Parameterizing turbulent diffusion through the joint probability density

The convective mass flux parameterization often used in meteorological modeling expresses the vertical flux of a transported scalar as proportional to the product of the difference in mean values of the scalar in updrafts and downdrafts and their characteristic velocity. The proportionality factor is a constant to be specified. We show that this proportionality factor also appears in the relaxed eddy accumulation technique of Businger and Oncley. That associates the surface-layer flux of a scalar with the product of the standard deviation of vertical velocity and the mean concentration difference between updrafts and downdrafts.We show that this constant (b) is determined uniquely by the joint probability density (jpd) of vertical velocity and the scalar. Using large-eddy simulation, we generate this jpd for a conservative scalar diffusing through a convective boundary layer. It has quite different forms in top-down and bottom-up diffusion geometries. The bottom-up jpd is fairly well represented by a jointly Gaussian form and implies b ~ 0.6, in good agreement with the surface-layer value reported by Businger and Oncley. The top-down jpd is strikingly non-Gaussian and gives b ~ 0.47. Updrafts carry the bulk of the scalar flux - 70% in the bottom-up case, 60% in the top-down case.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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     

On the turbulence structure in the stable boundary layer over the Greenland ice sheet

Turbulence measurements from a 30 m tower in the stably stratifiedboundary layer over the Greenland ice sheet are analyzed. The observationsinclude profile and eddy-correlation measurements at various levels. Atfirst, the analysis of the turbulence data from the lowest level (2 m aboveground) shows that the linear form of the non-dimensional wind profile(m) is in good agreement with the observations for z/L <0.4, whereL represents the Obukhov length. A linear regression yieldsm=1+5.8z/L. The non-dimensional temperature profile (h) at the2m level shows no tendency to increase with increasing stability. The datafrom the upper levels of the tower are analyzed in terms of both localscaling and surface-layer scaling. The m and the h values show atendency to level off at large stability (z/>0.4) where represents the local Obukhov length. Hence, the linear form of the functions is no longer appropriate under such conditions. The bestcorrespondence to the data can be achieved when using the expression ofBeljaars and Holtslag for m and h. The vertical profiles of theturbulent fluxes, the wind velocity variances and temperature variance arealso determined. The momentum flux profile and the profiles of wind speedvariances are in general agreement with other observations if a welldeveloped low-level wind maximum occurs, and the height of this maximum isused as a height scale.     

Bioaccumulation of Cobalt in Parmelia sulcata

Six locations across mainland Portugal were selected for exposing Parmelia sulcata, for a one-year period (8 months for one site), with simultaneous measurement of total (dry + wet) deposition (one-month periods). The exposed lichens and the total (dry + wet) deposition were analysed for cobalt contents by INAA (instrumental neutron activation analysis) and ICP-MS (inductively coupled plasma mass spectroscopy), respectively. The designated wet deposition was evaluated through the collected water volume; the designated dry deposition was assessed after the (dried) residual mass of the wet deposition. An excellent agreement between Co contents in exposed lichens and the cumulative (1) Co contents in the dry deposition, (2) dry deposition, and (3) wet deposition has been found for the locations with alternate drought and precipitation months, high dry deposition, and high Co contents in the latter. Continuous rainfall was found to hinder the Co accumulation in the lichen due to its release from the lichen and/or lower Co contents in the dry deposition. At three locations, P. sulcata Co contents, after subtraction of the background (before exposure), equalled or exceeded the Co contents in the cumulative dry deposition at the end of the exposure time. The optimal exposure period for this species likely depends on the exposure conditions.     

On Trajectory Curvature as a Selection Criterion for Valid Lagrangian Stochastic Dispersion Models

Recently Wilson and Flesch (Boundary-Layer Meteorology, 84, 411-426, 1997) suggested that the average increment d z to the orientation = arctan(w/u) of the Lagrangian velocity-fluctuation vector can be used to distinguish the better Lagrangian stochastic models within the well-mixed class. Here it is demonstrated that the specification of d z constitutes neither a sufficient or universally applicable criterion to distinguish the better Lagrangian stochastic models within the well-mixed class. The hypothesis made by Wilson and Flesch that Lagrangian stochastic models with /P_E irrotational are zero-spin models, having d z=0, is proven     

