An efficient PBL model for global circulation models-design and validation

An efficient, pianetary boundary layer (PBL) model is developed and validated with empirical data for applications in general circulation models (GCMs). The purpose of this PBL model is to establish the turbulent surface fluxes as a function of the principal external PBL parameters in a numerically efficient way. It consists of a surface layer and a mixed layer matched together with the conditions of constant momentum and heat flux at the interface. An algebraic solution to the mean momentum equations describes the mixed-layer velocity profile and thus determines the surface wind vector. The velocity profile is globally valid by incorporating the effect of variable Coriolis force without becoming singular at the equator. Turbulent diffusion depends on atmospheric stability and is modeled in the surface layer by a drag law and with first-order closure in the mixed layer. Radiative cooling in the stably stratified PBL is considered in a simple manner. The coupled system is solved by an iterative method. In order to preserve the computational efficiency of the large-scale model, the PBL model is implemented into the GISS GCM by means of look-up tables with the bulk PBL Richardson number, PBL depth, neutral drag coefficient, and latitude as independent variables.A validation of the PBL model with observed data in the form of Rossby number similarity theory shows that the internal feedback mechanisms are represented correctly. The model, however, underpredicted the sensible heat-flux. A subsequent correction in the turbulence parameterization yields better agreement with the empirical data. The behavior of the principal internal PBL quantities is presented for a range of thermal stabilities and latitudes.     

Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift

Recent technological advances in current measuring devices has resulted in a large observational database related to wind-driven motions in the upper ocean mixed layer. This has served to highlight the fact that transient motions make up a substantial contribution of the resulting Ekman currents. At the same time, certain discrepancies have emerged between the observed angular deflections of the steady-state currents from the surface wind stress, both at the surface and at sub-surface depths, which cannot be reconciled using the classical Ekman model. This paper seeks to tackle these two issues.First a general analytical method is presented for solving the time dependent horizontal momentum Ekman equations. Analysis of the unsteady terms that arise from simple special cases shows how the evolution proceeds through three stages. At early times, the Coriolis acceleration is insignificant, and the current is unidirectional and deepens through downward diffusion of momentum. Later Coriolis acceleration deflects the current vectors in the upper layers, whilst downward diffusion of momentum continues to deepen the layer. Finally, once diffusion has penetrated down to the depth of the steady-state current, then the transients decay on the inertial or diffusive timescale, depending upon the boundary conditions of the particular problem.In the second half of the paper, a new steady-state model is developed that includes the effects of wind-generated waves, through the action of their Stokes drift on the planetary vorticity. Comparisons between observations and the theoretical predictions, demonstrate that inclusion of the Stokes drift is the key to reconciling the discrepancies in the angular deflections of the steady-state currents. This leads to the conclusion that Ekman layer currents are significantly influenced by the surface waves.     

Stable Boundary-Layer Scaling Regimes: The Sheba Data

Turbulent and mean meteorological data collected at five levels on a 20-m tower over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are analyzed to examine different regimes of the stable boundary layer (SBL). Eleven months of measurements during SHEBA cover a wide range of stability conditions, from the weakly unstable regime to very stable stratification. Scaling arguments and our analysis show that the SBL can be classified into four major regimes: (i) surface-layer scaling regime (weakly stable case), (ii) transition regime, (iii) turbulent Ekman layer, and (iv) intermittently turbulent Ekman layer (supercritical stable regime). These four regimes may be considered as the basic states of the traditional SBL. Sometimes these regimes, especially the last two, can be markedly perturbed by gravity waves, detached elevated turbulence (‘upside down SBL’), and inertial oscillations. Traditional Monin–Obukhov similarity theory works well in the weakly stable regime. In the transition regime, Businger–Dyer formulations work if scaling variables are re-defined in terms of local fluxes, although stability function estimates expressed in these terms include more scatter compared to the surface-layer scaling. As stability increases, the near-surface turbulence is affected by the turning effects of the Coriolis force (the turbulent Ekman layer). In this regime, the surface layer, where the turbulence is continuous, may be very shallow (< 5 m). Turbulent transfer near the critical Richardson number is characterized by small but still significant heat flux and negligible stress. The supercritical stable regime, where the Richardson number exceeds a critical value, is associated with collapsed turbulence and the strong influence of the earth’s rotation even near the surface. In the limit of very strong stability, the stress is no longer a primary scaling parameter.     

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.     

