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.     

Scavenging Efficiency of ‘Aerosol Carbon’ and Sulfate in Supercooled Clouds at Mt. Sonnblick (3106 m a.s.l., Austria)

Cloud water and interstitial aerosol samples collected at Mt. Sonnblick (SBO) were analyzed for sulfate and aerosol carbon to calculate in-cloud scavenging efficiencies. Scavenging efficiencies for sulfate (_SO) ranged from 0.52 to 0.99 with an average of 0.80. Aerosol carbon was scavenged less efficiently with an average value (_AC) of 0.45 and minimum and maximum values of 0.14 and 0.81, respectively. Both _SO and _AC showed a marked, but slightly different, dependence on the liquid water content (LWC) of the cloud. At low LWC, _SO increased with rising LWC until it reached a relatively constant value of 0.83 above an LWC of 0.3 g/m³. In the case of aerosol carbon, we obtained a more gradual increase of _AC up to an LWC of 0.5 g/m³. At higher LWCs, _{_} remained relatively constant at 0.60. As the differences between _SO and _A varied across the LWC range observed at SBO, we assume that part of the aerosol carbon was incorporated into the cloud droplets independently from sulfate. This hypothesis is supported by size classified aerosol measurements. The differences in the size distributions of sulfate and total carbon point to a partially external mixture. Thus, the different chemical nature and the differences in the size and mixing state of the aerosol particles are the most likely candidates for the differences in the scavenging behavior.     

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.     

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     

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     

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.     

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.     

Estimating product yields of carbon-containing products from the atmospheric photooxidation of ambient air alkenes

The yields of products have been calculated for the reactions of hydroxyl radicals and ozone with 19 of the two-through-six carbon anthropogenic alkenes. Based on their rate of reaction, mechanisms of reactions and the ambient air distribution for these alkenes their seasonal ambient air yields have been estimated.Aldehydes predominate as products irrespective of season, with smaller yields of several ketones. Other minor products include carboxylic acids, carbon monoxide, carbon dioxide, and alkenes. About a two-fold increase is estimated in the yields of hot biradicals and their products from summer to winter.One sensitivity analysis was made by recomputing yields at a different OH radical to O₃ concentration than assumed most likely in the calculations discussed above. In addition, the sensitivity of product yields to an estimated range of seasonally averaged sunset-to-sunrise NO₃ radical concentrations was calculated. The effects of free radical reactions are discussed, but these are believed to make a relatively minor contribution within the NO _x -rich atmospheres that contain anthropogenic alkenes.The uncertainties in product yields associated with the range of NO₃ radical concentrations assumed present is relatively small for aldehydes, as is the decrease in yield of the one carbon hot biradical. Larger uncertainties occur for ketones. Significant decreases in yields occur for larger hot biradicals, especially the branched-chain hot radicals in the presence of NO₃ radicals.     

Drag and drag partition on rough surfaces

An analytic treatment of drag and drag partition on rough surfaces is given. The aims are to provide simple predictive expressions for practical applications, and to rationalize existing laboratory and atmospheric data into a single framework. Using dimensional analysis and two physical hypotheses, theoretical predictions are developed for total stress (described by the square root of the canopy drag coefficient), stress partition (described by the ratio _S/ of the stress _s on the underlying ground surface to total stress ), zero-plane displacement and roughness length. The stress partition prediction is the simple equation _S/= 1/(1+), where = C_RC_S the ratio of element and surface drag coefficients. This prediction agrees very well with data and is free of adjustable constants. Other predictions also agree well with a range of laboratory and atmospheric data.     

Final results of the CONDORS convective diffusion experiment

TheConvectiveDiffusionObserved byRemoteSensors (CONDORS) field experiment conducted at the Boulder Atmospheric Observatory used innovative techniques to obtain three-dimensional mappings of plume concentration fields, /Q, of oil fog detected by lidar and chaff detected by Doppler radar. It included extensive meteorological measurements and, in 1983, tracer gases measured at a single sampling arc. Final results from ten hours of elevated and surface release data are summarized here. Many intercomparisons were made. Oil fog /Q measured 40m above the arc are mostly in good agreement withSF ₆ values, except in a few instances with large spacial inhomogeneities over short distances. After a correction scheme was applied to compensate for the effect of its settling speed, chaff dy/Q agreed well with those of oil except in two cases of oil fog hot spots. Mass or frequency distribution vs. azimuth or elevation angle comparisons were made for chaff, oil, and wind, with mostly good agreements. Spacial standard deviations, _y and _z, of chaff and oil agree overall and are consistent at short range with velocity standard deviations _vand _w 0.6w^* (the convective scale velocity), as measured atz>100m. Surface release _y is enhanced up to 60% at smallx, consistent with the Prairie Grass measurements and with larger _v and reduced wind speed measured near the surface. Decreased _y at small dimensionless average times is also noted. Finally, convectively scaled dy, C _y, were plotted versus dimensionlessx andz for oil, chaff, and corrected chaff for each 30–60 min period. Aggregated CONDORSC _y fields compare well with laboratory tank and LES numerical simulations; surface-released oil fog compares expecially well with the tank experiments. However, large deviations from the norm occurred in individual averaging periods; these deviations correlated strongly with anomalies in measured distributions.On assignment to the US Environmental Protection Agency, Atmospheric Research and Exposure Assessment Laboratory, RTP, NC.     

