investigation of the local behaviour of the solution to a mesoscale model with Newtonian nudging when observed winds are time varying. The analysis examines each Fourier component of the time series of observed winds. Unlike the case with a constant observed wind, the nudged wind vector does not asymptotically approach the observed wind. In response to sinusoidal oscillation of the observed wind, the nudged wind vector is always on a half circle connecting the vector ends of the observed and un-nudged modelled winds. When nudging parameter 0, the nudged wind vector approaches the un-nudged wind; when , the nudged wind vector approaches the observed wind. For commonly used values of nudging parameter , the modelled wind field always carries errors.A target nudging scheme is devised in this study in order to ensure the model result is identical to observed winds with sinusoidal oscillation. Investigation shows that such a target wind exists for a finite value of , and the magnitude of the target-nudging term is about the same as that of a normal nudging term if f, wheref is the Coriolis parameter and is the frequency of the wind oscillation.With 7 Figures     

AN E – ε – ℓ TURBULENCE CLOSURE SCHEME FOR PLANETARY BOUNDARY-LAYER MODELS: THE NEUTRALLY STRATIFIED CASE

The standard E – model generates aplanetary boundary layerthat appears to be much too deep. The cause of theproblem is traced to the equation for the dissipationrate () of turbulent kinetic energy (E), specifically theparameterization of dissipation production anddestruction. In the context of atmosphericboundary-layer modelling, we argue that a part of thedissipation production should be modelled as the inputto the spectral cascade from the energy-containingpart of the spectrum, with a characteristic length , while the equilibrium imbalancebetween local production and destruction ofdissipation is modelled as proportional toE2/E, as in the standard model. Wepropose an E – – turbulence closurescheme, in which both the mixing length, m, and are prescribed. The importance ofthe equation is diminished, though itstill determines the dissipation rate in the Eequation.