The Ekman momentum approximation and its application

In the boundary layer, the flow is basically an equilibrium of three forces: Coriolis, pressure gradient and frictional. This means that it is an Ekman flow while the basic flow in the free atmosphere is an equilibrium of two forces: Coriolis and pressure gradient, and is a geostrophic flow. Therefore, it is natural to try to modify the geostrophic momentum approximation in the free atmosphere to become an Ekman momentum approximation in the boundary layer. The physical explanation and foundation of the Ekman momentum approximation are discussed.     

日间对流边界层中的非局地动量混合

日间对流边界层最显著的结构特征是在热力作用下所形成的组织化对流。与小尺度湍涡不同的是，组织化对流具有边界层尺度的垂直相干性，可实现垂直贯穿边界层的非局地物质和能量传输。本文针对对流边界层中的动量混合，探究组织化对流对动量输送的贡献。以高精度大涡模拟数据为研究资料，通过傅里叶变换、本征正交分解和经验模态分解3种滤波方法，分离组织化对流和背景湍涡，计算与两者相关的非局地和局地动量通量，发现与组织化对流相关的非局地动量通量是总通量的重要组成部分，并主导混合层中的垂直动量输送。而后，基于协谱和相位谱分析，探究组织化对流的空间结构对动量传输的影响，发现在热力主导的不稳定环境中，单体型环流结构对动量的传输效率较低。而在风切较强的近中性环境中，滚涡型组织化结构可使垂直和水平流向扰动速度的相位差减小，从而提升动量传输效率。研究结果表明，边界层方案需要包含非局地动量通量项，其参数化应考虑整体稳定度对传输效率的影响。     

植物冠层动量交换特征的实验研究

使用湍流梯度测试资料，对植物冠层动量交换特征进行了详细研究，结果表明:森林冠层内惯性副区能谱曲线仍可用幂指数描述，但斜率比-2/3更负；森林冠层内湍流尺度有变小的趋势；森林上层的耗散系数比下层大；由植被吸收引起动量及动量通量随冠层深度增加而明显减小；冠层下层的动量通量和耗散系数分别与上层的量有好的正相关；森林冠层内耗散系数和动量通量随大气稳定度有明显变化。     

强风天气下边界层结构特征

近地层观测的强风运动表明,叠加在平均流动之上的脉动通常有两种,一种是随机的湍流脉动,还有一种具有相干结构的阵风扰动。分析表明,上层强风的剪切运动产生阵风,并向下传递能量,对近地层的通量传输起到重要作用。本文利用北京325 m气象塔、位于海拔1257 m的妙峰山测风塔和位于海拔1688 m的灵山测风塔的资料,分析了强风天气下,边界层上层出现阵风并向下传递的过程,进一步证实无论在近地层还是边界层上层,强风期间,叠加在平均流动上除了高频湍流脉动之外,还有周期为1~10分钟的阵风,即相干结构。阵风峰期有下沉运动,阵风谷期有上升运动。这些相干结构在边界层上层产生,向下运动和传播过程中受到平均气流梯度的切变作用和地面摩擦,破碎为湍流结构。边界层上层的阵风和湍流产生的动量通量向下传递,使得强风期间,边界层中阵风和湍流对通量具有同样的输送能力,对边界层中沙尘、污染物等气溶胶的传输具有重要作用。本研究为模式中进行通量输送参数化方案的修正提供了观测和理论依据。     

A multi-limit formulation for the equilibrium depth of a stably stratified boundary layer

Currently no expression for the equilibrium depth of the turbulent stably-stratified boundary layer is available that accounts for the combined effects of rotation, surface buoyancy flux and static stability in the free flow. Various expressions proposed to date are reviewed in the light of what is meant by the stable boundary layer. Two major definitions are thoroughly discussed. The first emphasises turbulence and specifies the boundary layer as a continuously and vigorously turbulent layer adjacent to the surface. The second specifies the boundary layer in terms of the mean velocity profile, e.g. by the proximity of the actual velocity to the geostrophic velocity. It is shown that the expressions based on the second definition are relevant to the Ekman layer and portray the depth of the turbulence in the intermediate regimes, when the effects of static stability and rotation essentially interfere. Limiting asymptotic regimes dominated by either stratification or rotation are examined using the energy considerations. As a result, a simple equation for the depth of the equilibrium stable boundary layer is developed. It is valid throughout the range of stability conditions and remains in force in the limits of a perfectly neutral layer subjected to rotation and a rotation-free boundary layer dominated by surface buoyancy flux or stable density stratification at its outer edge. Dimensionless coefficients are estimated using data from observations and large-eddy simulations. Well-known and widely used formulae proposed earlier by Zilitinkevich and by Pollard, Rhines and Thompson are shown to be characteristic of the above interference regimes, when the effects of rotation and static stability (due to either surface buoyancy flux, or stratification at the outer edge of the boundary layer) are roughly equally important.     