Surface-Layer Fluxes in Stable Conditions

Micrometeorological tower data from the Microfronts experiment are analyzed. Scale-dependencies of the flux and flux sampling error are combined to automatically determine Reynolds turbulence cut-off time scales for computing fluxes from time series. The computed downward heat flux at the 3 m height averaged over nine nights with 7.3 hours each night is 20% greater than the downward heat flux computed at the 10 m height. In contrast, there is only a 1.2% difference between 3 m and 10 m heat fluxes averaged over daytime periods, and there is less than a 2% difference between 3 m and 10 m momentum fluxes whether averaged over nighttime or daytime periods.Stability functions, M(z/L) and H(z/L) are extended to z/L up to 10, where z is the observational height and L is the Obukhov length. For 0.01 < z/L < 1 the estimated functions generally agree with Businger-Dyer formulations, though the H estimates include more scatter compared to the M estimates. For 1 < z/L < 10, the flux intermittency increases, the flux Richardson number exceeds 0.2, and the number of flux samples decreases. Nonetheless the estimates of the stability function M based on 3-m fluxes are closer to the formula proposed by Beljaars and Holtslag in 1991 while the M functions based on 10-m fluxes appears to be closer to the formula proposed by Businger et al. in 1971. The stability function H levels off at z/L = 0.5.     

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 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.     

Turbulent transport from an arctic lead: A large-eddy simulation

The upward transfer of heat from ocean to atmosphere is examined for an Arctic lead, a break in the Arctic ice which allows contact between the cold atmosphere and the relatively warm ocean. We employ a large-eddy model to compute explicitly the three-dimensional turbulent response of the atmosphere to a lead of 200 m width. The surface heat flux creates a turbulent plume of individual quasi-random eddies, not a continuous updraft, which penetrate into the stable atmosphere and transport heat upward.Maximum updraft velocities and turbulence occur downwind of the lead rather than over the lead itself, because the development time of an individual thermal eddy is longer than its transit time across the lead. The affected vertical region, while shallow over the lead itself, grows to a height of 65m at 600 m downwind of the lead; beyond that, the depth of the turbulent region decreases as the eddies weaken. The maximum vertical turbulent heat flux occurs at the downwind edge of the lead, beyond which a relative maximum extends upward into the plume. Negative surface heat flux immediately downwind of the lead creates a growing stable layer, but above that internal boundary layer the turbulent heat flux is still positive. Updraft maxima are typically 28 cm/s, but compensating downdrafts result in time-averaged vertical velocities of less than 1 cm/s in the plume. Conditional sampling separates the updraft and downdraft contributions. Formulas for the horizontal eddy development distance and for the vertical plume penetration height are presented. The relative importance of mean and turbulent transport is compared for both vertical and horizontal heat transfer: turbulence dominates the vertical heat transport whereas mean advection dominates the horizontal transport, these offsetting transports producing a quasi-stationary state.     

Modelling of turbulence over low hills and varying surface roughness

Neutral surface layer flow over low hills and varying surface roughness is considered with emphasis on closure schemes in relation to the prediction of turbulence quantities. The equations are linearised, Fourier transformed in the two horizontal directions and solved by means of a finite difference method in the vertical. Three closure schemes are. employed, namely mixing length, E- and e-- closure where E, and indicate that differential equations are used for turbulent kinetic energy, dissipation rate and shear stress. Model calculations are compared with experimental data for the step in roughness problem and for the Askervein hill. The mean flow results turn out to be relatively insensitive to the closure scheme. The shear stress and the dimensionless shear, however, are much better predicted with the E- equations than with mixing length closure. In the outer layer of the hill problem, advection of shear stress becomes important. An equation for is needed here.     

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     

Thermal comfort of man in different urban environments

Summary On July 29, 1985, a hot summer day, biometeorological measurements were performed simultaneously in three different urban structures within the city of Munich and in the trunk space of a nearby tall spruce forest. Based on the results of these experiments the following thermophysiologically relevant biometeorological indices were calculated: Predicted mean vote, skin wettedness and physiologically equivalent temperature. These three indices are derived from different models for the human energy balance. They allow the assessment of the thermal components of the microclimates at the selected sites with regard to application in urban planning. The results quantitatively show the great heat stress in the urban structure street canyon, exposed to south, whereas in the trunk space of the tall spruce forest there is nearly an optimal climate even on hot summer days. Between these extremes the results for street canyon, exposed to north show a little higher heat load than for backyard with trees.

