The use of σ T as a temperature scale in the atmospheric surface layer

The standard deviation of temperature _T is proposed as a temperature scale and as a velocity scale to describe the behaviour of turbulent flows in the Atmospheric Surface Layer (ASL), instead of _* andu _* of the Monin—Obukhov similarity theory, and ofT _f andU _f used for free convection stability conditions. On the basis of experimental evidence reported in the literature, it is shown that _T T _f andv _* U _f in the free convection region, and _{T *} andv _* U _* in nearneutral and stable conditions. This implies that the proposed scales can be applied for all stabilities. Furthermore, a new length scale is proposed and its relation with Obukhov length is given. Also, a simple semi-empirical expression is presented with which _T andv _* can be evaluated in a rather simple way. Some examples of practical applications are given, e.g., a stability classification for unstable conditions.     

The behaviour of aerosol optical depth during clear summer days in Athens,Greece

Summary The integral aerosol optical depths (k ) at the hour of 08:20 Local Standard Time (LST), are compared with those calculated previously at 11:20 and 14:20 LST, for clear days during summer in Athens over the period 1962–1988. The mean values at 08:20 LST were consistently lower than the values at 11:20 and 14:20 LST. The influence of the vertical wind profile on the values ofk was also investigated. A comparison was made of the wind profiles at 02:00 and 14:00 LST, for days in which the 11:20 and 14:20 LST values ofk were 0.200 andk 0.350, respectively. The corresponding bulk wind shear s was also found for the period 1980–1988. The most significant results occurred with the first category of days. The resultant wind velocities from the surface to the 900 hPa level, in each hour were higher by 2–4 m·s^–1 with respect to the corresponding values for the second category. At 02:00 LST the bulk wind shear showed a considerable difference (1.8) between the two categories of days in the surface to 700 hPa layer at 02:00 LST. Finally, the associated weather conditions that appear to initiate a period of low values ofk (k 0.200) at 11:20 and 14:20 LST were examined for the period 1980–1988. Fifteen such cases were identified and it was found that they all occurred after the passage of weak cold fronts.With 6 Figures     

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.     

A Richardson Number criterion for the air-sea interface

It is shown that the observationally determined roughness relation z ₀ = u _* ²/g in which g is the acceleration of gravity, u _*, is the friction velocity in air, and = 0.0185 (Wu, 1982) for the wind profile over the sea surface relative to the surface current, is consistent with the existence of a Richardson Number criterion at the air-sea interface in which the critical Richardson Number, Ri_c = 1, such that all the shear energy is converted into potential energy.     

Über die mittlere lineare sukzessive Differenz und ihre Anwendung auf die Untersuchung meteorologischer Beobachtungsreihen

Zusammenfassung Eine endliche Reihe (Sequenz) wird als eine der möglichen Permutationen ihrer Glieder aufgefaßt. Es wird gezeigt, daß die Summe der absoluten Differenzen der aufeinanderfolgenden Glieder gleich ist , wo die natürliche Zahlen sind und nur von der Rangordnung der Glieder der Reihe (von der Permutation) abhängen; die _j sind von der Reihenfolge unabhängig und werden durch die Dispersion der Reihenglieder bestimmt. Die _j und die _j werden separat untersucht; der Erwartungswert der erwähnten Differenzsumme wird abgeleitet. Verschiedene bereits bekannte und auch erstmalig hier vorgeschlagene Maßzahlen werden geprüft. An Reihen jährlicher Regenmengen wird die Rolle der _j und der _j und das Verhalten der besprochenen Maßzahlen veranschaulicht.

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Summary A series ofn members can be considered as one of the possible permutations of its members. It is shown that the sum of the linear successive differences is equal to the expression , where the _j are positive integers, dependent only upon the rank-order (the permutation) of the members, while the _j are independent of the order of the succession and are determined by the dispersion of the members of the series. The factors _j and _j are separately investigated; the expected value of the sum of the linear successive differences is established. Various related statistical measures, already in usage and new ones suggested here, are discussed. Series of yearly rainfall amounts are used to show the effects of the _j and _j and to discuss the behaviour of the various measures.

