Simulation of a Stably Stratified Atmospheric Boundary Layer Using One-Dimensional Turbulence

One-dimensional turbulence (ODT) is a single-column simulation in which vertical motions are represented by an unsteady advective process, rather than their customary representation by a diffusive process. No space or time averaging of mesh-resolved motions is invoked. Molecular-transport scales can be resolved in ODT simulations of laboratory-scale flows, but this resolution of these scales is prohibitively expensive in ODT simulations of the atmospheric boundary layer (ABL), except possibly in small subregions of a non-uniform mesh.Here, two methods for ODT simulation of the ABL on uniform meshes are described and applied to the GABLS (GEWEX Atmospheric Boundary Layer Study; GEWEX is the Global Energy and Water Cycle Experiment) stable boundary-layer intercomparison case. One method involves resolution of the roughness scale using a fixed eddy viscosity to represent subgrid motions. The other method, which is implemented at lower spatial resolution, involves a variable eddy viscosity determined by the local mesh-resolved flow, as in multi-dimensional large-eddy simulation (LES). When run at typical LES resolution, it reproduces some of the key high-resolution results, but its fidelity is lower in some important respects. It is concluded that a more elaborate empirically based representation of the subgrid physics, closely analogous to closures currently employed in LES of the ABL, might improve its performance substantially, yielding a cost-effective ABL simulation tool. Prospects for further application of ODT to the ABL, including possible use of ODT as a near-surface subgrid closure framework for general circulation modeling, are assessed.     

Effects of turbulent dispersion of atmospheric balance motions of planetary boundary layer

New Reynolds' mean momentum equations including both turbulent viscosity and dispersion are used to analyze atmospheric balance motions of the planetary boundary layer. It is pointed out that turbulent dispersion with r 0 will increase depth of Ekman layer, reduce wind velocity in Ekman layer and produce a more satisfactory Ekman spiral lines fit the observed wind hodograph. The wind profile in the surface layer including tur-bulent dispersion is still logarithmic but the von Karman constant k is replaced by k1 = 1 -2/k, the wind increasesa little more rapidly with height.     

Modelling the One-Dimensional Stable Boundary Layer with an E−ℓ Turbulence Closure Scheme

The atmospheric boundary layer (ABL) model of Weng and Taylor with E−ℓ turbulence closure is applied to simulate the one-dimensional stably stratified ABL. The model has been run for nine hours from specified initial wind, potential temperature and turbulent kinetic energy profiles, and with a specified cooling rate applied at the surface. Different runs are conducted for different cooling rates, geostrophic winds and surface roughnesses. The results are discussed and compared with other models, large-eddy simulations and published field data.     

农林复合带一维非静力大气边界层模式及其模拟分析

建立了一个农林复合带地区一维非静力大气边界层能量闭合模式，对1000m以下的大气边界层内的风、温、湿作了24h的预报，并对下垫面3种不同参数化方案(农作物、森林、无植被)的输出结果与实测值进行了分析和比较；同时通过敏感性试验，突出比较了农作物和森林下垫面对大气边界层垂直流场，湍流垂直交换和湍能的影响。结果表明，本模式能改善边界层风速、位温和湿度预报的模拟效果，下垫面植被对边界层气象要素大小和分布有显著的作用，对湍能垂直分布有一定影响。     

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.     

Comparison of Kansas Data with High-resolution Large-eddy Simulation Fields

The surface layer of an atmospheric boundary layer (ABL) is most accessible to field measurements and hence its ensemble-mean structure has been well established. The Kansas field measurements were the first detailed study of this layer, providing numerous benchmark statistical profiles for a wide range of stability states. Large-eddy simulation (LES), in contrast, is most suitable for studying the mixed layer of the ABL where the energy-containing range of the vertical velocity field is well resolved. In the surface layer, typical large-eddy simulations barely resolve the energy-containing vertical-velocity fields and hence do not provide sufficient data for a detailed analysis.We carried out a nested-mesh simulation of a moderately convective ABL (-z_i/L = 8) in which the lower 6% of the boundary layer had an effective grid resolution of 512³. We analyze the LES fields above the 6th vertical grid level (z = 23 m) where the vertical velocity field has a well formed inertial subrange, for a detailed comparison with the Kansas results. Various terms in the budgets of turbulent kinetic energy, temperature variance, Reynolds stress, temperature flux, and some higher order moments are compared. The agreement is generally quite good; however, we do observe certain discrepancies, particularly in the terms involving pressure fluctuations.     

