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).     

Parameterization for the depth of the entrainment zone above the convectively mixed layer

It has been noted that when the convective Richardson number Ri* is used to characterize the depth of the entrainment zone, various parameterization schemes can be obtained. This situation is often attributed to the invalidity of parcel theory. However, evidence shows that the convective Richardson number Ri^* might be an improper characteristic scaling parameter for the entrainment process. An attempt to use an innovative parameter to parameterize the entrainment-zone thickness has been made in this paper.Based on the examination of the data of water-tank experiments and atmospheric measurements, it is found that the total lapse rate of potential temperature across the entrainment zone is proportional to that of the capping inversion layer. Inserting this relationship into the so-called parcel theory, it thus gives a new parameterization scheme for the depth of the entrainment zone. This scheme includes the lapse rate of the capping inversion layer that plays an important role in the entrainment process. Its physical representation is reasonable. The new scheme gives a better ordering of the data measured in both watertank and atmosphere as compared with the traditional method using Ri^*. These indicate that the parcel theory can describe the entrainment process suitably and that the new parameter is better than Ri^*.     

Parameterization of sheared entrainment in a well-developed CBL. Part I: Evaluation of the scheme through large-eddy simulations

The entrainment flux ratio A _e and the inversion layer (IL) thickness are two key parameters in a mixed layer model. A _e is defined as the ratio of the entrainment heat flux at the mixed layer top to the surface heat flux. The IL is the layer between the mixed layer and the free atmosphere. In this study, a parameterization of A _e is derived from the TKE budget in the firstorder model for a well-developed CBL under the condition of linearly sheared geostrophic velocity with a zero value at the surface. It is also appropriate for a CBL under the condition of geostrophic velocity remaining constant with height. LESs are conducted under the above two conditions to determine the coefficients in the parameterization scheme. Results suggest that about 43% of the shear-produced TKE in the IL is available for entrainment, while the shear-produced TKE in the mixed layer and surface layer have little effect on entrainment. Based on this scheme, a new scale of convective turbulence velocity is proposed and applied to parameterize the IL thickness. The LES outputs for the CBLs under the condition of linearly sheared geostrophic velocity with a non-zero surface value are used to verify the performance of the parameterization scheme. It is found that the parameterized A _e and IL thickness agree well with the LES outputs.     

Airborne Lidar Observations of the Transition Zone Between the Convective Boundary Layer and Free Atmosphere During the International H<Subscript>2</Subscript>O Project (IHOP) in 2002

Airborne, light detection and ranging (lidar) backscatter observations of the convective boundary layer from the International H₂O Project (IHOP) in 2002 are analysed to study the structure of the transition zone; the backscatter gradient between the convective boundary layer and free atmosphere. A new mathematical algorithm is developed and used to extract high-resolution (15 m) transition-zone boundaries from 6,500 km (flight legs) of airborne observations. The cospectra of transition-zone boundaries and its thickness indicate that thickness changes occur from boundaries moving in opposite directions (vertically) at small wavelengths (<1 km), while at longer wavelengths (>1 km) both boundaries move coherently, with the lower boundary changing altitude more rapidly. Daily probability distributions of the transition-zone thickness are positively skewed with a mode of 60 m. The structure of the transition zone shows no dependence on the “overall” Richardson number, unlike the entrainment zone. This study provides the first quantitative characterization of the structure of the instantaneous transition zone, a contribution towards an improved understanding of convective boundary-layer entrainment.     

