Flux Footprints in the Convective Boundary Layer: Large-Eddy Simulation and Lagrangian Stochastic Modelling

We investigated the flux footprints of receptors at different heights in the convective boundary layer (CBL). The footprints were derived using a forward Lagrangian stochastic (LS) method coupled with the turbulent fields from a large-eddy simulation model. Crosswind-integrated flux footprints shown as a function of upstream distances and sensor heights in the CBL were derived and compared using two LS particle simulation methods: an instantaneous area release and a crosswind linear continuous release. We found that for almost all sensor heights in the CBL, a major positive flux footprint zone was located close to the sensor upstream, while a weak negative footprint zone was located further upstream, with the transition band in non-dimensional upwind distances −X between approximately 1.5 and 2.0. Two-dimensional (2D) flux footprints for a point sensor were also simulated. For a sensor height of 0.158 z _i, where z _i is the CBL depth, we found that a major positive flux footprint zone followed a weak negative zone in the upstream direction. Two even weaker positive zones were also present on either side of the footprint axis, where the latter was rotated slightly from the geostrophic wind direction. Using CBL scaling, the 2D footprint result was normalized to show the source areas and was applied to real parameters obtained using aircraft-based measurements. With a mean wind speed in the CBL of U = 5.1 m s⁻¹, convective velocity of w _* = 1.37 m s⁻¹, CBL depth of z _i = 1,000 m, and flight track height of 159 m above the surface, the total flux footprint contribution zone was estimated to range from about 0.1 to 4.5 km upstream, in the case where the wind was perpendicular to the flight track. When the wind was parallel to the flight track, the total footprint contribution zone covered approximately 0.5 km on one side and 0.8 km on the other side of the flight track.     

A Similarity Model of Subfilter-Scale Energy for Large-Eddy Simulations of the Atmospheric Boundary Layer

A scale-similarity model to estimate the subfilter-scale energy using the trace of the Leonard stress tensor is proposed and evaluated for large-eddy simulations of the atmospheric boundary layer (ABL). The model is derived from a stability-dependent model of the energy spectrum in the ABL, which accounts for the effects of buoyancy and mean shear as a function of z/L, the Monin–Obukhov stability variable. An a priori test using ABL turbulence data demonstrates that the model has accurate performance for dimensionless filter widths of Δ/z = 2, 1, and 0.5 for stabilities of −1 ≤ z/L ≤ 0.5, and improves considerably upon a similar model that is derived using an infinite κ ^−5/3 spectrum. This improvement is especially significant in the first several grid points near the surface in large-eddy simulations of the ABL, where Δ/z is necessarily large. The modelling procedure is then extended to develop a similarity model for the subfilter-scale scalar variance; it is shown to have robust performance for temperature.     

Nesting Turbulence in an Offshore Convective Boundary Layer Using Large-Eddy Simulations

The applicability of the one-way nesting technique for numerical simulations of the heterogeneous atmospheric boundary layer using the large-eddy simulation (LES) framework of the Weather Research and Forecasting model is investigated. The focus of this study is on LES of offshore convective boundary layers. Simulations were carried out using two subgrid-scale models (linear and non-linear) with two different closures [diagnostic and prognostic subgrid-scale turbulent kinetic energy (TKE) equations]. We found that the non-linear backscatter and anisotropy model with a prognostic subgrid-scale TKE equation is capable of providing similar results when performing one-way nested LES to a stand-alone domain having the same grid resolution but using periodic lateral boundary conditions. A good agreement is obtained in terms of velocity shear and turbulent fluxes, while velocity variances are overestimated. A streamwise fetch of 14 km is needed following each domain transition in order for the solution to reach quasi-stationary results and for the velocity spectra to generate proper energy content at high wavelengths, however, a pile-up of energy is observed at the low-wavelength portion of the spectrum on the first nested domain. The inclusion of a second nest with higher resolution allows the solution to reach effective grid spacing well within the Kolmogorov inertial subrange of turbulence and develop an appropriate energy cascade that eliminates most of the pile-up of energy at low wavelengths. Consequently, the overestimation of velocity variances is substantially reduced and a considerably better agreement with respect to the stand-alone domain results is achieved.     

