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.     

Measurements Of Thermal Updraft Intensity Over Complex Terrain Using American White Pelicans And A Simple Boundary-Layer Forecast Model

An examination of boundary-layer meteorological and avian aerodynamic theories suggests that soaring birds can be used to measure the magnitude of vertical air motions within the boundary layer. These theories are applied to obtain mixed-layer normalized thermal updraft intensity over both flat and complex terrain from the climb rates of soaring American white pelicans and from diagnostic boundary-layer model-produced estimates of the boundary-layer depth z_i and the convective velocity scale w_*. Comparison of the flatland data with the profiles of normalized updraft velocity obtained from previous studies reveals that the pelican-derived measurements of thermal updraft intensity are in close agreement with those obtained using traditional research aircraft and large eddy simulation (LES) in the height range of 0.2 to 0.8 z_i. Given the success of this method, the profiles of thermal vertical velocity over the flatland and the nearby mountains are compared. This comparison shows that these profiles are statistically indistinguishable over this height range, indicating that the profile for thermal updraft intensity varies little over this sample of complex terrain. These observations support the findings of a recent LES study that explored the turbulent structure of the boundary layer using a range of terrain specifications. For terrain similar in scale to that encountered in this study, results of the LES suggest that the terrain caused less than an 11% variation in the standard deviation of vertical velocity.     

The diurnal wind variation in a variable eddy viscosity semi-geostrophic Ekman boundary-layer model: Analytical study

Summary ?A time-dependent semi-geostrophic Ekman boundary-layer model (SG), including slowly varying eddy diffusivity with height and inertial term effects, is developed to investigate the diurnal wind variation in the planetary boundary layer (PBL). An approximate analytical solution of this model is derived by using the WKB method, which extends the Tan and Farahani (1998)’s solution by including the vertical variable eddy viscosity. The features of the diurnal wind variation in the PBL mainly depend on three factors: the latitude, horizontal momentum advection and eddy viscosity. The vertical variable eddy viscosity has little influence on diurnal wind variation in the PBL at the low latitude, however its effect may be exacerbated in the mid- and high latitudes. In comparing with the constant eddy viscosity case, the decreasing (increasing) with height eddy viscosity produces a large (small) maximum wind speed (MWS) in the PBL, however, the eddy viscosity that has a mid-layer peak in the vertical gives rise to a higher height of occurrence of MWS. For the boundary-layer wind structure, there is a singular point when the modified SG inertial oscillation frequency η equals the forcing frequency ω. The isotachs of boundary-layer wind speed have almost no tilt to left or right relative to time evolution and the occurrence time of the MWS is the earliest at the singular point. The feature will be enhanced in the decreasing with height eddy viscosity case and weakened in the eddy viscosity initially increasing with height case. Received April 6, 2001; accepted December 27, 2001     

大气对黑潮延伸区中尺度海洋涡旋的响应——冬季暖、冷涡个例分析

采用动态合成、带通滤波等方法,通过对冬季黑潮延伸区暖、冷两个中尺度海洋涡旋的分析,研究了大气对中尺度海洋涡旋的响应特征。结果表明,海表温度（SST）与近海面风速的正相关关系在涡旋的动态合成图上清晰可见,暖（冷）涡上空对应10 m风速的极大（小）值,即海洋对大气的强迫作用在日时间尺度上表现显著;SST高低值中心基本对应10 m风无辐散区,暖（冷）涡上空为异常正（负）涡度分布;暖（冷）涡上空潜热、感热通量增大（减小）,降低（增大）大气稳定度,从而加强（减弱）边界层垂直混合作用,使得海洋大气边界层增厚（变薄）。暖（冷）涡旋上空对应摩擦速度极大（小）值,反映了湍流粘性力在高（低）海温中心增大（减小）的特征,表明动量垂直混合机制在中小尺度海气相互作用中起着主要作用。中尺度海洋涡旋能够影响大气瞬变扰动,大气瞬变扰动强度在暖（冷）涡下游上空出现极大（小）值,该影响不仅表现在海洋大气边界层,在自由大气中低层也有较为清晰的反映。此外,从能量转换的角度入手,发现斜压能量转换在中尺度海洋涡旋影响大气瞬变扰动强度中贡献明显。     

