A. Pier Siebesma

A Combined Eddy-Diffusivity Mass-Flux Approach for the Convective Boundary Layer

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.

CGILS: Results from the First Phase of an International Project to Understand the Physical Mechanisms of Low Cloud Feedbacks in Single Column Models

CGILS—the CFMIP-GASS Intercomparison of Large Eddy Models (LESs) and single column models (SCMs)—investigates the mechanisms of cloud feedback in SCMs and LESs under idealized climate change perturbation. This paper describes the CGILS results from 15 SCMs and 8 LES models. Three cloud regimes over the subtropical oceans are studied: shallow cumulus, cumulus under stratocumulus, and well-mixed coastal stratus/stratocumulus. In the stratocumulus and coastal stratus regimes, SCMs without activated shallow convection generally simulated negative cloud feedbacks, while models with active shallow convection generally simulated positive cloud feedbacks. In the shallow cumulus alone regime, this relationship is less clear, likely due to the changes in cloud depth, lateral mixing, and precipitation or a combination of them. The majority of LES models simulated negative cloud feedback in the well-mixed coastal stratus/stratocumulus regime, and positive feedback in the shallow cumulus and stratocumulus regime. A general framework is provided to interpret SCM results: in a warmer climate, the moistening rate of the cloudy layer associated with the surface-based turbulence parameterization is enhanced; together with weaker large-scale subsidence, it causes negative cloud feedback. In contrast, in the warmer climate, the drying rate associated with the shallow convection scheme is enhanced. This causes positive cloud feedback. These mechanisms are summarized as the “NESTS” negative cloud feedback and the “SCOPE” positive cloud feedback (Negative feedback from Surface Turbulence under weaker Subsidence—Shallow Convection PositivE feedback) with the net cloud feedback depending on how the two opposing effects counteract each other. The LES results are consistent with these interpretations.

A New Subcloud Model for Mass-Flux Convection Schemes: Influence on Triggering, Updraft Properties, and Model Climate

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.

A Simple Parameterization for Detrainment in Shallow Cumulus

Abstract 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 depe...

Analogies between Mass-Flux and Reynolds-Averaged Equations

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.

Parameterization of the Vertical Velocity Equation for Shallow Cumulus Clouds

AbstractThe application of a steady-state vertical velocity equation for parameterized moist convective updrafts in climate and weather prediction models is currently common practice. This equation usually contains an advection, a buoyancy, and a lateral entrainment term, whereas the effects of pressure gradient and subplume contributions are typically incorporated as proportionality constants a and b for the buoyancy and the entrainment terms, respectively. A summary of proposed values of these proportionality constants a and b in the literature demonstrates that there is a large uncertainty in their most appropriate values. To shed new light on this situation an analysis is presented of the full vertical budget equation for shallow cumulus clouds obtained from large eddy simulations of three different Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) intercomparison cases. It is found that the pressure gradient term is the dominant sink term in the vertical velocity budget, wher...

Stochastic Parameterization of Convective Area Fractions with a Multicloud Model Inferred from Observational Data

AbstractObservational 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 ge...

Variability of Local Structure Parameters in the Convective Boundary Layer

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,r2. 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,Δ2 in the convective boundary layer. The local formulation used to calculate Cn,Δ2 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–convec...

Large-Eddy Simulations of EUCLIPSE–GASS Lagrangian Stratocumulus-to-Cumulus Transitions: Mean State, Turbulence, and Decoupling

AbstractResults of four Lagrangian stratocumulus-to-shallow-cumulus transition cases as obtained from six different large-eddy simulation models are presented. The model output is remarkably consistent in terms of the representation of the evolution of the mean state, which is characterized by a stratocumulus cloud layer that rises with time and that warms and dries relative to the subcloud layer. Also, the effect of the diurnal insolation on cloud-top entrainment and the moisture flux at the top of the subcloud layer are consistently captured by the models. For some cases, the models diverge in terms of the liquid water path (LWP) during nighttime, which can be explained from the difference in the sign of the buoyancy flux at cloud base. If the subcloud buoyancy fluxes are positive, turbulence sustains a vertically well-mixed layer, causing a cloud layer that is relatively cold and moist and consequently has a high LWP. After some simulation time, all cases exhibit subcloud-layer dynamics that appear to ...

A mixed‐layer model study of the stratocumulus response to changes in large‐scale conditions

A mixed-layer model is used to study the response of stratocumulus equilibrium state solutions to perturbations of cloud controlling factors which include the sea surface temperature, the specific humidity and temperature in the free troposphere, as well as the large-scale divergence and horizontal wind speed. In the first set of experiments, we assess the effect of a change in a single forcing condition while keeping the entrainment rate fixed, while in the second set, the entrainment rate is allowed to respond. The role of the entrainment rate is exemplified from an experiment in which the sea surface temperature is increased. An analysis of the budget equation for heat and moisture demonstrates that for a fixed entrainment rate, the stratocumulus liquid water path (LWP) will increase since the moistening from the surface evaporation dominates the warming effect. By contrast, if the response of the entrainment rate to the change in the surface forcing is sufficiently strong, enhanced mixing of dry and warm inversion air will cause a thinning of the cloud layer. If the entrainment warming effect is sufficiently strong, the surface sensible heat flux will decrease, as opposed to an increase which will occur for a fixed entrainment rate. It is argued that the surface evaporation will always increase for an increase in the sea surface temperature, and this change will be enlarged if the entrainment rate increases. These experiments aid the interpretation of results of similar simulations with single-column model versions of climate models carried out in the framework of the CFMIP-GCSS Intercomparison of Large-Eddy and Single-Column Models (CGILS) project. Because in a large-scale models, the entrainment response to changes in the large-scale forcing conditions depends on the details of the parameterization of turbulent and convective transport, intermodel differences in the sign of the LWP response may be well attributable to differences in the entrainment response.