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Christian Jakob and A. Pier Siebesma

Abstract

All convection parameterizations in models of the atmosphere include a decision tree to decide on at least the occurrence, and often the type, of convection in a model grid volume. This decision tree is sometimes referred to as the “trigger function.” This study investigates the role that the decision-making processes play in the simulation of convection in the European Centre for Medium-Range Weather Forecasts global forecast model.

For this purpose, a new simple parcel-ascent model based on an entraining plume model is developed to replace the currently used undilute ascent in the initial decision making. The consequences of the use of the more realistic model for the behavior of convection itself and its impact on the model climate are investigated. It is shown that there are profound changes to both the convection characteristics, and consequently, the model climate. The wider implications of the findings here for the general design of a mass-flux convection parameterization are discussed.

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Sylvain Cheinet and A. Pier Siebesma

Abstract

The propagation of optical and acoustical waves is affected by the atmospheric turbulence through the local instantaneous refractive index structure parameter in a volume of characteristic size r, denoted Cn ,r 2. Often r is well within the inertial–convective range. In this study, a large-eddy simulation (LES) of spatial resolution Δ is used to analyze the distribution of Cn 2 in the convective boundary layer. The local formulation used to calculate Cn 2 is described and is found to back up the subgrid parameterization of atmospheric LES.

The mean vertical profile behaves according to the mixed layer similarity theory. The spatial organization relates to the presence of buoyant ascending plumes. This structure is associated with some bimodal probability density functions of the inertial–convective range variables, in agreement with experimental results. The standard model of jointly lognormal statistics is challenged. The intermittency of these variables is characterized, and its inertial–convective range component quantitatively agrees with experimental estimates.

The present LES results are used to document the bias produced by averaging the dissipation rates of TKE and temperature variance to estimate the average structure parameters. Comparing with nonconvective turbulence measurements, the bias for CT ,r 2 is found to depend on the stability. A physical explanation is offered that emphasizes the role of the large-scale turbulence under convective conditions.

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Wim C. de Rooy and A. Pier Siebesma

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For a wide range of shallow cumulus convection cases, large-eddy simulation (LES) model results have been used to investigate lateral mixing as expressed by the fractional entrainment and fractional detrainment rates. It appears that the fractional entrainment rates show much less variation from hour to hour and case to case than the fractional detrainment rates. Therefore, in the parameterization proposed here, the fractional entrainment rates are assumed to be described as a fixed function of height, roughly following the LES results. Based on the LES results a new, more flexible parameterization for the detrainment process is developed that contains two important dependencies. First, based on cloud ensemble principles it can be understood that deeper cloud layers call for smaller detrainment rates. All current mass flux schemes ignore this cloud-height dependence, which evidently leads to large discrepancies with observed mass flux profiles. The new detrainment formulation deals with this dependence by considering the mass flux profile in a nondimensionalized way. Second, both relative humidity of the environmental air and the buoyancy excess of the updraft influence the detrainment rates and, therefore, the mass flux profiles. This influence can be taken into account by borrowing a parameter from the buoyancy-sorting concept and using it in a bulk sense. LES results show that with this bulk parameter, the effect of environmental conditions on the fractional detrainment rate can be accurately described. A simple, practical but flexible parameterization for the fractional detrainment rate is derived and evaluated in a single-column model (SCM) for three different shallow cumulus cases, which shows the clear potential of this parameterization. The proposed parameterization is an attractive and more robust alternative for existing, more complex, buoyancy-sorting-based mixing schemes, and can be easily incorporated in current mass flux schemes.