Observations and Large-Eddy Simulations of Entrainment in the Sheared Sahelian Boundary Layer

At the top of the planetary boundary layer, the entrainment of air, which incorporates dry and warm air from the free troposphere into the boundary layer, is a key process for exchanges with the free troposphere since it controls the growth of the boundary layer. Here, we focus on the semi-arid boundary layer where the entrainment process is analyzed using aircraft observations collected during the African Monsoon Multidisciplinary Analysis experiment and large-eddy simulations. The role of the entrainment is specifically enhanced in this region where very large gradients at the planetary boundary-layer top can be found due to the presence of the moist, cold monsoon flow on which the dry, warm Harmattan flow is superimposed. A first large-eddy simulation is designed based on aircraft observations of 5 June 2006 during the transition period between dry conditions and the active monsoon phase. The simulation reproduces the boundary-layer development and dynamics observed on this day. From this specific case, sensitivity tests are carried out to cover a range of conditions observed during seven other flights made in the same transition period in order to describe the entrainment processes in detail. The combination of large-eddy simulations and observations allows us to test the parametrization of entrainment in a mixed-layer model with zero-order and first-order approximations for the entrainment zone. The latter representation of the entrainment zone gives a better fit with the conditions encountered in the Sahelian boundary layer during the transition period because large entrainment thicknesses are observed. The sensitivity study also provides an opportunity to highlight the contribution of shear stress and scalar jumps at the top of the boundary layer in the entrainment process, and to test a relevant parametrization published in the recent literature for a mixed-layer model.     

An Improved Ekman Layer Approximation for Smooth Eddy Diffusivity Profiles

The Ekman boundary-layer model is extended analytically for a gradually varying eddy diffusivity K(z) ≥ 0, z ≥ 0. A solution for the Ekman layer is provided having similar structure to the constant-K case; that is, exponentially decaying sine functions for the two horizontal wind components. The analytical asymptotic solution compares well with its numerical counterpart for various K(z). The result can be useful in theoretical studies such as Ekman pumping, for efficient estimation of the Ekman layer profiles in various analyses with near-neutral stratifications, or for a rapid initialization of mesoscale models.     

An Approximate Analytical Solution For The Baroclinic And Variable Eddy Diffusivity Semi-Geostrophic Ekman Boundary Layer

The WKB method has been used to develop an approximate solutionof the semi-geostrophic Ekman boundary layer with height-dependenteddy viscosity and a baroclinic pressure field. The approximate solutionretains the same simple form as the classical Ekman solution. Behavioursof the approximate solution are discussed for different eddy viscosityand the pressure systems. These features show that wind structure inthe semi-geostrophic Ekman boundary layer depends on the interactionbetween the inertial acceleration, variable eddy viscosity and baroclinicpressure gradient. Anticyclonic shear has an acceleration effect on theair motion in the boundary layer, while cyclonic shear has a decelerationeffect. Decreasing pressure gradient with height results in a super-geostrophicpeak in the wind speed profile, however the increasing pressure gradient withheight may remove the peak. Anticyclonic shear and decreasing the variableeddy viscosity with height has an enhanced effect on the peak.Variable eddy viscosity and inertial acceleration has an important role in thedivergence and vorticity in the boundary layer and the vertical motion at the top of the boundary layer that is called Ekman pumping. Compared to the constanteddy viscosity case, the variable eddy diffusivity reduces the absolute value ofEkman pumping, especially in the case of eddy viscosity initially increasing with height. The difference in the Ekman pumping produced by different eddy diffusivity assumptions is intensified in anticyclonic flow and reduced in cyclonic flow.     

