The numerical experiments on applicating geostrophic momentum approximation to the baroclinic and non-neutral PBL

In this paper, Wu and Blumen’s boundary layer geostrophic momentum approximation model (Wu and Blumen, 1982) is applied to baroclinic and non-neutral PBL, the motion equations for the PBL under the geostrophic momentum approximation are solved, in which the eddy transfer coefficient is a function of the distributions of the wind and temperature. The results are compared with those in barotropic and neutral conditions with the geostrophic momentum approximation. It is found that in the baroclinic condition, the wind distribution has both the characteristics of a steady, homogeneous and baroclinic PBL and those caused by the geostrophic momentum approximation. Those in non-neutral conditions show that they retain the intrinsic characteristics for the wind in non-neutral PBL, at the same time, the effects of the large-scale advection and local variation are also included. We can predict the wind in the non-neutral and baroclinic PBL by use of the geostrophic mo-mentum approximation when the temporal and spatial distributions of the geostrophic wind, as well as the po-tential temperatures and their variation rates at the upper and lower boundary of the PBL are given by large-scale model. Finally, the model is extended to the case over sea surface.     

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。     

地转动量近似下边界层中风场的调整

本文利用地转动量近似,并假设气压场为定常的圆形涡旋和初始风场不满足四力平衡(气压梯度力、科里奥利力、湍流粘性力和半地转惯性力)的条件下,求解了正压边界层中风场向气压场调整的初边值问题,得到了一些初步结论。本工作为利用四力平衡下的风速分布来诊断预报边界层风场提供了理论依据。     

Ekman动量近似下中间边界层模式中的风场结构

发展了一个准三维的、中等复杂的边界层动力学模式，该模式包含了EKman动量近似下的惯性加速度和Blackadar的非线性湍流粘性系数，它进一步改进了Tan和Wu(1993）提出的边界层理论模型。该模型在数值计算复杂性上与经典Ekman模式相类似，但由于包含了Ekman动量近似下的惯性项，使得该模式比传统Ekman模式更近于实际过程。中详细地比较了该模式与其他简化边界层模式在动力学上的差异，结果表明：在经典的Ekman模式中，由于忽略了流动的惯性项作用，导致在气旋性切变气流（反气旋性切变气流）中风速和边界层顶部的垂直速度的高估（低估），而在半地转边界层模式中，由于高估了流动惯性项的作用，结果与经典Ekman模式相反。同样，该模式可以应用于斜压边界层，对于Ekman动量下的斜压边界层风场同时具有经典斜压边界层和Ekman动量近似边界层的特征。     

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     

Analysis of aircraft measurements of momentum flux in the subcloud layer over the tropical atlantic ocean during gate

The momentum flux data obtained by the gust probe aboard the NOAA DC-6 aircraft during GATE are analyzed. Vertical profiles are obtained for Phases I and III and correlated with vertical wind velocity profiles using the geostrophic departure method. Reasonable agreement is obtained using the horizontal equations of motion with negligible advective acceleration. The vertical profiles of momentum flux and wind speed variance compare well with the numerical model results of Deardorff (1972) and Wyngaard et al. (1974). Vertical distributions of power spectra for vertical eddy motion and cospectra corresponding to the momentum flux components are obtained along with the height variation of the dominant length scales of vertical eddy motion and the dissipation rate of turbulence kinetic energy. When normalized by mixed-layer similarity, these results agree well with previous determinations in the boundary layer over tropical oceans and over land.     

An Analytical Study of the Diurnal Variations of Wind in a Semi-geostrophic Ekman Boundary Layer Model

A time-dependent semi-geostrophic Ekman boundary-layer model based on the geostrophic momentum approximation is used to study the diurnal wind variation in the planetary boundary layer (PBL) and the evolution of the low-level nocturnal jet (LLJ). The coefficient of eddy viscosity varies periodically with time, varies linearly with height in the surface layer and is constant above the surface layer. The influence of horizontal advection of momentum on the diurnal wind variation in the PBL, the development of inertial oscillations (IOs) and the formation of the LLJ are examined.In comparison with the Ekman solutions, the diurnal wind variation in semi-geostrophic Ekman boundary-layer dynamics has the following features: (1) the phase angle of the diurnal wind wave shifts with height, the rate of shifting is increased in anticyclonic regions and decreased in cyclonic regions, (2) the time of occurrence of the low-level maximum wind speed is later in anticyclonic regions and earlier in cyclonic regions, (3) the height of occurrence of the maximum wind speed is higher in the anticyclonic and lower in cyclonic regions, (4) the wind speed maximum and the amplitude of the diurnal wind variation are larger in anticyclonic and smaller in cyclonic regions, (5) the period of IOs is larger in anticyclonic regions and smaller in cyclonic regions, (6) anticyclonic vorticity is conducive to the generation of LLJ in the PBL. These features are interpreted by means of the physical properties of semi-geostrophic Ekman boundary-layer dynamics and inertial oscillation dynamics.     

