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J. C. Weil

Abstract

A Lagrangian stochastic model of particle trajectories is used to investigate the asymmetry in vertical diffusion from area sources at the bottom and top of an inhomogeneous turbulent boundary layer. Such an asymmetry was discovered in the large-eddy simulations (LES) of the convective boundary layer (CBL) by Wyngaard and Brost (1984) and Moeng and Wyngaard (1984).

For inhomogeneous Gaussian turbulence, a diffusion asymmetry results from the vertical asymmetry in the vertical velocity variance about the midplane of the boundary layer. For small turbulence time scales, this is predictable from eddy-diffusion (K) theory. However, for large time scales, K theory is inapplicable as evidenced by countergradient flux regions and K singularities. The fundamental causes of the K model breakdown are the memory (large time scale) and vertical inhomogeneity of the turbulence, which lead to a mean vertical acceleration of particles away from the source and a “drift” velocity.

A positive skewness in vertical velocity enhances the drift velocity for a bottom source and suppresses it for a top source, thus leading to a greater diffusion asymmetry than in Gaussian turbulence; this is independent of the variance profile. The asymmetry due to skewness is caused by the bias in the probability density function of vertical velocity (w)—larger positive w values and smaller negative ones than in Gaussian turbulence. The results for inhomogeneous skewed turbulence are in good agreement with the LES results for the CBL.

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J. C. Weil

Abstract

Most diffusion models currently used in air quality applications are substantially out of date with understanding of turbulence and diffusion in the planetary boundary layer. Under a Cooperative Agreement with the Environmental Protection Agency, the American Meteorological Society organized a workshop to help improve the basis of such models, their physics and hopefully their performance. Reviews and recommendations were made on models in three areas: diffusion in the convective boundary layer (CBL), diffusion in the stable boundary layer (SBL), and model uncertainty.

Progress has been made in all areas, but it is most significant and ready for application to practical models in the case of the CBL. This has resulted from a clear understanding of the vertical structure and diffusion in the CBL, as demonstrated by laboratory experiments, numerical simulations, and field observations. All of these investigations have shown the importance of the convective scaling parameter: w *, the convective velocity scale and zi, the CBL height. This knowledge and the non-Gaussian nature of vertical diffusion have already been incorporated in some applied models and show much promise. The workshop has made a number of recommendations concerning the use of this information, with perhaps the most important being the use of w *, zi directly in expressions for the dispersion parameters (σy, σz).

Understanding of turbulence structure and diffusion in the SBL is less complete and not yet ready for general use in applications. However, some promising new developments include a similarity framework for turbulence structure over ideal terrain and models to predict vertical dispersion in terms of the local structure. Further development and testing of these models are required, with new data sets—laboratory, numerical, and field—being especially beneficial.

As for model uncertainty, it is recommended that natural variability estimates ultimately become an integral part of air quality predictions. Some general frameworks for these estimates include the meandering plume and Eulerian similarity models, with the former being of more immediate utility. However, further evaluation of these models is necessary before they can be recommended for applications.

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Whither the Stable Boundary Layer?

A Shift in the Research Agenda

H. J. S. Fernando and J. C. Weil
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T. W. Horst and J. C. Weil

Abstract

Correction to Volume 11, Issue 4, pages 1018-1025.

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T. W. Horst and J. C. Weil

Abstract

Recent model estimates of the flux footprint are used to examine the fetch requirements for accurate micro-meteorological measurement of surface fluxes of passive, conservative scalars within the surface flux layer. The required fetch is quantified by specifying an acceptable ratio of the measured flux to the local surface flux. When normalized by the measurement height zm, the fetch is found to be a strong function of atmospheric stability as quantified by zm/L, where L is the Obukhov length, and a weaker function of the normalized measurement height zm/zo, where zo is the roughness length. Stable conditions are found to require a much greater fetch than do unstable conditions, and the fetch required for even moderately stable conditions is for many situations considerably greater than 100 times the measurement height.

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J. C. Weil, R. I. Sykes, and A. Venkatram

Abstract

Over the past decade, much attention has been devoted to the evaluation of air-quality models with emphasis on model performance in predicting the high concentrations that are important in air-quality regulations. This paper stems from our belief that this practice needs to be expanded to 1) evaluate model physics and 2) deal with the large natural or stochastic variability in concentration. The variability is represented by the root-mean- square fluctuating concentration (σc about the mean concentration (C) over an ensemble—a given set of meteorological, source, etc. conditions. Most air-quality models used in applications predict C, whereas observations are individual realizations drawn from an ensemble. For σcC large residuals exist between predicted and observed concentrations, which confuse model evaluations.

This paper addresses ways of evaluating model physics in light of the large σc the focus is on elevated point-source models. Evaluation of model physics requires the separation of the mean model error-the difference between the predicted and observed C—from the natural variability. A residual analysis is shown to be an elective way of doing this. Several examples demonstrate the usefulness of residuals as well as correlation analyses and laboratory data in judging model physics.

In general, σc models and predictions of the probability distribution of the fluctuating concentration (c′), Ω(c′, are in the developmental stage, with laboratory data playing an important role. Laboratory data from point-source plumes in a convection tank show that Ω(c′ approximates a self-similar distribution along the plume center plane, a useful result in a residual analysis. At pmsent,there is one model—ARAP—that predicts C, σc, and &Omega(c for point-source plumes. This model is more computationally demanding than other dispersion models (for C only) and must be demonstrated as a practical tool. However, it predicts an important quantity for applications— the uncertainty in the very high and infrequent concentrations. The uncertainty is large and is needed in evaluating operational performance and in predicting the attainment of air-quality standards.

