Improvement Of The Mellor–Yamada Turbulence Closure Model Based On Large-Eddy Simulation Data

On the basis of data constructed with large-eddy simulation (LES), an attempt is made to improve the Mellor–Yamada (M–Y) turbulence closure model. Firstly, stably-stratified and convective planetary boundary layers without moisture are simulated by a LES model to obtain a database for the improvement. Secondly, based on the LES data, closure constants are re-evaluated and a new diagnostic equation for the master length scale L is proposed. The new equation is characterized by allowing L in the surface layer to vary with stability instead of constant kz, where k is the von Kármán constant, and z is height.The non-dimensional eddy-diffusivity coefficients calculated from the modifiedM–Y model are in satisfactory agreement with those from the LES data. It isfound that the modified M–Y model improves the original one largely, and thatthe improvement is achieved by considering buoyancy effects on the pressurecovariances andby using the newly proposed equation for L.     

一个对流边界层大涡模式的建立与调试

本文介绍一个适合于对流边界层的大涡模式的建立及其调试结果。该大涡模式建立过程中注重于计算的节省，同时也强调原理与方法的简单和合理性。模式的调试表明，对于平坦均一地形的情况，模拟可以获得合理的结果。调试同时显示了模式对较低水平分辨率的适用条件，以及模式应用于模拟较大水平范围问题的可能性。     

Development of a Single-Column Model in RegCM4 and Its Preliminary Application for Evaluating PBL Schemes in Simulating the Dry Convection Boundary Layer

A single-column model (SCM) is developed in the regional climate model RegCM4. The evolution of a dry convection boundary layer (DCBL) is used to evaluate this SCM. Moreover, four planetary boundary layer (PBL) schemes, namely the Holtslag-Boville scheme (HB), Yonsei University scheme (YSU), and two University of Washington schemes (UW01, Grenier-Bretherton-McCaa scheme and UW09, Bretherton-Park scheme), are compared by using the SCM approach. A large-eddy simulation (LES) of the DCBL is performed as a benchmark to examine how well a PBL parameterization scheme reproduces the LES results, and several diagnostic outputs are compared to evaluate the schemes. The results show that the SCM is proper constructed. In general, with the DCBL case, the YSU scheme performs best for reproducing the LES results, which include well-mixed features and vertical sensible heat fluxes; the simulated wind speed, turbulent kinetic energy, entrainment flux, and height of the entrainment zone are all underestimated in the UW09; the UW01 has all those biases of the UW09 but larger, and the simulated potential temperature is not well mixed; the HB is the least skillful scheme, by which the PBL height, entrainment flux, height of the entrainment zone, and the vertical gradients within the mixed layer are all overestimated, and a inversion layer near the top of the surface layer is wrongly simulated.Although more cases and further testing are required, these simulations show encouraging results towards the use of this SCM framework for evaluating the simulated physical processes by the RegCM4.     

Subgrid-Scale Dynamics of Water Vapour, Heat, and Momentum over a Lake

We examine the dynamics of turbulence subgrid (or sub-filter) scales over a lake surface and the implications for large-eddy simulations (LES) of the atmospheric boundary layer. The analysis is based on measurements obtained during the Lake-Atmosphere Turbulent EXchange (LATEX) field campaign (August–October, 2006) over Lake Geneva, Switzerland. Wind velocity, temperature and humidity profiles were measured at 20 Hz using a vertical array of four sonic anemometers and open-path gas analyzers. The results indicate that the observed subgrid-scale statistics are very similar to those observed over land surfaces, suggesting that the effect of the lake waves on surface-layer turbulence during LATEX is small. The measurements allowed, for the first time, the study of subgrid-scale turbulent transport of water vapour, which is found to be well correlated with the transport of heat, suggesting that the subgrid-scale modelling of the two scalars may be coupled to save computational resources during LES.     

Improvement of the K-profile Model for the Planetary Boundary Layer based on Large Eddy Simulation Data

Modifications of the widely used K-profile model of the planetary boundary layer (PBL), reported by Troen and Mahrt (TM) in 1986, are proposed and their effects examined by comparison with large eddy simulation (LES) data. The modifications involve three parts. First, the heat flux from the entrainment at the inversion layer is incorporated into the heat and momentum profiles, and it is used to predict the growth of the PBL directly. Second, profiles of the velocity scale and the Prandtl number in the PBL are proposed, in contrast to the constant values used in the TM model. Finally, non-local mixing of momentum was included. The results from the new PBL model and the original TM model are compared with LES data. The TM model was found to give too high PBL heights in the PBL with strong shear, and too low heights for the convection-dominated PBL, which causes unrealistic heat flux profiles. The new PBL model improves the predictability of the PBL height and produces profiles that are more realistic. Moreover, the new PBL model produces more realistic profiles of potential temperature and velocity. We also investigated how each of these three modifications affects the results, and found that explicit representation of the entrainment rate is the most critical.     

