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.     

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。     

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.     

An Investigation into Ridge-Top Turbulence Characteristics During Neutral and Weakly Stable Conditions: Velocity Spectra and Isotropy

An investigation into high Reynolds number turbulent flow over a ridge top in New Zealand is described based on high-resolution in-situ measurements, using ultrasonic anemometers for two separate locations on the same ridge with differing upwind terrain complexity. Twelve 5-h periods during neutrally stratified and weakly stable atmospheric conditions with strong wind speeds were sampled at 20 Hz. Large (and small) turbulent length scales were recorded for both vertical and longitudinal velocity components in the range of 7–23 m (0.7–3.3 m) for the vertical direction and 628–1111 m (10.5–14.5 m) for the longitudinal direction. Large-scale eddy sizes scaled to the WRF (Weather Research and Forecasting) numerical model simulated boundary-layer thickness for both sites, while small-scale turbulent features were a function of the complexity of the upwind terrain. Evidence of a multi-scale turbulent structure was obtained at the more complex terrain site, while an assessment of the three-dimensional isotropy assumption in the inertial subrange of the spectrum showed anisotropic turbulence at the less complex site and evidence of isotropic turbulence at the more complex site, with a spectral ratio convergence deviating from the 4/3 or unity values suggested by previous theory and practice. Existing neutral spectral models can represent locations along the ridge top with simple upwind complexity, especially for the vertical wind spectra, but sites with more orographic complexity and strong vertical wind speeds are often poorly represented using these models. Measured spectra for the two sites exhibited no significant diurnal variation and very similar large-scale and small-scale turbulent length scales for each site, but the turbulence energy measured by the variances revealed a strong diurnal difference.     

Dynamics of the planetary boundary layer with fine structure in the large scale background field

Summary On the basis of Wu and Blumen's work (1982) on the geostrophic momentum approximation (GMA) in the planetary boundary layer (PBL) and Tan and Wu (1992, 1994) on the Ekman momentum approximation (EMA) in the PBL, some improvements about the eddy exchange coefficientK, the advective inertial force and the lower boundary condition of the PBL are developed in this paper: (1) apply theK which is a gradually varying function of height instead of a constant value in the Ekamn layer, and introduce a surface layer; (2) take the effect of the vertical advective inertial force into account; (3) the solution technique is extended from level terrain to orographically formed terrain. Under the condition of the equilibrium among four forces (the pressure — gradient force, Coriolis force, eddy viscous force and inertial force including horizontal and vertical advective inertial forces), we have obtained the analytical solutions of the distributions of the wind and the vertical velocity. The computation of an individual example shows that: (1) both the wind velocity near surface and the angle between which and the non-viscous wind are more consistent with usual observations than that of Wu and Blumen (1982); (2) comparing with the horizontal advective inertial force, the vertical advective inertial force can not be neglected, when the orography is considered, the effect of the latter is even more important than the former.With 3 Figures     

The Baroclinic, Variable Eddy Viscosity Ekman Layer

The WKB method is used in conjunction with the variation of parameters technique to find an approximate analytical solution for Ekman layers with eddy viscosity and horizontal pressure gradient that are each variable with height from the surface. Behaviour of the solution is illustrated by comparing model output when several eddy viscosity and horizontal pressure gradient profiles are used. Cases where the pressure gradient decreases with height accentuate the super-geostrophic peak in the wind velocity profile, with decreasing eddy viscosity with height further enhancing this effect. Increasing pressure gradient with height reduces or eliminates the peak. The model output when using an eddy viscosity that has a low-level peak fits marine boundary-layer data taken during ASTEX better than the classic solution - the model giving greater low-level mixing which is seen in ASTEX data as well as in data from ERICA.     

An analytical study of diurnal wind-structure variations in the boundary layer and the low-level nocturnal jet