Synoptic Controls on Boundary-Layer Characteristics

We report the characteristics of the three-dimensional, time evolving, atmospheric boundary layer that develops beneath an idealised, dry, baroclinic weather system. The boundary-layer structure is forced by thermal advection associated with the weather system. Large positive heat fluxes behind the cold front drive a vigorous convective boundary layer, whereas moderate negative heat fluxes in the warm sector between the cold and warm fronts generate shallow, stably stratified or neutral boundary layers. The forcing of the boundary-layer structure is quantified by forming an Eulerian mass budget integrated over the depth of the boundary layer. The mass budget indicates that tropospheric air is entrained into the boundary layer both in the vicinity of the high-pressure centre, and behind the cold front. It is then transported horizontally within the boundary layer and converges towards the cyclone’s warm sector, whence it is ventilated out into the troposphere. This cycling of air is likely to be important for the ventilation of pollution out of the boundary layer, and for the transformation of the properties of large-scale air masses.     

Effects of mesoscale sea-surface temperature fronts on the marine atmospheric boundary layer

A numerical modelling study is presented focusing on the effects of mesoscale sea-surface temperature (SST) variability on surface fluxes and the marine atmospheric boundary-layer structure. A basic scenario is examined having two regions of SST anomaly with alternating warm/cold or cold/warm water regions. Conditions upstream from the anomaly region have SST values equal to the ambient atmosphere temperature, creating an upstream neutrally stratified boundary layer. Downstream from the anomaly region the SST is also set to the ambient atmosphere value. When the warm anomaly is upstream from the cold anomaly, the downstream boundary layer exhibits a more complex structure because of convective forcing and mixed layer deepening upstream from the cold anomaly. An internal boundary layer forms over the cold anomaly in this case, generating two distinct layers over the downstream region. When the cold anomaly is upstream from the warm anomaly, mixing over the warm anomaly quickly destroys the shallow cold layer, yielding a more uniform downstream boundary-layer vertical structure compared with the warm-to- cold case. Analysis of the momentum budget indicates that turbulent momentum flux divergence dominates the velocity field tendency, with pressure forcing accounting for only about 20% of the changes in momentum. Parameterization of surface fluxes and boundary-layer structure at these scales would be very difficult because of their dependence on subgrid-scale SST spatial order. Simulations of similar flow over smaller scale fronts (<5 km) suggest that small-scale SST variability might be parameterized in mesoscale models by relating the effective heat flux to the strength of the SST variance.     

An Evaluation of Boundary-Layer Depth,Inversion and Entrainment Parameters by Large-Eddy Simulation

Studies of entrainment across the top of the boundary layer rely to a great extent on identification of the boundary-layer top, inversion properties, entrainment-zone depth, and the temporal changes in all of these. A variety of definitions and techniques have been used to provide automated and objective estimates; however, direct comparisons between studies is made difficult by the lack of consistency in techniques. Here we compare boundary-layer depth, entrainment-zone thickness, and entrainment rate derived from several commonly used techniques applied to a common set of large-eddy simulations of the idealized, dry, convective boundary layer. We focus in particular on those techniques applicable to lidar backscatter measurements of boundary-layer structure. We find significant differences in all the quantities of interest, and further that the behaviour as functions of common scaling parameters, such as convective Richardson number, also differ, sometimes dramatically. The discretization of the possible values of some quantities imposed by the vertical grid is found to affect some of the results even when changes to model resolution does not affect the entrainment rate or scaling behaviour. This is a particular problem where entrainment parameters are derived from a single mean profile (e.g. the buoyancy-flux profile), but not where they are derived from the statistical properties of large numbers of individual profiles (e.g. the probability distribution of the local boundary-layer top at each model grid point).     