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J. C. Weil, L. A. Corio, and R. P. Brower

Abstract

A probability density function (PDF) dispersion model is presented for buoyant plumes in the convective boundary layer (CBL), where the mean concentration field C is obtained from the PDFs p y and p z of tracer particle position in the lateral y and vertical z directions. The p y is assumed to be Gaussian, whereas the p z is derived from the the vertical velocity PDF, which is skewed. Three primary sources contribute to the modeled C field: 1) the “direct” or real source at the stack, 2) an “indirect” source to account for the slow downward dispersion of lofting plumes from the CBL top, and 3) a “penetrated” source to treat material that initially penetrates the elevated inversion but later fumigates into the CBL. Image sources are included to satisfy the zero-flux conditions at the ground and the CBL top.

Comparisons between the modeled crosswind-integrated concentration fields C y and convection tank data show fair to good agreement in the lower half of the CBL. In particular, the C y profiles at the surface agree with the data over a wide range of the dimensionless buoyancy flux F∗ and show a systematic decrease in C y with F∗.

Comparisons between the modeled and observed ground-level concentrations around several power plants exhibit good agreement on average and are considerably better than those obtained with a standard Gaussian plume model. A residual analysis suggests some areas for future model development.

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C-H. Moeng, J. C. McWilliams, R. Rotunno, P. P. Sullivan, and J. Weil

Abstract

The performance of a two-dimensional (2D) numerical model in representing three-dimensional (3D) planetary boundary layer (PBL) convection is investigated by comparing the 2D model solution to that of a 3D large- eddy simulation. The free convective PBL has no external forcing that would lead to any realizable 2D motion, and hence the 2D model represents a parameterization (not a simulation) of such a convective system. The present solutions show that the fluxes of conserved scalars, such as the potential temperature, are somewhat constrained and hence are not very sensitive to the model dimensionality. Turbulent kinetic energy (TKE), surface friction velocity, and velocity variances are sensitive to the subgrid-scale eddy viscosity and thermal diffusivity in the 2D model; these statistics result mostly from model-generated hypothetical 2D plumes that can be tuned to behave similarly to their 3D counterparts. These 2D plumes are comparable in scale with the PBL height due to the capping inversion. In the presence of shear, orienting the 2D model perpendicular to the mean shear is essential to generate a reasonable momentum flux profile, and hence mean wind profile and wind- related statistics such as the TKE and velocity variances.

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Peter P. Sullivan, James C. McWilliams, Jeffrey C. Weil, Edward G. Patton, and Harindra J. S. Fernando

Abstract

Turbulent flow in a weakly convective marine atmospheric boundary layer (MABL) driven by geostrophic winds U g = 10 m s−1 and heterogeneous sea surface temperature (SST) is examined using fine-mesh large-eddy simulation (LES). The imposed SST heterogeneity is a single-sided warm or cold front with temperature jumps Δθ = (2, −1.5) K varying over a horizontal distance between [0.1, −6] km characteristic of an upper-ocean mesoscale or submesoscale regime. A Fourier-fringe technique is implemented in the LES to overcome the assumptions of horizontally homogeneous periodic flow. Grid meshes of 2.2 × 109 points with fine-resolution (horizontal, vertical) spacing (δx = δy, δz) = (4.4, 2) m are used. Geostrophic winds blowing across SST isotherms generate secondary circulations that vary with the sign of the front. Warm fronts feature overshoots in the temperature field, nonlinear temperature and momentum fluxes, a local maximum in the vertical velocity variance, and an extended spatial evolution of the boundary layer with increasing distance from the SST front. Cold fronts collapse the incoming turbulence but leave behind residual motions above the boundary layer. In the case of a warm front, the internal boundary layer grows with downstream distance conveying the surface changes aloft and downwind. SST fronts modify entrainment fluxes and generate persistent horizontal advection at large distances from the front.

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Peter P. Sullivan, James C. McWilliams, Jeffrey C. Weil, Edward G. Patton, and Harindra J. S. Fernando

Abstract

Turbulent flow in a weakly convective marine atmospheric boundary layer (MABL) driven by geostrophic winds V g = 10 m s−1 and heterogeneous sea surface temperature (SST) is examined using fine-mesh large-eddy simulation (LES). The imposed SST heterogeneity is a single-sided warm or cold front with jumps Δθ = (2, −1.5) K varying over a horizontal x distance of 1 km characteristic of an upper-ocean mesoscale or submesoscale front. The geostrophic winds are oriented parallel to the SST isotherms (i.e., the winds are alongfront). Previously, Sullivan et al. examined a similar flow configuration but with geostrophic winds oriented perpendicular to the imposed SST isotherms (i.e., the winds were across-front). Results with alongfront and across-front winds differ in important ways. With alongfront winds, the ageostrophic surface wind is weak, about 5 times smaller than the geostrophic wind, and horizontal pressure gradients couple the SST front and the atmosphere in the momentum budget. With across-front winds, horizontal pressure gradients are weak and mean horizontal advection primarily balances vertical flux divergence. Alongfront winds generate persistent secondary circulations (SC) that modify the surface fluxes as well as turbulent fluxes in the MABL interior depending on the sign of Δθ. Warm and cold filaments develop opposing pairs of SC with a central upwelling or downwelling region between the cells. Cold filaments reduce the entrainment near the boundary layer top that can potentially impact cloud initiation. The surface-wind–SST-isotherm orientation is an important component of atmosphere–ocean coupling. The results also show frontogenetic tendencies in the MABL.

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