Fluid Modelling Of Atmospheric Dispersion In The Convective Boundary Layer

A laboratory convection tank has been established following thepioneering work of Willis and Deardorff, but with many improvements and enhancements thattake advantage of modern technology. The main emphasis in the current design was toprovide the ability to conduct a virtually unlimited number of realizations under essentiallyidentical conditions in order to obtain reliable statistics on the dispersion of plumes and puffsreleased within the simulated atmospheric convective boundary layer. Described herein is the tankitself and its auxiliary systems, including a laser-induced-fluorescence and video-imaging system for makingnon-intrusive, full-field measurements of concentrations, and the interfacing of varioussubsystems with a master controller that automates essentially all operation and measurement functions.The current system provides unprecedented resolution, control, and data volumes. Exampleresults are presented from two types of releases: continuous plumes and instantaneous puffs.These data sets clearly show penetration of the highly buoyant plumes and puffs into theinversion above the convective boundary layer, gravity spreading within the inversion, andrapid diffusion within the mixed layer. They also show extreme `spottiness' in the instantaneousconcentration cross-sections.     

Turbulent Pressure Statistics in the Atmospheric Boundary Layer from Large-Eddy Simulation

We use large-eddy simulation (LES) to study the turbulent pressure field in atmospheric boundary layers with free convection, forced convection, and stable stratification. We use the Poisson equation for pressure to represent the pressure field as the sum of mean-shear, turbulence–turbulence, subfilter-scale, Coriolis, and buoyancy contributions. We isolate these contributions and study them separately. We find that in the energy-containing range in the free-convection case the turbulence–turbulence pressure dominates over the entire boundary layer. That part dominates also up to midlayer in the forced-convection case; above that the mean-shear pressure dominates. In the stable case the mean-shear pressure dominates over the entire boundary layer.We find evidence of an inertial subrange in the pressure spectrum in the free and forced-convection cases; it is dominated by the turbulence–turbulence pressure and has a three-dimensional spectral constant of about 4.0. This agrees well with quasi-Gaussian predictions but is a factor of 2 less than recent results from direct numerical simulations at moderate Reynolds numbers. Measurements of the inertial subrange pressure spectral constant at high Reynolds numbers, which might now be possible, would be most useful.     

A Variable Mesh Spacing for Large-Eddy Simulation Models in the Convective Boundary Layer

A variable vertical mesh spacing for large-eddy simulation (LES) models in a convective boundary layer (CBL) is proposed. The argument is based on the fact that in the vertical direction the turbulence near the surface in a CBL is inhomogeneous and therefore the subfilter-scale effects depend on the relative location between the spectral peak of the vertical velocity and the filter cut-off wavelength. From the physical point of view, this lack of homogeneity makes the vertical mesh spacing the principal length scale and, as a consequence, the LES filter cut-off wavenumber is expressed in terms of this characteristic length scale. Assuming that the inertial subrange initial frequency is equal to the LES filter cut-off frequency and employing fitting expressions that describe the observed convective turbulent energy one-dimensional spectra, it is feasible to derive a relation to calculate the variable vertical mesh spacing. The incorporation of this variable vertical grid within a LES model shows that both the mean quantities (and their gradients) and the turbulent statistics quantities are well described near to the ground level, where the LES predictions are known to be a challenging task.     

大气对流边界层发展的模拟研究

室内水槽模拟是大气边界层研究的一种重要手段。利用室内模拟水槽对大气边界层的发展进行了模拟,通过处理平均温度廓线和光斑图像得到了对流边界层顶部位置h2和边界层高度zi。结果表明,不同测量方法得到的结果一致性很好,与实际大气的边界层发展情况也较为接近。同时,根据试验情况确定初始条件和边界条件,使用边界层参数化模型进行了数值模拟,其结果与室内模拟的结果也较吻合。     

Large-Eddy Simulation of air Pollution Dispersion in the Nocturnal Cloud-Topped Atmospheric Boundary Layer

Effects of stratocumulus clouds on the dispersion of contaminants are studied in the nocturnal atmospheric boundary layer. The study is based on a large-eddy simulation (LES) model with a bulk parametrization of clouds. Computations include Lagrangian calculations of atmospheric dispersion of a passive tracer released from point sources at various heights above the ground. The results obtained show that the vertical diffusion is non-Gaussian and depends on the location of a source in the boundary layer.     