Effects of Sea-Surface Waves and Ocean Spray on Air-Sea Momentum Fluxes

The effects of sea-surface waves and ocean spray on the marine atmospheric boundary layer(MABL) at different wind speeds and wave ages were investigated. An MABL model was developed that introduces a wave-induced component and spray force to the total surface stress. The theoretical model solution was determined assuming the eddy viscosity coefficient varied linearly with height above the sea surface. The wave-induced component was evaluated using a directional wave spectrum and growth rate. Spray force was described using interactions between ocean-spray droplets and wind-velocity shear. Wind profiles and sea-surface drag coefficients were calculated for low to high wind speeds for wind-generated sea at different wave ages to examine surface-wave and ocean-spray effects on MABL momentum distribution. The theoretical solutions were compared with model solutions neglecting wave-induced stress and/or spray stress. Surface waves strongly affected near-surface wind profiles and sea-surface drag coefficients at low to moderate wind speeds. Drag coefficients and near-surface wind speeds were lower for young than for old waves. At high wind speeds, ocean-spray droplets produced by wind-tearing breaking-wave crests affected the MABL strongly in comparison with surface waves, implying that wave age affects the MABL only negligibly. Low drag coefficients at high wind caused by ocean-spray production increased turbulent stress in the sea-spray generation layer, accelerating near-sea-surface wind. Comparing the analytical drag coefficient values with laboratory measurements and field observations indicated that surface waves and ocean spray significantly affect the MABL at different wind speeds and wave ages.     

A Large-Eddy Simulation Study of Turbulent Flow Over Multiscale Topography

Most natural landscapes are characterized by multiscale (often multifractal) topography with well-known scale-invariance properties. For example, the spectral density of landscape elevation fields is often found to have a power-law scaling behaviour (with a −2 slope on a log–log scale) over a wide span of spatial scales, typically ranging from tens of kilometres down to a few metres. Even though the effect of topography on the atmospheric boundary layer (ABL) has been the subject of numerous studies, few have focussed on multiscale topography. In this study, large-eddy simulation (LES) is used to investigate boundary-layer flow over multiscale topography, and guide the development of parametrizations needed to represent the effects of subgrid-scale (SGS) topography in numerical models of ABL flow. Particular emphasis is placed on the formulation of an effective roughness used to account for the increased aerodynamic roughness associated with SGS topography. The LES code uses the scale-dependent Lagrangian dynamic SGS model for the turbulent stresses and a terrain-following coordinate transformation to explicitly resolve the effects of the topography at scales larger than the LES resolution. The terrain used in the simulations is generated using a restricted solid-on-solid landscape evolution model, and it is characterized by a −2 slope of the elevation power spectrum. Results from simulations performed using elevation fields band-pass filtered at different spatial resolutions indicate a clear linear relation between the square of the effective roughness and the variance of elevation.     

The Morning Transition of the Nocturnal Boundary Layer

Six years of observations from a surface instrument site have been analysed to determine timings and factors influencing developmental changes in the near-surface wind and turbulent heat fluxes during the morning heating of the atmospheric boundary layer. A simple relationship has been found between near-surface wind speed and screen temperature, together with a predictive equation for the morning transition air temperature. Profile measurements from a probe mounted on a tethered balloon have beenused to supplement the surface data and study the processes underlying these surface relationships. The results have confirmed earlier work and have shown that both before and immediately after morning transition, almost all heating in the surface layer is due to turbulent diffusion from above. In order to explain the mechanisms involved in the relationships, a simple finite difference model has been run and validated against the profile data. The model predictions are compared with observations during both the morning and evening and the differences related to the different temperature profiles. Numerical forecasting rules for the surface wind speed and transition temperature are derived from the results.     