The wind in the baroclinic boundary layer with three sublayers incorporating the weak non-linear effect

In considering the weak non-linear effect, and using the small parameter expansion method, the analyt-ical expressions of the wind distribution within PBL (planetary boundary layer) and the vertical velocity at the top of the PBL are obtained when the PBL is divided into three layers and different eddy transfer coefficients K are adopted for the three layers. The conditions of barotropy and neutrality for the PBL are extended to that of baroclinity and non-neutral stratification. An example of a steady circular vortex is used to display the characteristics of the horizontal wind within the PBL and the vertical velocity at the top of the PBL. Some new results have been obtained, indicating that the magnitude of the speed in the lower height calculated by the present model is larger than that by the model in which k is a constant within the whole boundary layer, for example, in the classical Ekman boundary layer model and the model by Wu (1984). The angle between the wind at the top of the PBL and the wind near the surface calculated by the present model is less than that calculated by the single K model. These results are in agreement with the observations.     

The wind field in the nonlinear multilayer planetary boundary layer

By use of the small parameter expansion method, the nonlinear planetary boundary layer (PBL) is studied in this paper. The PBL is divided into the surface layer and the Ekman layer, which is divided into several sublayers. In the surface-layer, the eddy coefficient K is taken as a linear function of height; in the Ekman layer, different constant K values are taken within different sublayers: these values are determined from O'Brien's formula (O'Brien, 1970) approximately. Under the upper and lower boundary conditions and the continuity conditions of the wind velocities and turbulent stresses at each boundary between sublayers, analytical expressions for wind velocity in all sublayers and the vertical velocity at the top of the PBL are obtained. A specific example of steady axisymmetrical circular high and low pressure areas is analysed, and some new conclusions are obtained. The results are in better agreement with reality than previous results. This example also shows that the vertical velocity at the top of the PBL caused by friction approaches zero near the center of a high or low pressure system for this model, but attains its maximum absolute values near the center of the high or low pressure area for Wu's (1984) model. This is due to the fact that in our model, the geostrophic wind speed near the center of this specific vortex approaches zero, which causes the wind shear and the friction effect to be very weak. Therefore the wind distribution in the PBL is very sensitive to the type of eddy coefficient.     

A numerical experiment of the PBL with geostrophic momentum approximation

In this paper, a numerical experiment of the motion in the PBL (planetary boundary layer) is perform-ed with geostrophic momentum approximation, in which a nonlinear eddy transfer coefficient is used. Some results are obtained for the boundary layer winds in cyclone-anticyclone and trough-ridge systems. This treat-ment improves W-B’s work. The effects of geostrophic wind tendency and the advection of the geostrophic wind on the winds in the PBL are also discussed.     

斜压大气中海面边界层摩擦偏角的动力学研究

本文在Ekman动量近似下，引入关于水面粗糙度的Charnock公式，求得了斜压大气中海面边界层的风速的解析表达式，进一步得到边界层摩擦偏角的公式，并获得了边界层摩擦偏角的有关结论。例如海面的摩擦偏角远小于陆地的摩擦偏角；低纬的摩擦偏角比高纬的要大：理论分析和个例计算均表明，垂直平流惯性力与水平平流惯性力对摩擦偏角分别起着减小和增大的相反作用，而且反气旋性涡度处与气旋性涡度处的摩擦偏角可相差达20多度。冷暖平流下的摩擦偏角相差很大，甚至可达七、八十度。这些结论对斜压大气中的海面边界层风场摩擦偏角的预后都具有指导性作用。     

Momentum flux in the subcloud layer of a microburst-producing thunderstorm determined from JAWS Dual-Doppler data

