Improving Non-local Parameterization of the Convective Boundary Layer

We propose improvements in the “non-local” parameterization scheme of the convective boundary layer. The countergradient terms for components of the momentum fluxes are introduced in a form analogous to those for other scalars. The scheme also includes explicit expressions for entrainment fluxes of momentum, temperature, and humidity. A simplified procedure for calculating the boundary-layer height is proposed, consisting of two steps: the evaluation of the convection level, followed by the assessment of the depth of the interfacial layer.     

Non-local mixing of momentum in the convective boundary layer

Recently Frech and Mahrt proposed a closure scheme which includes alarge-scale stress term to represent the effects of non-local momentummixing in the convective boundary layer. Here large-eddy simulation (LES)datasets are used to evaluate the performance of this scheme across a rangeof stabilities between neutral and highly convective conditions, and as afunction of baroclinity. Generally the inclusion of the non-local term inthe closure model leads to results in better agreement with LES, althoughsome modifications to the model formulation are suggested.     

Length Scales of Scalar Diffusion in the Convective Boundary Layer: Laboratory Observations

A laboratory study of scalar diffusion in the convective boundary layer has found results that are consistent with a 1999 large-eddy simulation (LES) study by Jonker, Duynkerke and Cuijpers. For bottom-up and top-down scalars (introduced as ‘infinite’ area sources of passive tracer at the surface and inversion, respectively) the dominant length scale was found to be much larger than the length scale for density fluctuations, the latter being equal to the boundary-layer depth h. The variance of the normalized passive scalar grew continuously with time and its magnitude was about 3–5 times larger for the top-down case than for the bottom-up case. The vertical profiles of the normalized passive scalar variance were found to be approximately constant through the convective boundary layer (CBL) with a value of about 3–8c_*² for bottom-up and 10–50c_*² for top-down diffusion. Finally, there was some evidence of a minimum in the variance and dominant length scale for scalar flux ratios (top-down to bottom-up flux) close to −0.5. All these convection tank results confirm the LES results and support the hypothesis that there is a distinct difference in behaviour between the dynamic and passive variables in the CBL.     

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 Parameterization of Third-order Moments for the Dry Convective Boundary Layer

We describe one-dimensional (1D) simulations of the countergradient zone of mean potential temperature observed in the convective boundary layer (CBL). The method takes into account the third-order moments (TOMs) in a turbulent scheme of relatively low order, using the turbulent kinetic energy equation but without prognostic equations for other second-order moments. The countergradient term is formally linked to the third-order moments and , and a simple parameterization of these TOMs is proposed. It is validated for several cases of a dry CBL, using large-eddy simulations that have been realized from the MESO-NH model. The analysis of the simulations shows that TOMs are responsible for the inversion of the sign of in the higher part of the CBL, and budget analysis shows that the main terms responsible for turbulent fluxes and variances are now well reproduced.     

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.     

城市边界层动量和保守物通量的特征

利用2005年1-5月北京325 m气象塔47 m高度的湍流脉动资料(风速、温度、水汽和CO2),对城市边界层冠层内的湍流运动统计特征(相似关系、高阶矩、通量和谱等)进行了分析。其中,谱分析的结果表明,城市冠层内稳定度对湍流谱的影响比较小,而水平风速的影响比较大。因此,速度和温度的相似关系在夜间稳定条件下也成立。但是,由于水汽和CO2还受其他因素的影响,相似关系并不适用。更高阶矩的研究表明它们的陡峭度与偏斜度之间存在平方关系。而水汽和CO2之间也存在差异,它们的通量日变化特征明显不同,CO2通量的日变化更能体现人类活动的影响。同时,感热通量、潜热通量和CO2通量存在季节变化,尤其是潜热通量季节差异很大。     

Wave-Modified Flux and Plume Dispersion in the Stable Boundary Layer

The effects of a pressure jump and a following internal gravity wave on turbulence and plume diffusion in the stable planetary boundary layer are examined. The pressure jump was accompanied by a sudden increase in turbulence and plume dispersion. The effects of wave perturbations on turbulence statistics are analysed by calculating fluxes and variances with and without the wave signal for averaging times ranging from 1 to 30 min. The wave signals are obtained using a band-pass filter. It is shown that second-order turbulence quantities calculated without first subtracting the wave perturbations from the time are greater than those calculated when the wave signal is separated from the turbulence. Estimates of the vertical dispersion of an elevated tracer plume in the stable boundary layer are made using an elastic backscatter lidar. Plume dispersion observed 25 m downwind of the source increases rapidly with the arrival of the flow disturbances. Measured plume dispersion and plume centreline height correlate with the standard deviation of the vertical velocity but not with the wave signal.     