An analytical framework is proposed for studying variations in the diurnal wind structure in the planetary boundary layer (PBL) and the evolution of the low-level nocturnal jet. A time-dependent eddy-diffusivity coefficient corresponding to solar input is proposed, and an appropriate coordinate transformation ensures that mixing height varies continuously with ground heat-flux changes. The solution exhibits the receding character of the daytime PBL as evening approaches, thereby dividing the PBL into two regimes — the one just above the ground, representing the nocturnal boundary layer, and the region above it. It is assumed that inertial oscillations (IO) are triggered in the upper layer at about the time of sunset when the reversal in the direction of ground heat flux is felt in the upper layer. Two approaches are adopted to determine the characteristic features of IO and the evolution of the nocturnal low-level jet. The first one is based on the physical principle that release of horizontal momentum due to deviation from the geostrophic wind gives rise to the IO. The solution captures all the characteristic features of the IO, such as phase shift and decreasing amplitude of the IO with increasing height. According to this analysis the IO is triggered at a level as soon as the top of the receding boundary layer leaves that level. The solution is discontinuous with respect to the vertical coordinate. In the second approach we solve an initial-value problem to determine the solution in the upper layer, assuming that at about the time of sunset there is a rapid collapse of the daytime PBL to the steady, nocturnal boundary layer. The assumption is based on the mixing-height profiles prepared from climatological data collected at Delhi. The solution for the nocturnal boundary-layer regime is then obtained as a boundary-value problem. The solutions so obtained are continuous throughout the domain of interest and exhibit the characteristic features of an IO. The analysis leads to the conditions under which a low-level nocturnal jet is produced and provides quantitative estimates of the parameters, such as length of night, latitude, mixing height at sunset and nocturnal mixing height, that are conducive to the generation of a jet. The nocturnal wind profile produced by this approach compares well both with typical atmospheric data observed at Delhi and with output from a mesoscale numerical model. There is still some uncertainty related to the time of initiation of the IO as a function of latitude.     

Evaluation of MM5 mesoscale model at local scale for air quality applications over the Swedish west coast: Influence of PBL and LSM parameterizations

Summary The performance of MM5 mesoscale model (Version 3.6.3) using different planetary boundary layer (PBL) and land surface model (LSM) parameterizations is evaluated and compared using high temporal and spatial resolution G?TE2001 campaign data at local scale (a few kilometers) over the Greater G?teborg area along the Swedish west coast during 7–20 May 2001. The focus is on impact of PBL and LSM parameterizations on simulated meteorological variables important for air quality applications such as global radiation, diurnal cycle of near-surface air temperature and wind, diurnal cycle intensity, near-surface vertical temperature gradient, nocturnal temperature inversion, boundary layer height, and low-level jet (LLJ). The model performance for daytime and nighttime and under different weather conditions is also discussed. The purpose is to examine the performance of the model using different PBL and LSM parameterizations at local scale in this area for its potential applications in air quality modeling. The results indicate that the influence of PBL and LSM parameterizations on simulated global radiation, diurnal cycle of near-surface air temperature and wind speed, diurnal cycle intensity, vertical temperature gradient, nocturnal temperature inversion and PBL heights, which are critical parameters for air quality applications, is evident. Moreover, the intensity and location of LLJ are simulated well by all schemes, but there also exist some differences between simulated results by using different PBL and LSM schemes. Therefore, the choice of PBL and LSM parameterizations is important for MM5 applications to air quality studies. Correspondence: Junfeng Miao, Department of Earth Sciences, G?teborg University, P.O. Box 460, 405 30 G?teborg, Sweden     

Some aspects of modelling low-level jets

An improved non-stationary two-layer model is presented for the simulation of wind speed maxima in the nocturnal boundary layer. The model is based on the idea of Blackadar (1957), who proposed as forcing mechanism an inertial oscillation of the ageostrophic component of the wind vector in the levels above the top of the nocturnal radiation inversion. First, the time-dependent variation of the nocturnal boundary-layer height is studied by means of prognostic equations; there is a good agreement between observed and calculated height data for three days of the Wangara experiment. Furthermore, a diurnal variation of the drag coefficient is considered in the lower layer by decreasing the coefficient by a factor of 10–20 due to stabilization of this layer during the night. The marked temporal decrease (increase) of the drag coefficient in the first hours after sunset (sunrise) is described by a function . The incorporation of these two effects into the model gives results which are in good agreement with observed wind data for Wangara days 13/14, 30/31, and 33/34.     