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Résumé Une série, constituée parn valeurs, est regardée comme une des possibles permutations de ces valeurs. L'auteur montre que la somme des différences absolues, qui se présentent entre les valeurs consécutives de la série, est égale à l'expression . Les _j sont des nombres entiers positifs et ne dépendent que de l'ordre des membres de la série, tandis que les _j, indépendants de l'ordre, sont déterminés par la dispersion des membres. Les facteurs _j et _j sont étudiés séparément; l'espérance mathématique de la somme mentionnée est dérivée. Des paramètres statistiques déjà connus ou proposés ici pour la première fois, sont discutés. Le rôle des _j et des _j et le comportement des divers paramètres sont montrés à l'aide de séries de totaux annuels de pluies.

     

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.     

Calculation of sensible and latent heat fluxes,and surface resistance from profile data

A set of semi-continuous measurements of temperature, wind and moisture gradients as well as of net radiation and ground heat flux covering a period of about one and a half years has been analysed to give a corresponding set of complete surface energy balance data on an hourly basis. An analysis of the evaporation data so obtained is given.It is shown that surface resistance r _S exhibits a diurnal trend: values are smallest (ca. 150 s m^-1) a few hours before noon and increase to as much as 800 s m^-1 towards dusk. The minimum values tend to be higher during dry periods when the soil moisture is low. There is also some indication that r _S decreases rapidly soon after rainfall.An exponential relation is found between the fraction of available energy used as evaporative flux, , and r _S for values of r _I/r_S <0.70, where r _I is the climatological resistance. On the other hand, the ratio of r _I to r _S is linearly correlated with , implying that an equilibrium state is established between the grass surface and the atmosphere, at least from mid-morning to mid-afternoon when the leaves are dry. Near-noon values calculated by Stewart and Thom for Thetford Forest also follow a linear trend.The above two regression results (In (r _S) versus r _I/r_S versus ) are combined to obtain an empirical relation of the form r _I=m exp (a-b) which is used to estimate evaporative flux. The estimates are found to be within 20% of calculated values.Guest Scientist from Department of Physics, University of Cape Coast, Cape Coast, Ghana.     

The effects of orography on precipitation

In this paper, a model simulating the effects of topography and altitude on precipitation is presented. Topography has its maximum effect on precipitation when the angle which the wind makes with the slope direction approaches zero and the inclination of the slope is near 45°. The smaller the angle , the greater the influence of slope on precipitation. When <45°, the larger the inclination, the greater the influence of slope on precipitation and the less the difference in precipitation between the windward and the leeward slopes. When <45°, the reverse holds. But for in the range of 0°–45° and in the range 30°–60°, differences in precipitation on both the windward and leeward slopes are not so well marked and can be neglected in general. In condition of uniform slope inclination, precipitation on the windward slope increases with altitude at first and then decreases after attaining a height (H _m ) of maximum precipitation; alsoH _m is greater, the drier the air mass. When the terrain on the windward side is stepped in shape, it is possible that more than one height of maximum precipitation will occur.     

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.     

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     

A Generalized Structure-Activity Relationship for the Decomposition of (Substituted) Alkoxy Radicals

A novel and readily applicable Structure-Activity Relationship (SAR) for predicting the barrier height E_b to decomposition by C-C scission of (substituted) alkoxy radicals is presented. Alkoxy radicals are pivotal intermediates in the atmospheric oxidation of (biogenic) volatile organic compounds, and their fate is therefore of crucial importance to the understanding of atmospheric VOC degradation mechanisms. The SAR is based on available theoretical energy barriers and validated against barriers derived from experimental data. The SAR is expressed solely in terms of the number(s) N_i of alkyl-, hydroxy- and/or oxo-substituents on the - and -carbons of the breaking bond: E_b(kcal/mol) =17.5 – 2.1 × N(alk) – 3.1 ×N(alk) – 8.0 × N_,(OH) – 8.0 × N(O=) – 12 × N(O=). For barriers below 7 kcal/mol, an additional, second-order term accounts for the curvature. The SAR reproduces the available experimental and theoretical data within 0.5 to 1 kcal/mol. The SAR generally allows conclusive predictions as to the fate of alkoxy radicals; several examples concerning oxy radicals from prominent atmospheric VOC are presented. Specific limitations of the SAR are also discussed. Using the predicted barrier height E_b, the high-pressure rate coefficient for alkoxy decomposition k _diss (298 K) can be obtained from k _diss (298 K) = L ×1.8 × 10¹³ exp(–E_b/RT) s^–1, with L the reaction path degeneracy.     

