Turbulent dispersion in the atmospheric surface layer

By non-dimensionalizing a trajectory-simulation (TS) model of turbulent dispersion, it is shown that the dimensionless concentration z ₀cu_*/kQ (cu _*/kQ) due to a continuous line (area) source of strength Q in the atmospheric surface layer depends only on z/z ₀, x/z ₀, z ₀/L and z _s/z₀, where z _s is the source height. The TS model is used to tabulate concentration profiles due to ground-level line and area sources. Concentration profiles generated by the TS model for elevated sources are shown to be inconsistent with the Reciprocal Theorems of Smith (1957) and it is suggested that this is because the flux-mean gradient closure scheme inherent in the Reciprocal Theorem is invalid for an elevated source.     

Turbulent carbon exchange in very stable conditions

Turbulent fluxes obtained using the conventional eddy covariance approach result in erratic results with large time fluctuations in extremely stable conditions. This can limit efforts to estimate components of the nocturnal energy budget and respiratory CO₂ fluxes. Well-organized fluxes that show a clear dependence on turbulent intensity were obtained when multiresolution decomposition was used to estimate turbulent exchanges. CO₂, heat and water vapour fluxes were observed at a site in the eastern Amazon basin that had been cleared for agricultural purposes. Temporal scales of the carbon transfer were determined and shown to be similar to those of latent heat, but as much as three times larger than those of sensible heat. CO₂ eddy diffusivities at the temporal scales on which most of the vertical CO₂ exchange occurs are shown to be 50 times larger than the eddy diffusivity for heat. A process associated with the vertical scale of the scalar accumulation layer is suggested to explain these different scales and turbulent diffusivities of carbon and sensible heat transfer. For an appreciable range of turbulence intensities, the observed vertical turbulent carbon exchange is insufficient to account for the locally respired CO₂ estimated independently. Evidence that shallow drainage currents may account for this is given.     

Turbulent exchange over a surface with chessboard-type inhomogeneities

The results of an experiment carried out in the summer of 1988 in the forest-steppe region of the USSR are given. The aim of the experiment was to study turbulent exchange between the atmosphere and a non-homogeneous underlying surface consisting of a patchwork quilt of agricultural lands sown with different crops (hereafter called chessboard-type inhomogeneities). Simultaneous measurements of turbulent fluxes of heat, momentum and humidity by the eddy-correlation methods and also the measurements of the mean wind velocity and temperature are described. The values of turbulent fluxes calculated from the profile measurements are in good agreement with those obtained from the eddy-correlation measurements. Thus it may be concluded that the universal functions of Monin-Obukhov similarity theory (determined from measurements over a flat and homogeneous underlying surface) pertain also to a non-homogeneous (chessboard-type) underlying surface.     

Estimating the Monin-Obukhov length in the stable boundary layer for dispersion calculations

Analysis of data collected during the Prairie Grass, Kansas and Minnesota experiments reveals the following empirical relationship between the Monin-Obukhov length L and the friction velocity u _*: L = Au _* ², A = 1.1 × 10³s²m^-1. This result combined with the formulation for the height of the stable boundary layer h suggested by Zilitinkevich (1972) leads to h u _* ^3/2 f–^1/2 where f is the Coriolis parameter. Data from the Minnesota study (Caughey et al., 1979) provide ample support for this expression.These empirical equations for L and h are useful for routine dispersion estimates during stable conditions.     

A numerical study on the meso-scale pollutant dispersion over a sloped surface in the stable boundary layer

A numerical model is used to study the properties of pollutant dispersion over a large uniformly-sloped surface in the stable atmospheric boundary layer. By simulating the structure of boundary layer flow to improve the advective wind field and vertical eddy diffusivities included in the advection-diffusion equa-tion, this numerical model permits an estimation of the distribution of pollutant concentration for more real-istic atmospheric diffusion conditions.     

A suggested refinement for O'Brien's convective boundary layer Eddy exchange coefficient formulation

With observational data collected and interpreted by Crane et al. (1977), the adequacy of the O'Brien polynomial to represent the exchange profile of heat and pollution in a convective boundary layer is examined and a refinement suggested. Also, it is shown that the height of the surface layer, h=0.04 z _i , developed by Blackadar and Tennekes (1968) for a neutrally stratified boundary layer (with z _z =0.25u _*/f) appears to be equally valid for the convective boundary layer where z _i , defined as the top of the mixed layer, is used.     