Dual-Doppler winds at 1647 MDT for the 14 July, 1982 convective storm collected during the Joint Airport Weather Studies (JAWS) project at Denver's Stapleton International Airport were objectively analyzed to produce a three-dimensional wind field. The domain of interest had dimensions of 10 × 10 × 8.5 km centered on the microburst. Vertical velocities were computed by integrating the anelastic continuity equation downward from the storm's top. A variational approach was then employed to adjust the derived three-dimensional wind field. Subsequently, fields of deviation perturbation pressure and virtual temperature were retrieved from a detailed wind field using the three momentum equations. These retrieved fields were subjected to internal consistency checks to determine the level of confidence before interpetation. The fields were then used to calculate the generation of the vertical transport of horizontal momentum in the subcloud layer of a microburst-producing storm during the quasi-steady mature stage. Results show that the microburst occurrence in the atmospheric boundary layer (ABL) enhances eddy transfer of momentum. Direct calculation of the vertical transport of u- and v-momentum reveals that momentum was being transferred downward from the mid-levels of the storm to the microburst. The dominant processes contributing to the generation/dissipation of horizontal momentum flux were the total buoyancy production, pressure effects, vertical mean wind shear and vertical transport of momentum. The above processes play an important role in maintaining the strength of the microburst outflow in the ABL during the quasi-steady mature stage of the microburst life cycle.     

Atmospheric Response to Mesoscale Ocean Eddies over the South China Sea

The South China Sea(SCS) is an eddy-active area. Composite analyses based on 438 mesoscale ocean eddies during 2000–2012 revealed the status of the atmospheric boundary layer is influenced remarkably by such eddies. The results showed cold-core cyclonic(warm-core anticyclonic) eddies tend to cool(warm) the overlying atmosphere and cause surface winds to decelerate(accelerate). More than 5% of the total variance of turbulent heat fluxes, surface wind speed and evaporation rate are induced by mesoscale eddies. Furthermore, mesoscale eddies locally affect the columnar water vapor, cloud liquid water, and rain rate. Dynamical analyses indicated that both variations of atmospheric boundary layer stability and sea level pressure are responsible for atmospheric anomalies over mesoscale eddies. To reveal further details about the mechanisms of atmospheric responses to mesoscale eddies, atmospheric manifestations over a pair of cold and warm eddies in the southwestern SCS were simulated. Eddy-induced heat flux anomalies lead to changes in atmospheric stability. Thus, anomalous turbulence kinetic energy and friction velocity arise over the eddy dipole, which reduce(enhance) the vertical momentum transport over the cold(warm) eddy, resulting in the decrease(increase) of sea surface wind. Diagnoses of the model's momentum balance suggested that wind speed anomalies directly over the eddy dipole are dominated by vertical mixing terms within the atmospheric boundary layer, while wind anomalies on the edges of eddies are produced by atmospheric pressure gradient forces and atmospheric horizontal advection terms.     

Velocity profiles,the resistance law and the dissipation rate of mean flow kinetic energy in a neutrally and stably stratified planetary boundary layer

The logarithmic + polynomial approximation is suggested for vertical profiles of velocity components in a planetary boundary layer (PBL) at neutral and stable stratification. The resistance law functions A and B are determined on the basis of this approximation, using integral relations derived from the momentum equations, the Monin-Obukhov asymptotic formula for the wind profile in a stably stratified near-surface layer and the known expressions for the PBL depth. This result gives a realistic and convenient method for calculating the surface friction velocity and direction and the total dissipation rate of mean flow kinetic energy in terms of geostrophic velocity, buoyancy flux at the surface, the roughness parameter and the Coriolis parameter. In the course of these derivations a review is given of current views on the main problems of the neutral and stable PBL.     

山地边界层中场变量的动力学研究

采用与实测较接近的二次函数来表达Ｅｋｍａｎ层中的湍流粘性系数Ｋ，在圆形气压场条件下，求得了山地上空边界层中的风速，进而求得散度、涡度和垂直速度等场变量随高度的分布。并作图分析了这些场变量的一些动力学特征。改进了以往在求解析解时，略去运动方程中湍流粘性力项中的关于高度的一阶导数项，以及取山坡面上风速为零作下边界条件等欠合理欠精确的做法。所求得的风速、散度、涡度和垂直速度均用简单的初等函数表示出来，有助于边界层参数化和深化对边界层动力学的认识。     