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Louise Nuijens, Bjorn Stevens, and A. Pier Siebesma

Abstract

Quantitative estimates of precipitation in a typical undisturbed trade wind region are derived from 2 months of radar reflectivity data and compared to the meteorological environment determined from soundings, surface flux, and airborne-lidar data. Shallow precipitation was ubiquitous, covering on average about 2% of the region and contributing to at least half of the total precipitation. Echo fractions on the scale of the radar domain range between 0% and 10% and vary greatly within a period from a few hours to a day. Variability in precipitation relates most strongly to variability in humidity and the zonal wind speed, although greater inversion heights and deeper clouds are also evident at times of more rain. The analysis herein suggests that subtle fluctuations in both the strength of the easterlies and in subsidence play a major role in regulating humidity and hence precipitation, even within a given meteorological regime (here, the undisturbed trades).

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A. Pier Siebesma, Pedro M. M. Soares, and João Teixeira

Abstract

A better conceptual understanding and more realistic parameterizations of convective boundary layers in climate and weather prediction models have been major challenges in meteorological research. In particular, parameterizations of the dry convective boundary layer, in spite of the absence of water phase-changes and its consequent simplicity as compared to moist convection, typically suffer from problems in attempting to represent realistically the boundary layer growth and what is often referred to as countergradient fluxes. The eddy-diffusivity (ED) approach has been relatively successful in representing some characteristics of neutral boundary layers and surface layers in general. The mass-flux (MF) approach, on the other hand, has been used for the parameterization of shallow and deep moist convection. In this paper, a new approach that relies on a combination of the ED and MF parameterizations (EDMF) is proposed for the dry convective boundary layer. It is shown that the EDMF approach follows naturally from a decomposition of the turbulent fluxes into 1) a part that includes strong organized updrafts, and 2) a remaining turbulent field. At the basis of the EDMF approach is the concept that nonlocal subgrid transport due to the strong updrafts is taken into account by the MF approach, while the remaining transport is taken into account by an ED closure. Large-eddy simulation (LES) results of the dry convective boundary layer are used to support the theoretical framework of this new approach and to determine the parameters of the EDMF model. The performance of the new formulation is evaluated against LES results, and it is shown that the EDMF closure is able to reproduce the main properties of dry convective boundary layers in a realistic manner. Furthermore, it will be shown that this approach has strong advantages over the more traditional countergradient approach, especially in the entrainment layer. As a result, this EDMF approach opens the way to parameterize the clear and cumulus-topped boundary layer in a simple and unified way.

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Stephan R. de Roode, Peter G. Duynkerke, and A. Pier Siebesma

Abstract

In many large-scale models mass-flux parameterizations are applied to prognose the effect of cumulus cloud convection on the large-scale environment. Key parameters in the mass-flux equations are the lateral entrainment and detrainment rates. The physical meaning of these parameters is that they quantify the mixing rate of mass across the thermal boundaries between the cloud and its environment.

The prognostic equations for the updraft and downdraft value of a conserved variable are used to derive a prognostic variance equation in the mass-flux approach. The analogy between this equation and the Reynolds-averaged variance equation is discussed. It is demonstrated that the prognostic variance equation formulated in mass-flux variables contains a gradient-production, transport, and dissipative term. In the latter term, the sum of the lateral entrainment and detrainment rates represents an inverse timescale of the dissipation.

Steady-state solutions of the variance equations are discussed. Expressions for the fractional entrainment and detrainment coefficients are derived. Also, solutions for the vertical flux of an arbitrary conserved variable are presented. For convection in which the updraft fraction equals the downdraft fraction, the vertical flux of the scalar flows down the local mean gradient. The turbulent mixing coefficient is given by the ratio of the vertical mass flux and the sum of the fractional entrainment and detrainment coefficients. For an arbitrary updraft fraction, however, flux correction terms are part of the solution. It is shown that for a convective boundary layer these correction terms can account for countergradient transport, which is illustrated from large eddy simulation results. In the cumulus convection limit the vertical flux flows down the “cloud” gradient. It is concluded that in the mass-flux approach the turbulent mixing coefficients, and the correction terms that arise from the transport term, are very similar to closures applied to the Reynolds-averaged equations.

