Connection between mass flux transport and eddy diffusivity in convective atmospheric boundary layers

AbstractEddy diffusivity models are a common method to parameterize turbulent fluxes in the atmospheric sciences community. However, their inability to handle convective boundary layers leads to the addition of a nondiffusive flux component (usually called nonlocal) alongside the original diffusive term (usually called local). Both components are often modeled for convective conditions based on the shape of the eddy diffusivity profile for neutral conditions. This assumption of shape is traditionally employed due to the difficulty of estimating both components based on numerically simulated turbulent fluxes without any a priori assumptions. In this manuscript we propose a novel method to avoid this issue and estimate both components from numerical simulations without having to assume any a priori shape or scaling for either. Our approach is based on optimizing results from a modeling perspective and taking as much advantage as possible from the diffusive term, thus maximizing the eddy diffusivity. We use our method to diagnostically investigate four different large-eddy simulations spanning different stability regimes, which reveal that nondiffusive fluxes are important even when trying to minimize them. Furthermore, the calculated profiles for both diffusive and nondiffusive fluxes suggest that their shapes change with stability, which is an effect that is not included in most models currently in use. Finally, we use our results to discuss modeling approaches and identify opportunities for improving current models.

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An Eddy Diffusivity–Mass Flux Approach to the Vertical Transport of Turbulent Kinetic Energy in Convective Boundary Layers

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-11-06.1 ◽

2011 ◽

Vol 68 (10) ◽

pp. 2385-2394 ◽

Cited By ~ 13

Author(s):

Marcin L. Witek ◽

Joao Teixeira ◽

Georgios Matheou

Keyword(s):

Kinetic Energy ◽

Turbulent Kinetic Energy ◽

Boundary Layers ◽

Vertical Velocity ◽

Mass Flux ◽

Eddy Diffusivity ◽

Vertical Transport ◽

Convective Boundary ◽

Global Circulation Models ◽

Convective Boundary Layers

Abstract In this study a new approach to the vertical transport of the turbulent kinetic energy (TKE) is proposed. The principal idea behind the new parameterization is that organized updrafts or convective plumes play an important role in transferring TKE vertically within convectively driven boundary layers. The parameterization is derived by applying an updraft environment decomposition to the vertical velocity triple correlation term in the TKE prognostic equation. The additional mass flux (MF) term that results from this decomposition closely resembles the features of the TKE transport diagnosed from the large-eddy simulation (LES) and accounts for 97% of the LES-diagnosed transport when the updraft fraction is set to 0.13. Another advantage of the MF term is that it is a function of the updraft vertical velocity and can be readily calculated using already existing parameterization. The new MF approach, combined with several eddy diffusivity (ED) formulations, is implemented into a simplified 1D TKE prognostic model. The 1D model results, compared against LES simulations of dry convective boundary layers, show substantial improvement in representing the vertical structure of TKE. The new combined ED–MF parameterization, as well as the MF term alone, surpasses in accuracy the ED parameterizations. The proposed TKE transport parameterization shows large potential of improving TKE simulations in mesoscale and global circulation models.

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A Unified Model for Moist Convective Boundary Layers Based on a Stochastic Eddy-Diffusivity/Mass-Flux Parameterization

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-12-0106.1 ◽

2013 ◽

Vol 70 (7) ◽

pp. 1929-1953 ◽

Cited By ~ 56

Author(s):

Kay Sušelj ◽

João Teixeira ◽

Daniel Chung

Keyword(s):