Coherence and Scale of Vertical Velocity in the Convective Boundary Layer from a Doppler Lidar

We utilized a Doppler lidar to measure integral scale and coherence of vertical velocity w in the daytime convective boundary layer (CBL). The high resolution 2 μm wavelength Doppler lidar developed by the NOAA Environmental Technology Laboratory was used to detect the mean radial velocity of aerosol particles. It operated continuously in the zenith-pointing mode for several days in the summer 1996 during the “Lidars in Flat Terrain” experiment over level farmland in central Illinois. We calculated profiles of w integral scales in both the alongwind and vertical directions from about 390 m height to the CBL top. In the middle of the mixed layer we found, from the ratio of the w integral scale in the vertical to that in the horizontal direction, that the w eddies are squashed by a factor of about 0.65 as compared to what would be the case for isotropic turbulence. Furthermore, there is a significant decrease of the vertical integral scale with height. The integral scale profiles and vertical coherence show that vertical velocity fluctuations in the CBL have a predictable anisotropic structure. We found no significant tilt of the thermal structures with height in the middle part of the CBL.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Doppler Lidar Measurements of Vertical Velocity Spectra in the Convective Planetary Boundary Layer

We utilized a Doppler lidar to measure spectra of vertical velocity w from 390m above the surface to the top of the daytime convective boundary layer (CBL). The high resolution 2μm wavelength Doppler lidar developed by the NOAA Environmental Technology Laboratory was used to detect the mean radial velocity of aerosol particles. It operated continuously during the daytime in the zenith-pointing mode for several days in summer 1996 during the Lidars-in-Flat-Terrain experiment over level farmland in central Illinois, U.S.A. The temporal resolution of the lidar was about 1 s, and the range-gate resolution was about 30m. The vertical cross-sections were used to calculate spectra as a function of height with unprecedented vertical resolution throughout much of the CBL, and, in general, we find continuity of the spectral peaks throughout the depth of the CBL. We compare the observed spectra with previous formulations based on both measurements and numerical simulations, and discuss the considerable differences, both on an averaged and a case-by-case basis. We fit the observed spectra to a model that takes into account the wavelength of the spectral peak and the curvature of the spectra across the transition from low wavenumbers to the inertial subrange. The curvature generally is as large or larger than the von Kármán spectra. There is large case-to-case variability, some of which can be linked to the mean structure of the CBL, especially the mean wind and the convective instability. We also find a large case-to-case variability in our estimates of normalized turbulent kinetic energy dissipation deduced from the spectra, likely due for the most part to a varying ratio of entrainment flux to surface flux. Finally, we find a relatively larger contribution to the low wavenumber region of the spectra in cases with smaller shear across the capping inversion, and suggest that this may be due partly to gravity waves in the inversion and overlying free atmosphere.     

Modelling Mean and Turbulence Fields in the Dry Convective Boundary Layer with the Eddy-Diffusivity/Mass-Flux Approach

The treatment of turbulence closure in atmospheric models is examined in the context of the dry convective boundary layer (CBL) and the eddy-diffusivity/mass-flux (EDMF) approach. The EDMF approach is implemented into a model called TAPM to use a coupled two-equation prognostic turbulence closure and the mass-flux approach to represent turbulence in the CBL. This work also extends the range of turbulence variables that can be derived from the mass-flux component of the model and uses these along with their values from the prognostic scheme to provide total turbulence fields that can be used to compare to data and/or to feed into other components of TAPM, including those needed to drive Eulerian and Lagrangian air pollution dispersion modules. Model results are presented for the afternoon of a simulated summer day and are compared to both laboratory and field observations in a mixed-layer scaled framework. The results show that the EDMF approach works well within TAPM and can provide good predictions of mean and turbulence fields, including in the upper levels of the CBL. The EDMF approach has several attractive features, including the potential to be one approach to unify the treatment of turbulence and dry and moist convection in atmospheric models.     

The Role of Shear in the Morning Transition Boundary Layer

We use large-eddy simulation (LES) to better define the early stages of the morning transition boundary layer. Previous LES studies relating to the morning transition boundary layer focus on the role of the entraining convective boundary layer (CBL). By using a combination of different domain sizes and grid lengths, the full evolution from the stable boundary layer (SBL) to the CBL is modelled here. In the early stages of the morning transition the boundary layer is shown to be a combination of a shallow mixed layer capped by a significant shear driven stable boundary layer (the so-called mixed CBL–SBL state). The mixed CBL–SBL state is the key to understanding the sensitivity to shear. Turbulent kinetic energy budgets also indicate that it is shear driven. The negative flux from the mixed CBL–SBL state extends much further above the minimum than is typically found for the CBL later in the day, and the depth of penetration scales as w _m /N _i , where w _m is the combined friction and convective velocity scale and N _i the static stability at the inversion top.     

