Examination of the empirical flux-profile models in the atmospheric surface boundary layer

Values of Richardson number (Ri) and the wind profile Deacon number () in the atmospheric surface layer are evaluated from various experimental data sources. The relationship between Ri and shows some scatter, but gives agreement with the relations derived by the several empirical models available for both unstable and inversion conditions.     

A study of a fair weather boundary layer in TOGA-COARE: Parameterization of surface fluxes in large scale and regional models for light wind conditions

The study focuses on a way to parameterize the effect of subgrid scale convective motions on surface fluxes in large scale and regional models for the case of light surface winds. As previously proposed, these subgrid effects are assumed to scale with the convection intensity through the relationship: where is the mean velocity of the wind, U₀ the velocity of the mean wind, w_* the free convection velocity, and an empirical coefficient to be determined. Both observations and numerical simulation are presently used to determine the free convection coefficient .Large eddy simulation of a fair weather convective boundary layer case observed during TOGA-COARE is performed. Comparisons between observations and the simulation of surface properties and vertical profiles in the planetary boundary layer are presented. The simulated vertical turbulent fluxes of heat, moisture and buoyancy range well within estimates from aircraft measurements.The most important result is that the true free convection coefficient , directly estimated from simulation, leads to a value of 0.65, smaller than the ones estimated from temporal and spatial variances. Using observations and simulation, estimates of from temporal and spatial variances are obtained with similar values 0.8. From both theoretical derivations and numerical computations, it is shown that estimates of the true from variances are possible but only after applying a correction factor equal to 0.8. If this correction is not used, is overestimated by about 25%. The time and space sampling problem is also addressed in using numerical simulations.     

Analytical solutions for the Ekman layer

The PBL equation that governs the transition from the constant-stress surface layer to the geostrophic wind in a neutrally stratified atmosphere for which the eddy viscosityK(z) is assumed to vary smoothly from the surface-layer value U _*z (0.4,U _*=friction velocity,z=elevation) to the geostrophic asymptoteK _GU _*d forzd is solved through an expansion in fd/U _*1 (f=Coriolis parameter). The resulting solution is separated into Ekman's constant-K solution an inner component that reduces to the classical logarithmic form forzd and isO() relative to the Ekman component forzd. The approximationKU _*d is supported by the solution of Nee and Kovasznay's phenomenological transport equation forK(z), which yieldsK–U _*d exp(–z/d), where is an empirical constant for which observation implies, 1. The parametersA andB in Kazanskii and Monin's similarity relation forG/U _* (G=geostrophic velocity) are determined as functions of . The predicted values ofG/U _* and the turning angle are in agreement with the observed values for the Leipzig wind profile. The predicted value ofB based on the assumption of asymptotically constantK is 4.5, while that based on the Nee-Kovasznay model is 5.1; these compare with the observed value of 4.7 for the Leipzig profile. A thermal wind correction, an asymptotic solution for arbitraryK(z) and 1, and an exact (unrestricted ) solution forK(z)=U _*d[1–exp(–z/d)] are developed in appendices.     

An improved calibration for tethered balloon wind measurements

A previously published technique for using tethered spherical balloons as anemometers for measuring light low-level winds has been further developed. Earlier data on the relationship between the aerodynamic drag coefficient and the Reynolds number of spherical rubber balloons were combined with a large number of new data and re-analysed; and the errors in the relationship were estimated. The results allowed a more accurate calculation of wind speed from the deflection of a tethered balloon from the vertical. When combined with a new technique for calculating the effects of the tether, this enabled light to moderate low-level winds at fixed heights up to 600 m or more to be measured with simple, cheap, and readily mobile equipment; and a slight modification of the technique allowed measurement of winds in and above fog. Wind speeds measured by the ballon technique showed reasonably good agreement with measurements by an anemometer carried beneath the balloon.Glossary of Symbols a, b, c Coefficients in the relationship between lnC _d and lnR - A Quantity under square root in solution for lnV whena0 - C _d Wind drag coefficient for balloon - C _dc Value ofC _d given by calibration curve of Table I - D Dynamic wind pressure force on balloon - F Buoyant free lift of balloon with load - Re Reynold's number of balloon (sphere) - R = Re/10⁵ - r Radius of sphere - T Tension in tether - V Wind speed - ₈₃() =(lnC _dc -lnC _d ) when 83° , or 0 for other - Error in lnC _d - Elevation of tether where attached to balloon - Elevation of balloon from ground tether point - Molecular viscosity of air - Ratio of circumference to diameter of circle - Density of air     

