Gervásio Annes Degrazia

Derivation of an Eddy Diffusivity Depending on Source Distance for Vertically Inhomogeneous Turbulence in a Convective Boundary Layer

Abstract Accounting for the current knowledge of the convective boundary layer structure and characteristics, a new formulation for the eddy diffusivities to be used in atmospheric dispersion models has been derived. That is, expressions for the eddy diffusivities, depending on source distance, for inhomogeneous turbulence are proposed. The classical statistical diffusion theory, the observed spectral properties, and observed characteristics of energy-containing eddies are used to estimate these parameters. In addition, a vertical eddy diffusivity was introduced into an air pollution model, validated with the data of Copenhagen experiments, and compared with an improved Gaussian model. The results of this new method are shown to agree with the measurements of Copenhagen and also with those of the Gaussian model. Furthermore, the current study suggests that the inclusion of the memory effect, important in regions near an elevated continuous point source, improves the description of the turbulent transport ...

Evaluation of a new eddy diffusivity parameterisation from turbulent Eulerian spectra in different stability conditions

Abstract A parameterisation for the vertical diffusivity has been recently derived by some of the authors. The formulation, based on the Taylors statistical theory, the Hay and Pasquill working approximation concerning the relationship between Lagrangian and Eulerian turbulence spectra and a model for Eulerian spectra, relates plume dispersion in a boundary layer mainly to the turbulent eddies acting in the planetary boundary layer (PBL). The formulation represents in a realistic way both shear and buoyant turbulent mechanisms, which characterise the various regimes of the PBL and gives continuous values at any elevation and all stability conditions from unstable to stable. In this paper, the K-parameterisations, included in an advanced analytical model, have been tested and compared with a vertical dispersion scheme reported in literature, using experimental data in different emission conditions (low and tall stacks) and in several meteorological conditions ranging from stable to convective. Results show that (i) the dispersion model with the K-parameterisation included, produces a good fitting of the measured ground-level concentration data in all the experimental conditions considered; (ii) there are no big differences between the parameterisation proposed and the alternative taken from literature. The main advantage of the proposed model with respect to existing formulations consists mainly in its continuity at all elevations and for different stability regimes, resulting more physically correct.

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.

A THEORETICAL MODEL FOR THE STUDY OF CONVECTIVE TURBULENCE DECAY AND COMPARISON WITH LARGE-EDDY SIMULATION DATA

The development of a theoretical model fora decaying convective boundary layeris considered. The model relies on thedynamical energy spectrumequation in which the buoyancy andinertial transfer terms are retained,and a closure assumptionmade for both. The parameterization for thebuoyancy term is given providing a factorizationbetween the energy source termand its temporal decay. Regarding the inertialtransfer term a hypothesis ofsuperposition is used to describe theconvective energy source and time variationof velocity correlation separately.The solution of the budget equation for theturbulent kinetic energy spectrum is possible,given the three-dimensional initial energyspectrum. This is doneutilizing a version of the Kristensen et al.(see Boundary-Layer Meteorol.47, 149–193)model valid for non-isotropic turbulence. During thedecay the locus of the spectralpeak remains at about the sameposition as the heat flux decreases.Comparison of the theoretical modelis performed against large-eddy simulationdata for a decaying convectiveboundary layer.

A Simplified Model for Intermittent Turbulence in the Nocturnal Boundary Layer

A model for the exchange between the surface and the atmosphere under stable conditions is proposed. It is based on the classical scheme first suggested by Blackadar and comprises prognostic equations for the wind components and air and ground temperature. The main difference from previous works consists in the fact that the turbulent intensity is determined by a prognostic equation for turbulent kinetic energy (TKE), rather than by using stability functions that arbitrarily relate it to atmospheric stability. Results show that the model reproduces the condition of connection and disconnection between the surface and upper levels. Furthermore, it leads to periodic turbulence bursts when one level within the stable boundary layer (SBL) is considered and the use of additional levels increasingly leads to more complex solutions, characterizing the occurrence of global intermittency. Such turbulence bursts occur in the disconnected state and cause large fluctuations of the variables near the surface. The boundary layer height plays a role in the sense that for the same geostrophic winds, connection is favored for shallower layers. Although playing a role in the intermittency characteristics, soil type is not determinant to their existence, as the bursts occur even for very high values of heat capacity. Vertical profiles for both the intermittent and connected state are analyzed and in general agree with observations. It is shown that, near the surface, weak turbulence bursts favor the exchange between the air and the cooler ground, leading to a local temperature decrease, while stronger events that mix the air deeper in the SBL cause an average warming tendency. An opposite pattern occurs at the upper SBL. Intermittency is favored over a range of low geostrophic winds and clear skies, in agreement with previous suggestions. The vertical structure of the intermittent events is analyzed, and it shown that they are generated at the surface by a local shear increase above a threshold, propagating upward through the turbulence transfer term in the TKE equation. It is proposed that such events constitute a natural characteristic of the disconnected SBL, which occurs along with low large-scale winds and clear skies.