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     

Microwave vegetation optical depth and inverse modelling of soil emissivity using Nimbus/SMMR satellite observations

Summary A radiative transfer model has been used to determine the large scale effective 6.6 GHz and 37 GHz optical depths of the vegetation cover. Knowledge of the vegetation optical depth is important for satellite-based large scale soil moisture monitoring using microwave radiometry. The study is based on actual observed large scale surface soil moisture data and observed dual polarization 6.6 and 37 GHz Nimbus/SMMR brightness temperatures over a 3-year period. The derived optical depths have been compared with microwave polarization differences and polarization ratios in both frequencies and with Normalized Difference Vegetation Index (NDVI) values from NOAA/AVHRR. A synergistic approach to derive surface soil emissivity from satellite observed brightness temperatures by inverse modelling is described. This approach improves the relationship between satellite derived surface emissivity and large scale top soil moisture fromR ²=0.45 (no correction for vegetation) toR ²=0.72 (after correction for vegetation). This study also confirms the relationship between the microwave-based MPDI and NDVI earlier described and explained in the literature.List of Symbols f frequency [Hz] - f _i(p) fractional absorption at polarizationp - h surface roughness - h h cos² - H horizontal polarization - n _i complex index of refraction - p polarization (H orV) - R _s microwave surface reflectivity - T _B(p) brightness temperature at polarizationp - T ^* normalized brightness temperature - T polarization difference (T _v-T _H) - T _s temperature of soil surface - T _c temperature of canopy - T _max daily maximum air temperature - T _min daily minimum air temperature - V vertical polarization - soil moisture distribution factor; also used for the constant to partition the influence of bound and free water components to the dielectric constant of the mixture - empirical complex constant related to soil texture - microwave transmissivity of vegetation (=e ^–) - ^* effective transmissivity of vegetation (assuming =0) - microwave emissivity - _s emissivity of smooth soil surface - _rs emissivity of rough soil surface - _vs emissivity of vegetated surface - soil moisture content (% vol.) - K dielectric constant [F·m^–1] - K _fw dielectric constant of free water [F·m^–1] - K _ss dielectric constant of soil solids [F·m^–1] - K _m dielectric constant of mixture [F·m^–1] - K _o permittivity of free space [8.854·10^–12 F·m^–1] - high frequency limit ofK _wf [F·m^–1] - wavelength [m] - incidence angle [degrees from nadir] - polarization ratio (T _H/T _V) - b soil bulk density [gr·cm^–3] - s soil particle density [gr·cm^–3] - R surface reflectivity in red portion of spectrum - NIR surface reflectivity in near infrared portion of spectrum - _eff effective conductivity of soil extract [mS·cm^–1] - vegetation optical depth - _6.6 vegetation optical depth at 6.6 GHz - ₃₇ vegetation optical depth at 37 GHz - ^* effective vegetation optical depth (assuming =0) - single scattering albedo of vegetation With 12 Figures     

Temperature distribution and current system in a convectively mixed lake

During spring and autumn, many lakes in temperate latitudes experience intensive convective mixing in the vertical, which leads to almost isothermal conditions with depth. Thus the regime of turbulence appears to be similar with that characteristic of convective boundary layers in the atmosphere. In the present paper a simple analytical approach, based on boundary-layer theory, is applied to convective conditions in lakes. The aims of the paper are firstly to analyze in detail the temperature distribution during these periods, and secondly to investigate the current system, created by the horizontal temperature gradient and wind action. For these purposes, simple analytical solutions for the current velocities are derived under the assumption of depth-constant temperatures. The density-induced current velocities are shown to be small, in the order of a few mm/sec. The analytical model of wind-driven currents is compared with field data. The solution is in good qualitative agreement with observed current velocities under the condition that the wind field is steady for a relatively long time and that residual effects from former wind events are negligible.The effect of the current system on an approximately depth-constant temperature distribution is then checked by using the obtained current velocity fields in the heat transfer equation and deriving an analytical solution for the corrected temperature field. These temperature corrections are shown to be small, which indicates that it is reasonable to describe the temperature distribution with vertical isotherms.Notation T temperature - t time - x, y, z cartesian coordinates - molecular viscosity - _h , _v horizontal and vertical turbulent viscosity - K _h ,K _v horizontal and vertical turbulent conductivity - Q heat flux through the water surface - D depth - u, v, w average current velocity components inx, y andz directions - f Coriolis parameter - p pressure - density - g gravity acceleration - a constant in the freshwater state equation - h _s deviation from the average water surface elevation - L _*,H _* length and depth scale - U _*,W _* horizontal and vertical velocity scale - T temperature difference scale - bottom slope - u _* friction velocity at the water surface - von Karman constant - L Monin-Obukhov length scale - buoyancy parameter - l turbulence length scale - C ₁,C ₂,C ₃ dimensionless constants in the expressions for the vertical turbulent viscosity - , dimensionless vertical coordinate and dimensionless local depth - angle between surface stress direction andx-axis - T _bx ,T _by bottom stress components - c bottom drag coefficient     

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).     