Simulating Dispersion in the Evening-Transition Boundary Layer

We investigate dispersion in the evening-transition boundary layer using large-eddy simulation (LES). In the LES, a particle model traces pollutant paths using a combination of the resolved flow velocities and a random displacement model to represent subgrid-scale motions. The LES is forced with both a sudden switch-off of the surface heat flux and also a more gradual observed evolution. The LES shows ‘lofting’ of plumes from near-surface releases in the pre-transition convective boundary layer; it also shows the subsequent ‘trapping’ of releases in the post-transition near-surface stable boundary layer and residual layer above. Given the paucity of observations for pollution dispersion in evening transitions, the LES proves a useful reference. We then use the LES to test and improve a one-dimensional Lagrangian Stochastic Model (LSM) such as is often used in practical dispersion studies. The LSM used here includes both time-varying and skewed turbulence statistics. It is forced with the vertical velocity variance, skewness and dissipation from the LES for particle releases at various heights and times in the evening transition. The LSM plume spreads are significantly larger than those from the LES in the post-transition stable boundary-layer trapping regime. The forcing from the LES was thus insufficient to constrain the plume evolution, and inclusion of the significant stratification effects was required. In the so-called modified LSM, a correction to the vertical velocity variance was included to represent the effect of stable stratification and the consequent presence of wave-like motions. The modified LSM shows improved trapping of particles in the post-transition stable boundary layer.     

Large-Eddy Simulation of Flow and Pollutant Dispersion in High-Aspect-Ratio Urban Street Canyons with Wall Model

A large-eddy simulation (LES) with a one-equation subgrid-scale (SGS) model was developed to investigate the flow field and pollutant dispersion inside street canyons of high aspect ratio (AR). A 1/7th power-law wall model was implemented near rigid walls to mitigate the demanding near-wall resolution requirements in LES. This LES model had been extensively validated against experimental results for street canyons of AR = 1 and 2 before it was applied to the cases of AR = 3 and 5. A ground-level passive pollutant line source, located in the middle of the street, was used to simulate vehicular emissions. Three and five vertically aligned primary recirculations were developed in the street canyons of AR 3 and 5, respectively. The ground-level mean wind speed was less than 0.5% of the free stream value, which makes it difficult for the pollutant to be transported upward for removal. High pollutant concentration and variance were found near the buildings where the air flow is upwards. It was found that the velocity fluctuation, pollutant concentration and variance were all closely related to the interactions between the primary recirculations and/or the free surface layer. Several quantities, which are non-linear functions of AR, were introduced to quantify the air quality in street canyons of different configurations.     

Study of the Probability Density Functions From a Large-Eddy Simulation for a Stably Stratified Boundary Layer

Turbulence in a non-strongly stably stratified large-eddy simulation (LES) case is studied through probability density functions (PDFs) to obtain additional information than that provided by classical LES averages. The PDFs are computed for one hour within the steady-state regime at three different levels: near the surface, in the middle and at the top of the boundary layer, for the wind components and the temperature. The physical significance of these PDFs from LES is discussed and they are compared to those obtained from observations. The analysis of the eddy structures within the stably stratified boundary layer is made through the combined study of the fields, the spectra and the statistical moments obtained from the PDFs and joint PDFs. The homogeneity of the fields is inspected through a comparison of the ensemble to the temporal and the spatial PDFs, showing that the ergodic theorem is not fulfilled. To this end, the sensitivity of the PDF moments to the LES resolution is explored.     

Footprints in Homogeneously and Heterogeneously Driven Boundary Layers Derived from a Lagrangian Stochastic Particle Model Embedded into Large-Eddy Simulation

A Lagrangian stochastic (LS) model, which is embedded into a parallelised large-eddy simulation (LES) model, is used for dispersion and footprint evaluations. For the first time an online coupling between LES and LS models is applied. The new model reproduces concentration patterns, which were obtained in prior studies, provided that subgrid-scale turbulence is included in the LS model. Comparisons with prior studies show that the model evaluates footprints successfully. Streamwise dispersion leads to footprint maxima that are situated less far upstream than previously reported. Negative flux footprints are detected in the convective boundary layer (CBL). The wide range of applicability of the model is shown by applying it under neutral and stable stratification. It is pointed out that the turning of the wind direction with height leads to a considerable dependency of source areas on height. First results of an application to a heterogeneously heated CBL are presented, which emphasize that footprints are severely affected by the inhomogeneity.     

A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows

A long-standing problem in large-eddy simulations (LES) of the planetary boundary layer (PBL) is that the mean wind and temperature profiles differ from the Monin-Obukhov similarity forms in the surface layer. This shortcoming of LES has been attributed to poor grid resolution and inadequate sub-grid-scale (SGS) modeling. We study this deficiency in PBL LES solutions calculated over a range of shear and buoyancy forcing conditions. The discrepancy from similarity forms becomes larger with increasing shear and smaller buoyancy forcing, and persists even with substantial horizontal grid refinement. With strong buoyancy forcing, however, the error is negligible.In order to achieve better agreement between LES and similarity forms in the surface layer, a two-part SGS eddy-viscosity model is proposed. The model preserves the usual SGS turbulent kinetic energy formulation for the SGS eddy viscosity, but it explicitly includes a contribution from the mean flow and a reduction of the contributions from the turbulent fluctuations near the surface. Solutions with the new model yield increased fluctuation amplitudes near the surface and better correspondence with similarity forms out to a distance of 0.1–0.2 times the PBL depth, i.e., a typical surface-layer depth. These results are also found to be independent of grid anisotropy. The new model is simple to implement and computationally inexpensive.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.     