Turbulent mixing of reactive gases in the convective boundary layer

We study the interactions of chemistry and turbulent mixing of tracersin the convective boundary layer with a second-order closure model,including higher order chemistry terms. In order to limit the number of predictive equations we prescribe the profiles for ¯w¯, ¯w¯ ¯ and the lengthscale l. However, for model validation we treat temperature and humidity asinert tracers, and compare the results with profiles observed during theAir Mass Transformation Experiment, and with similarity expressions for thesurface layer. We find good agreement of the mean profiles, but the (co-)variances are slightly underpredicted. Furthermore, the model usesdiagnostic equations expressing third moments of concentration in terms ofsecond moments and their vertical derivatives. They are compared withlarge-eddy model results, showing good agreement and, therefore, thesimplifications are justified. The model is applied to the transport of two gases subject to one bimolecular reaction. The importance of concentration correlations on themean transformation rate is studied. For two gases diffusing in oppositedirections we find for moderate and fast chemistry a 50% and90% decreased transformation rate due to the negatively correlatedconcentrations. These values are similar to large-eddy results of Schumannand Sykes et al. For two bottom-up tracers we find that the covariance ofboth reactive species is either positive or negative, increasing or reducingthe effective transformation rate depending on the Damköhler number (the ratio of the turbulent and the chemistry timescale). A significantdirect influence of chemistry on the flux divergence is found in bothcases. According to the model the effective transport to mid-levels of theboundary layer is increased when two reactive tracers diffuse in oppositedirections, and decreased in the case of two bottom-up tracers.     

Laboratory and Numerical Studies of the Convective Boundary Layer Capped by a Strong Inversion

The convective boundary layer (CBL) with a wide range of stability is simulated experimentally using a thermally stratified wind tunnel, and numerically by direct numerical simulation (DNS). The turbulence structures and flow characteristics of various CBL flows, capped by a strong temperature inversion and affected by surface shear, are investigated. The various vertical profiles of turbulence statistics similar to those from the observed CBL in the field are successfully simulated in both the wind-tunnel experiment and in DNS. The comparison of the wind-tunnel data and DNS results with those of atmospheric observations and water-tank studies shows the crucial dependence of the turbulence statistics in the upper part of the layer on the strength of the inversion layer, as well as the modification of the CBL turbulence regime by the surface shear.     

Discussion and Applications of Slab Models of the Convective Boundary Layer based on Turbulent Kinetic Energy Budget Parameterisations

Some of the most widely used slab model formulations for applications in the convective boundary layer are analysed and discussed. Three main classes are identified based on different approximations of the turbulent kinetic energy equation. The models appear to be quite insensitive to the initial values for boundary-layer height, and temperature discontinuity at the boundary-layer top. The slab models are applied to a case of sea-land transition from the literature, and a case of convective boundary layer time evolution over a homogeneous terrain at San Pietro Capofiume (Bologna, Italy). The different parameterisations turn out to be almost equivalent for the cases studied. The models generally underpredict the value for the height, while all give very good estimates for the mean mixed-layer temperature.     

Fluxes and Gradients in the Convective Surface Layer and the Possible Role of Boundary-Layer Depth and Entrainment Flux

We study the relation between fluxes and gradients in the very unstable surface layer by comparing recent proposals in the literature with the well-known Businger–Dyer functions. The recent proposals include results from large-eddy simulation (LES), which account for entrainment effects and effects of the boundary-layer depth. A comparison of the relationships is made with experimental data. The LES-based gradient functions show the impact of entrainment in the surface layer, but the scatter in the field data is too large to confirm this. Therefore this result is preliminary and future tests against new observations are recommended. It appears that the Businger–Dyer relationship behaves differently to the alternatives, and that it deviates from observations for large stability.     

Simulated Airborne Flux Measurements in a LES generated Convective Boundary Layer

One aim of past boundary-layer experiments with aircraft was the determination of areally averaged heat fluxes. In spite ofsophisticated instrumentation the measured fluxes extrapolated to the ground differed significantly from fluxes measured directly at ground stations. This studypresents simulated sensible heat flux measurements with aircraft flightsthrough a synthetic convective boundary layer created by a401 × 401 × 42 cubic-grid large eddy simulation (LES) with agrid spacing of 50 m. After some considerations with respect to necessary measurement lengths using results ofLenschow and Stankov (1986 – J. Atmos. Sci. 43, 1198–1209), simulated measurementcampaigns were carried out in three modelruns. During each model run five sets ofmeasurement runs were carried out successively.During each set of runs 10 aircraftflew at 10 altitudes with a ground speedof 100 m s^-1 simultaneously throughtime and space. In total, 150 legs were carried out, 15 at each flight level. The resulting`measured' heat fluxes were compared withthose of the `true' flux profiles obtaineddirectly from the ensemble-averagedLES-generated data. No significant systematic error between `measured' and `true' profiles was observed. Furthermore, the comparison of the resulting relative error with the theory ofLenschow and Stankov showed a good agreement at allmeasurement levels.     

Growth Of The Summer Daytime Convective Boundary Layer At Anand

The heights of the daytime convective boundary layer (CBL), computed by a one-dimensional model for a bare soil surface at a semi-arid station,Anand, during the dry and hot summer month of May 1997, are presented. As input, the model requires surface heat flux, friction velocity and air temperature as functions of time. Temperature data at the one-metre level from a tower and sonic anemometer data at 9.5 m collected during the period 13–17 May 1997 in the Land Surface Processes Experiment (LASPEX-97) are used to compute hourly values of surface heat flux, friction velocity and Obukhov length following the operational method suggested by Holtslag and Van Ulden [J. Climate Appl. Meteorol. 22,517–529 (1983)]. The model has been tested with different values for the potential temperature gradient ( ) above the inversion. The model-estimated CBL heights comparefavourably with observed heights obtained from radiosonde ascents.