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.     

The growth of the mixed layer in a stratified fluid due to penetrative convection

This paper describes a theoretical and experimental study of penetrative convection within an initially thermally stably stratified fluid heated from below. Emphasis is placed on the experimental investigation of the growth of the mixed layer and the entrainment at its boundary. Both processes play an important role in density-induced geophysical phenomena such as the lifting of an inversion layer during the morning and the deepening of a thermocline in a lake during the fall.Many laboratory experiments with water as the experimental fluid were performed, in which the convection process was generated and visualised. The height of the mixed layer, heat transfer across the bottom interface and temperature profiles were measured as functions of time.Theoretically-based analytical equations are given, which predict the thickness and temperature of the mixed layer. The equations involve one empirical factor characterising the entrainment rate at the interface between the mixed and the upper stable layer.The experimental results confirm the theoretical equations and show that the empirical factor is a constant. From this, an entrainment rate is calculated which agrees well with values presented in the meteorological literature.Work performed at Sonderforschungsbereich 80, University of Karlsruhe.     

基于激光雷达遥感和参数化模式研究城市混合层的发展机制

利用北京大学的微脉冲激光雷达(MPL)观测的偏南气流条件下的混合层高度和夹卷层厚度探测资料,研究简单天气条件下城市混合层的发展机制并与GB94的参数化方案相互映证.通过激光雷达遥感的混合层高度和夹卷层厚度计算了混合层顶的夹卷率A,得到其平衡夹卷阶段的值为0.24.在不考虑机械混合前提下反演了地面感热通量,结果表明遥感的反演值与梯度法的计算值有系统性偏差,但总体上仍旧有较好的相关.偏差量的大小反映了影响混合层发展的机械湍流的参数B,进一步通过GB91模式的模拟确定该参数的最佳值约为3.5.在此基础上讨论了混     

Development of a Single-Column Model in RegCM4 and Its Preliminary Application for Evaluating PBL Schemes in Simulating the Dry Convection Boundary Layer

A single-column model (SCM) is developed in the regional climate model RegCM4. The evolution of a dry convection boundary layer (DCBL) is used to evaluate this SCM. Moreover, four planetary boundary layer (PBL) schemes, namely the Holtslag-Boville scheme (HB), Yonsei University scheme (YSU), and two University of Washington schemes (UW01, Grenier-Bretherton-McCaa scheme and UW09, Bretherton-Park scheme), are compared by using the SCM approach. A large-eddy simulation (LES) of the DCBL is performed as a benchmark to examine how well a PBL parameterization scheme reproduces the LES results, and several diagnostic outputs are compared to evaluate the schemes. The results show that the SCM is proper constructed. In general, with the DCBL case, the YSU scheme performs best for reproducing the LES results, which include well-mixed features and vertical sensible heat fluxes; the simulated wind speed, turbulent kinetic energy, entrainment flux, and height of the entrainment zone are all underestimated in the UW09; the UW01 has all those biases of the UW09 but larger, and the simulated potential temperature is not well mixed; the HB is the least skillful scheme, by which the PBL height, entrainment flux, height of the entrainment zone, and the vertical gradients within the mixed layer are all overestimated, and a inversion layer near the top of the surface layer is wrongly simulated.Although more cases and further testing are required, these simulations show encouraging results towards the use of this SCM framework for evaluating the simulated physical processes by the RegCM4.     

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.     

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.     

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^*.     

Resolved Versus Parametrized Boundary-Layer Plumes. Part II: Continuous Formulations of Mixing Rates for Mass-Flux Schemes

The conditional sampling of coherent structures in large-eddy simulations of the convective boundary layer (Couvreux et al. Boundary-layer Meteorol 134:441–458, 2010) is used to propose and evaluate formulations of fractional entrainment and detrainment rates for mass-flux schemes. The proposed formulations are physically-based and continuous from the surface to the top of clouds. Entrainment is related to the updraft vertical velocity divergence, while detrainment depends on the thermal vertical velocity, on buoyancy and on the moisture contrast between the mean plume and its environment. The proposed formulations are first directly evaluated in simulations of shallow clouds. They are then tested in single-column simulations with the thermal plume model, a mass-flux representation of boundary-layer thermals.     

A lidar study of the atmospheric entrainment zone and mixed layer over Hong Kong

In this paper we present the lidar study of the atmospheric boundary layer using the City University of Hong Kong lidar system. Three cases of determination of the entrainment zone thickness and the mixed layer depth in the atmospheric boundary layer over Hong Kong were selected for detailed study. The data collected have been analysed using the visual inspection method and the Steyn et al. [J. Atmos. Ocean. Technol. 16 (1999) 953] detection method. During the cold front passage, the mixed layer depth stayed at the level almost constant over the transition period, and the entrainment zone was thickening at a steady entrainment rate.     

