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.     

Statistical Variability of Dispersion in the Convective Boundary Layer: Ensembles of Simulations and Observations

A Lagrangian particle dispersion model (LPDM) driven by velocity fields from large-eddy simulations (LESs) is used to determine the mean and variability of plume dispersion in a highly convective planetary boundary layer (PBL). The total velocity of a “particle” is divided into resolved and unresolved or random (subfilter scale, SFS) velocities with the resolved component obtained from the LES and the SFS velocity from a Lagrangian stochastic model. This LPDM-LES model is used to obtain an ensemble of dispersion realizations for calculating the mean, root-mean-square (r.m.s.) deviation, and fluctuating fields of dispersion quantities. An ensemble of 30 realizations is generated for each of three source heights: surface, near-surface, and elevated. We compare the LPDM calculations with convection tank experiments and field observations to assess the realism of the results. The overall conclusion is that the LPDM-LES model produces a realistic range of dispersion realizations and statistical variability (i.e., r.m.s. deviations) that match observations in this highly convective PBL, while also matching the ensemble-mean properties. This is true for the plume height or trajectory, vertical dispersion, and the surface values of the crosswind-integrated concentration (CWIC), and their dependence on downstream distance. One exception is the crosswind dispersion for an elevated source, which is underestimated by the model. Other analyses that highlight important LPDM results include: (1) the plume meander and CWIC fluctuation intensity at the surface, (2) the applicability of a similarity theory for plume height from a surface source to only the very strong updraft plumes—not the mean height, and (3) the appropriate variation with distance of the mean surface CWIC and the lower bound of the CWIC realizations for a surface source.     

Turbulent Statistics of Neutrally Stratified Flow Within and Above a Sparse Forest from Large-Eddy Simulation and Field Observations

Turbulent statistics of neutrally stratified shear-driven flow within and above a sparse forest canopy are presented from a large-eddy simulation (LES) and compared with those from observations within and above a deciduous forest with similar height and foliage density. First- and second-order moments from the LES agree with observations quite well. Third-order moments from the LES have the same sign and similar vertical patterns as those from the observations, but the LES yields smaller magnitudes of such higher-order moments. Turbulent spectra and cospectra from the LES agree well with observations above the forest. However, at the highest frequencies, the LES spectra have steeper slopes than observations. Quadrant and conditional analyses of the LES resolved-scale flow fields also agree with observations. For example, both LES and observation find that sweeps are more important than ejections for the transport of momentum within the forest, while inward and outward interaction contributions are both small, except near the forest floor. The intermittency of the transport of momentum and scalar increases with depth into the forest. Finally, ramp structures in the time series of a passive scalar at multiple levels within and above the forest show similar features to those measured from field towers. Two-dimensional (height-time cross-section) contours of the passive scalar and wind vectors show sweeps and ejections, and the characteristics of the static pressure perturbation near the ground resemble those deduced from field tower-based measurements. In spite of the limited grid resolution (2 m × 2 m × 2 m) and domain size (192 m × 192 m × 60 m) used in this LES, we demonstrate that the LES is capable of resolving the most important characteristics of the turbulent flow within and above a forest canopy.     

A grid nesting method for large-eddy simulation of planetary boundary-layer flows

