scholarly journals A Diagnostic for Evaluating the Representation of Turbulence in Atmospheric Models at the Kilometric Scale

2011 ◽  
Vol 68 (12) ◽  
pp. 3112-3131 ◽  
Author(s):  
Rachel Honnert ◽  
Valéry Masson ◽  
Fleur Couvreux
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Potential Temperature ◽  
Similarity Function ◽  
Mixing Ratio ◽  
Atmospheric Models ◽  
Convective Boundary ◽  
Similarity Functions ◽  
Partial Similarity ◽  
Convective Boundary Layers

Abstract Turbulence is well represented by atmospheric models at very fine grid sizes, from 10 to 100 m, for which turbulent movements are mainly resolved, and by atmospheric models with grid sizes greater than 2 km, for which those movements are entirely parameterized. But what happens at intermediate scales, Wyngaard’s so-called terra incognita? Here an original method is presented that provides a new diagnostic by calculating the subgrid and resolved parts of five variables at different scales: turbulent kinetic energy (TKE), heat and moisture fluxes, and potential temperature and mixing ratio variances. They are established at intermediate scales for dry and cumulus-topped convective boundary layers. The similarity theorem allows the determination of the dimensionless variables of the problem. When the subgrid and resolved parts are studied, a new dimensionless variable, the dimensionless mesh size , needs to be added to the Deardorff free convective scaling variables, where h is the boundary layer height and hc is the height of the cloud layer. Similarity functions for the subgrid and resolved parts are assumed to be the product of the similarity function of the total (subgrid plus resolved) variables and a “partial” similarity function that depends only on . In order to determine the partial similarity function form, large-eddy simulations (LES) of five dry and cloudy convective boundary layers are used. The resolved and subgrid parts of the variables at coarser grid sizes are then deduced from the LES fields. The evolution of the subgrid and resolved parts in the boundary layer with is as follows: fine grids mainly resolve variables. As the mesh becomes coarser, more eddies are subgrid. Finally, for very large meshes, turbulence is entirely subgrid. A scale therefore exists for which the subgrid and resolved parts are equal. This is obtained for in the case of TKE, 0.4 for the potential temperature variance, and 0.8 for the mixing ratio variance, indicating that the velocity structures are smaller than those for the potential temperature, which are smaller than those for the mixing ratio. Furthermore, boundary layers capped by convective clouds have structures larger than dry boundary layer ones as displayed by the scaling in the partial similarity functions. This new diagnostic gives a reference for evaluating current and future parameterizations at kilometric scales. As an illustration, the parameterizations of a mesoscale model are eventually evaluated at intermediate scales. In its standard version, the model produces too many resolved movements, as the turbulence scheme does not sufficiently represent the impact of the subgrid thermal. This is not true when a mass-flux scheme is introduced. However in this case, a completely subgrid thermal is modeled leading to an overestimation of the subgrid part.

scholarly journals Predictability of Dry Convective Boundary Layers: An LES Study

2016 ◽  
Vol 73 (7) ◽  
pp. 2715-2727 ◽  
Author(s):  
Siddhartha Mukherjee ◽  
Jerôme Schalkwijk ◽  
Harmen J. J. Jonker
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Strong Dependence ◽  
Second Phase ◽  
Error Growth ◽  
Convective Boundary ◽  
Boundary Layer Height ◽  
Eddy Simulation ◽  
Convective Boundary Layers ◽  
Two Phases

Abstract The predictability horizon of convective boundary layers is investigated in this study. Large-eddy simulation (LES) and direct numerical simulation (DNS) techniques are employed to probe the evolution of perturbations in identical twin simulations of a growing dry convective boundary layer. Error growth typical of chaotic systems is observed, marked by two phases. The first comprises an exponential error growth as , with δ0 as the initial error, δ(t) as the error at time t, and Λ as the Lyapunov exponent. This phase is independent of the perturbation wavenumber, and the perturbation energy grows following a self-similar spectral shape dominated by higher wavenumbers. The nondimensional error growth rate in this phase shows a strong dependence on the Reynolds number (Re). The second phase involves saturation of the error. Here, the error growth follows Lorenz dynamics with a slower saturation of successively larger scales. An analysis of the spectral decorrelation times reveals two regimes: an Re-independent regime for scales larger than the boundary layer height and an Re-dependent regime for scales smaller than , which are found to decorrelate substantially faster for increasing Reynolds numbers.