On the analytical solution for two-dimensional convective plume and analytical modeling of the entrainment zone thickness

Analytical solution for two-dimensional thermal plume updraft velocity is obtained under the assumption of a uniform temperature excess inside the plume. In this way, the thermal plume motion is modeled in both mixed layer and entrainment zone. Also, a semi-analytical solution is obtained using an empirical model for the plume temperature excess in the mixed layer. In addition, an analytical model for entrainment zone thickness is obtained by computing the overshoot distance of the modeled plumes, and a semi-analytical model by using the empirical model for plume temperature. By using a nonlinear profile for the lapse rate in the surface layer based on the Monin–Obukhov similarity theory, our model predicts that the characteristics of the surface layer plays an important role in the structure of the entrainment zone. Finally, our solutions for plume velocity allow us to consider the effect of the lateral entrainment on the plume excess temperature and velocity in the convective boundary layer. It is shown that the lateral entrainment has an important role on the plume dynamics and the solutions in the zero entrainment limit offer large overestimated values for the plume velocity, which also result in overestimated values of the entrainment zone thickness.     

Effect of the Entrainment Flux Ratio on the Relationship between Entrainment Rate and Convective Richardson Number

The parameterization of the dimensionless entrainment rate (w _e /w _*) versus the convective Richardson number (Ri _δθ ) is discussed in the framework of a first-order jump model (FOM). A theoretical estimation for the proportionality coefficient in this parameterization, namely, the total entrainment flux ratio, is derived. This states that the total entrainment flux ratio in FOM can be estimated as the ratio of the entrainment zone thickness to the mixed-layer depth, a relationship that is supported by earlier tank experiments, and suggesting that the total entrainment flux ratio should be treated as a variable. Analyses show that the variability of the total entrainment flux ratio is actually the effect of stratification in the free atmosphere on the entrainment process, which should be taken into account in the parameterization. Further examination of data from tank experiments and large-eddy simulations demonstrate that the different power laws for w _e /w _* versus Ri _δθ can be interpreted as the variability of the total entrainment flux ratio. These results indicate that the dimensionless entrainment rate depends not only on the convective Richardson number but also upon the total entrainment flux ratio.     

Distribution of convective energy at upper level in South Korea and the possibility of artificial showery rain caused by activated CAPE

This paper reports a theoretical study on the possibility of inducing artificial showery rain using the convective available potential energy, which is naturally stored in the troposphere. We calculated the environmental parameters (frequency of climatic values, extreme value of stability index, etc.) in the upper troposphere using rawinsonde data from six main stations in Korea from 2001 to 2008 and examined the temporal spatial convective energy according to region. Our results showed that convective available potential energy, which can induce artificial rainfall, existed in the troposphere mainly in summer and were low in other seasons. Its value was found to be highest during late afternoon and in inland regions. We examined the vertical structure of the atmosphere using moisture convergence and vertical velocity (omega) and found that precipitation occurred under strong real latent instability conditions with high convective available potential energy (>3,000?J/kg) in summer and was characterized by moisture convergence at 1,000?C400?hPa, moisture divergence at 400?C300?hPa, and continuous ascending air current at 1,000?C300?hPa (?C??), on average. However, precipitation still did not occur in more than half the cases with high convective available potential energy because, according to the analysis, convective rainfall is affected to a greater extent by the value of convective inhibition than by convective available potential energy. It was also verified that in spite of zero convective inhibition, if the updrafts at a lower level were not sufficient to generate high convective available potential energy at a level higher than the level of free convection, convective rainfall would not occur under real latent instability. Therefore, we suggest it might be possible during the summer to secure the water resources in regions without precipitation by inducing ascending air current artificially under unstable atmospheric conditions to induce showery rain.     

气溶胶辐射效应对边界层结构及夹卷特征影响的观测分析

2017年12月22日至2018年1月18日利用无人机携带温、湿和颗粒物浓度探测仪对南京地区灰霾污染条件下大气边界层垂直结构开展加密观测。通过比较不同灰霾污染条件下温度、湿度和PM_2.5（直径小于2.5微米的颗粒物）浓度的垂直结构差异,结合地面热通量、2米空气温度、相对湿度、风速、风向及主要大气污染物（如臭氧和PM_2.5）浓度,定量评估了气溶胶辐射效应对边界层和夹卷过程的影响。分析表明,灰霾或气溶胶削弱到达地表太阳辐射,减小地表感热通量,延迟边界层发展,增加近地层大气稳定度,降低边界层高度,并加重灰霾污染。灰霾污染物在混合层顶处累积,导致PM_2.5浓度最大变化出现在边界层顶部而不是近地层。气溶胶辐射效应对夹卷特征及其特征参数有重要影响。灰霾浓度升高时,夹卷区厚度增加;无量纲化夹卷速度随对流理查逊数的变化不再符合负1次方幂函数关系,与大涡模拟结果一致。本研究进一步指出,为提高重霾污染条件下天气和空气质量数值预报水平,必须考虑气溶胶辐射效应对边界层和夹卷参数化的影响。     