A method for performing nested grid calculations with a large-eddy simulation code is described. A common numerical method is used for all meshes, and the grid architecture consists of a single outer or coarse grid, and nested or fine grids, which overlap in some common region. Inter-grid communication matches the velocity, pressure and potential temperature fields in the overlap region. Resolved and sub-grid scale (SGS) turbulent fluxes and kinetic energy on the fine grid are averaged to the coarse grid using a conservation rule equivalent to Germano's identity used to develop dynamic SGS models.Simulations of a slightly convective, strong shear planetary boundary layer were carried out with varying surface-layer resolutions. Grid refinements in the (x, y, z) directions of up to (5, 5, 2) times were employed. Two-way interaction solutions on the coarse and fine meshes are successfully matched in the overlap region on an instantaneous basis, and the turbulent motions on the fine grid blend smoothly into the coarse grid across the grid interface. With surface-layer grid nesting, significant increases in resolved eddy fluxes and variances are found. The energy-scale content of the vertical velocity, and hence vertical turbulent fluxes, appear to be most influenced by increased grid resolution. Vertical velocity spectra show that the dominant scale shifts towards higher wavenumbers (smaller scales) and the magnitude of the peak energy is increased by more than a factor of 3 with finer resolution. Outside of the nested region the average heat and momentum fluxes and spectra are slightly influenced by the fine resolution in the surface layer. From these results we conclude that fine resolution is required to resolve the details of the turbulent motions in the surface layer. At the same time, however, increased resolution in the surface layer does not appreciably alter the ensemble statistics of the resolved and SGS motions outside of the nested region.     

Comparison of a computer-simulated stratus-topped boundary layer with aircraft observations

To assess the realism of large-eddy simulation (LES) of the stratus-topped boundary layer and its predicted turbulent structure, we performed detailed data analyses on a LES (which has a 12.5 m grid size in all three directions), in a manner similar to those used by Nicholls (1989) on aircraft measurements. The first analysis retrieves the primary convective elements, i.e., the negatively buoyant downdrafts, which are driven mainly by cloud-top radiative cooling, through a conditional sampling technique. Comparison shows that the LES of this resolution reflects most of the observed downdraft features; most of the discrepancies that exist between the obervations and the LES can be explained by decoupling of the cloud layer from the underlying flow that exists in the former but not in the latter. The second analysis shows the vertical velocity spectrum and its agreement with the measurements. In the third analysis, showing the turbulent kinetic energy budgets, the discrepancy in the turbulent transport term (i.e., the divergence of the third-moment quantity , the turbulent-kinetic-energy flux) between the LES and measurements exists even with such a fine resolution LES. This discrepancy is related mainly to the different behavior in between the LES and observations, which may again be associated with decoupling.An advantage of LES over aircraft observations is that the former can provide three-dimensional flow structure at any instant. In this paper, we examined the instantaneous flow structure and observed closed cellular patterns near the cloud top in which updrafts occupy the broad centers and relatively strong downdrafts occur in the narrow edges. In the intersections of these cell boundaries, there exist weak downdrafts, consisting of relatively cold and dry air, that are the most likely origins of the strong downdrafts extending throughout the mixed layer.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Entrainment Processes in the Convective Boundary Layer with Varying Wind Shear

Large-eddy simulations (LES) are performed to investigate the entrainment andthe structure of the inversion layer of the convective boundary layer (CBL) withvarying wind shears. Three CBLs are generated with the constant surface kinematicheat flux of 0.05 K m s^-1 and varying geostrophic wind speeds from 5 to 15m s^-1. Heat flux profiles show that the maximum entrainment heat flux as afraction of the surface heat flux increases from 0.13 to 0.30 in magnitude withincreasing wind shear. The thickness of the entrainment layer, relative to the depthof the well-mixed layer, increases substantially from 0.36 to 0.73 with increasingwind shear. The identification of vortices and extensive flow visualizations nearthe entrainment layer show that concentrated vortices perpendicular to the meanboundary-layer wind direction are identified in the capping inversion layer for thecase of strong wind shear. These vortices are found to develop along the mean winddirections over strong updrafts, which are generated by convective rolls and to appearas large-scale wavy motions similar to billows generated by the Kelvin–Helmholtzinstability. Quadrant analysis of the heat flux shows that in the case of strong windshear, large fluctuations of temperature and vertical velocity generated by largeamplitude wavy motions result in greater heat flux at each quadrant than that inthe weak wind shear case.     