Dynamical Initialization of Boundary-Layer Data

A procedure for the dynamic initialization of wind and temperature fields within the atmospheric boundary layer (ABL) is presented. The procedure uses transilient turbulence theory to assess the turbulent fluxes from observed wind and temperature data, which are used to estimate the eddy transfer coefficients, so enabling a local closure ABL model to be integrated forward in time to a new steady state. The method has been applied to initialize kytoon data taken at Kharagpur (22.3° N, 87.2° E) during the MONTBLEX field programme. Results of a case study for 17 June 1990 are discussed.     

Observations of atmospheric boundary layer evolution above the Gulf Stream frontal zone

Ship borne measurements of atmospheric boundary layer (ABL) parameters, sea-surface temperature and radar signals are analyzed to reveal the effects of the ABL transformation above the Gulf Stream temperature frontal zone. It was found that local changes in vertical gradients of wind speed and air temperature are well correlated with sub-mesoscale (~ 10 km) sea surface temperature variations. These effects are accompanied by appropriate variations in surface wind stresses that were identified from microwave backscatter.For steady atmospheric conditions the same effects were observed on spatial scales of 100 km, demonstrating positive radar signal contrast of the Gulf Stream warm waters with respect to surrounding Sargasso sea and shelf water areas. A simplified model of the ABL, accounting for an effect of spatial inhomogeneity by introducing an internal boundary layer, is used to analyze field observations. The model is able to reproduce both sub-mesoscale and mesoscale ABL evolution.     

On the Possible Impact of a Following-Swell on the Atmospheric Boundary Layer

A simple model of the atmospheric boundary layer over the ocean where the swell impact on the atmosphere is explicitly accounted for is suggested. The model is based on Ekman’s equations, where the stress in the wave boundary layer is split into two parts: the turbulent and wave-induced stress. The turbulent stress is parameterized traditionally via the eddy viscosity proportional to the generalized mixing length. The wave-induced stress directed upward (from swell to the atmosphere) is parameterized using the formalism of the wind-over-waves coupling theory. The model can be seen as an extension of the model by Kudryavtsev and Makin (J Phys Oceanogr 34:934–949, 2004) to the scale of the entire atmospheric boundary layer by including the Coriolis force into the momentum conservation equation and generalizing the definition of the mixing length. The regime of low winds for swell propagating along the wind direction is studied. It is shown that the impact of swell on the atmosphere is governed mainly by the swell parameter—the coupling parameter that is the product of the swell steepness and the growth rate coefficient. When the coupling parameter drops below − 1 the impact of swell becomes significant and affects the entire atmospheric boundary layer. The turbulent stress is enhanced near the surface as compared to the no-swell case, and becomes negative above the height of the inner region. The wind profile is characterized by a positive gradient near the surface and a negative gradient above the height of the inner region forming a characteristic bump at the height of the inner region. Results of the model agree at least qualitatively with observations performed in the atmosphere in presence of swell.     

On the consideration of mesoscale transports in climate modelling

Summary The dynamical effect of land surface heterogeneity on heat fluxes in the atmospheric boundary layer (ABL) is investigated using numerical simulations with a non-hydrostatic model over a wide range of grid resolutions. It is commonly assumed that mesoscale or dynamical fluxes associated with mesoscale and convective circulations simulated by a high-resolution model (subgrid (SG) model) on the subgrid scale of a climate model (large-scale (LS) model) represent additional processes in the ABL, which are not considered by the turbulence scheme of the LS-model, and which can be parameterized using the SG-model. The present study investigates the usefulness of this methodology for small-scale and large-scale idealized heterogeneities using a SG-model resolving mesoscale or even microscale circulations to compute the mesoscale fluxes on the scale of the LS-model. It is shown that the dynamical transports as derived from the SG-model should not be used to correct the parameterized turbulent fluxes of the LS-model. The reason is that the subgrid circulations simulated by the SG-model interact with the fields of wind and scalars in the ABL, which results in reduced turbulent fluxes in the ABL. Thus the methodology of previous studies to use mesoscale/dynamical fluxes for the correction of flux profiles simulated by climate models seems to be questionable.     