Impact of Eddy Characteristics on Turbulent Heat and Momentum Fluxes in the Urban Roughness Sublayer

Eddy-covariance observations above the densely built-up Centre of Nanjing were made from December 2011 to August 2012. Separate eddy-covariance systems installed at two levels on a 36-m tower located on a rooftop were operated simultaneously, and observations grouped into two sectors (A, B) according to the prevalent wind directions. For sector A, where the nearby buildings are all below the lower measurement level, the sensible heat and momentum fluxes are generally greater at the upper level. For sector B, where several high-rise buildings are located upwind, the sensible heat and momentum fluxes at the upper level are close to those at the lower level. The analysis shows that the turbulent eddy characteristics differ between the two wind sectors, leading to a different behaviour of turbulent exchange between the two levels. A hypothesis is proposed that addresses the vertical variation of turbulent fluxes in the urban roughness sublayer (RSL). For sector A, the buildings block the flow, change the trajectory of scalars, and distort the footprint of scalar fluxes; this ‘blocking effect’ is believed to lead to a smaller sensible heat flux above the canopy layer. Such an effect should decrease with height in the RSL, explaining the increase of the observed turbulent heat flux with height. In addition, the presence of non-uniform building heights adversely affects turbulence organization around the canopy top, and likely elevates the inflection point of the mean flow to a higher elevation close to the upper measurement level, where larger shear results in a larger momentum flux. For sector B, wake effects from the nearby high-rise buildings strongly reduce turbulence organization at higher elevations, leading to similar sensible heat and momentum fluxes at both measurement levels.     

Inertia and diurnal oscillations of Ekman layers in atmosphere and ocean

A 1D model, including a time variation of eddy viscosity and mixed layer depth, is applied to study Ekman spirals. It simulates a weak velocity in the atmosphere but a jet in the upper oceanic mixed layer during daytime; and a strong velocity in the atmosphere but a weak, uniform velocity in the ocean at night. The mean spirals in both atmosphere and ocean are close to the average spirals at midday and midnight, they are not flat as suggested by previous studies but consistent with the observations of Polton et al (2013). Our results also show shorter length scale for magnitude decay than for rotation of mean velocity as observed in the ocean, which comes from the combined effects of the diurnal variation of PBL and the Coriolis force. The latter becomes more important away from the surface. In the upper oceanic mixed layer, the mean velocity mainly comes from the strong jets in the late afternoon and early evening. Near and below the depth of Ekman depth, the weak velocities change with time and cancel out each other if averaged timing is longer than the inertia period. It results in diminishing of magnitude of the mean velocity, but the amplitude of individual parcel oscillating can still be quite large near the Ekman depth. Meanwhile, the change of velocity angle from the surface is near or less than 90 degree. Hence, shorter length scale for magnitude decay than for rotation of the mean velocity is not controlled by viscosity alone. Meanwhile, the model does not need two viscosities as suggested previously.The results also show that either the diurnal variation of surface stress or eddy viscosity alone can create a diurnal oscillation of velocity in the ocean. The interactions between PBL force and the Coriolis force can create a weak instability in the atmosphere and ocean at 30° and 90°. This weak instability may explain the observed nocturnal LLJ near 30 °N on the lee of the Rocky Mountains and the intensification of mesoscale circulation simulated by Sun and Wu (1992).     

Impact of cyclone Nilam on tropical lower atmospheric dynamics

A deep depression formed over the Bay of Bengal on 28 October 2012, and developed into a cyclonic storm. After landfall near the south coast of Chennai, cyclone Nilam moved north-northwestwards. Coordinated experiments were conducted from the Indian stations of Gadanki(13.5?N, 79.2?E) and Hyderabad(17.4?N, 78.5?E) to study the modification of gravity-wave activity and turbulence by cyclone Nilam, using GPS radiosonde and mesosphere–stratosphere–troposphere radar data. The horizontal velocities underwent large changes during the closest approach of the storm to the experimental sites. Hodograph analysis revealed that inertia gravity waves(IGWs) associated with the cyclone changed their directions from northeast(control time) to northwest following the path of the cyclone. The momentum flux of IGWs and short-period gravity waves(1–8 h) enhanced prior to, and during, the passage of the storm(±0.05 m2s-2and ±0.3 m2s-2, respectively), compared to the flux after its passage. The corresponding body forces underwent similar changes, with values ranging between ±2–4m s-1d-1and ±12–15 m s-1d-1. The turbulence refractivity structure constant(C2n) showed large values below 10 km before the passage of the cyclone when humidity in the region was very high. Turbulence and humidity reduced during the passage of the storm when a turbulent layer at ～17 km became more intense. Turbulence in the lower troposphere and near the tropopause became weak after the passage of the cyclone.     