Equilibrium evaporation beneath a growing convective boundary layer

Expressions for the equilibrium surface Bowen ratio ( _s ) and equilibrium evaporation are derived for a growing convective boundary layer (CBL) in terms of the Bowen ratio at the top of the mixed layer _i and the entrainment parameter A _R . If A_R is put equal to zero, the solution for _s becomes-that previously obtained for the zero entrainment or closed box model. The Priestley-Taylor parameter is also calculated and plotted in terms ofA _R and _i . Realistic combinations of the atmospheric parameters give values of in the range 1.1 to 1.4.     

The Value Of The β Coefficient In The Relaxed Eddy Accumulation Method In Terms Of Fourth-Order Moments

The commonly measured value of in the relaxed eddy accumulationmethod of about 0.56is shown to arise from the non-Gaussiannature of turbulence. Fourth-orderGram–Charlier functions forthe two-dimensional probability distributionsof variation in the horizontal component of wind velocityand concentrations of water vapour, carbondioxide and methane with respect to thevertical component of wind velocity are used to examinethe value of .An analytical solution for ispresented in terms of fourth-order moments.Under mean conditions, this solution givesa value for of0.557. Variation of is shown to be controlledprimarily by the ratio of the mean ofc'w3 (where c'is relevant to the entity of interest andw' is vertical component of windvelocity) to the correlationcoefficient between the entity concentrationand vertical component of wind velocity.     

Modelling radiation quantities and photolysis frequencies in the troposphere

STAR (System for Transfer of Atmospheric Radiation) was developed to calculate accurately and efficiently the irradiance, the actinic flux, and the radiance in the troposphere. Additionally a very efficient calculation scheme to computer photolysis frequencies for 21 different gases was evolved. STAR includes representative data bases for atmospheric constituents, especially aerosol particles. With this model package a sensitivity study of the influence of different parameter on photolysis frequencies in particular of O₃ to Singlet D oxygen atoms, of NO₂, and of HCHO was performed. The results show the quantitative effects of the influence of the solar zenith angle, the ozone concentration and vertical profile, the aerosol particles, the surface albedo, the temperature, the pressure, the concentration of NO₂, and different types of clouds on the photolysis frequencies.Notation I _A(, ) actinic flux - I _H(, ) irradiance - L(, , , ) radiance - wavelength - azimuth angle - cosine of zenith angle - _s cosine of solar zenith angle - optical depth - _s scattering coefficient - _c extinction coefficient - _o single scattering albedo - p _mix mixed phase function - g _mix mixed asymmetry factor - J _gas photolysis frequency     

A study of the sensitivity of bare soil evaporation schemes to soil surface wetness,using the coupled soil moisture and surface temperature prediction model,BARESOIL

Summary The performance of evaporation schemes with and approach and their combination within resistance representation of evaporation from bare soil surface is discussed. For this purpose nine schemes, based on different functions of or , on the ratio of the volumetric soil moisture content and its saturated value are used.The quality of the chosen schemes has been evaluated using the results of time integration by the coupled soil moisture and surface temperature prediction model, BARESOIL, using in situ data. A sensitivity analysis was made using two sets of data derived from the volumetric soil moisture content of the top soil layer. One with values below the wilting point (0.17 m³m^–3) and the second with values above 0.20m³m^–3. Data sets were obtained at the experimental site Rimski anevi, Yugoslavia, from the bare surface of a chernozem soil.With 4 Figures     

Effects of water vapour on the structure parameter of the refractive index for near-infrared radiation