Parameterization of Entrainment in a Sheared Convective Boundary Layer Using a First-order Jump Model

Basic entrainment equations applicable to the sheared convective boundary layer (CBL) are derived by assuming an inversion layer with a finite depth, i.e., the first-order jump model. Large-eddy simulation data are used to determine the constants involved in the parameterizations of the entrainment equations. Based on the integrated turbulent kinetic energy budget from surface to the top of the CBL, the resulting entrainment heat flux normalized by surface heat flux is a function of the inversion layer depth, the velocity jumps across the inversion layer, the friction velocity, and the convection velocity. The developed first-order jump model is tested against large-eddy simulation data of two independent cases with different inversion strengths. In both cases, the model reproduces quite reasonably the evolution of the CBL height, virtual potential temperature, and velocity components in the mixed layer and in the inversion layer.The part of this work was done when the first author visited at NCAR.     

A laboratory study of the turbulent velocity characteristics in the convective boundary layer

Based on the measurement of the velocity field in the convective boundary layer （CBL） in a convection water tank with the particle image velocimetry （PIV） technique, this paper studies the characteristics of the CBL turbulent velocity in a modified convection tank. The experiment results show that the velocity distribution in the mixed layer clearly possesses the characteristics of the CBL thermals, and the turbulent eddies can be seen obviously. The comparison of the vertical distribution of the turbulent velocity variables indicates that the modeling in the new tank is better than in the old one. The experiment data show that the thermal＇s motion in the entrainment zone sometimes fluctuates obviously due to the intermittence of turbulence. Analyses show that this fluctuation can influence the agreement of the measurement data with the parameterization scheme, in which the convective Richardson number is used to characterize the entrainment zone depth. The normalized square velocity wi^2/w＊^2. at the top of the mixed layer seems to be time-dependent, and has a decreasing trend during the experiments. This implies that the vertical turbulent velocity at the top of the mixed layer may not be proportional to the convective velocity （w＊）.     

Sensitivity of tropical Atlantic climate to mixing in a coupled ocean–atmosphere model

The sensitivity of tropical Atlantic climate to upper ocean mixing is investigated using an ocean-only model and a coupled ocean–atmosphere model. The upper ocean thermal structure and associated atmospheric circulation prove to be strongly related to the strength of upper ocean mixing. Using the heat balance in the mixed layer it is shown that an excessively cold equatorial cold tongue can be attributed to entrainment flux at the base of the oceanic mixed layer, that is too large. Enhanced entrainment efficiency acts to deepen the mixed layer and causes strong reduction in the upper ocean divergence in the central equatorial Atlantic. As a result, the simulated sea surface temperature, thermocline structure, and upwelling velocities are close to the observed estimates. In the coupled model, the seasonal migration of the Intertropical Convergence Zone (ITCZ) reduces when the entrainment efficiency in the oceanic mixed layer is enhanced. The precipitation rates decrease in the equatorial region and increase along 10°N, resulting in a more realistic Atlantic Marine ITCZ. The reduced meridional surface temperature gradient in the eastern tropical Atlantic prohibits the development of convective precipitation in the southeastern part of the tropical Atlantic. Also, the simulation of tropical Atlantic variability as expressed in the meridional gradient mode and the eastern cold tongue mode improves when the entrainment efficiency is enhanced.     

Three-dimensional numerical study of turbulence in an entraining mixed layer

The mean structure calculated by a three-dimensional numerical model of a heated planetary boundary layer, in simulation of DAY 33 of the Australian Wangara data, has been previously described. The present study supplements it by describing properties of the calculated turbulence.A major finding is the importance of entrainment upon turbulence statistics relating to specific humidity, relative to those for potential temperature. The variances, skewness and spectra of velocity, temperature and humidity are presented, as are budget equations for kinetic energy, temperature and humidity variances and heat/moisture fluxes. These are interpreted with regard to the relative importance of the surface flux vs the flux due to entrainment at the top of the mixed layer, and in regard to the structure which would occur if the entrainment were to vanish.The Rotte-type closure assumption is tested for the correlation between the pressure fluctuation and the vertical gradient of vertical velocity, potential temperature, or specific humidity, and found to be qualitatively correct except near the top of the mixed layer.NCAR is sponsored by the National Science Foundation (U.S.A.).     