Planetary boundary layer of equatorial waves and critical latitude

The boundary-layer solutions for oscillatory interior flow in a neutral fluid show that, away from the critical latitude, the planetary boundary-layer flow is composed of two vertically propagating waves; one is of shorter vertical wavelength and attenuates faster with height while the other is of longer wavelength and attenuates slowly with height. At the critical latitude, the longer wave is of the nature of an inertial oscillation and penetrates the entire depth of the fluid and gives rise to a rather stronger (but finite) vertical motion than in the surroundings at great height, but below 2 km this difference is not very great. In general, the vertical velocity of the boundary-layer flow depends on both the vorticity and the divergence of the interior flow, and the influence of the former is to intensify while that of the latter is to diminish the existing vertical motion. The influence of the stable stratification above a mixed, neutral surface layer on the boundary-layer flow of the equatorial waves is analyzed in detail. It is shown that the boundary-layer flow is greatly impeded by the stable layer and the horizontal velocities of the boundary-layer flows are made to change their directions in the upper part of the mixed layer and above, so that the vertical velocity is greatly reduced. The effect of the critical latitude is almost absent in the antisymmetric Rossby waves under stable stratification.     

Comments on: ‘The Neutral, Barotropic Planetary Boundary Layer, Capped by a Low-Level Inversion’ by G. D. Hess, Boundary-Layer Meteorology (2004) 110, pp. 319–355

Precision measurements indicate that the stability capping of the neutral planetary boundary layer (PBL) that leads to a reduced PBL height is caused by the very stable upper part of the PBL, rather than by an overlying inversion. Radiative processes related to liquid water in boundary-layer clouds seem to play the key role for the formation of the stable upper PBL. The famous Leipzig Profile – generally considered as an example of a neutral PBL – has been included in Hess’s analysis because its PBL height is considerably lower than the ca. 3000 m to be expected by numerical models in truly neutral conditions. An analysis of the original observations reveals that the Leipzig PBL was stable and that it can be consistently treated as a ‘normal’ stable PBL with a height of ca. 700 m. A further finding is that the super-geostrophic PBL wind speed maxima predicted by almost all models are not observed in near-steady-state conditions. For the ‘ranking’ of analytical models versus numerical models, the comparisons with measurements show that the analytical models perform comparably well and even partially better than the numerical models.     

Evaluation of the Weather Research and Forecast/Urban Model Over Greater Paris

Meteorological modelling in the planetary boundary layer (PBL) over Greater Paris is performed using the Weather Research and Forecast (WRF) numerical model. The simulated meteorological fields are evaluated by comparison with mean diurnal observational data or mean vertical profiles of temperature, wind speed, humidity and boundary-layer height from 6 to 27 May 2005. Different PBL schemes, which parametrize the atmospheric turbulence in the PBL using different turbulence closure schemes, may be used in the WRF model. The sensitivity of the results to four PBL schemes (two non-local closure schemes and two local closure schemes) is estimated. Uncertainties in the PBL schemes are compared to the influence of the urban canopy model (UCM) and the updated Coordination of Information on the Environment (CORINE) land-use data. Using the UCM and the CORINE land-use data produces more realistic modelled meteorological fields. The wind speed, which is overestimated in the simulations without the UCM, is improved below 1,000 m height. Furthermore, the modelled PBL heights during nighttime are strongly modified, with an increase that may be as high as 200 %. At night, the impact of changing the PBL scheme is lower than the impact of using the UCM and the CORINE land-use data.     

The impact of the PBL scheme and the vertical distribution of model layers on simulations of Alpine foehn

Summary This paper investigates the influence of the planetary boundary-layer (PBL) parameterization and the vertical distribution of model layers on simulations of an Alpine foehn case that was observed during the Mesoscale Alpine Programme (MAP) in autumn 1999. The study is based on the PSU/NCAR MM5 modelling system and combines five different PBL schemes with three model layer settings, which mainly differ in the height above ground of the lowest model level (z ₁). Specifically, z ₁ takes values of about 7 m, 22 m and 36 m, and the experiments with z ₁ = 7 m are set up such that the second model level is located at z = 36 m. To assess if the different model setups have a systematic impact on the model performance, the simulation results are compared against wind lidar, radiosonde and surface measurements gathered along the Austrian Wipp Valley. Moreover, the dependence of the simulated wind and temperature fields at a given height (36 m above ground) on z ₁ is examined for several different regions. Our validation results show that at least over the Wipp Valley, the dependence of the model skill on z ₁ tends to be larger and more systematic than the impact of the PBL scheme. The agreement of the simulated wind field with observations tends to benefit from moving the lowest model layer closer to the ground, which appears to be related to the dependence of lee-side flow separation on z ₁. However, the simulated 2 m-temperatures are closest to observations for the intermediate z ₁ of 22 m. This is mainly related to the fact that the simulated low-level temperatures decrease systematically with decreasing z ₁ for all PBL schemes, turning a positive bias at z ₁ = 36 m into a negative bias at z ₁ = 7 m. The systematic z ₁-dependence is also observed for the temperatures at a fixed height of 36 m, indicating a deficiency in the self-consistency of the model results that is not related to a specific PBL formulation. Possible reasons for this deficiency are discussed in the paper. On the other hand, a systematic z ₁-dependence of the 36-m wind speed is encountered only for one out of the five PBL schemes. This turns out to be related to an unrealistic profile of the vertical mixing coefficient. Correspondence: Günther Z?ngl, Meteorologisches Institut der Universitat München, 80333 München, Germany     