A Scale-Dependent Dynamic Model for Scalar Transport in Large-Eddy Simulations of the Atmospheric Boundary Layer

An important challenge in large-eddy simulationsof the atmospheric boundarylayer is the specification of the subgrid-scale(SGS) model coefficient(s)and, in particular, how to account for factorssuch as position in the flow,grid/filter scale and atmospheric stability.A dynamic SGS model (thatassumes scale invariance of the coefficients)is implemented in simulationsof a neutral boundary layer with a constantand uniform surface flux of apassive scalar. Results from our simulationsshow evidence that the lumpedcoefficient in the eddy-diffusion modelcomputed with the dynamic proceduredepends on scale. This scale dependence isstronger near the surface, and itis more important for the scalar than for thevelocity field (Smagorinskycoefficient) due to the stronger anisotropicbehaviour of scalars. Based onthese results, a new scale-dependent dynamicmodel is developed for theeddy-diffusion lumped coefficient. The newmodel, which is similar to theone proposed earlierfor the Smagorinsky coefficient,is fully dynamic, thus not requiring anyparameter specification or tuning.Simulations with the scale-dependent dynamicmodel yield the expected trendsof the coefficients as functions of positionand filter/grid scale.Furthermore, in the surface layer the newmodel gives improved predictionsof mean profiles and turbulence spectra ascompared with the traditionalscale-invariant dynamic model.     

Large-Eddy Simulation Of A Nocturnal Stratocumulus-Topped Marine Atmospheric Boundary Layer: An Uncertainty Analysis

A large-eddy simulation (LES) model has been used to study a nocturnalstratocumulus-topped marine atmospheric boundary layer. The main objectivesof our study have been first to investigate the statistical significance of LES-derived data products. Second, to test the sensitivity of our LES results with respect to the representation of subgrid-scale mixing and microphysical processes, and third to evaluate and to quantify the parametric uncertainty arising from the incomplete knowledge of the environmental parameters that are required to specify the initial and boundary conditions of a particular case study. Model simulations were compared with observations obtained in solid stratocumulus during the third flight of the first 'Lagrangian' experiment of the Atlantic Stratocumulus Transition Experiment (ASTEX). Based on these simulations the following conclusions could be drawn. Resolution(50 × 50 × 25 m³) and domain size (3.2 × 3.2 × 1.5 km³) of the LES calculations were adequate from a numerical point of view to represent the essential features of the stratocumulus-topped boundary layer. However, the ensemble runs performed in our study to investigate the statistical significance of LES-derived data products demonstrate that the area-time averaging procedure for the second-order moments produces only a low degree of statistical reliability in the model results. This illustratesthe necessity of having LES model results that are not only of adequate resolution but also of sufficiently large domain. The impact of different subgrid schemes was small, but the primary effects of drizzle were found to influence the boundary-layer structure in a climatologically significant way. The parametric uncertainty analysis revealed that the largest contribution to the variance of the LES-derived data products is due to theuncertainties in the cloud-top jump of total water mixing ratio and the net radiative forcing. The differences between the model and measurements for most of the simulated quantities were within the modelling uncertainties, but the calculated precipitation rate was found to differ significantly from that derived in the observations.     

A Modulated-Gradient Parametrization for the Large-Eddy Simulation of the Atmospheric Boundary Layer Using the Weather Research and Forecasting Model

The performance of the modulated-gradient subgrid-scale (SGS) model is investigated using large-eddy simulation (LES) of the neutral atmospheric boundary layer within the weather research and forecasting model. Since the model includes a finite-difference scheme for spatial derivatives, the discretization errors may affect the simulation results. We focus here on understanding the effects of finite-difference schemes on the momentum balance and the mean velocity distribution, and the requirement (or not) of the ad hoc canopy model. We find that, unlike the Smagorinsky and turbulent kinetic energy (TKE) models, the calculated mean velocity and vertical shear using the modulated-gradient model, are in good agreement with Monin–Obukhov similarity theory, without the need for an extra near-wall canopy model. The structure of the near-wall turbulent eddies is better resolved using the modulated-gradient model in comparison with the classical Smagorinsky and TKE models, which are too dissipative and yield unrealistic smoothing of the smallest resolved scales. Moreover, the SGS fluxes obtained from the modulated-gradient model are much smaller near the wall in comparison with those obtained from the regular Smagorinsky and TKE models. The apparent inability of the LES model in reproducing the mean streamwise component of the momentum balance using the total (resolved plus SGS) stress near the surface is probably due to the effect of the discretization errors, which can be calculated a posteriori using the Taylor-series expansion of the resolved velocity field. Overall, we demonstrate that the modulated-gradient model is less dissipative and yields more accurate results in comparison with the classical Smagorinsky model, with similar computational costs.     