Turbulent characteristics of a shallow convective internal boundary layer

Turbulent characteristics of a 50 to 100 m deep convective internal boundary layer (I.B.L.) have been studied. The data were gathered at a flat coastal site (Näsudden on the island of Gotland, Sweden) during three consecutive days in May 1980 which were characterized by a steady, very stable stratified marine approach flow. The site is situated on a flat area ca. 1500 m from the shoreline. Only daytime runs have been analysed in the present paper. The sensible heat flux at the ground was typically 200 W m^-2 and was found to decrease more or less linearly with height throughout the I.B.L., being slightly negative at greater heights. The momentum flux was also found to decrease with height, but nevertheless shear production of turbulent kinetic energy was found to be large throughout the entire I.B.L. The analysis shows that the turbulent regime has a mixed character. Certain characteristics, such as the rate of growth of the I.B.L., appear to be almost entirely controlled by mechanical turbulence, while others, notably temperature variance and the spectrum of vertical velocity, scale remarkably well with w _* and z _i, in accordance with the results found in fully convective conditions during the experiments at Minnesota and Aschurch. Other turbulent characteristics, such as spectra of the horizontal wind components measured near the top of the I.B.L. tend to adhere to mixed-layer scaling in the high frequency range, exhibiting much increased energy in the lower (reduced) frequency range. Spectra of the velocity components from 10 m are shown to be in general agreement with findings from ‘ideal’, homogeneous sites (Kansas) when properly normalized, although the low frequency part of u- and v-spectra are slightly reduced compared to the case with deep convection.     

Step-like temperature fluctuations associated with inverted ramps in a stable surface layer

Ensemble averages of temperature before and after step-like temperature fluctuations reveal the presence of inverted ramps in a stable surface layer. Normalized frequency of upward steps increases with increasing stability, whereas normalized magnitude of the temperature step decreases with stability and becomes constant at about R _i = 1. These results suggest that the significance of temperature steps increases as stability increases. In moderate stability, the temperature pattern shows a gradual decrease after an upward step, which can be called a time-inverted ramp. Descending air and large downward heat flux are observed in a time-inverted ramp, suggesting a contribution from an ordered motion in wind. On the other hand, the temperature steps are related to gravity waves in strong stability.     

Turbulent exchange above a pine forest II. Organized structures

Data from two 100-min runs on the turbulent atmospheric wind, temperature and humidity fields above a pine forest have been analysed using conditional sampling techniques. With the aid of the temperature time series, ramp events were identified and all fields were averaged in order to remove smaller scale turbulence and random low-frequency turbulence, and to map the organized structures revealed in this way. It is shown that the turbulent fluxes of momentum, heat and humidity, determined from these ramp-events, in fact constitute a large part of the total fluxes, about 90% during the actual events.On average, the duration of and the time between ramps were found to be about 35 s and 100 s, respectively. These periods were also found in the uw-, wT- and wq-cospectra, not only in the data analysed in this paper, but in the major part of all day-time data from this forest site (about 80 runs of 60 or 100 min). This indicates that the ramp events described arc a rather common phenomenon. The organized structures also have remarkable resemblance to near-wall structures observed in the laboratory.     

The energy exchange within a vegetation layer

Summary The concept of vegetation as a multi-layered heat exchange system is discussed with reference to measurements in a barley field. These measurements included the monitoring of net radiation at various levels inside the crop and the conducted heat flux in the soil for typical clear and overcast days. The diurnal variations of the components of the heat balance throughout the crop are discussed, computing the combined flux of sensible and latent heat as a remainder term. The results show a complete reversal of the flux of sensible and latent heat from the top of the crop to the soil surface: during the night the surface loses heat by eddy diffusion as well as radiation and during the day it gains heat through both these processes. The total heat exchange between the crop and the atmosphere gives the usual heat gains by eddy diffusion during the night and losses during the day. The radiation absorbed by a layer of vegetation is converted into sensible and latent heat and 80% of the total energy exchange takes place in the upper half of the crop. The magnitude of the exchange process falls off rapidly with depth in the crop.

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Zusammenfassung Die Vegetation wird als mehrschichtiges System im Hinblick auf den Wärmeaustausch betrachtet, wobei Messungen in einem Gerstenfeld verwendet werden. Die Messungen umfaßten die Registrieuung der Wärmebilanz in verschiedenen Höhen im Getreidestand und des Wärmeflusses im Boden an typischen klaren und bedeckten Tagen. Der Tagesgang der Komponenten der Wärmebilanz durch die Vegetationsschicht wird untersucht, dabei wird die Summe des Fluesses von fühlbarer und von latenter Wärme als Restglied berechnet. Die Resultate zeigen eine vollkommene Umkehr des Flusses von fühlbarer und latenter Wärme von der Obergrenze des Getreidestandes zum Boden: während der Nacht verliert die Erdoberfläche Wärme sowohl durch turbulenten Austausch wie durch Strahlung, während des Tages nimmt sie durch beide Prozesse Wärme auf. Der gesamte Wärmeastausch zwischen dem Getreidefeld und der Atmosphäre ergibt die gewöhnlichen Wärmegewinne durch turbulenten Austausch bei Nacht und die Wärmeverluste bei Tag. Die von der Vegetationsschicht absorbierte Strahlung wird in fühlbare und latente Wärme umgesetzt, wobei 80% des gesamten Wärmeaustausches in der oberen Hälfte der Vegetationsschicht erfolgen. Die Größe des Austauschprozesses vermindert sich rasch mit der Tiefe in der Vegetationsschicht.