A generalized scaling for convective shear flows

During the last two decades, different scalings for convective boundary layer (CBL) turbulence have been proposed. For the shear-free regime, Deardorff (1970) introduced convective velocity and temperature scales based on the surface potential temperature flux,Q _s , the buoyancy parameter, , and the time-dependent boundary-layer depth,h. Wyngaard (1983) has proposed decomposition of turbulence into two components, bottom-up (b) and top-down (t), the former characterized byQ _s , the latter, by the potential temperature flux due to entrainment,Q _h . Sorbjan (1988) has devised height-dependent velocity and temperature scales for both b- and t-components of turbulence.Incorporating velocity shear, the well known similarity theory of Monin and Obukhov (1954) has been developed for the atmospheric surface layer. Zilitinkevich (1971, 1973) and Betchov and Yaglom (1971) have elaborated this theory with the aid of directional dimensional analysis for a particular case when different statistical moments of turbulence can be alternatively attributed as being of either convective or mechanical origin.In the present paper, we attempt to create a bridge between the two approaches pointed out above. A new scaling is proposed on the basis of, first, decomposition of statistical moments of turbulence into convective (c), mechanical (m) and covariance (c&m) contributions using directional dimensional analysis and, second, decomposition of these contributions into bottom-up and top-down components using height-dependent velocity and temperature scales. In addition to the statistical problem, the scaling suggests a new approach of determination of mean temperature and velocity profiles with the aid of the budget equations for the mean square fluctuations.Notation ATL alternative turbulence layer - CBL convective boundary layer - CML convective and mechanical layer - FCL free convection layer - MTL mechanical turbulence layer     

Penetrative convection in rapidly rotating flows: preliminary results from numerical simulation

Turbulent convection forced by a surface heat flux into a stably stratified region is a feature of both the atmospheric and oceanic planetary boundary layers. Of particular interest is the interface between the convective layer and the stable stratification, where the entrainment of fluid into the convective layer by penetrating plumes may lead to a reverse buoyancy flux, and an enhancement of the stable stratification. Whereas in the atmosphere the influence of rotation on this penetrative convection is negligible, oceanic convection may be subjected to lower Rossby numbers and hence greater rotational influence. To isolate the effects of rotation, we present three numerical solutions for turbulent penetrative convection, characterised by different rotation rates, with all other parameters being held constant. Our results indicate that at lower Rossby numbers the lateral scale of the plumes is reduced, whereas the vertical vorticity of the plumes is much enhanced. Vertical transports of buoyancy and kinetic energy across the convective layer are reduced, leading to less efficient penetration at the interface with the stratified layer, and hence less reverse buoyancy flux in this region.     

Atmospheric boundary-layer structure observed during a haze event due to forest-fire smoke