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

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

Large-Eddy Simulation of the Daytime Boundary Layer in an Idealized Valley Using the Weather Research and Forecasting Numerical Model

A three-dimensional numerical meteorological model is used to perform large-eddy simulations of the upslope flow circulation over a periodic ridge-valley terrain. The subgrid-scale quantities are modelled using a prognostic turbulence kinetic energy (TKE) scheme, with a grid that has a constant horizontal resolution of 50 m and is stretched along the vertical direction. To account for the grid anisotropy, a modified subgrid length scale is used. To allow for the response of the surface fluxes to the valley-flow circulation, the soil surface temperature is imposed and the surface heat and momentum fluxes are computed based on Monin–Obukhov similarity theory. The model is designed with a symmetrical geometry using periodic boundary conditions in both the x and y directions. Two cases are simulated to study the influence of along-valley geostrophic wind forcing with different intensities. The presence of the orography introduces numerous complexities both in the mean properties of the flow and in the turbulent features, even for the idealized symmetric geometry. Classical definitions for the height of the planetary boundary layer (PBL) are revisited and redefined to capture the complex structure of the boundary layer. Analysis of first- and second-moment statistics, along with TKE budget, highlights the different structure of the PBL at different regions of the domain.     

A HIGH RESOLUTION MODEL FOR CHEMICAL SPECIES EXCHANGE IN TROPOSPHERE

Based on the regional acid deposition model(RADM),a high resolution model for species exchange in thetroposphere(EM3)is designed.EM3 differs considerably in the following 5 aspects from RADM.First,the vertical gridlevels in the planetary boundary layer(PBL)are increased.Second,layered vertical eddy diffusivity patterns in thetroposphere(TL)are considered.Third,layered horizontal eddy diffusivity patterns within TL is used.Fourth,new drydeposition velocity pattern including the effect of plant canopy layer(CL)vertical structure is adopted.Fifth,advectivescheme of second-order moment conservation with less numerical diffusion is used.OSCAR 4 case is comparativelysimulated with both EM3 and RADM.The results show that 3-D distribution laws of chemical species in whole TL areforecasted by EM3 better than by RADM.Under the same conditions,all ratios of the central concentrations simulatedwith both models in lower PBL are more than 1.8,the maximum can be more than 3.     

The influence of the geostrophic wind advection approximation on a well-mixed layer

Numerical results indicate that advection of momentum in the boundary layer may significantly alter both the structure of the planetary boundary layer and its influence on the overlying free atmosphere. However, due to the nonlinearity of the inertial terms, it is always difficult to obtain the analytical solution of the boundary-layer model that retains the flow acceleration. In order to overcome this difficulty, the geostrophic momentum (hereafter GM) approximation has been introduced into boundary-layer models. By replacing the advected momentum with the geostrophic wind, the effect of the flow acceleration is partially considered and the original nonlinear partial differential equation set is converted to ordinary differential equations, the solutions of which can be obtained easily with standard techniques. However, the model employing GM fails to capture the features of the boundary layer when the spatio-temporal variation of the boundary-layer flow cannot be properly approximated by the geostrophic wind. In the present work, a modified boundary-layer model with the inertial acceleration in a different approximate form is proposed, in which the advecting wind instead of the advected momentum is approximated by the geostrophic wind (hereafter GAM).Comparing the horizontal velocity and boundary-layer pumping obtained from the classical Ekman theory, and the model incorporating (i) GM and (ii) GAM, it is found that the model with GAM describes most facets of the steady well-mixed layer beneath a north-westerly flow with embedded mesoscale perturbations that is considered in the present work. Inspection of the solution of the model with GAM shows that, within the limit of the validation of the model (i.e., the Rossby number R_O is not very large and the drag coefficient C_D is not too small), the horizontal convergence (divergence) is strengthened by the effect of the inertial acceleration in the region of maximum positive (negative) geostrophic vorticity. Consequently, the boundary-layer pumping there is intensified. It is found that the intensification is firstly strengthened and then weakened as R_O or C_D increases.     

一个诊断非平坦地形上边界层风的数值模式

根据半地转大气边界层模式，由大尺度数值模式并考虑了下垫面地形及粗糙度的水平非均匀性及大尺度气压场的时空变化，给出了一个诊断边界层风的数值模式。对低纬度运用塔层风模式进行诊断。诊断结果与实测资料比较，风向风速均达到了一定的精确度。