Large-Eddy Simulation Of The Stably Stratified Planetary Boundary Layer

In this work, we study the characteristics of a stably stratifiedatmospheric boundary layer using large-eddy simulation (LES).In order to simulate the stable planetary boundary layer, wedeveloped a modified version of the two-part subgrid-scalemodel of Sullivan et al. This improved version of themodel is used to simulate a highly cooled yet fairly windy stableboundary layer with a surface heat flux of(W)_o = -0.05 m K s^-1and a geostrophic wind speed of U_g = 15 m s^-1.Flow visualization and evaluation of the turbulencestatistics from this case reveal the development ofa continuously turbulent boundary layer with small-scalestructures. The stability of the boundary layercoupled with the presence of a strong capping inversionresults in the development of a dominant gravity wave atthe top of the stable boundary layer that appears to be relatedto the most unstable wave predicted by the Taylor–Goldsteinequation. As a result of the decay of turbulence aloft,a strong-low level jet forms above the boundary layer.The time dependent behaviour of the jet is compared with Blackadar'sinertial oscillation analysis.     

An Observational Study of Wind Profiles in the Baroclinic Convective Mixed Layer

A comprehensive planetary boundary-layer (PBL) and synoptic data set is used to isolate the mechanisms that determine the vertical shear of the horizontal wind in the convective mixed layer. To do this, we compare a fair-weather convective PBL with no vertical shear through the mixed layer (10 March 1992), with a day with substantial vertical shear in the north-south wind component (27 February). The approach involves evaluating the terms of the budget equations for the two components of the vertical shear of the horizontal wind; namely: the time-rate-of-change or time-tendency term, differential advection, the Coriolis terms (a thermal wind term and a shear term), and the second derivative of the vertical transport of horizontal momentum with respect to height (turbulent-transport term). The data, gathered during the 1992 STorm-scale Operational and Research Meteorology (STORM) Fronts Experiments Systems Test (FEST) field experiment, are from gust-probe aircraft horizontal legs and soundings, 915-MHz wind profilers, a 5-cm Doppler radar, radiosondes, and surface Portable Automated Mesonet (PAM) stations in a roughly 50 × 50 km boundary-layer array in north-eastern Kansas, nested in a mesoscale-to-synoptic array of radiosondes and surface data.We present evidence that the shear on 27 February is related to the rapid growth of the convective boundary layer. Computing the shear budget over a fixed depth (the final depth of the mixed layer), we find that the time-tendency term dominates, reflecting entrainment of high-shear air from above the boundary layer. We suggest that shear within the mixed layer occurs when the time-tendency term is sufficiently large that the shear-reduction terms – namely the turbulent-transport term and differential advection terms – cannot compensate. In contrast, the tendency term is small for the slowly-growing PBL of 10 March, resulting in a balance between the Coriolis terms and the turbulent-transport term. Thus, the thermal wind appears to influence mixed-layer shear only indirectly, through its role in determining the entrained shear.     

An evaluation of neutral and convective planetary boundary-layer parameterizations relative to large eddy simulations

This paper compares a number of one-dimensional closure models for the planetary boundary layer (PBL) that are currently in use in large-scale atmospheric models. Using the results of a large-eddy simulation (LES) model as the standard of comparison, the PBL models are evaluated over a range of stratifications from free convective to neutral and a range of surface shear stresses. Capping inversion strengths for the convective cases range from weakly to strongly capped. Six prototypical PBL models are evaluated in this study, which focuses on the accuracy of the boundary-layer fluxes of momentum, heat, and two passive scalars. One scalar mimics humidity and the other is a top-down scalar entrained into the boundary layer from above. A set of measures based on the layer-averaged differences of these fluxes from the LES solutions is developed. In addition to the methodological framework and suite of LES solutions, the main result of the evaluation is the recognition that all of the examined PBL parameterizations have difficulty reproducing the entrainment at the top of the PBL, as given by the LES, in most parameter regimes. Some of the PBL models are relatively accurate in their entrainment flux in a subset of parameter regimes. The sensitivity of the PBL models to vertical resolution is explored, and substantive differences are observed in the performance of the PBL models, relative to LES, at low resolution typical of large scale atmospheric models.