Long-term study of coherent structures in the atmospheric surface layer

A long-term study of coherent turbulence structures in the atmospheric surface layer has been carried out using 10 months of turbulence data taken on a 30-m tower under varying meteorological conditions. We use an objective detection technique based on wavelet transforms. The applied technique permits the isolation of the coherent structures from small-scale background fluctuations which is necessary for the development of dynamical models describing the evolution and properties of these phenomena. It was observed that coherent structures occupied 36% of the total time with mean turbulent flux contributions of 44% for momentum and 48% for heat. The calculation of a transport efficiency parameter indicates that coherent structures transport heat more efficiently than momentum. Furthermore, the transport efficiency increases with increasing contribution of the structures to the overall transport.     

Role of horizontal density advection in seasonal deepening of the mixed layer in the subtropical Southeast Pacific

The mechanisms behind the seasonal deepening of the mixed layer(ML) in the subtropical Southeast Pacific were investigated using the monthly Argo data from 2004 to 2012. The region with a deep ML(more than 175 m) was found in the region of(22?–30?S, 105?–90?W), reaching its maximum depth(～200 m) near(27?–28?S, 100?W) in September. The relative importance of horizontal density advection in determining the maximum ML location is discussed qualitatively. Downward Ekman pumping is key to determining the eastern boundary of the deep ML region. In addition, zonal density advection by the subtropical countercurrent(STCC) in the subtropical Southwest Pacific determines its western boundary, by carrying lighter water to strengthen the stratification and form a "shallow tongue" of ML depth to block the westward extension of the deep ML in the STCC region. The temperature advection by the STCC is the main source for large heat loss from the subtropical Southwest Pacific. Finally, the combined effect of net surface heat flux and meridional density advection by the subtropical gyre determines the northern and southern boundaries of the deep ML region: the ocean heat loss at the surface gradually increases from 22?S to 35?S, while the meridional density advection by the subtropical gyre strengthens the stratification south of the maximum ML depth and weakens the stratification to the north. The freshwater flux contribution to deepening the ML during austral winter is limited. The results are useful for understanding the role of ocean dynamics in the ML formation in the subtropical Southeast Pacific.     

Boundary-layer structure near the cold front of a marine cyclone during “ERICA”

The boundary layer in the warm sector of a moderately deepening winter cyclone during the Experiment on Rapidly Intensifying Cyclones over the Atlantic (ERICA) is studied near the cold front. Data from the National Center for Atmospheric Research Electra research aircraft are used to examine mean and turbulence quantities. The aircraft data and supplemental data from ships, drifting buoys and moored buoys reveal an equivalent-barotropic pressure field. The area is found to be dominated by gradients in temperature and in turbulent fluxes, with changes occurring over 100 km horizontally being comparable to changes over 350 m vertically. The horizontal components of the gradients are found to be a maximum in a direction perpendicular to the front. Cross-sections perpendicular to the front are used to illustrate boundary-layer structure. Profiles of wind speed, stress, wind direction and stress direction are estimated from an Ekman model that is modified to take into account the equivalent-barotropic pressure field. Comparison of profiles from the model to the aircraft-measured data show reasonable agreement far from the front (100 km) when the model uses a constant eddy viscosity of approximately 6 kg m^–1 s^–1. Near the front there is less agreement with the model. Profiles of turbulent fluxes of momentum, heat and latent heat are divergent, with along-wind momentum flux negative and decreasing upward, cross-wind momentum flux positive and increasing upward, and heat flux and latent heat flux small, positive and decreasing upward. Far from the front, the turbulent kinetic energy budget shows that dissipation balances shear production. However, near-front behavior has an imbalance at low altitude, with shear production appearing as a TKE sink.     

Some Characteristics of the Surface Boundary Layer of a Strong Cold Air Process over Southern China

In southern China,cold air is a common weather process during the winter season;it can cause strong wind,sharp temperature decreases,and even the snow or freezing rain events.However,the features of the atmospheric boundary layer during cold air passage are not clearly understood due to the lack of comprehensive observation data,especially regarding turbulence.In this study,four-layer gradient meteorological observation data and one-layer,10-Hz ultrasonic anemometer-thermometer monitoring data from the northern side of Poyang Lake were employed to study the main features of the surface boundary layer during a strong cold-air passage over southern China.The results show that,with the passage of a cold air front,the wind speed exhibits low-frequency variations and that the wind systematically descends.During the strong wind period,the wind speed increases with height in the surface layer.Regular gust packets are superimposed on the basic strong wind flow.Before the passage of cold air,the wind gusts exhibit a coherent structure.The wind and turbulent momentum fluxes are small,although the gusty wind momentum flux is slightly larger than the turbulent momentum flux.However,during the invasion of cold air,both the gusty wind and turbulent momentum fluxes increase rapidly with wind speed,and the turbulent momentum flux is larger than the gusty wind momentum flux during the strong wind period.After the cold air invasion,this structure almost disappears.     

