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  • Author or Editor: A. Pier Siebesma x
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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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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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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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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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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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Arthur C. Petersen
,
Cees Beets
,
Han van Dop
,
Peter G. Duynkerke
, and
A. Pier Siebesma

Abstract

The transport of nonreactive and reactive bottom-up and top-down diffusing scalars in a solid-lid convective boundary layer is studied using large-eddy simulation (LES). The chemistry considered consists of an irreversible, binary reaction involving the bottom-up and top-down diffusing scalars. The mass-flux or top-hat characteristics of the reactive flow are determined. Also, several mass-flux schemes are run in an off-line mode, that is, with prescribed profiles of the mass flux and the updraft area fraction, and are compared to the LES. Top-hat approximations are found to capture about 25% of the covariance between two arbitrary (nonreacting or reacting) scalars and about 65% of the flux. Subplume fluxes are located either in the updraft for bottom-up diffusing scalars or in the downdraft for top-down diffusing scalars. The mass-flux scheme that is nearly identical to the exact plume-budget equations gives the best performance. For the parameterization of lateral exchange this mass-flux scheme includes gross exchange across the interface between updrafts and downdrafts, that is, includes also subinterface-scale exchange processes (like the other dynamical quantities also prescribed in an off-line mode using LES data). A simpler mass-flux scheme, which does not include the more sophisticated parameterizations of subplume fluxes and subinterface-scale lateral exchange, is found to perform only slightly worse. The results of this paper are also valid for the surface layer and lower mixed layer of the entraining convective boundary layer but not for the entrainment zone.

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Steven J. Böing
,
Harm J. J. Jonker
,
A. Pier Siebesma
, and
Wojciech W. Grabowski

Abstract

The rapid transition from shallow to deep convection is investigated using large-eddy simulations. The role of cold pools, which occur due to the evaporation of rainfall, is explored using a series of experiments in which their formation is suppressed. A positive feedback occurs: the presence of cold pools promotes deeper, wider, and more buoyant clouds with higher precipitation rates, which in turn lead to stronger cold pools. To assess the influence of the subcloud layer on the development of deep convection, the coupling between the cloud layer and the subcloud layer is explored using Lagrangian particle trajectories. As shown in previous studies, particles that enter clouds have properties that deviate significantly from the mean state. However, the differences between particles that enter shallow and deep clouds are remarkably small in the subcloud layer, and become larger in the cloud layer, indicating different entrainment rates. The particles that enter the deepest clouds also correspond to the widest cloud bases, which points to the importance of convective organization within the subcloud layer.

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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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Jessica M. Loriaux
,
Geert Lenderink
,
Stephan R. De Roode
, and
A. Pier Siebesma

Abstract

Previously observed twice-Clausius–Clapeyron (2CC) scaling for extreme precipitation at hourly time scales has led to discussions about its origin. The robustness of this scaling is assessed by analyzing a subhourly dataset of 10-min resolution over the Netherlands. The results confirm the validity of the previously found 2CC scaling for extreme convective precipitation.

Using a simple entraining plume model, an idealized deep convective environmental temperature profile is perturbed to analyze extreme precipitation scaling from a frequently used relation based on the column condensation rate. The plume model simulates a steady precipitation increase that is greater than Clausius–Clapeyron scaling (super-CC scaling). Precipitation intensity increase is shown to be controlled by a flux of moisture through the cloud base and in-cloud lateral moisture convergence. Decomposition of this scaling relation into a dominant thermodynamic and additional dynamic component allows for better understanding of the scaling and demonstrates the importance of vertical velocity in both dynamic and thermodynamic scaling. Furthermore, systematically increasing the environmental stability by adjusting the temperature perturbations from constant to moist adiabatic increase reveals a dependence of the scaling on the change in environmental stability. As the perturbations become increasingly close to moist adiabatic, the scaling found by the entraining plume model decreases to CC scaling. Thus, atmospheric stability changes, which are expected to be dependent on the latitude, may well play a key role in the behavior of precipitation extremes in the future climate.

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