Baroclinic Planetary Boundary-Layer Model for Neutral and Stable Stratification Conditions

The temperature and wind profiles in abaroclinic atmospheric boundary layer (ABL) are investigated.Assuming stationary conditions, the turbulent state in the ABL forstable and neutral conditions is uniquely determined by the Rossbynumber, the external stratification parameter and two externalbaroclinic parameters. A simple two-layer baroclinic model isdeveloped. It consists of a surface layer (SL) and overlyingEkman-type layer. The system of dynamic and heat transfer equations isclosed using K-theory. In the SL the turbulent exchangecoefficient is consistent with the results of similarity theorywhile in the Ekman layer it is assumed constant. The universalfunctions in the resistance, heat and humidity transfer laws arededuced from the analytical solutions for the wind and temperatureprofiles. The solutions of the ABL resistance laws for theinternal ABL parameters, necessary for the calculations of the ABLprofiles, are approximated in terms of the external ABLparameters. Favourable agreement of model results with theavailable experimental data is demonstrated.     

The Impact of Land-Surface Parameter Properties and Resolution on the Simulated Cloud-Topped Atmospheric Boundary Layer

A method to simulate characteristics of wind speed in the boundary layer of tropical cyclones in an idealized manner is developed and evaluated. The method can be used in a single-column modelling set-up with a planetary boundary-layer parametrization, or within large-eddy simulations (LES). The key step is to include terms in the horizontal velocity equations representing advection and centrifugal acceleration in tropical cyclones that occurs on scales larger than the domain size. Compared to other recently developed methods, which require two input parameters (a reference wind speed, and radius from the centre of a tropical cyclone) this new method also requires a third input parameter: the radial gradient of reference wind speed. With the new method, simulated wind profiles are similar to composite profiles from dropsonde observations; in contrast, a classic Ekman-type method tends to overpredict inflow-layer depth and magnitude, and two recently developed methods for tropical cyclone environments tend to overpredict near-surface wind speed. When used in LES, the new technique produces vertical profiles of total turbulent stress and estimated eddy viscosity that are similar to values determined from low-level aircraft flights in tropical cyclones. Temporal spectra from LES produce an inertial subrange for frequencies \(\gtrsim \)0.1 Hz, but only when the horizontal grid spacing \(\lesssim \)20 m.     

Spatial representativeness of single tower measurements and the imbalance problem with eddy-covariance fluxes: results of a large-eddy simulation study

A large-eddy simulation (LES) study is presented that investigates the spatial variability of temporal eddy covariance fluxes and the systematic underestimation of representative fluxes linked to them. It extends a prior numerical study by performing high resolution simulations that allow for virtual measurements down to 20 m in a convective boundary layer, so that conditions for small tower measurement sites can be analysed. It accounts for different convective regimes as the wind speed and the near-surface heat flux are varied. Moreover, it is the first LES imbalance study that extends to the stable boundary layer. It reveals shortcomings of single site measurements and the necessity of using horizontally-distributed observation networks. The imbalances in the convective case are attributed to a locally non-vanishing mean vertical advection due to turbulent organised structures (TOS). The strength of the TOS and thus the imbalance magnitude depends on height, the horizontal mean wind and the convection type. Contrary to the results of a prior study, TOS cannot generally be responsible for large energy imbalances: at low observation heights (corresponding to small towers and near-surface energy balance stations) the TOS related imbalances are generally about one order of magnitude smaller than those in field experiments. However, TOS may cause large imbalances at large towers not only in the case of cellular convection and low wind speeds, as found in the previous study, but also in the case of roll convection at large wind speeds. In the stably stratified boundary layer for all observation heights neither TOS nor significant imbalances are observed. Attempting to reduce imbalances in convective situations by applying the conventional linear detrending method increases the systematic flux underestimation. Thus, a new filter method is proposed.     