The refractive index of air (n) mainly depends on temperature andwater vapour content. For near-infrared radiation, temperature isthe main determining factor. To determinethe structure parameter of temperature ( ) fromthe structure parameter of the refractive index( ), the influence ofwater vapour content on n needs to be taken into account as acorrection. Three levels of approximation are presented. The firstinvolves the standard deviations of T and q (_T and_q) as well as the correlation coefficient betweenT and q (R_Tq). The second approximation involvesR_Tq and the Bowen ratio (), and the last uses only the Bowen ratio.The latter is the classical Bowen ratio correction.Evaluation of the validity of the assumptions used in the derivationreveals that a large error may be introduced (for situations withR_Tq < 0.8) by replacing _T/_qwith the Bowen ratio.Consequently, estimating from using the Bowen ratiocan contain errors of 5–40% for || < 1. Adding R_Tqas extra information reduces the errors only marginally. For || > 1,the correction is small, and all three approximations give errors of lessthan 1% in . When is used to compute the sensible heat flux,the influence of the quality of the correction forwater vapour fluctuations on the measured energy balance is small: forsmall ||, the correction is large, but the absolute value ofthe heat flux is small, whereas for large ||, the correctionis insignificant.     

The validation of various schemes for parameterizing evaporation from bare soil for use in meteorological models: A numerical study using in situ data

Parameterization of evaporation from a non-plant-covered surface is very important in the hierarchy strategy of modelling land surface processes. One of the representations frequently used in its computation is the resistance formulation. The performance of the evaporation schemes using the , , and their combination resistance approaches to parameterize evaporation from bare soil surfaces is discussed. For that purpose, the nine schemes, based on a different dependence of and on volumetric soil moisture content and its saturated value, are used.The tests of performances of the considered schemes are based on time integrations by the land surface module (BARESOIL) using observed data. The 23 data sets at a bare surface experimental site in Rimski anevi, Yugoslavia on chernozem soil, were used for the resistance algorithm evaluation. The quality of the schemes was compared with the observed values of the latent heat flux using several statistical parameters.     

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).     

Interaction between the atmospheric and oceanic boundary layers

The two-layer system of an atmosphere over water bodies is reduced to a single-layer problem. Values of the interfacial quantities, such as the friction velocity, the surface velocity, the angles, and , between the surface shear stress and the geostrophic wind velocity and the surface wind velocity, respectively, and the surface roughness, all of which depend upon external parameters, such as the geostrophic wind and stratifications, are obtained. The geostrophic drag coefficient C _d, the geostrophic wind coefficient C _f, and the angles , and , of the turbulent flow at the sea-air interface are functions of a dimensionless number, mfG/kg, with S ₁ and S ₂ as two free stratification parameters. The surface roughness is uniquely determined from the geostrophic wind rather than from the wind profile in the boundary layer.Formerly Visiting Research Associate, Applied Physics Branch, Earth Observations Division, NASA-Manned Spacecraft Center, Houston, Texas.     

Gas and Particle Products Distribution from the Reaction of β-Caryophyllene with Ozone

Gas and particulate reaction products from the ozonolysis of -caryophyllene (I) in the presence of atmospheric air were investigated using a combination of gas chromatography-mass spectrometry (GC-MS) and high performance liquid chromatography (HPLC). A Scanning Mobility Particle Sizer system (3936, TSI) and a Condensation Particle Counter (3025A, TSI) were used to study secondary organic aerosol formation. The nighttime oxidation was carried out in a large outdoor smog chamber (190 m³). A wide range of ring retaining and ring opening products in the gas and particle phase are reported over the course of the reaction. On average, measured gas and particle phase products accounted for 64% of the reacted -caryophyllene (I) carbon. Measurements show that a number of reaction products with low vapor pressure (e.g., -caryophyllone aldehyde (IV), -norcaryophyllone aldehyde (V), -caryophyllonic acid (VIII), -14-hydroxycaryophyllonic acid (XIV)) were found in the sample taken during the first 20 min of the reaction and may play an important role in the early formation of secondary organic aerosol. A detailed mechanism is proposed to account for most products observed in this investigation.     