Mechanisms and products of the reactions of NO3 with cycloalkenes

The NO₃ radical initiated oxidation of cyclopentene, cyclohexene and 1-methyl-cyclohexene has been studied. The products formed in an N₂O₅-NO₂-N₂-O₂-cycloalkene-static reactor system, at 0.1 MPa and 296 K, were investigated using long path FTIR. The principal products were aldehydes formed via a ring opening process. The reactions also resulted in significant yields of three types of ring retaining nitrooxy-substituted compounds. The average yields of alkyl nitrates from, e.g., reactions with cycloalkene were 25.1% 2-oxo-cyclohexyl nitrate, 22.8% 2-hydroxy-cyclohexyl nitrate and 4.0% 1,2-cyclohexyl dinitrate. The mechanisms involved resembles those proposed for acyclic alkenes. In absence of NO, -oxo and -hydroxy-cycloalkyl nitrates are formed via self reactions of -nitrooxy substituted cycloalkyl peroxy radicals. Estimated branching ratios for the reactants leading to ring retaining products in the presence and in the absence of NO are given and the possible relevance of these reactions for cycloalkenes under tropospheric conditions is discussed.     

A generalization of the Kolmogorov-von Kármán relationship and some further implications on the values of the constants

A general relation between the Kolmogorov (₁) and von Kármán (k) constants appropriate to flows in the surface boundary layer is obtained by including stability and divergence dependent terms in the development. The result is used to show that the author's earlier inference of the valuek = 0.36 drawn from the observed value ,k ^4/3=0.141 cannot have been underestimated due to the neglect of stability or divergence effects. It is concluded that if k is to be 0.4, then ₁ must be 0.5.Work performed under the auspices of the U.S. Energy Research and Development Administration.     

Experimental determination of HONO mass accommodation coefficients using two different techniques

The mass accommodation coefficient _HONO of gaseous nitrous acid on water surfaces has been determined in a cooperation between the Universities of Strasbourg and Bonn. The droplet train technique (Strasbourg) yielded 0.04<_HONO<0.09 for an estimated surface temperature of 245 K, while the liquid jet technique (Bonn) yielded 0.03<_HONO<0.15 for a surface temperature of 297 K. The uncertainty ranges allow for experimental scatter and estimated uncertainties in diffusion coefficients. The same HONO source and analytical equipment were used for both experiments, which were run in parallel. The results indicate that the exchange rate of HONO between atmospheric water droplets and interstitial air is not inhibited by interfacial resistance.     

Gaseous and Particulate Oxidation Products Analysis of a Mixture of α-pinene + β-pinene/O3/Air in the Absence of Light and α-pinene + β-pinene/NOx/Air in the Presence of Natural Sunlight

The gas and particle phase reaction products of a mixture of the atmospherically important terpenes -pinene and -pinene with the atmospheric oxidants O₃ and OH/NO_x were investigated using both gas chromatography-mass spectrometry (GC-MS) and high performance liquid chromatography (HPLC) for identification and quantification of reaction products. The nighttime oxidation of a mixture of -pinene and -pinene in the presence of O₃/air, and the daytime oxidation of a mixture of -pinene + -pinene with NO_x air in the presence of natural sunlight were carried out in the University of North Carolina's large outdoor smog chamber (190 m³) located in Chatham County, North Carolina. Mass balances for gaseous and aerosol reaction products are reported over the course of the reaction. More than twenty-nine products were identified and/or quantified in this study. On average, measured gas and particle phase products accounted for 74 to 80% of the reacted -pinen/-pinene mixture carbon. Measurements show that a number of reaction products were found in both O₃ and NO_x system [pinonaldehyde, pinic acid, pinonic acid, pinalic-3-acid, 4-hydroxypinalic-3-acid, 4-oxonopinone, 1-hydroxy-nopinone, 3-hydroxy-nopinone, and nopinone]. Pinonic acid, pinic acid, pinalic-3-acid, 4-hydroxypinalic-3-acid, and 10-hydroxypinonic acid were observed in the early stage in the aerosol phase and may play an important role in the early formation of secondary aerosols.     

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.