Steady State ◽

Boundary Layers ◽

Mass Flux ◽

Eddy Diffusivity ◽

Cloud Base ◽

Entrainment Rate ◽

Subgrid Scale ◽

Convective Boundary ◽

Main Challenge ◽

Convective Boundary Layers

Abstract A single-column model (SCM) is developed for representing moist convective boundary layers. The key component of the SCM is the parameterization of subgrid-scale vertical mixing, which is based on a stochastic eddy-diffusivity/mass-flux (EDMF) approach. In the EDMF framework, turbulent fluxes are calculated as a sum of the turbulent kinetic energy–based eddy-diffusivity component and a mass-flux component. The mass flux is modeled as a fixed number of steady-state plumes. The main challenge of the mass-flux model is to properly represent cumulus clouds, which are modeled as moist plumes. The solutions have to account for a realistic representation of condensation within the plumes and of lateral entrainment into the plumes. At the level of mean condensation within the updraft, the joint pdf of moist conserved variables and vertical velocity is used to estimate the proportion of dry and moist plumes and is sampled in a Monte Carlo way creating a predefined number of plumes. The lateral entrainment rate is modeled as a stochastic process resulting in a realistic decrease of the convective cloudiness with height above cloud base. In addition to the EDMF scheme, the following processes are included in the SCM: a pdf-based parameterization of subgrid-scale condensation, a simple longwave radiation, and one-dimensional dynamics. Note that in this approach there are two distinct pdfs, one representing the variability of updraft properties and the other one the variability of thermodynamic properties of the surrounding environment. The authors show that the model is able to capture the essential features of moist boundary layers, ranging from stratocumulus to shallow-cumulus regimes. Detailed comparisons, which include pdfs, profiles, and integrated budgets with the Barbados Oceanographic and Meteorological Experiment (BOMEX), Dynamics and Chemistry of Marine Stratocumulus (DYCOMS), and steady-state large-eddy simulation (LES) cases, are discussed to confirm the quality of the present approach.

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An Integrated Turbulence Scheme for Boundary Layers with Shallow Cumulus Applied to Pollutant Transport

Journal of Applied Meteorology ◽

10.1175/jam2284.1 ◽

2005 ◽

Vol 44 (9) ◽

pp. 1436-1452 ◽

Cited By ~ 33

Author(s):

Wayne M. Angevine

Keyword(s):

Kinetic Energy ◽

Turbulent Kinetic Energy ◽

Boundary Layers ◽

Mass Flux ◽

Eddy Diffusivity ◽

Cloud Base ◽

Entrainment Rate ◽

Convective Boundary ◽

Standard Case ◽

Shallow Cumulus

Abstract A scheme is described that provides an integrated description of turbulent transport in free convective boundary layers with shallow cumulus. The scheme uses a mass-flux formulation, as is commonly found in cumulus schemes, and a 1.5-order closure, involving turbulent kinetic energy and eddy diffusivity. Both components are active in both the subcloud and cloud layers. The scheme is called “mass flux–diffusion.” In the subcloud layer, the mass-flux component provides nonlocal transport. The scheme combines elements from schemes that are conceptually similar but differ in detail. An entraining plume model is used to find the mass flux. The mass flux is continuous through the cloud base. The lateral fractional entrainment rate is constant with height, while the detrainment-rate profile reduces the mass flux smoothly to zero at the cloud top. The eddy diffusivity comes from a turbulent kinetic energy–length scale formulation. The scheme has been implemented in a simple one-dimensional (single column) model. Results of simulations of a standard case that has been used for other model intercomparisons [Atmospheric Radiation Measurement (ARM), 21 June 1997] are shown and indicate that the scheme provides good results. The model also simulates the profile of a conserved scalar; this capability is applied to a case from the 1999 Southern Oxidants Study Nashville (Tennessee) experiment, where it produces good simulations of vertical profiles of carbon monoxide in a cloud-topped boundary layer.

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Subcloud-Layer Feedbacks Driven by the Mass Flux of Shallow Cumulus Convection over Land

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-13-0192.1 ◽

2014 ◽

Vol 71 (3) ◽

pp. 881-895 ◽

Cited By ~ 21

Author(s):

Bart J. H. van Stratum ◽

Jordi Vilá-Guerau de Arellano ◽

Chiel C. van Heerwaarden ◽

Huug G. Ouwersloot

Keyword(s):