Evaporation from a blanket bog in a foggy coastal environment

Frequent fog severely restricts evaporation from blanket bogs in Newfoundland because it more than halves the radiant energy input, and it eliminates the vapor pressure deficit, resulting in evaporation at the equilibrium rate (average = 0.99 during fog). During these periods, there is no surface resistance to evaporation because the bog has been wetted by fog drip, and although the latent heat flux dominates over sensible heat (average = 0.8), both are small. In contrast, the surface dries during clear periods, increasing the surface resistance to evaporation so that sensible heat becomes more important ( = 1.05). When the mosses are dry, evaporation is below the equilibrium rate ( = 0.87), although the higher available energy ensures that actual evaporation is higher. During clear periods, daily evaporation averaged 2.5 mm, compared to 1.1 and 0.7 mm for fog and rain, respectively. The suppressed evaporation at this site is important in maintaining appropriate hydrological conditions for blanket bog development.     

Latitudinal variation of tropospheric temperature lapse rate

Summary The latitudinal variation of tropospheric temperature lapse rate is examined on the basis of recently published data for the northern hemisphere. In January, the lapse rate systematically decreases from 6.4°C/km. for the equator to 3.6°C/km. for 70°N; in July, the lapse rate is nearly constant in respect of latitude between the equator and 50°N, but decreases from the latter poleward. The average January–July lapse rate decreases systematically from 6.3°C/km. for the equator to 4.7°C/km. for 70°N. This variation is closely described by the equation =6.25–2 sin⁴, where is the lapse rate, in °C/km, for latitude . For the north pole, the equation gives a lapse rate of 4.25°C/km.

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Zusammenfassung Die Änderung des vertikalen Gradienten der Troposphärentemperatur mit der geographischen Breite wird auf Grund neuen Zahlenmaterials für die Nordhemisphäre untersucht. Im Januar nimmt der Temperaturgradient allmählich von 6.4°C/km am Äquator bis zu 3.6°C/km in 70°N Breite ab; im Juli ist der Temperaturgradient in den Breiten zwischen dem Äquator und 50°N Breite fast gleich und nimmt von hier aus polwärts ab. Der mittlere Temperaturgradient für Januar–Juli nimmt allmählich von 6.3°C/km am Äquator bis auf 4.7°C/km in 70°N Breite ab. Die Breitenabhängigkeit läßt sich gut durch die Gleichung =6.25–2 sin⁴ darstellen, in der der Temperaturgradient in °C/km in der Breite ist. Für den Nordpol ergibt die Gleichung einen Temperaturgradienten von 4.25°C/km.

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Résumé La variation latitudinale du gradient thermique vertical de la température troposphérique est examinée en se basant sur des données publiées récemment d'une valeur de 6.4°C/km pour l'équateur à 3.6°C/km pour 70°N; en juillet le gradient est presque constant pour les latitudes situées entre l'équateur et 50°N, mais il diminue d'ici vers le pôle. Le gradient moyen janvier/juillet diminue systématiquement de 6.3°C/km pour l'équateur à 4.7°C/km pour 70°N. Cette variation peut être représentée par l'équation =6.25–2 sin⁴ où est le gradient en °C/km pour la latitude . Pour le pôle nord, l'équation donne un gradient de 4.25°C/km.

     

Turbulence mechanisms at an agricultural site

An extensive set of turbulence data from the 3- and 12-m heights taken over an agricultural site (Marsta, Sweden) are analyzed and compared with data from ideal sites.In unstable air, Monin-Obukhov similarity is found to be valid for the non-dimensional gradients of wind, _m , temperature, _h , and humidity, _e , for (only a few data), for _T /|T _*|,/ _E /|E _*| and for the non-dimensionalized inertial subrange spectra of temperature and humidity. Where comparison is possible, the unstable data also agree with those found in the Kansas study, with one remarkable exception, the inertial subrange constant of the temperature spectrum, ₁, being only 0.39, compared to the value 0.80 found at the Kansas site.On the stable side, most similarity predictions break down, with most of the data differing systematically from the corresponding Kansas results, the only exception being . The inertial subrange constants for temperature, ₁, and for humidity, ₁ are found to have the same values, 0.39 and 0.30, respectively, as they do on the unstable side. Remarkable similarity is found for the shape of the stable u- and - and e-spectra. In addition, this shape is found to be identical with that found in Kansas. The peak wavelength of the stable u-, and -spectra is found to be about four times larger than it is for the corresponding Kansas spectra. This is interpreted to be a result of the increased macro-roughness at the Marsta site as compared with that at the Kansas site. A possible explanation for the low ₁-value is discussed, suggesting that ₁ is not a universal constant, but instead dependent on the turbulent structure.     