变化涡动沾性系数的Ekman动量近似模式风场结构

在边界层动力学中，涡动粘性系数是影响边界层风场结构的一个重要参数。本文利用边界层动力学中的Ekman动量近似理论，给出了涡动粘性系数随高度缓变条件下的Ekman动量近似边界层模式解，着重讨论了边界层的风场结构、水平散度、垂直涡度以及边界层顶部的垂直速度。结果分析表明：与常值涡动粘性系数情况相比，在边界层低层随高度增加的涡动粘性系数可以导致低层边界层风速随高度迅速增加，即风速垂直切变增加，同时风速矢与地转风之间的夹角减小。惯性项作用可以导致上述作用在气旋性区域减小、而在反气旋性区域增大。随高度增加的涡动粘性系数导致水平散度绝对值、垂直涡度绝对值以及边界层顶部的垂直速度绝对值在气旋性区域减小，而在反气性旋区域增大。涡动粘性系数与惯性之间的非线性相互作用是边界层动力学中重要过程。     

Discussion and Applications of Slab Models of the Convective Boundary Layer based on Turbulent Kinetic Energy Budget Parameterisations

Some of the most widely used slab model formulations for applications in the convective boundary layer are analysed and discussed. Three main classes are identified based on different approximations of the turbulent kinetic energy equation. The models appear to be quite insensitive to the initial values for boundary-layer height, and temperature discontinuity at the boundary-layer top. The slab models are applied to a case of sea-land transition from the literature, and a case of convective boundary layer time evolution over a homogeneous terrain at San Pietro Capofiume (Bologna, Italy). The different parameterisations turn out to be almost equivalent for the cases studied. The models generally underpredict the value for the height, while all give very good estimates for the mean mixed-layer temperature.     

The Moist Boundary Layer under a Mid-latitude Weather System

Mid-latitude weather systems are key contributors to the transport of atmospheric water vapour, but less is known about the role of the boundary layer in this transport. We expand a conceptual model of dry boundary-layer structure under synoptic systems to include moist processes, using idealised simulations of cyclone waves to investigate the three-way interaction between the boundary layer, atmospheric moisture and large-scale dynamics. Forced by large-scale thermal advection, boundary-layer structures develop over large areas, analogous to the daytime convective boundary layer, the nocturnal stable boundary layer and transitional regimes between these extremes. A budgeting technique demonstrates the key role of boundary-layer processes in the transport of moisture. Moisture is evaporated from the ocean behind the cold front and in the high-pressure part of the wave, and transported large distances within the boundary layer into the footprint of the warm-conveyor belt. The warm-conveyor belt forms one of the two main processes of boundary-layer ventilation, with shallow cumulus convection being of similar importance.     

A simple model of the atmospheric boundary layer; sensitivity to surface evaporation

A simple formulation of the boundary layer is developed for use in large-scale models and other situations where simplicity is required. The formulation is suited for use in models where some resolution is possible within the boundary layer, but where the resolution is insufficient for resolving the detailed boundary-layer structure and overlying capping inversion. Surface fluxes are represented in terms of similarity theory while turbulent diffusivities above the surface layer are formulated in terms of bulk similarity considerations and matching conditions at the top of the surface layer. The boundary-layer depth is expressed in terms of a bulk Richardson number which is modified to include the influence of thermals. Attention is devoted to the interrelationship between predicted boundary-layer growth, the turbulent diffusivity profile, countergradient heat flux and truncation errors.The model predicts growth of the convectively mixed layer reasonably well and is well-behaved in cases of weak surface heat flux and transitions between stable and unstable cases. The evolution of the modelled boundary layer is studied for different ratios of surface evaporation to potential evaporation. Typical variations of surface evaporation result in a much greater variation in boundary-layer depth than that caused by the choice of the boundary-layer depth formulation.     

A comparison of boundary layer diffusion schemes in unstable conditions over land

We compare the results of a local and a nonlocal scheme for vertical diffusion in the atmospheric boundary layer with observations at the 200 m tower at Cabauw. This is done for a 12 h period during daytime on 31 May 1978, which is characterised by strong insolation, clear skies, moderately strong winds and weak advection. The local diffusion scheme uses an eddy diffusivity determined independently at each point along the vertical based on local vertical gradients of wind and virtual potential temperature, similar to the usual approach in atmospheric models. The nonlocal scheme determines an eddy diffusivity profile based on a diagnosed boundary-layer height and a turbulent velocity scale. It also incorporates nonlocal (vertical) transport effects for heat and moisture. The boundary-layer diffusion schemes are forced with the locally observed fluxes for heat and moisture. The outputs of the scheme are compared with the observed mean structure along the Cabauw tower, and the radiosonde profile at a nearby location (De Bilt). Overall, the nonlocal scheme transports moisture away from the surface more rapidly than the local scheme, and deposits the moisture at higher levels. The local scheme tends to saturate the lowest model levels unrealistically in comparison with the observations. We also compare the outputs of the two diffusion schemes with the results of a transilient model simulation. Subsequently, we study the impact on the model behaviour by varying important parameters in both diffusion schemes and we investigate the sensitivity to uncertainty in the environmental conditions. Finally, we study the interaction of the diffusion schemes with a simple surface flux scheme.     