During a haze event in Baltimore, U.S.A. from July 6 to 8, 2002, smoke from forest fires in the Québec region (Canada), degraded air quality and impacted upon local climate, decreasing solar radiation and air temperature. The smoke particles in and above the atmospheric boundary layer (ABL) served as a tracer and provided a unique opportunity to investigate the ABL structure, especially entrainment. Elastic backscatter lidar measurements taken during the haze event distinctly reveal the downward sweeps (or wisps) of smoke-laden air from the free atmosphere into the ABL. Visualisations of mechanisms such as dry convection, the entrainment process, detrainment, coherent entrainment structures, and mixing inside the ABL, are presented. Thermals overshooting at the ABL top are shown to create disturbances in the form of gravity waves in the free atmosphere aloft, as evidenced by a corresponding ripple structure at the bottom of the smoke layer. Lidar data, aerosol ground-based measurements and supporting meteorological data are used to link free atmosphere, mixed-layer and ground-level aerosols. During the peak period of the haze event (July 7, 2002), the correlation between time series of elastic backscatter lidar data within the mixed layer and the scattering coefficient from a nephelometer at ground level was found to be high (R=0.96 for z =324 m, and R=0.89 for z=504 m). Ground-level aerosol concentration was at a maximum about 2 h after the smoke layer intersected with the growing ABL, confirming that the wisps do not initially reach the ground.     

A Parameterization of Dry Thermals and Shallow Cumuli for Mesoscale Numerical Weather Prediction

For numerical weather prediction models and models resolving deep convection, shallow convective ascents are subgrid processes that are not parameterized by classical local turbulent schemes. The mass flux formulation of convective mixing is now largely accepted as an efficient approach for parameterizing the contribution of larger plumes in convective dry and cloudy boundary layers. We propose a new formulation of the EDMF scheme (for Eddy Diffusivity\Mass Flux) based on a single updraft that improves the representation of dry thermals and shallow convective clouds and conserves a correct representation of stratocumulus in mesoscale models. The definition of entrainment and detrainment in the dry part of the updraft is original, and is specified as proportional to the ratio of buoyancy to vertical velocity. In the cloudy part of the updraft, the classical buoyancy sorting approach is chosen. The main closure of the scheme is based on the mass flux near the surface, which is proportional to the sub-cloud layer convective velocity scale w _*. The link with the prognostic grid-scale cloud content and cloud cover and the projection on the non- conservative variables is processed by the cloud scheme. The validation of this new formulation using large-eddy simulations focused on showing the robustness of the scheme to represent three different boundary layer regimes. For dry convective cases, this parameterization enables a correct representation of the countergradient zone where the mass flux part represents the top entrainment (IHOP case). It can also handle the diurnal cycle of boundary-layer cumulus clouds (EUROCS\ARM) and conserve a realistic evolution of stratocumulus (EUROCS\FIRE).     

Observations of temperature microstructure in the atmosphere

In order to provide data of atmospheric temperature microstructure for the investigation of light prop-agation we measured fluctuations of atmospheric temperature below the height of 300 m with a platinum wire thermometer in Tianjin in May and September, 1980. The results measured in daytime revealed some properties of the temperature structure parameter and spectrum. It has been confirmed that there is a max-imum in the profile of the structure parameter produced probably by the entrainment in the interfacial layer at the top of convective boundary layer. The average of C2t in the interfacial layer and its Wyngaard calculating method are discussed, and the thickness of the interfacial layer is obtained.It is shown by spectrum analysis that a wide inertial subrange exists in the convective boundary layer and the strong turbulent zone in the free atmosphere. The spectral law with the power of -2.5 was measured within the upper half of boundary layer over the sea in vicinity of Tanggu.     

Entrainment Processes in the Convective Boundary Layer with Varying Wind Shear

Large-eddy simulations (LES) are performed to investigate the entrainment andthe structure of the inversion layer of the convective boundary layer (CBL) withvarying wind shears. Three CBLs are generated with the constant surface kinematicheat flux of 0.05 K m s^-1 and varying geostrophic wind speeds from 5 to 15m s^-1. Heat flux profiles show that the maximum entrainment heat flux as afraction of the surface heat flux increases from 0.13 to 0.30 in magnitude withincreasing wind shear. The thickness of the entrainment layer, relative to the depthof the well-mixed layer, increases substantially from 0.36 to 0.73 with increasingwind shear. The identification of vortices and extensive flow visualizations nearthe entrainment layer show that concentrated vortices perpendicular to the meanboundary-layer wind direction are identified in the capping inversion layer for thecase of strong wind shear. These vortices are found to develop along the mean winddirections over strong updrafts, which are generated by convective rolls and to appearas large-scale wavy motions similar to billows generated by the Kelvin–Helmholtzinstability. Quadrant analysis of the heat flux shows that in the case of strong windshear, large fluctuations of temperature and vertical velocity generated by largeamplitude wavy motions result in greater heat flux at each quadrant than that inthe weak wind shear case.     