Numerical experiments with alternative boundary layer formulations using bomex data

The basic numerical air-sea boundary-layer model described in Pandolfo (1969a, b) was varied to produce a set of models with differing atmospheric boundary-layer formulas, four of which are discussed here. Model I is the basic model itself, with stability and sea-state dependent eddy viscosity, conductivity and diffusivity which may, in certain ranges ofRi, be unequal. This model is applied on a relatively fine grid. Model II, applied on the same grid, uses formulas which yield equal eddy conductivity, diffusivity, and viscosity. The calculated eddy coefficients depend only on the height and wind shear. Model III uses the same exchange coefficient formulas as Model II. However, the surface-layer eddy flux in Model III is calculated by assuming that logarithmic profiles of the transported variables are present in this layer. Model IV is the same as Model III in these respects, but employs a relatively coarse vertical grid. This model, therefore, includes boundary layer formulas most like those conventionally used in large scale atmospheric models (e.g. Miyakoda, 1969).The four models were integrated numerically with identical inputs of initial, boundary, and auxiliary data prepared from observations made over the eastern half of the BOMEX observational area during June 21–25, 1969.Models I and IV are, in general, in better agreement with each other than either is with Model II. This is true for the model-generated upper and lower boundary fluxes of mean momentum and latent heat; and for the internal boundary layer production of mean kinetic energy by the cross-isobaric flow component. Model I agrees, on balance, about as well with Model IV as does Model III. The solutions for Models I, III, and IV are also, in general, more consistent with observed data, viz. 5-day average temperature profiles in the layer from the surface to 1000 meters, and 5-day averages of sea surface temperature and of surface-layer atmospheric humidity. Solutions for Model I are in better overall agreement with the observed data, and with the average observed surface-layer wind.The results show that, under the limitations implicit in these preliminary experiments, accurate simulations of observed data are possible with boundary-layer formulas of the type used in Model IV, and even more accurate simulation with the modest refinements represented by Model I. Piecemeal imposition of such refinements could, however, lead to models, like Model II, with significantly different energetic properties and less simulative accuracy. Specifically, the results support the speculation (Miyakodaet al., 1969) that the shallowness of the simulated Trades noted in some large-scale models is due to deficiencies in the boundary-layer eddy stress formulations used.     

Evaluation of the Diurnal Cycle in the Atmospheric Boundary Layer Over Land as Represented by a Variety of Single-Column Models: The Second GABLS Experiment

We present the main results from the second model intercomparison within the GEWEX (Global Energy and Water cycle EXperiment) Atmospheric Boundary Layer Study (GABLS). The target is to examine the diurnal cycle over land in today??s numerical weather prediction and climate models for operational and research purposes. The set-up of the case is based on observations taken during the Cooperative Atmosphere-Surface Exchange Study-1999 (CASES-99), which was held in Kansas, USA in the early autumn with a strong diurnal cycle with no clouds present. The models are forced with a constant geostrophic wind, prescribed surface temperature and large-scale divergence. Results from 30 different model simulations and one large-eddy simulation (LES) are analyzed and compared with observations. Even though the surface temperature is prescribed, the models give variable near-surface air temperatures. This, in turn, gives rise to differences in low-level stability affecting the turbulence and the turbulent heat fluxes. The increase in modelled upward sensible heat flux during the morning transition is typically too weak and the growth of the convective boundary layer before noon is too slow. This is related to weak modelled near-surface winds during the morning hours. The agreement between the models, the LES and observations is the best during the late afternoon. From this intercomparison study, we find that modelling the diurnal cycle is still a big challenge. For the convective part of the diurnal cycle, some of the first-order schemes perform somewhat better while the turbulent kinetic energy (TKE) schemes tend to be slightly better during nighttime conditions. Finer vertical resolution tends to improve results to some extent, but is certainly not the solution to all the deficiencies identified.     

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.