Statistics of Scalar Fields in the Atmospheric Boundary Layer Based on Large-Eddy Simulations. Part II: Forced Convection

Forced convection in a quasi-steady atmospheric boundary layer is investigated based on a large-eddy simulation (LES) model. The performed simulations show that in the upper portion of the mixed layer the dimensionless (in terms of mixed layer scales) vertical gradients of temperature, humidity, and wind velocity depend on the dimensionless height z/z _i and the Reech number Rn. The peak values of variances and covariances at the top of the mixed layer, scaled in terms of the interfacial scales, are functions of the interfacial Richardson number Ri. As a result expressions for the entrainment rates, in the case when the interfacial layer has a finite depth, and a condition for the presence of moistening or drying regimes in the mixed layer, are derived. Profiles of dimensionless scalar moments in the mixed layer are proposed to be expressed in terms of two empirical similarity functions F _m and F _i , dependent on dimensionless height z/z _i , and the interfacial Richardson number Ri. The obtained similarity expressions adequately approximate the LES profiles of scalar statistics, and properly represent the impact of stability, shear, and entrainment. They are also consistent with the parameterization proposed for free convection in the first part of this paper.     

An embedded mixed-layer-ocean circulation model

The rationale and numerical technique of embedding an oceanic bulk mixed-layer model with a multi-level primitive equation model is presented. In addition to the usual prognostic variables that exist in a multi-level primitive equation model, the embedded model predicts the depth of the well-mixed layer as well as the jumps in temperature and velocity that occur at the base of that layer. The depth of the mixed layer need not coincide with any of the fixed-model levels used in the primitive equations calculations.In addition to advective changes, the mixed layer can deepen by entrainment and it can reform at a shallower depth in the absence of entrainment. When the mixed layer reforms at a shallower depth, the vertical profile of temperature below the new, shallower mixed layer is adjusted to fit the fixed-level structure used in the primitive equations calculations using a method which conserves heat, momentum and potential energy. Finally, a dynamic stability condition, which includes a consideration of both the vertical current shear and the vertical temperature gradient, is introduced in place of the traditional ‘convective adjustment’.A two-dimensional version of the model is used to test the embedded model formulations and to study the response of the ocean to a stationary axisymmetric hurricane. The model results indicate a strong interdependence between vertical turbulent mixing and advection of heat.     

Stratocumulus-capped mixed layers derived from a three-dimensional model

Results of a three-dimensional numerical model are analysed in a study of turbulence and entrainment within mixed layers containing stratocumulus with or without parameterized cloud-top radiative cooling. The model eliminates most of the assumptions invoked in theories of cloud-capped mixed layers, but suffers disadvantages which include poor resolution and large truncation errors in and above the capping inversion.For relatively thick mixed layers with relatively thick capping inversions, the cloud-top radiative cooling is found to be lodged mostly within the capping inversion when the cooling is confined locally to the upper 50 m or less of the cloud. It does not then contribute substantially towards increased buoyancy flux and turbulence within the well mixed layer just below.The optimal means of correlating the entrainment rate, or mixed-layer growth rate, for mixed layers of variable amounts of stratocumulus is found to be through functional dependence upon an overall jump Richardson number, utilizing as scaling velocity the standard deviation of vertical velocity existing at the top of the mixed layer (near the center of the capping inversion). This velocity is found to be a fraction of the generalized convective velocity for the mixed layer as a whole which is greater for cloud-capped mixed layers than for clear mixed layers.     

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.     

Radiative and Evaporative Cooling in the Entrainment Zone of Stratocumulus – the Role of Longwave Radiative Cooling Above Cloud Top

A mixing fraction determines the relative amount of above-cloud-top air that has been mixed into a cloudy air parcel. A method, based on the use of mixing fractions, to calculate the cooling effects due to mixing, longwave radiation and phase changes at cloud top is derived and discussed. We compute cooling effects for the whole range of mixing fraction for two observed cases of the stratocumulus-topped marine boundary layer. In both cases the total radiative cooling effect is found to be the most dominant contributor to the negative buoyancy excess found at cloud top. The largest radiative cooling rates are found for clear-air parcels immediately adjacent to cloud top rather than inside the cloud. With the help of a simple longwave radiation model, we show this to be caused by clear-air radiative cooling due to the temperature inversion at cloud top. Further we show that flux profiles in the entrainment zone can be computed from data obtained from a horizontal level run that is half the time in cloud and half the time out of cloud.     

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.