Passive scalar diffusion from surface sources in the convective boundary layer

We examine vertical and horizontal diffusion of a passive scalar puff from a surface point source in a convective boundary layer (CBL). Numerical results are presented from a large-eddy simulation (LES) with embedded subgrid Lagrangian particle simulation (LPS). There is good agreement in most respects with previous laboratory and numerical studies. Analytical approximations for the concentration, horizontal flux and vertical flux are found to work reasonably well; they are based on the assumption that the concentration follows a Gaussian function in the horizontal and vertical, and that the dimensionless width and height scales of the puff follow simple functions of time. Fluxes and concentration gradients are related through a continuity relationship, without the need for an eddy diffusivity assumption. The instantaneous, point-source fields can be integrated for any source geometry. We compare predictions from the LES/LPS model for a sinusoidal surface flux with previous results from an LES with sinusoidal buoyancy flux and confirm that the buoyancy perturbations diffuse like a passive scalar. We also consider a continuous point source and derive footprint functions for vertical flux measurements above the surface layer.     

Resolution Sensitivity and Scaling of Large-Eddy Simulations of the Stable Boundary Layer

Large-eddy simulations (LES) of the continuously turbulent quasi-equilibrium stable boundary layer (SBL) are conducted with grid lengths in the range of 12.5 m to 2 m, in order to explore resolution sensitivity, and determine at what point grid convergence occurs. The structure of the mean potential temperature, winds, and turbulent fluxes varies significantly over this resolution range. The highest resolution simulations show a significant degree of convergence. The dimensionless momentum diffusivity asymptotes to a value of 0.06, corresponding to a limiting flux Richardson number of 0.15.Using the converged simulations, some scaling hypotheses underpinning first-order and second-order closure models are revisited. The effective Richardson number stability functions of the LES are compared with the forms often used in numerical weather prediction (NWP). The mixing implied by the LES is less than that used in NWP. The commonly used similarity profiles for heat and momentum fluxes, and the scalings for dissipation and pressure covariances are compared with the LES. This information could provide guidance for the next generation of SBL parametrization schemes.     

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.     

Third-Order Moments for Shear Driven Boundary Layer

A new third-order model for shear driven boundary layer is presented and tested against large-eddy simulation (LES) data. Numerical solutions are obtained using mean flow components and second-order moments as input. The calculated vertical profiles of the variances and turbulent kinetic energy fluxes and those provided by a LES experiment are compared and discussed     

Large-Eddy Simulation of the Stable Atmospheric Boundary Layer using Dynamic Models with Different Averaging Schemes

Large-eddy simulation (LES) of a stable atmospheric boundary layer is performed using recently developed dynamic subgrid-scale (SGS) models. These models not only calculate the Smagorinsky coefficient and SGS Prandtl number dynamically based on the smallest resolved motions in the flow, they also allow for scale dependence of those coefficients. This dynamic calculation requires statistical averaging for numerical stability. Here, we evaluate three commonly used averaging schemes in stable atmospheric boundary-layer simulations: averaging over horizontal planes, over adjacent grid points, and following fluid particle trajectories. Particular attention is focused on assessing the effect of the different averaging methods on resolved flow statistics and SGS model coefficients. Our results indicate that averaging schemes that allow the coefficients to fluctuate locally give results that are in better agreement with boundary-layer similarity theory and previous LES studies. Even among models that are local, the averaging method is found to affect model coefficient probability density function distributions and turbulent spectra of the resolved velocity and temperature fields. Overall, averaging along fluid pathlines is found to produce the best combination of self consistent model coefficients, first- and second-order flow statistics and insensitivity to grid resolution.     

Two-Point Properties Of Atmospheric Turbulence Very Close To The Ground: Comparison Of A High Resolution Les With Theoretical Models

Using the tools of large-eddy simulation (LES), rapid distortion theory andEulerian kinematic simulation, two-point properties of turbulenceare studied. It is shown how the boundary conditions in thepresent LES model are fully consistent with the new top-down understanding ofatmospheric turbulence close to the ground, wherethe turbulence is analysed in terms of turbulent eddies impinging ontothe ground, being distorted by the shear and the blocking by the wall,and experiencing the creation of an internal boundary layer within aneddy surface layer (ESL) with a height of a dozen metres.The question of very large streamwise structures is addressed, and itis shown that the k^-1 range measured in spectra for the streamwisevelocity in the ESL in several recent field experiments can be found in LES, and corresponds to streaky structures. However, thesestreaky structures are different from the low Reynolds number streaks,which induce a k^-2 range in the spectrum. Finally, two-point verticalcorrelations are studied. In particular, effects of shear and of the slope of thespectrum are analysed.