Boundary Layers ◽

Mixed Layer ◽

Mass Flux ◽

Large Eddy Simulations ◽

Cloud Layer ◽

Layer Model ◽

Flux Transport ◽

Shallow Cumulus ◽

Large Eddy ◽

Mixed Layer Model

Abstract The processes and feedbacks associated with the mass flux of shallow cumulus clouds over land are studied by analyzing the results from large-eddy simulations and a mixed-layer model. The primary focus is to study the development of the (well mixed) subcloud layer and understand the four primary feedbacks between the subcloud-layer dynamics and cumulus mass flux. Guided by numerical experiments in large-eddy simulations that show the transition from clear to cloudy boundary layers at midlatitudes over land, the feedbacks introduced by shallow cumuli are first conceptually described. To study the complex interplay between the subcloud and cloud layer, a mixed-layer model is proposed and validated with large-eddy simulations for the Atmospheric Radiation Measurement Southern Great Plains case. The mixed-layer model is shown to identify and reproduce the most relevant feedbacks in the transition from clear to cloudy boundary layers: a reduced mixed-layer growth and drying of the subcloud layer by enhanced entrainment and mass flux transport of moisture to the cloud layer. To complete the study, the strength of the different feedbacks is further quantified by an analysis of the individual contributions to the tendency of the relative humidity at the top of the mixed layer.

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

Journal of the Atmospheric Sciences ◽

10.1175/jas3888.1 ◽

2007 ◽

Vol 64 (4) ◽

pp. 1230-1248 ◽

Cited By ~ 193

Author(s):

A. Pier Siebesma ◽

Pedro M. M. Soares ◽

João Teixeira

Keyword(s):

Boundary Layer ◽

Boundary Layers ◽

Mass Flux ◽

Convective Boundary Layer ◽

Weather Prediction ◽

Eddy Diffusivity ◽

Moist Convection ◽

Convective Boundary ◽

New Approach ◽

Convective Boundary Layers

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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An Integrated TKE-Based Eddy Diffusivity/Mass Flux Boundary Layer Closure for the Dry Convective Boundary Layer

Journal of the Atmospheric Sciences ◽

10.1175/2011jas3548.1 ◽

2011 ◽

Vol 68 (7) ◽

pp. 1526-1540 ◽

Cited By ~ 20

Author(s):

Marcin L. Witek ◽

Joao Teixeira ◽

Georgios Matheou

Keyword(s):

Boundary Layer ◽

Kinetic Energy ◽

Boundary Layers ◽

Mass Flux ◽

Model Comparison ◽

Eddy Diffusivity ◽

Heat Fluxes ◽

Convective Boundary ◽

1D Model ◽

Convective Boundary Layers

Abstract This study presents a new approach to the eddy diffusivity/mass flux (EDMF) framework for the modeling of convective boundary layers. At the root of EDMF lies a decomposition of turbulent transport mechanisms into strong ascending updrafts and smaller-scale turbulent motions. The turbulent fluxes can be therefore described using two conventional approaches: mass flux (MF) for the organized thermals and eddy diffusivity (ED) for the remaining turbulent field. Since the intensities of both MF and ED transports depend on the kinetic energy of the turbulent motions, it seems reasonable to formulate an EDMF framework based on turbulent kinetic energy (TKE). Such an approach allows for more physical and less arbitrary formulations of parameters in the model. In this study the EDMF–TKE coupling is achieved through the use of (i) a new parameterization for the lateral entrainment coefficient ɛ and (ii) the MF contribution to the buoyancy source of TKE. Some other important features of the EDMF parameterization presented here include a revised mixing length formulation and Monin–Obukhov stability scaling for the surface layer. The scheme is implemented in a one-dimensional (1D) model. Several cases of dry convective boundary layers (CBL) with different surface sensible heat fluxes in the free-convection limit are investigated. Results are compared to large-eddy simulation (LES). Good agreement between LES and the 1D model is achieved with respect to mean profiles, boundary layer evolution, and updraft characteristics. Some disagreements between the models are found to most likely relate to deficiencies in the TKE simulation in the 1D model. Comparison with other previously established ɛ parameterizations shows that the new TKE-based formulation leads to equally accurate, and in many respects better, simulation of the CBL. The encouraging results obtained with the proposed EDMF framework indicate that full integration of EDMF with higher-order closures is possible and can further improve boundary layer simulations.

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