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.     

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.     

Convective plumes in the atmospheric boundary layer as observed with an acoustic Doppler sodar

The vertical velocity field and the convective plumes in the atmospheric boundary layer have been observed during morning hours with the acoustic Doppler sounder of the C.R.P.E. A method for plume determination using acoustic soundings in the well-mixed layer is presented. Using Telford's 1970 and Manton's 1975 models, a comparison is made between the predictions of the models and the plume properties as observed by the Doppler sodar. The mean plume velocity is found to be parabolic. It is shown, restricting Monin and Obukhov similarity to conditions inside plumes and using only vertical velocity within plumes, that the observed convective plumes carry nearly sixty percent of the sensible heat flux at the top of the surface 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.     

A one-dimensional model for the parameterization of deep convection in the ocean

A one-dimensional penetrative plume model has been constructed to parameterize the process of deep convection in ocean general circulation models (OGCMs). This research is motivated by the need for OGCMs to better model the production of deep and intermediate water masses. The parameterization scheme takes the temperature and salinity profiles of OGCM grid boxes and simulates the subgrid-scale effects of convection using a one-dimensional parcel model. The model moves water parcels from the surface layer down to their level of neutral buoyancy, simulating the effect of convective plumes. While in transit, the plumes exchange water with the surrounding environment; however, the bulk of the plume water mass is deposited at e level of neutral buoyancy. Weak upwelling around the plumes is included to maintain an overall mass balance. The process continues until the negative buoyant energy of the one-dimensional vertical column is minimized. The parameterized plume entrainment rate, which plays a central role in the parameterization, is calculated using modified equations based on the physics of entraining buoyant plumes. This scheme differs from the convective adjustment techniques currently used in OGCMs, because the parcels penetrate downward with the appropriate degree of mixing until they reach their level of neutral stability.     

Design criteria for water tank models of dispersion in the planetary convective boundary layer

Design criteria for laboratory water-analogs of clear-air penetrative convection in the atmosphere are described. Consideration is given to the range of factors relevant to modelling both turbulent penetrative convection and the dispersion of buoyant point-source plumes within the convective boundary layer. Scaling arguments based on mixed-layer and plume scaling show that at typical laboratory scales, saline convection can satisfy the requirements for modelling buoyant plume dispersion under strongly convective (light wind) conditions better than heated water tanks or wind tunnels.     

A similarity model for maximum ground-level concentration in a height-invariant,stably stratified atmospheric boundary layer

A model is presented for determining the location and magnitude of the maximum ground-level concentration arising from an elevated buoyant source in a very stable atmospheric boundary layer. The development combines the turbulent structure of such a boundary layer, Lagrangian similarity of the diffusion process, and similarity solutions of the conservation equations of the buoyant plume with mass conservation to produce a simple, experimentally verifiable formulation. Functional analogy with previous results for the constant flux layer and a deep convectively unstable layer suggest a heuristic model by which to visualize the process.     

A saline laboratory model of the planetary convective boundary layer

A laboratory water-analog of clear-air penetrative convection in the atmosphere has been constructed to continue studies of the turbulent dispersion of buoyant plumes in the convective boundary layer (CBL). A unique feature is the utilization of saline rather than thermal convection, which has been made possible by the development of a reliable method for delivering a controllable buoyancy flux through a porous membrane. It has been shown in an earlier paper that at typical laboratory scales, a saline convection tank is well suited to modelling buoyant plume dipersion under strongly convective (light wind) conditions.A range of experiments has clearly demonstrated the validity of the model. Results for density and velocity variances show much less scatter than most comparable measurements because of the greatly improved sampling that is possible in the tank. The results are generally in good agreement with field data and other laboratory simulations but the improved accuracy of the data has highlighted the anomalously low values for the horizontal velocity variances produced by large-eddy simulations of the CBL. The cause of this apparent underprediction remains unresolved.     