南海台风边界层湍流小波分析

利用小波变换（WT）对香港天文台飞机观测台风“妮妲”（1604）资料进行分析,研究在不稳定、不均匀的台风边界层中湍流涡旋的垂直传输作用。在0.1~5 Hz惯性子区内横风和顺风分量功率谱密度能较好符合-5/3幂律。小波分析显示:横风的小波功率谱峰值集中在1 km之下,顺风分量的小波功率谱峰值集中在1~6 km之间;眼区动量通量的主要贡献尺度为2.3 km,眼区外主要贡献尺度在1~2 km,中低层为较小尺度（< 1.0 km）;湍流功能(TKE)的生成尺度主要集中在4 km之下。这项研究定量描述了南海北部台风边界层各个区域湍流结构的差异特征,讨论了对台风边界层通量参数化的可能影响。      

Experiment on Dust Flux During Duststorm Periods over Desert Area

The present study investigates the characteristics of turbulent transfer and the conditions for dust emission and transport using the dust concentration and micrometeorological data obtained during dust events occurring in the spring of 2004 over the Hunshandake desert area. The turbulent exchange coefficients and turbulent fluxes of momentum and heat are calculated. The relationships between dust flux, friction velocity, and wind speed are also explored. The results show that thermal turbulence is dominant during daytime of non-dusty days. The dynamic turbulence increases obviously and the sensible heat flux reduces by different degrees during dust events. There is an efficient downward transfer of momentum before duststorm occurrence, and both the dynamic turbulence and the thermal turbulence are important in the surface layer. The dynamic turbulence even exceeds the thermal turbulence during severe duststorm events. The values of dust flux vary in the range of -5 5, -30 30, and -200-300 μg m^-2 s^-1 during non-dusty days, blowing dust, and duststorm events, respectively. A slight upward transport of dust is observed during non-dusty days. The dust flux gradually varies from positive to negative during duststorm periods, which indicates the time evolution of dust events from dust rising to stably suspending and then deposition. The dust flux is found to be proportional to u＊^3. The threshold values of wind speed and friction velocity are about 6 and 0.4 m s^-1, respectively.     

Role of Convective Structures and Background Turbulence in the Dry Convective Boundary Layer

We quantify the role of the convective buoyant structures and the remainder turbulence, here called background turbulence, in the convective atmospheric boundary layer in horizontally homogeneous, dry and barotropic conditions. Three filtering methods to separate the structures and the background turbulence are first evaluated. These are: short-time averaging, Fourier filtering and proper orthogonal decomposition. The Fourier method turns out to be the most appropriate for the present purpose. The decomposition is applied to two cases: one with no mean flow and another with moderate mean wind speed. It is shown that roughly 85 % of the vertical flux of the potential temperature and about 72 % of the kinetic energy is carried by the structures in the mixed layer in both cases. The corresponding percentage for the potential temperature variance is 81 % in the zero mean-wind case and 76 % in the moderate mean-wind case. The structures are responsible for as much as 94 % of the momentum flux in the mixed layer of the moderate mean-wind case. In the surface layer the background turbulence is generally more important than the structure contribution in both cases. The budget of the potential temperature flux is analyzed in detail and it is shown that its turbulent transport term is mostly built up by the structures but also the interaction between the structures and the background turbulence plays a significant role. The other important budget terms are shown to be dominated by the structures except for the pressure–temperature gradient covariance.     

The nocturnal boundary layer over Northern Germany: An observational study

The stable boundary layer which evolved over the lowland of Northern Germany during a clear night with moderate geostrophic winds is studied. Because of the lack of turbulence measurements, a vertical flux-profile of heat and momentum is derived from a mean wind and temperature profile using an integral method. The stability parameter h/L _* = 17 indicates that turbulence was sporadic during this particular night. This result is confirmed by the observed inertial oscillations, which occur not only in the residual layer but also in the boundary layer below.The case study shows that turbulent cooling overrules radiational cooling in the lower part of the surface inversion layer. Additionally, warm-air advection occurs. In the upper part, cold-air advection and radiational cooling dominate, while turbulent cooling is reduced. Subsidence warming can be neglected throughout the boundary layer during this particular night.