Free convection frequency spectra of atmospheric turbulence over the sea

Frequency spectra of atmospheric turbulenceS (f) in the inertial subrange are considered in the free convection regime over the sea surface in a case of motionless instrument measurements (Eulerian frequency spectra). The frequency spectra formulaef _* S (f)/ ² =c (f _*/f)^5/3 for wind velocity (=1–3), temperature (=t) and humidity (=e) fluctuations are derived on the basis of similarity theory and the –5/3 law. These relations also can be derived from a consideration of convective large-scale advection of small eddies. The frequency scalef _* = (N ^{1 2}/)^1/2 (H/z ²)^1/3 is the lower bound of the inertial subrange and it is of order 10^–2 Hz.The spectra formulae are compared with direct measurements of atmospheric turbulence from the fixed research tower in the coastal zone of the Black Sea in calm weather. It is shown that these formulae are realized at least over two to three decades of the frequency range (approximately from 10^–2 to 10 Hz) and values of the numerical coefficients are found. The derived formulae can be used for calculations of sensible and latent heat fluxes by measuring the high-frequency range of spectra at a fixed point at low wind speeds when the conventional inertial dissipation method is not applicable.     

An explicit three-dimensional nonhydrostatic numerical simulation of a tropical cyclone

Summary A nonhydrostatic numerical simulation of a tropical cyclone is performed with explicit representation of cumulus on a meso- scale grid and for a brief period on a meso- scale grid. Individual cumulus plumes are represented by a combination of explicit resolution and a 1.5 level closure predicting turbulent kinetic energy (TKE).The results demonstrate a number of expected and unexpected important scale interaction processes. Within the central core of the developing cyclone, meso- convective regions grow and breakdown into propagating inertiagravity waves throughout the lifecycle of the cyclone. In the early stages, the amplitude of pressure fluctuations associated with the meso- scale convection exceed the central pressure of the cyclone and strongly modulate its intensity. With each meso- scale pulsation, the cyclone core increases in strength, measured by the central pressure deficit. The increasingly strong inertial frequency of the storm core acts to increasingly trap the convection induced heating within the core by balancing the tangential wind against the low central pressure, before the meso- scale convection breaks down and sends the warmth away as a propagating wave. Eventually, the slow manifold's amplitude exceeds the amplitude of the meso- scale oscillations and a stable eye region is formed. As inertial instability increases, increasingly high thermal warmth can be protected in the core, allowing persistent subsidence to form and to clear out the cyclone eye.On the outside of the eye wall, strong inertial stability gradients in the troposphere cause convective warming to split the inflow to the eye wal! and spawn outwardly propagating inertia gravity waves. These waves carry away all of the heating forced by convection that is not inertially trapped by the eye wall and act as a moderating influence on storm intensity.Inertia gravity waves are also spawned in the stratosphere at the top of the eye wall by the revolution of asymmetric cumulus structures. In all instances, the tropospheric waves are coupled to the propagating stratospheric waves which both move at 35 ms^–1, although there are many instances where the stratospheric waves seem to have no tropospheric counterpart. Hence the anvil top forcing and low level breakdown are linked.The outwardly propagating inertia gravity waves act to initiate outer bands of convection. This initiation is with the assistance of low level boundary layer variations of density related to previous convection and to virga falling from the anvil which moistens and destabilizes the mid levels of _e minimum. The convection initiated by these waves does not move substantially outward with the wave, although may appear to develop outward discontinuously.With 12 Figures     

Hilfsdiagramme für dent-Test

Zusammenfassung Es werden Diagramme für dent-Test gegeben, aus denen man bei Kenntnis vonf, d undS allein entscheiden kann, ob die Stichprobe einent-Wert ergäbe, der größer alst ist, oder nicht.

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Summary Graphs are given for thet-test, by means of which one can decide whether the smaple would give a value oft large thant or not, only from the knowledge off, d andS.

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Résumé L'auteur présente, pour le test t, des diagrammes qui permettent de dire si la valeur det dépasse celle det ou non, à la seule connaissance def, d etS.

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Mit 5 Textabbildungen