Atmospheric estimates of power-law exponents Μ and Μθ

Measurements in the atmospheric surface layer of sixth-order velocity structure functions and of sixth-order mixed velocity-temperature structure functions support values of and previously obtained in the laboratory at moderate turbulence Reynolds numbers.     

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.     

The influence of surface cover and climate on energy partitioning and evaporation in a subarctic wetland

Energy partitioning and evaporation were measured over three wetland surfaces in a subarctic coastal marsh during pre-growing and growing periods. These surfaces included an alder/willow woodland, a sedge marsh and a raised backshore sedge meadow. A combination model analysis was used to assess the relative importance of surface resistance and meteorological conditions on the magnitude of the Bowen ratio, , during the growing period.Overall, the three surfaces experienced important site-to-site and seasonal differences in and evaporation, Q _E. During the non-foliated period, Q _E was largest and was smallest for the open water marsh, while the dry backshore site experienced the smallest Q _E and largest . The non-foliated woodland assumed intermediate values of and Q _E. After the vegetation covers were established, the woodland assumed the smallest and largest Q _E flux. It was also found that at the marsh site increased with the presence of a vegetation cover.Wind direction was always an important factor in determining Q _E and at all sites. was substantially larger and Q _E was smaller for onshore winds (i.e., originating from James Bay) than for offshore winds. The combination model analysis showed that canopy resistance at all sites was largest during warm offshore winds, which were associated with large saturation deficits. However, the effect of increased canopy resistance on during offshore winds was offset by a large climatological resistance, resulting in small values and large Q _E. When winds originated from James Bay, canopy resistance was smaller than for offshore winds, but the climatological resistance also was much smaller, resulting in larger and small Q _E. The results have important implications for changes in land cover and climate on the regional water balance.     

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.     

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.     

On characteristics of wind direction fluctuations in the surface layer

It is shown that the ratio of standard deviation of lateral velocity to the friction velocity, /u _*, and therefore wind direction fluctuations, are sensitive to mesoscale terrain properties. Under neutral conditions, /u _* is almost 40% larger in rolling terrain than over a horizontal surface. In the lee of a low mountain, the fluctuations may be 2.5 times as strong as over horizontal terrain. In contrast, vertical velocity fluctuations are little influenced by mesoscale terrain features.Now with Air Weather Service, Offutt AFB, Omaha, Nebraska.     

A dynamical analysis of the drag conditions at the sea surface

When applied to a sea surface, shortcomings are noted for the ordinary classification of drag conditions at rigid underlying surfaces according to the Reynolds roughness number Re _s . It is shown that in the case of mobile underlying surfaces, it would be more natural to use the dynamical classification of drag conditions according to the order of magnitude of the ratio ( = /) of the momentum flux toward the waves ( _w) to the viscous momentum flux through the surface ( _w). The relevant estimates of for the main stages of development of the wind waves indicate that the observed values of the drag coefficient of the sea surface correspond to the case of underdeveloped roughness.     

Gas and Particulate Products Distribution from the Photooxidation of α-Humulene in the Presence of NOx, Natural Atmospheric Air and Sunlight

The photooxidation of -humulene in the presence of NO_x, natural sunlight, and rural background air was investigated using a combination of gas chromatography-mass spectrometry (GC-MS) and high performance liquid chromatography (HPLC). Identification and quantification of gas and particulate reaction products were reported over the course of the reaction. The daytime photooxidation 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. On average, measured gas and particle phase products accounted for 44% of the reacted -humulene carbon. Measurements show that a number of reaction products with low vapor pressures (e.g. 3-seco--humulone aldehyde, 7-seco--humulone aldehyde, -humulal aldehyde, -humulene 3-oxide or -humulene 7-oxide, -humulaic/alic acid isomers, and 3-seco--14-hydroxyhumulone aldehyde) were found in the early stage 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.     

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     

Estimation of the Monin-Obukhov similarity functions from a spectral model

From measured one-dimensional spectra of velocity and temperature variance, the universal functions of the Monin-Obukhov similarity theory are calculated for the range –2 z/L + 2. The calculations show good agreement with observations with the exception of a range –1 z/L 0 in which the function _m , i.e., the nondimensional mean shear, is overestimated. This overestimation is shown to be caused by neglecting the spectral divergence of a vertical transport of turbulent kinetic energy. The integral of the spectral divergence over the entire wave number space is suggested to be negligibly small in comparison with production and dissipation of turbulent kinetic energy.Notation a,b,c contants (see Equations (–4)) - C_i constants i=u, v, w, (see Equation (5) - k_me,k_mT peak wave numbers of 3-d moel spectra of turbulent kinetic energy and of temperature variance, respectively - k_mi peak wave numbers of 1-d spectra of velocity components i=u, v, w and of temperature fluctuations i= - k_sb, k_c characteristics wave numbers of energy-feeding by mechanical effects being modified by mean buoyancy, and of convective energy feeding, respectively - L Monin-Obukhov length - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gabeivayaaraaaaa!3C5B!\[{\rm{\bar T}}\] difference of mean temperature and mean potential temperature - T* Monin-Obukhov temperature scale - velocity of mean flow in positive x-direction - u* friction velocity - u, v, w components of velocity fluctuations - z height above ground - von Kármanán constant - temperature fluctuation - _m nondimensional mean shear - _H nondimensional mean temperature gradient - nondimensional rate of lolecular dissipation of turbulent kinetic energy - _D nondimensional divergence of vertical transports of turbulent linetic energy