Application of a model system for the study of transport and diffusion in complex terrain to the TRACT experiment

Abstract The transport and diffusion processes of a tracer gas released near the ground in the Rhine valley region, in Central Europe, during the 1992 TRACT field experiment, are simulated by a computational model system for complex terrain. This system (RMS) is composed of the prognostic mesoscale model RAMS, the Lagrangian stochastic dispersion model SPRAY and the interface code MIRS, which links RAMS to SPRAY. Three flow simulations were performed, with different initialisations and the one showing the best agreement with the measured flow was selected for the simulation of the TRACT tracer experiment. Tracer concentrations measured by an array of samplers at ground level and by an airplane aloft, are used to evaluate the 3-D concentration field simulated by the model system. The analysis of the simulation results generated by RMS shows that our model system very well reproduces the general behaviour of the contaminant plume, the temporal and spatial distribution of the concentration and the location of the concentration maxima.

Estimation of the lagrangian structure function constant C0 from surface-layer wind data

Eulerian turbulence observations, madein the surface layer under unstable conditions (z/L > 0),by a sonic anemometer were used to estimatethe Lagrangian structure function constant O. Twomethods were considered. The first one makes use of arelationship, widely used in the Lagrangian stochasticdispersion models, relating O to the turbulent kineticenergy dissipation rate ε, wind velocity variance andLagrangian decorrelation time. The second one employsa novel equation, connecting O to the constant of thesecond-order Eulerian structure function. Beforeestimating O, the measurements were processed in orderto discard non-stationary cases at least to a firstapproximation and cases in which local isotropy couldnot be assumed. The dissipation ε was estimated eitherfrom the best fit of the energy spectrum in theinertial subrange or from the best fit of the third-orderlongitudinal Eulerian structure function. Thefirst method was preferred and applied to the subsequentpart of the analysis. Both methods predict thepartitioning of O in different spatial components as aconsequence of the directional dependence of theEulerian correlation functions due to the isotropy.The O values computed by both methods are presented anddiscussed. In conclusion, both methods providerealistic estimates of O that compare well withprevious estimations reported in the literature, evenif a preference is to be attributed to the second method.

Validation of a New Turbulent Parameterization for Dispersion Models in Convective Conditions

A new parameterization for turbulentdispersion in a convective boundary layer isproposed. The model is based on turbulentkinetic energy spectra and Taylors diffusiontheory. The formulation, included in an advanceddispersion model, has been tested and comparedwith vertical and lateral dispersion schemesreported in the literature, using data from fieldexperiments. The application of a statisticalevaluation shows that the proposedparameterization has the best overall fit to the data.

Atmospheric Turbulence Decay During the Solar Total Eclipse of 11 August 1999

The studies of turbulence decay were based in the past on measurements carried out in neutrally stratified wind tunnels and, more recently, on large-eddy simulation runs. Here the atmospheric turbulence decay process during the solar total eclipse of 11 August 1999 is examined. Thus a rapid transition from convective boundary-layer turbulence to that of a neutral or slightly stable one is considered. A u-v-w propeller anemometer and a fast response temperature sensor located in northern France on top of a 9-m mast recorded the turbulence observations. The measurements, in terms of turbulent kinetic energy decay with time, were found to be in good agreement with those prescribed by a theoretical model of turbulence decay recently proposed. In particular, it was found that the exponent of the power law describing the decay process has the value -2.

An iterative Langevin solution for contaminant dispersion simulation using the Gram–Charlier PDF

Abstract An alternative numerical method to solve the three-dimensional stochastic Langevin equation applied to the air pollution dispersion is proposed and tested. We obtain a first-order differential equation whose solution is known and determined by an integrating factor. A Langevin model for inhomogeneous turbulence is obtained, considering the Gram–Charlier Probability Density Function (PDF) of turbulent velocity. The calculus process is based on an iterative scheme through the Picard Iterative Method. Numerical simulations and comparisons with measured data from two different tracer experiments are realized, showing a good agreement between predicted and observed values. Furthermore, the results obtained with the new approach are compared with the ones obtained by three different models.