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Zusammenfassung An einem heißen Sommertag, dem 29. Juli 1985, wurden in drei Stadtstrukturen in München und im Stammraum eines nahegelegenen Fichtenhochwaldes zeitgleich biometeorologische Messungen durchgeführt. Mit den Meßergebnissen wurden folgende thermophysiologisch relevante biometeorologische Indizes berechnet: Predicted mean vote, Hautbenetzungsgrad und physiologisch äquivalente Temperatur. Diese drei Indizes beruhen auf verschiedenen Modellen zur menschlichen Energiebilanz. Mit den drei Indizes wurden die thermischen Komponenten der Mikroklimate an den ausgewählten Meßplätzen im Hinblick auf Stadtplanungsaufgaben bewertet. Die Ergebnisse zeigen quantitativ die relativ große Hitzebelastung bei der Stadtstruktur Straßenschlucht, nach Süd exponiert, während im Stammraum des Fichtenhochwaldes selbst an heißen Sommertagen nahezu optimale Bedingungen herrschen. Zwischen diesen Extremen liegen die Ergebnisse für die anderen Meßplätze, wobei für Straßenschlucht, nach Nord exponiert die Wärmebelastung etwas höher als für Innenhof mit Bäumen ist.

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With 6 Figures     

Re-analysis of the nuclear winter phenomenon

Summary An analysis of the report of the (U.S.) National Academy of Sciences (NAS) on atmospheric effects of a nuclear exchange leads to conclusions that differ from those of the NAS and of the earlier TTAPS and AMBIO studies. Any cooling of the earth's surface is likely to beshort-lived because of rapid removal of the smoke clouds originating from nuclear burst-initiated fires, andminor because of appreciable green-house effects due to several distinct physical causes. (One of these, neglected in prior analyses, is the infrared absorption from cirrus clouds produced directly by the nuclear bursts.) Taken together, these effects may even induce slight surface warming (nuclear summer) instead of cooling (nuclear winter). The consequences to atmospheric ozone are similarly ambiguous; depending on the detailed nuclear scenario, the net ozone content may increase-rather than decrease as argued by TTAPS. Experiments could settle some uncertainties.With 2 Figures     

Numerical modeling of the nocturnal urban boundary layer

A numerical case study with a second-order turbulence closure model is proposed to study the role of urban canopy layer (UCL) for the formation of the nocturnal urban boundary layer (UBL). The turbulent diffusion coefficient was determined from an algebraic stress model. The concept of urban building surface area density is proposed to represent the UCL. Calculated results were also compared with field observation data. The height of the elevated inversion above an urban center was simulated and found to be approximately twice the average building height. The turbulent kinetic energy k, energy dissipation rate , and turbulence intensities u ² and w ² increase rapidly at the upwind edge of the urban area. The Reynolds stress uw displayed a nearly uniform profile inside the UBL, and the vertical sensible heat flux w had a negative value at the inversion base height. This indicates that the downward transport of sensible heat from the inversion base may play an important role in the formation of the nocturnal UBL.     

Numerical Simulation of Strongly Stratified Flow Over a Three-Dimensional Hill

A numerical study of stably stratified flow over a three-dimensional hill is presented. Large-eddy simulation is used here to examine in detail the laboratory experimental flows described in the landmark work of Hunt and Snyder about stratified flow over a hill. The flow is linearly stratified and U/Nh is varied from 0.2 to 1.0. Here N and U are the buoyancy frequency and freestream velocity respectively, and h is the height of the hill. The Reynolds number based on the hill height is varied from 365 to 2968. The characteristic flow patterns at various values of U/Nh have been obtained and they are in good agreement with earlier theoretical and experimental results. It is shown that the flow field cannot be predicted by Drazin's theory when recirculation exists at the leeside of the hill even at UNh 1. The wake structure agrees well with a two-dimensional wake assumption when U/Nh 1 but lee waves start to influence the wake structure as U/Nh increases. The dividing-streamline heights obtained in the simulation are in accordance with experimental results and Sheppard's formula. The energy loss along the dividing streamline due to friction/turbulence approximately offsets the energy gained from pressure field. When lee waves are present, linear theory always underestimates the amplitude and overestimates the wavelength of three-dimensional lee waves. The simulated variations of drag coefficients with the parameterK (=ND/ U) are qualitatively consistent with experimental data and linear theory. Here D is the depth of the tank.     

Recurrence statistics of concentration fluctuations in plumes within a near-neutral atmospheric surface layer

This study examines the statistical properties of the concentration derivative, , for a dispersing plume in a near-neutrally stratified atmospheric surface layer. Towards this goal, the probability density function (pdf) of , and the conditional pdf of given a fixed concentration level, , have been measured. These pdfs are found to be modeled well by a generalizedq-Gaussian (gqG) distribution with intermittency exponent,q, equal to 0.3 and 3/4, respectively. These results highlight the strong intermittency effect (patchiness) of the small-scale concentration eddy structures in the plume. The distribution of time intervals between successive high peaks in the squared derivative process, x², is found to be well approximated by a power-law distribution, implying that occurrences of these high peaks are much more clustered than would be predicted by a Poisson or shot-noise process. The results are used to improve models for the joint pdf of and , and for the expected number of upcrossings per unit time interval of a fixed concentration level that have been proposed by Kristensenet al. (1989). The predictions of the improved models are in accord with observations, and suggest that the intercorrelation between and must be explicitly incorporated if good estimates of the upcrossing intensity are to be obtained.     