Temporal Scales of Convective Coherent Structures Derived from Sodar Data

Summary The temporal variability of thermal turbulence and vertical velocity derived from sodar measurements during periods of atmospheric free convection is studied using both spectral and wavelet analysis. A promising approach to analyse atmospheric processes, an advanced high-resolution spectrum estimation technique is described. Variance spectra of meteorological and turbulent parameters are shown to have their specific comb shape at a low-frequency range. Spectra and wavelet transforms of the data obtained at different sites both indicate the existence of some representative predominant temporal scales in time variations of the convective boundary layer structure. The most evident temporal scales revealed are centered around 7–9 and 18–22 minutes. Received October 16, 1998 Revised April 15, 1999     

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 applied model for the height of the daytime mixed layer and the entrainment zone

A model is presented for the height of the mixed layer and the depth of the entrainment zone under near-neutral and unstable atmospheric conditions. It is based on the zero-order mixed-layer height model of Batchvarova and Gryning (1991) and the parameterization of the entrainment zone depth proposed by Gryning and Batchvarova (1994). However, most zero-order slab type models of mixed-layer height may be applied. The use of the model requires only information on those meteorological parameters that are needed in operational applications of ordinary zero-order slab type models of mixed-layer height: friction velocity, kinematic heat flux near the ground and potential temperature gradient in the free atmosphere above the entrainment zone. When information is available on the horizontal divergence of the large-scale flow field, the model also takes into account the effect of subsidence, although this is usually neglected in operational models of mixed-layer height owing to lack of data. Model performance is tested using data from the CIRCE experiment.     

A Similarity Model for Maximum Ground-Level Concentration in a Freely Convective Atmospheric Boundary Layer

A model of buoyancy- and momentum-driven industrial plumes in a freely convective boundary layer is proposed. The development combines the Lagrangian similarity models of Yaglom for non-buoyant releases in the convective surface layer with the Scorer similarity model for industrial plumes. Constraints on the validity of the extension of Yaglom’s model to the entire convective planetary boundary layer, arrived at by consideration of Batchelor’s formulation for diffusion in an inertial subrange, are often met in practice. The resulting formulation applies to an interval of time in which the entrainment of the atmosphere by the plume is balanced by the entrainment of the plume by the atmosphere. It is argued that during this interval, both maximum plume rise and ground contact are achieved. Further examination of the physical interrelationship with the Csanady-Briggs formulation serves to consolidate the model hypotheses, as well as to simplify the derivation of maximum ground-level concentrations. Experimental evidence is presented for the validity of the model, based on Moore’s published data.     

A numerical study of daily transitions in the convective boundary layer

We examine daily (morning–afternoon) transitions in the atmospheric boundary layer based on large-eddy simulations. Under consideration are the effects of the stratification at the top of the mixed layer and of the wind shear. The results describe the transitory behaviour of temperature and wind velocity, their second moments, the boundary-layer height Z _m (defined by the maximum of the potential temperature gradient) and its standard deviation σ _m , the mixed-layer height z _i (defined by the minimum of the potential temperature flux), entrainment velocity W _e, and the entrainment flux H _i . The entrainment flux and the entrainment velocity are found to lag slightly in time with respect to the surface temperature flux. The simulations imply that the atmospheric values of velocity variances, measured at various instants during the daytime, and normalized in terms of the actual convective scale w_*, are not expected to collapse to a single curve, but to produce a significant scatter of observational points. The measured values of the temperature variance, normalized in terms of the actual convective scale Θ_*, are expected to form a single curve in the mixed layer, and to exhibit a considerable scatter in the interfacial layer.