A mixed-layer model for regional evaporation

A simple mixed-layer model is developed to describe evaporation into a convective planetary boundary layer (PBL). The model comprises volume budget equations for temperature and humidity, equations to describe transport through the surface layer which is treated as part of the lower boundary, and equations to describe entrainment at the top of the PBL. The ground surface is modelled as a canopy resistance. The model was integrated with canopy resistance, surface-layer resistance and available energy, (R _n – G), input as given functions of time, and the simulated PBL was allowed to grow into an atmosphere with known temperature and humidity profiles.Two variants of the mixed-layer model were tested using data from the KNMI tower site at Cabauw in the Netherlands. These variants differed only in the formulation of entrainment: one used a formulation developed by Driedonks (1982) while the other was a simpler formulation. Simulated evaporation agreed very well with observations irrespective of which entrainment formulation was used, despite discrepancies between simulated and observed PBL height growth which were sometimes quite large for the simpler formulation. Sensitivity analysis of the model confirms that good PBL height-growth predictions are not always a prerequisite for good evaporation predictions.     

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).     

我国西部高原大气边界层中的对流活动

利用 1 998年第 2次青藏高原野外试验中的多普勒声雷达探测、低空探测观测以及卫星观测资料对高原大气边界层内的对流现象进行分析研究。声雷达探测到了高原边界层内有强烈的对流活动。这种对流泡中心的垂直速度可超过 1m/s,并存在尺度为 1个多小时的周期性 ,表现为中小尺度的有组织的湍流活动。高原边界层强对流得以发展和维持的物理机制是 :强辐射加热、复杂的地形地貌形成的下垫面不均一性造成边界层斜压性、边界层内的平流活动等 ,这些现象都有利于对流的发展。在这些条件的作用下 ,边界层内可以产生一系列有组织的强湍流大涡旋活动 ,这些大涡旋形成的热泡在向上发展的过程中有的能够发生合并 ,变得更大也更为猛烈 ,达到凝结高度以上可形成对流云 ,并发生充分的对流混合。成云过程凝结潜热释放更有利于对流运动进一步发展 ,使对流云逐步发展成更大的对流云团 ,从而产生卫星云图中显示的云团发展过程。     

环境湍流对烟云抬升的作用

本文研究了中性层结环境中湍流对烟云抬升的连续作用。取外部湍流卷挟率正比于湍流特征速度并叠加于自身卷挟率,分析表明,即使在抬升的早期,环境湍流对弯曲烟云的路径有不可忽视的影响,并使烟云路径加速变平。电厂烟云的实测资料表明,平均抬升路径实际上不完全符合无湍流环境的三分之二规律,而与本文理论结果更为接近。 本研究也发现,最大抬升高度及其出现的下风距离都是大气湍流度的灵敏函数。据此,我们分析了几个常用抬升公式的局限性,并推荐了一种反映大气湍流度的改型公式。     

Convective Boundary-Layer Entrainment: Short Review and Progress using Doppler Lidar

The entrainment of air from the free atmosphere into the convective boundary layer is reviewed and further investigated using observations from a 2 μm Doppler lidar. It is possible to observe different individual processes entraining air into the turbulent layer, which develop with varying stability of the free atmosphere. These different processes are attended by different entrainment-zone thicknesses and entrainment velocities. Four classes of entrainment parametrizations, which describe relationships between the fundamental parameters of the process, are examined. Existing relationships between entrainment-zone thickness and entrainment velocity are basically confirmed using as scaling parameters boundary-layer height and convective velocity. An increase in the correlation coefficient between stability parameters based on the stratification of the free atmosphere and entrainment velocity (and entrainment-zone thickness respectively) up to 200% was possible using more suitable length and velocity scales.     

Diurnal cycle of precipitation over the Maritime Continent simulated by a spectral cumulus parameterization

The validity of a spectral cumulus parameterization (spectral scheme) for simulating a diurnal cycle of precipitation over the Maritime Continent (MC) was examined using a regional atmospheric model. The impacts of entrainment parameterization and each type of convective closure, i.e., non-equilibrium (or equilibrium) closure for deep convection, mid-level, and shallow convective closures, were also examined. When vertically variable entrainment and appropriate convective closures were employed, the model adequately simulated a diurnal cycle of precipitation over both land and ocean as compared to the observation. Analysis regarding the entrainment parameterization revealed that variable entrainment parameterization was needed not only for simulating better mean patterns of precipitation, but also for more realistic phases of diurnal cycles. The impacts of convective closures appeared in the differences in the precipitation amplitude. Analysis on diurnal cycles of convective properties and tendencies revealed that the cycles between boundary layer forcing and convective heating determined convection strength and were affected by each type of convective closure. It can be concluded that the spectral scheme with appropriate convective closures is able to simulate a realistic diurnal cycle over the MC.     