Periodicity of annual precipitation in different climate regions of Croatia

Summary The periodicity of a 100-year series of annual precipitation over Croatia has been studied by means of power spectrum analysis at 3 stations representing the different climatic regions of Croatia. The annual precipitation variance spectra in the continental lowland (Osijek) and at the north East Adriatic coast (Crikvenica) can be fitted by Markov white noise continuum, but in the transitional region between the Dinaric Alps and the Pannonian lowland (Zagreb-Gri) a non-white noise continuum is necessary. Quasi-periodic oscillations appear in two spectra ranges: short (2.2 and 4.7 years) and medium (25.0 and 33.3 years). These results are compared with those of other authors for other parts of the Europe.With 2 Figures     

Arctic hazes in summer over Greenland and the North American Arctic: II. Nature and concentrations of accumulation-mode and giant particles

Airborne measurements made during August 1985 over Greenland and its environs show that both accumulation-mode (0.1 m D2.0 m) and giant (D2 m) particles were present in relatively high concentrations in arctic haze layers and that the accumulation-mode particles dominated light scattering. Particles with diameters (D) between 1 and 4 m consisted predominately of mixed materials, small and dense inclusions, and probably organic compounds containing sulfur. Many of the particles from 0.1 to 1 m in diameter were also of mixed composition, with sulfuric acid, ammonium sulfate and organics probably the dominant constituents.     

SODAR-based estimation of TKE and momentum flux profiles in the atmospheric boundary layer: Test of a parameterization model

Summary A simple parameterization for the estimation of turbulent kinetic energy (TKE) and momentum flux profiles under near-neutral stratification based on sodar measurements of the vertical velocity variance has been tested using data from the LINEX-2000 experiment. Measurements included operation of a phased-array Doppler sodar DSDPA.90 and of a sonic anemometer USA-1 mounted at a meteorological tower at a height of 90m. Good agreement has been found between the TKE and momentum flux values derived from the sonic and sodar data (with correlation coefficients r>0.90 and a slope of the regression lines of about 1.01.1) suggesting the possible use of sodar measurements of _w ² to derive turbulence parameter profiles above the tower range.     

Experiments On Buoyant Plume Dispersion In A Laboratory Convection Tank

Plume dispersion in the convective boundary layer (CBL) is investigated experimentally in a laboratory convection tank. The focusis on highly-buoyant plumes that loft near or become trapped in the CBL capping inversion and resistdownward mixing. Such plumes are defined by dimensionless buoyancy fluxes F_* 0.1, where F_* = F_b/(U w_* ² z_i), F_b is the stack buoyancy flux,U is the mean wind speed, w_* is the convective velocity scale, and z_i is the CBL depth. The aim is to obtain statistically-reliable mean (C) and root-mean-square (rms, _c) concentration fields as a function of F_* and the dimensionless distance X = w_*x/(U z_i), where x is the distance downstream of the source.The experiments reveal the following mainresults: (1) For 3 X 4and F_* 0.1, the crosswind-integrated concentration (CWIC) fields exhibit distinctly uniform profiles below z_i with a CWIC maximum aloft, in contrast to the nonuniform profiles obtained earlier by Willis and Deardorff. (2) The lateral dispersion (_y) variation with X is consistent with Taylor's theory for _* 0.1 and a buoyancy-enhanced dispersion, _y/z_i F_* ^1/3X^2/3, forF_* = 0.2 and 0.4. (3) The entrapment, the plume fraction above z_i, has a mean (E) that follows a systematic variationwith X and F_*, and a variability (_e/E) that is broad ( 0.3 to 2) near the source but subsides to 0.25 far downstream. (4) Vertical profiles of the concentration fluctuation intensity (c/C) are uniform for z < z_i and X > 1.5, but exhibit significant increases: (a) at the surface and close to the source (X 1.5), and(b) in the entrainment zone. (5) The cumulative distribution functions (CDFs) of the scaled concentration fluctuations (c/_c) separate into mixed-layer and entrainment-layer CDFs for X 2, with the mixed-layer group collapsing to a single distribution independent of z.These are the first experiments to obtain all components of the lateral and vertical dispersion parameters (rms meander, relative dispersion, total dispersion) for continuous buoyant releases in a convection tank. They also are the first tank experiments to demonstrate agreement with field observations of: (1) the scaled ground-level concentration along the plume centreline, and (2) the dimensionless lateral dispersion _y/z_i of buoyant plumes.