Marginal mixing theories

Abstract

Mixing near the sloping boundaries of oceans or lakes may be a significant mechanism of diapycnal transport. The basic physics of this is reviewed, with emphasis on the reduction of the effectiveness of the process due to both reduced stratification and the restratifying secondary circulation driven by buoyancy forces. This re stratification is shown to reduce the effectiveness of intermittent mixing events as well as steady mixing. It is argued that for boundary mixing to be effective in the abyssal ocean it must extend sufficiently far from the boundary that the stratification can be maintained; this may be true for breaking bottom‐reflected internal waves. The alongslope flow implied by steady‐state boundary mixing theories is downwelling‐favourable and has a magnitude related to the thickness and other properties of the boundary layer. Mixing near a boundary may thus tend to drive a downwelling‐favourable mean circulation in the interior. If the interior circulation is imposed by other forces, the bottom boundary layer may evolve to a steady state if the interior flow is downwelling‐favourable, but if it is upwelling‐favourable initially a steady state seems unlikely and the downwelling‐favourable alongslope flow induced by the boundary mixing will tend to diffuse slowly into the interior. The nature of the solution in all these cases is sensitive to the Burger number, N² sin² θ/f², where θ is the bottom slope, and to the eddy Prandtl number.     

Turbulence Over Urban-type Roughness: Deductions from Wind-tunnel Measurements

Turbulence data from experiments conducted over a staggered cube array, modelling a neutrally stable atmospheric boundary layer in an urban environment, are presented. The results support the contention that organised eddy structures in the near-wall region differ significantly from those in regular smooth-wall flows or in rough-wall boundary layers with much smaller h/δ ratios (where δ and h are the boundary-layer thickness and the height of the roughness elements, respectively). Attention is concentrated on spatial correlations, spectra (and thus the dominant length and time scales), maps of anisotropy invariants and quadrant analyses of the stress tensor. Results are obtained within both the roughness sublayer (i.e. the region above the roughness but within which the flow is spatially inhomogeneous) and the canopy region (i.e. below the height of the roughness elements) and discussion includes consideration of the turbulence kinetic energy balance at various heights.     

Boundary-Layer Entrainment Estimation Through Assimilation of Radiosonde and Micrometeorological Data into a Mixed-Layer Model

In this study we estimate boundary-layer growth and entrainment bycombining radiosonde and micrometeorological observations with asimple coupled boundary-layer and land surface model. A variational(smoothing) approach is used to find the optimal estimate ofentrainment over the daytime window. This method is appealingbecause it accounts for the uncertainty in the various data streams,while enforcing the dynamics of the model (i.e., water and energybudgets in the boundary layer, mixed-layer growth, etc.). Thetraditional variational framework was modified in this study toinclude an ensemble approach, which not only yields a (mean) estimateof entrainment, but a measure of its uncertainty as well. Themethodology is applied to a field experiment site in Kansas. Resultsfrom this study indicate a much larger ratio of entrainment to surfacefluxes compared to early literature values from other sites. However,our results are consistent with recent estimates at the site usingindependent estimation methods. In tests where radiosonde data werewithheld, reasonable skill in entrainment estimation was still shown,suggesting the potential for more widespread applications where onlymicrometeorological data are available. Finally, the data assimilationframework presented here has not traditionally been used inatmospheric boundary-layer studies, and may provide a useful approachfor studying other aspects of the boundary layer in the future.