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Résumé On considère ici la végétation comme un système à plusieurs strates vis à vis des échanges de chaleur. Pour cela on se sert de mesures effectuées dans un champ d'orge. Ces mesures comprenaient l'enregistrement du bilan de chaleur à différentes hauteurs dans le dit champ ainsi que du flux de chaleur dans le sol à des jours typiques: couverts ou clairs. On étudie l'évolution diurne des composantes du bilan de chaleur au travers de la couche végétale. Pour ce faire, on clacule la somme du flux des chaleurs sensible et latente comme terme final de l'équation. Les résultats montrent une inversion complète du flux de ces deux chaleurs de la surface supérieure du champ jusqu'au sol. Pendant la nuit, la surface du sol perd de la chaleur aussi bien par des échanges turbulents que par rayonnement. Pendant le jour, le sol reçoit de la chaleur par ces deux processus. L'échange total de chaleur entre le champ d'orge et l'atmosphère présente les gains de chaleur ordinaire par turbulence de nuit et les pertes de jour. Le rayonnement absorbé par la couche végétale est transformé en chaleur latente et sensible. 80% de la totalité des échanges de chaleur se passent dans la moitié supérieure de la couche végétale. L'importance des processus d'échange diminue rapidement avec la profondeur de la couche végétale.

     

Turbulent dispersion in coastal atmospheric boundary layers: An application of a Lagrangian model

A Lagrangian model is applied to simulate the dispersion of passive tracers (in particular, water vapour) in coastal atmospheric boundary layers under onshore wind conditions. When applied to convective boundary layers over uniform surfaces, the model gives results in agreement with those of similar studies. Numerical simulation of turbulent dispersion in coastal areas also reproduces the basic features known from experimental studies. Under onshore wind conditions, the humidity field is plume-shaped with the maximum vertical transport being over land downstream of the coast line. The model shows that the surface sensible heat flux over land, the static stability of the onshore air flow and the onshore wind speed are the most important factors determining the basic features of turbulent dispersion in coastal areas.     

Analysis of turbulent exchange and coherent structures in the stable atmospheric boundary layer based on tower observations

Using data collected at the Spanish low troposphere research centre CIBA (Centro de Investigación de la Baja Atmósfera) and at the Cabauw Experimental Site for Atmospheric Research (CESAR) in the Netherlands, we analyzed the most significant features of different coherent structures occurring in the stable atmospheric boundary layer. In particular, we used both the Reynolds and wavelet methods to analyze a solitary wave, a gravity wave, a density current and a low-level jet. For each of these structures, we found that wavelet analysis had the capacity to distinguish the different scales involved in these events due to the different timing and heights of the thermal instabilities and downdrafts associated with the disturbances. In addition, the wavelet method highlights the different roles of turbulence and coherent structures in the transfer of heat, moisture and CO₂ in the nocturnal boundary layer.     

A model for eddy diffusivity in a stable boundary layer

Expressions for the vertical and the lateral diffusivity coefficients were derived from the Local Similarity Theory and the Statistical Diffusion Theory. For such, the spectral density energies for the turbulent velocities were used. The expressions here derived are compared with the diffusivity coefficients for momentum and heat suggested by Sorbjan (from the Minnesota experiments) and Nieuwstadt (from the Cabauw experiments). This comparison allows us to conclude that turbulence is equally efficient in transporting momentum, heat and contaminants in an ideally stable boundary layer.     

Concentration fluctuation measurements in a plume dispersing in a stable surface layer

A set of tracer experiments studying concentration fluctuations in a pollutant plume dispersing near the surface in a stably stratified nocturnal boundary layer is described, and the results are compared with those obtained in near-neutral stability conditions by Mylne and Mason (1991). The results highlight the importance of slow meandering of the plume which is characteristic of stable conditions. This meandering makes it impossible to conduct experiments under near-stationary conditions, resulting in considerable statistical variability in the results, but is important in reducing time-averaged concentrations. Spectral characteristics of the plume and general fluctuation statistics are qualitatively similar to those in near-neutral stability, but there are significant quantitative differences. Fluctuation time scales are shown to be substantially longer under stable conditions. This difference cannot be fully explained by the reduced windspeed alone, indicating that the length scale of plume elements is also longer. Some of the differences observed in stable conditions, particularly the longer time scales, are shown to substantially increase the potential hazard due to fluctuations in practical applications. A conceptual model of plume dispersion is described, which explains the observed plume structure under different conditions by relating it to the turbulent velocity spectra.     