A Large-Eddy Simulation and Lagrangian Stochastic Study of Heavy Particle Dispersion in the Convective Boundary Layer

Large-eddy simulation and Lagrangian stochastic dispersion models were used to study heavy particle dispersion in the convective boundary layer (CBL). The effects of various geostrophic winds, particle diameters, and subgrid-scale (SGS) turbulence were investigated. Results showed an obvious depression in the vertical dispersion of heavy particles in the CBL and major vertical stratification in the distribution of particle concentrations, relative to the passive dispersion. Stronger geostrophic winds tended to increase the dispersion of heavy particles in the lower CBL. The SGS turbulence, particularly near the surface, markedly influenced the dispersion of heavy particles in the CBL. For reference, simulations using passive particles were also conducted; these simulation results agreed well with results from previous convective tank experiments and numerical simulations.     

On Modelling the One-Dimensional Atmospheric Boundary Layer

Several commonly used turbulence closure schemes forthe atmospheric boundarylayer (ABL) are applied to simulate neutral, nocturnal and diurnal cyclesituations in a one-dimensional ABL. Results obtained with the differentschemes, E-, E- and its modified versions, and twoversions ofthe q ² Level 2.5, 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.     

Coherent Structures near the Surface in a Strongly Sheared Convective Boundary Layer Generated by Large-Eddy Simulation

Well-developed low speed and high temperature streaks in association with the alignment of convection cells are observed in a large-eddy-simulation (LES) generated strongly sheared convective boundary-layer flow, which is driven by a geostrophic wind speed of 15 m s^-1 and a surface kinematic heat flux of 0.05 K m s^-1. Vortices that drive streaky structures are identified through an eigenvalue method (lambda;₂method) near the surface. These vortices are highly elongated along the quasi-streamwise direction alternating sign of the x-component of vorticity (_x). By conditional sampling of fully developed vortices, a statistically significant coherent structure is educed. The educed vortex is elongated to the streamwise direction with the elevation angle of about 17° above the horizontal surface. However, the horizontal tilting is not clearly demonstrated in the present simulation. Fluctuation fields in the domain of the educed vortex show the existence of a low speed and high temperature streak as a direct consequence of momentum and heat transport by vortical motions. The strong ejection(upward transport of low momentum or high temperature)occurring at the higher level than that of the strong sweep (downward transport of high momentum and low temperature) can be explained from the spatial distribution of the fluctuationfields of velocity and temperature. The contribution of ejection to the Reynolds stress at z/h₁ = 0.18 is about 75%, which is slightly greater than that (70% at z/h₁ = 0.173) for the neutrally stratified atmospheric boundary layer. Ejection is also found to be dominant for the turbulent heat flux.     

A Large-Eddy Simulation Study of the Influence of Subsidence on the Stably Stratified Atmospheric Boundary Layer

The influence of the large-scale subsidence rate, S, on the stably stratified atmospheric boundary layer (ABL) over the Arctic Ocean snow/ice pack during clear-sky, winter conditions is investigated using a large-eddy simulation model. Simulations of two 24-h periods are conducted while varying S between 0, 0.001 and 0.002 ms⁻¹, and the resulting quasi-equilibrium ABL structures and evolutions are examined. Simulations conducted with S = 0 yield a boundary layer that is deeper, more strongly mixed and cools more rapidly than the observations. Simulations conducted with S > 0 yield improved agreement with the observations in the ABL height, potential temperature gradients and bulk heating rates. We also demonstrate that S > 0 limits the continuous growth of the ABL observed during quasi-steady conditions, leading to the formation of a nearly steady ABL of approximately uniform depth and temperature. Subsidence reduces the magnitudes of the stresses, as well as the implied eddy-diffusivity coefficients for momentum and heat, while increasing the vertical heat fluxes considerably. Subsidence is also observed to increases the Richardson number to values in excess of unity well below the ABL top.     