On the temperature spectrum in the convective boundary layer

A model for the temperature spectrum in the convective boundary layer is presented. The model is developed by using local similarity parameterization of the mixed layer. The model is compared with an idealized temperature spectrum obtained during the Minnesota experiment and exhibits behavior very similar to that observed in the atmosphere.     

Sensitivity of climate simulations to the parameterization of cumulus convection in the Canadian climate centre general circulation model

Abstract

A simplified cumulus parameterization scheme, suitable for use in GCMs, is presented. This parameterization is based on a plume ensemble concept similar to that originally proposed by Arakawa and Schubert (1974). However, it employs three assumptions which significantly simplify the formulation and implementation of the scheme. It is assumed that an ensemble of convective‐scale updrafts with associated saturated downdrafts may exist when the atmosphere is locally conditionally unstable in the lower troposphere. However, the updraft ensemble is comprised only of those plumes which are sufficiently buoyant to penetrate through this unstable layer. It is assumed that all such plumes have the same upward mass flux at the base of the convective layer. The third assumption is that moist convection, which occurs only when there is convective available potential energy (CAPE) for reversible ascent of an undiluted parcel from the sub‐cloud layer, acts to remove CAPE at an exponential rate with a specified adjustment time scale.

The performance of the scheme and its sensitivity to choices of disposable parameters is illustrated by presenting results from a series of idealized single‐column model tests. These tests demonstrate that the scheme permits establishment of a quasi‐equilibrium between large‐scale forcing and convective response. However, it is also shown that the strength of convective downdrafts is an important factor in determining the nature of the equilibrium state. Relatively strong down‐drafts give rise to an unsteady irregularly fluctuating state characterized by alternate periods of deep and shallow convection.

The effect of using the scheme for GCM climate simulations is illustrated by presenting selected results of a multi‐year simulation carried out with the Canadian Climate Centre GCM using the new parameterization (the CONV simulation). Comparison of these results with those for a climate simulation made with the standard model (the CONTROL simulation, as documented by McFarlane et al., 1992) reveals the importance of other parameterized processes in determining the ultimate effect of introducing the new convective scheme. The radiative response to changes in the cloudiness regime is particularly important in this regard.     

Simulating Dispersion in the Evening-Transition Boundary Layer

We investigate dispersion in the evening-transition boundary layer using large-eddy simulation (LES). In the LES, a particle model traces pollutant paths using a combination of the resolved flow velocities and a random displacement model to represent subgrid-scale motions. The LES is forced with both a sudden switch-off of the surface heat flux and also a more gradual observed evolution. The LES shows ‘lofting’ of plumes from near-surface releases in the pre-transition convective boundary layer; it also shows the subsequent ‘trapping’ of releases in the post-transition near-surface stable boundary layer and residual layer above. Given the paucity of observations for pollution dispersion in evening transitions, the LES proves a useful reference. We then use the LES to test and improve a one-dimensional Lagrangian Stochastic Model (LSM) such as is often used in practical dispersion studies. The LSM used here includes both time-varying and skewed turbulence statistics. It is forced with the vertical velocity variance, skewness and dissipation from the LES for particle releases at various heights and times in the evening transition. The LSM plume spreads are significantly larger than those from the LES in the post-transition stable boundary-layer trapping regime. The forcing from the LES was thus insufficient to constrain the plume evolution, and inclusion of the significant stratification effects was required. In the so-called modified LSM, a correction to the vertical velocity variance was included to represent the effect of stable stratification and the consequent presence of wave-like motions. The modified LSM shows improved trapping of particles in the post-transition stable boundary layer.     

Buoyant plume rise in a Lagrangian framework

For the dispersion of buoyant material, the interaction with the environment by entrainment forms a serious obstacle for a formulation in a Lagrangian framework. Nevertheless an outline is given here on how buoyant plume rise in a Lagrangian sense could be described. Though the method contains a number of heuristic elements, it has all the advantages of a Lagrangian formulation. It is shown that it is possible to formulate a Lagrangian model which both is able to recover the classical formulations for plume rise in a calm environment and to accomodate more recent Eulerian formulations in a turbulent environment. Moreover, the method offers excellent possibilities to include the turbulent characteristics of the plume's environment and arbitrary stratifications of the boundary layer. These facts make it attractive for various practical applications. Some examples are given which illustrate this.