Turbulent dispersion of gaseous pollutants: Numerical study of ground level concentration as a function of Eddy diffusivity parametrization on the atmospheric boundary layer

Theoretical and Applied Climatology - A numerical model of the dispersion of gaseous atmospheric pollutants based on the K-theory has been proposed, and the numerical procedure has been validated...     

Turbulent exchange above a pine forest,I: Fluxes and gradients

Measurements of gradients of wind, temperature and humidity and of the corresponding turbulent fluxes have been carried out over a sparse pine forest at Jädra»s in Sweden. In order to ascertain that correct gradient estimates were obtained, two independent measuring systems were employed: one system with sensors at 10 fixed levels on a 51 m tower and another with reversing sensors for temperature and humidity, covering the height interval 23 to 32 m. Turbulent fluxes were measured at three levels simultaneously. Data from three field campaigns: in June 1985, June 1987 and September 1987 have been analyzed. The momentum flux is found on the average to be virtually constant from tree top level, at 20 to 50 m. The average fluxes of sensible and latent heat are not so well behaved. The ratio of the non-dimensional gradients of wind and temperature to their corresponding values under ideal conditions (low vegetation) are both found to be small immediately above the canopy (about 0.3 for temperature and 0.4 for wind). With increasing height, the ratios increase, but the values vary substantially with wind direction. The ratios are not found to vary systematically with stability (unstable stratification only studied). The ratio of the non-dimensional humidity gradient to the corresponding non-dimensional potential temperature gradient (equivalent to k _h /k _w ) is found to be unity for (z – d)/L _v less than about –0.1 and about 1.4 for near neutral stratification, but the scatter of the data is very large.     

Turbulent mixing of reactive gases in the convective boundary layer

We study the interactions of chemistry and turbulent mixing of tracersin the convective boundary layer with a second-order closure model,including higher order chemistry terms. In order to limit the number of predictive equations we prescribe the profiles for ¯w¯, ¯w¯ ¯ and the lengthscale l. However, for model validation we treat temperature and humidity asinert tracers, and compare the results with profiles observed during theAir Mass Transformation Experiment, and with similarity expressions for thesurface layer. We find good agreement of the mean profiles, but the (co-)variances are slightly underpredicted. Furthermore, the model usesdiagnostic equations expressing third moments of concentration in terms ofsecond moments and their vertical derivatives. They are compared withlarge-eddy model results, showing good agreement and, therefore, thesimplifications are justified. The model is applied to the transport of two gases subject to one bimolecular reaction. The importance of concentration correlations on themean transformation rate is studied. For two gases diffusing in oppositedirections we find for moderate and fast chemistry a 50% and90% decreased transformation rate due to the negatively correlatedconcentrations. These values are similar to large-eddy results of Schumannand Sykes et al. For two bottom-up tracers we find that the covariance ofboth reactive species is either positive or negative, increasing or reducingthe effective transformation rate depending on the Damköhler number (the ratio of the turbulent and the chemistry timescale). A significantdirect influence of chemistry on the flux divergence is found in bothcases. According to the model the effective transport to mid-levels of theboundary layer is increased when two reactive tracers diffuse in oppositedirections, and decreased in the case of two bottom-up tracers.     

Turbulent diffusivity and diurnal variations in the atmospheric boundary layer

Diurnal variations of the vertical profiles of wind and temperature have been surveyed, and the diffusivity and the dimensionless gradient function in the atmospheric boundary layer have been estimated. Even in the middle of the atmospheric boundary layer (e.g., below a height of 442 m), the vertical wind profile normalized by the surface friction velocity has approximately a universal profile function different from that in the surface boundary layer. Under strong stability conditions, the dimensionless gradient function has a value of about 9.     

Observations of a multi-level turbulence structure in a very stable atmospheric boundary layer

Boundary-layer measurements conducted at the Marsta site in Sweden from a winter-time situation (23–25 Feb.) with stable stratification have been analysed. The data comprise wind and temperature profile measurements up to 30 m, turbulence measurements at 2, 6 and 30 m and Doppler acoustic sounder data up to about 150 m. The upwind fetch at the site is flat and free from obstacles to a distance of ca 5 km for the particular sector chosen for the experiment.During the night, a two-layer vertical structure developed. Analysis of power spectra, co-spectra and variances in a shallow and very stable turbulent boundary layer near the ground show that the turbulence is fully developed and follow the universal behaviour.Above, at a height of 30 m, another turbulent layer is produced by increased wind shear near a low-level jet. This turbulent upper layer can be regarded as a layer of free shear flow. At this height, there also exist wave-turbulence interactions at low frequencies which sometimes cause a countergradient heat flux.