On the Development of a Dynamic Non-linear Closure for Large-Eddy Simulation of the Atmospheric Boundary Layer

A dynamic procedure is developed to compute the model coefficients in the recently introduced modulated gradient models for both momentum and scalar fluxes. The magnitudes of the subgrid-scale (SGS) stress and the SGS flux are estimated using the local equilibrium hypothesis, and their structures (relative magnitude of each of the components) are given by the normalized gradient terms, which are derived from the Taylor expansion of the exact SGS stress/flux. Previously, the two model coefficients have been specified on the basis of theoretical arguments. Here, we develop a dynamic SGS procedure, wherein the model coefficients are computed dynamically according to the statistics of the resolved turbulence, rather than provided a priori or ad hoc. Results show that the two dynamically calculated coefficients have median values that are approximately constant throughout the turbulent atmospheric boundary layer (ABL), and their fluctuations follow a near log-normal distribution. These findings are consistent with the fact that, unlike eddy-viscosity/diffusivity models, modulated gradient models have been found to yield satisfactory results even with constant model coefficients. Results from large-eddy simulations of a neutral ABL and a stable ABL using the new closure show good agreement with reference results, including well-established theoretical predictions. For instance, the closure delivers the expected surface-layer similarity profiles and power-law scaling of the power spectra of velocity and scalar fluctuations. Further, the Lagrangian version of the model is tested in the neutral ABL case, and gives satisfactory results.     

A Simple Model for the Vertical Transport of Reactive Species in the Convective Atmospheric Boundary Layer

We have developed a simple, steady-state, one-dimensional second-order closure model to obtain continuous profiles of turbulent fluxes and mean concentrations of non-conserved scalars in a convective boundary layer without shear. As a basic tool we first set up a model for conserved species with standard parameterizations. This leads to formulations for profiles of the turbulent diffusivity and the ratio of temperature-scalar covariance to the flux of the passive scalar. The model is then extended to solving, in terms of profiles of mean concentrations and fluxes, the NO _x –O₃ triad problem. The chemical reactions involve one first-order reaction, the destruction of NO₂ with decay time τ, and one second-order reaction, the destruction of NO and O₃ with the reaction constant k. Since the fluxes of the sum concentrations of NO _x = NO + NO₂ and O₃ + NO₂ turn out to be constant throughout the boundary layer, the problem reduces to solving two differential equations for the concentration and the flux of NO₂. The boundary conditions are the three surface fluxes and the fluxes at the top of the boundary layer, the last obtained from the entrainment velocity, and the concentration differences between the free troposphere and the top of the boundary layer. The equations are solved in a dimensionless form by using 1/(kτ) as the concentration unit, the depth h of the boundary layer as the length unit, the convective velocity scale w _* as the velocity unit, and the surface temperature flux divided by w _* as the temperature unit. Special care has been devoted to the inclusion of the scalar–scalar covariance between the concentrations of O₃ and NO. Sample calculations show that the fluxes of the reactive species deviate significantly from those of non-reactive species. Further, the diffusivities, defined by minus the flux divided by the concentration gradient may become negative for reactive species in contrast to those of non-reactive species, which in the present model are never negative.     

A Large-Eddy Simulation Study of Water Vapour and Carbon Dioxide Isotopes in the Atmospheric Boundary Layer

A large-eddy simulation model developed at the National Center for Atmospheric Research (NCAR) is extended to simulate the transport and diffusion of C¹⁸OO, H₂¹⁸O and ¹³CO₂ in the atmospheric boundary layer (ABL). The simulation results show that the ¹⁸O compositions of leaf water and the ABL CO₂ are moderately sensitive to wind speed. The variations in the ¹⁸O composition of water vapour are an order of magnitude greater than those in the ¹³C and ¹⁸O compositions of CO₂ both at turbulent eddy scales and across the capping inversion. In a fully-developed convective ABL, these isotopic compositions are well mixed as with other conserved atmospheric quantities. The Keeling intercepts determined with the simulated high-frequency turbulence time series do not give a reliable estimate of the ¹⁸O composition of the surface water vapour flux and may be a reasonable approximation to the ¹³C and ¹⁸O compositions of the surface CO₂ flux in the late afternoon only after a deep convective ABL has developed. We suggest that our isotopic large-eddy simulation (ISOLES) model should be a useful tool for testing and formulating research hypotheses on land–air isotopic exchanges.