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Jerôme Schalkwijk, Harmen J. J. Jonker, and A. Pier Siebesma

Abstract

A modeling framework is developed that extends the mixed-layer model to steady-state cumulus convection. The aim is to consider the simplest model that retains the essential behavior of cumulus-capped layers. The presented framework allows for the evaluation of stationary states dependent on external parameters. These states are completely independent of the initial conditions, and therefore represent an asymptote that might help deepen understanding of the dependence of the cloudy boundary layer on external forcings. Formulating separate equations for the lifting condensation level and the mixed-layer height, the dry and wet energetics can be distinguished. Regimes that can support steady-state cumulus clouds and regimes that cannot are identified by comparison of the dry and wet buoyancy effects. The dominant mechanisms that govern the creation and eventual depth of the cloud layer are identified. Model predictions are tested by comparison with a large number of independent large-eddy simulations for varying surface and large-scale conditions and are found to be in good agreement.

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Jessica M. Loriaux, Geert Lenderink, and A. Pier Siebesma

Abstract

Large-eddy simulations with strong lateral forcing representative of precipitation over the Netherlands are performed to investigate the influence of stability, relative humidity (RH), and moisture convergence on precipitation. Furthermore, a simple climate perturbation is applied to analyze the precipitation response to increasing temperatures. Precipitation is decomposed to distinguish between processes affecting the precipitating area and the precipitation intensity. It is shown that amplification of the moisture convergence and destabilization of the atmosphere both lead to an increase in precipitation, but on account of different effects: atmospheric stability mainly influences the precipitation intensity, whereas the moisture convergence mainly controls the precipitation area fraction. Extreme precipitation intensities show qualitatively similar sensitivities to atmospheric stability and moisture convergence. Precipitation increases with RH due to an increase in area fraction, despite a decrease in intensity. The precipitation response to the climate perturbation shows a stronger response for the precipitation intensity than the overall precipitation, with no clear dependency on changes in atmospheric stability, moisture convergence, and relative humidity.

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Steven J. Böing, Harm J. J. Jonker, Witek A. Nawara, and A. Pier Siebesma

Abstract

Mixing processes in deep precipitating cumulus clouds are investigated by tracking Lagrangian particles in a large-eddy simulation. The trajectories of particles are reconstructed and the thermodynamic properties of cloud air are studied using mixing diagrams. The trajectory analysis shows that the in-cloud mixing is entirely dominated by lateral entrainment and that there is no significant vertical mixing by downdrafts originating from cloud top. Yet the thermodynamic properties of the particles are located close to a line in the mixing diagrams, which appears to be consistent with two-point vertical mixing. An attempt is made to resolve this paradox using the buoyancy-sorting model of Taylor and Baker, but it is found that this model does not provide a full explanation for the location of particles in the mixing diagram. However, it is shown that the mixing-line behavior can be well understood from a simple analytically solvable model that uses a range of different lateral entrainment rates. Two further factors that determine the location of particles in the mixing diagram are identified: the removal of noncloudy air and precipitation effects. Finally, a thermodynamic argument is given that explains the absence of coherent downdrafts descending from cloud top.

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Jesse Dorrestijn, Daan T. Crommelin, A. Pier Siebesma, Harmen J. J. Jonker, and Christian Jakob

Abstract

Observational data of rainfall from a rain radar in Darwin, Australia, are combined with data defining the large-scale dynamic and thermodynamic state of the atmosphere around Darwin to develop a multicloud model based on a stochastic method using conditional Markov chains. The authors assign the radar data to clear sky, moderate congestus, strong congestus, deep convective, or stratiform clouds and estimate transition probabilities used by Markov chains that switch between the cloud types and yield cloud-type area fractions. Cross-correlation analysis shows that the mean vertical velocity is an important indicator of deep convection. Further, it is shown that, if conditioned on the mean vertical velocity, the Markov chains produce fractions comparable to the observations. The stochastic nature of the approach turns out to be essential for the correct production of area fractions. The stochastic multicloud model can easily be coupled to existing moist convection parameterization schemes used in general circulation models.

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