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.     

Height dependence of diurnal variations of wind velocity and water temperature near the air-sea interface of the tropical Atlantic

From measurements during the Atlantic Trade Wind Experiment (ATEX) 1969, amplitudes and phases of the diurnal harmonic water-temperature variation between the sea surface and 50-m depth and of the semi-diurnal wind variation between 1 and 8 m were obtained. If the vertical diffusion of heat in the ocean is thought to be constant, a coefficient of K= 320 cm² s^–1 in the equation of diffusion fits best the observed data in the mixed layer. However, the measurements point to a decrease of K with depth.The height variation of the semi-diurnal zonal wind wave is caused by the influence of eddy viscosity. Our data are well fitted by results of the equation of diffusion, using the assumption of Lettau (1974) that the transfer coefficient of vertical transport of momentum is not only a function of height but also depends on time because of the semi-diurnal variation of surface stress.     

北京地区夏季边界层结构日变化的高分辨模拟对比

使用WRF中尺度数值模式, 分别选用两种不同的边界层参数化方案 (MYJ, YSU) 和3种陆面参数化方案 (SLAB, Noah, RUC), 对2004年7月1日08:00—7月4日20:00 (北京时) 北京地区夏季边界层结构进行1 km的高分辨模拟。对比分析了近地面层风场、温度场以及边界层的日变化特征, 结果发现:WRF模式基本模拟出了北京夏季边界层的日变化特征; 在边界层方案中, MYJ方案描述的边界层结构较YSU方案合理; Noah陆面模式较好地反映了城市的热岛效应; 无降水时, 风速及边界层高度对于陆面过程不敏感, 而降水发生后, 陆面过程对于边界层结构的影响增大; 各方案模拟的城区风速明显偏大, 这是因为没有充分考虑城市建筑物的阻力作用。     

Vertical Variation of Madden-Jullian Oscillations in the Normal Monsoon Season as Revealed Through MST Radar Wind Data

Summary  Mesosphere-Stratosphere-Troposphere (MST) Radar wind data for the period June through September 1996 have been examined to study vertical variation of Madden-Jullian Oscillations in wind and eddy kinetic energy (eke) in the normal monsoon season. The domain of analysis in the vertical is from 6 to 20 km with a height resolution of 150 m. Fast-Fourier-Transformation (FFT) has been applied to zonal (u), meridional(v) components of wind to extract the Madden-Jullian oscillations and eke. There are three dominant modes viz., 50–70, 30–40 and 10–20 day periodicity, which contain considerable fraction of energy and show high degree of vertical variability. The peak amplitude of 50–70 day mode in u, 30–40 mode in v and eke were observed at 16–17 km just below the tropopause level. The peak amplitudes of 30–40 day mode in u and 50–70 day mode in v were found in the height region of 13–16 km. To understand the origin and propagation of these waves, wave energy is calculated. The wave energy is higher at tropospheric heights than at lower stratospheric heights indicating that the origin of these waves is in the troposphere, and a part of the energy leaks into the stratosphere. Received September 17, 1998/Revised September 26, 1999     

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。     

Applicability of Temperature Discrete Equation to NMRF Boundary Layer Scheme in GRAPES Model

By deriving the discrete equation of the parameterized equation for the New Medium-Range Forecast(NMRF) boundary layer scheme in the GRAPES model, the adjusted discrete equation for temperature is obviously different from the original equation under the background of hydrostatic equilibrium and adiabatic hypothesis. In the present research, three discrete equations for temperature in the NMRF boundary layer scheme are applied, namely the original(hereafter NMRF), the adjustment(hereafter NMRF-go...