scholarly journals The Vertical Distribution of Radon in Clear and Cloudy Daytime Terrestrial Boundary Layers

2011 ◽  
Vol 68 (1) ◽  
pp. 155-174 ◽  
Author(s):  
Alastair G. Williams ◽  
Wlodek Zahorowski ◽  
Scott Chambers ◽  
Alan Griffiths ◽  
Jörg M. Hacker ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Similarity Theory ◽  
Ground Level ◽  
Structural Features ◽  
Rural Site ◽  
Convective Boundary ◽  
Characteristic Structure ◽  
Exchange Processes ◽  
Convective Boundary Layers

Abstract Radon (222Rn) is a powerful natural tracer of mixing and exchange processes in the atmospheric boundary layer. The authors present and discuss the main features of a unique dataset of 50 high-resolution vertical radon profiles up to 3500 m above ground level, obtained in clear and cloudy daytime terrestrial boundary layers over an inland rural site in Australia using an instrumented motorized research glider. It is demonstrated that boundary layer radon profiles frequently exhibit a complex layered structure as a result of mixing and exchange processes of varying strengths and extents working in clear and cloudy conditions within the context of the diurnal cycle and the synoptic meteorology. Normalized aircraft radon measurements are presented, revealing the characteristic structure and variability of three major classes of daytime boundary layer: 1) dry convective boundary layers, 2) mixed layers topped with residual layers, and 3) convective boundary layers topped with coupled nonprecipitating clouds. Robust and unambiguous signatures of important atmospheric processes in the boundary layer are identifiable in the radon profiles, including “top-down” mixing associated with entrainment in clear-sky cases and strongly enhanced venting and subcloud-layer mixing when substantial active cumulus are present. In poorly mixed conditions, radon gradients in the daytime atmospheric surface layer significantly exceed those predicted by Monin–Obukhov similarity theory. In two case studies, it is demonstrated for the first time that a sequence of vertical radon profiles measured over the course of a single day can consistently reproduce major structural features of the evolving boundary layer.

Structure Functions and Structure Parameters of Velocity Fluctuations in Numerically Simulated Atmospheric Convective Boundary Layer Flows

2020 ◽  
Vol 77 (10) ◽  
pp. 3619-3630
Author(s):  
Jeremy A. Gibbs ◽  
Evgeni Fedorovich
Keyword(s):  
Boundary Layer ◽  
Spectral Method ◽  
Boundary Layers ◽  
Convective Boundary Layer ◽  
Structure Functions ◽  
Inertial Subrange ◽  
Structure Parameters ◽  
Convective Boundary ◽  
Velocity Fluctuations ◽  
Convective Boundary Layers

AbstractWe extend our previous study, which dealt with structure functions of potential temperature fluctuations, and focus on the characteristics of second-order velocity structure functions and corresponding structure parameters in the atmospheric convective boundary layer. We consider the three previously reported methods to compute the structure parameters of turbulent velocity fields: the direct method, the true spectral method, and the approximate spectral method. The methods are evaluated using high-resolution gridded numerical data from large-eddy simulations of shear-free and shear-driven convective boundary layers. Results indicate that the direct and true spectral methods are more suitable than the approximate spectral method, which overestimates the structure parameters of velocity as a result of assuming the inertial-subrange shape of the velocity spectrum for all turbulence scales. Results also suggest that structure parameters of vertical velocity fluctuations are of limited utility because of violations of local isotropy, especially in shear-free convective boundary layers.

scholarly journals Analysis of Resolved and Parameterized Vertical Transports in Convective Boundary Layers at Gray-Zone Resolutions

2013 ◽  
Vol 70 (10) ◽  
pp. 3248-3261 ◽  
Author(s):  
Hyeyum Hailey Shin ◽  
Song-You Hong
Keyword(s):  
Boundary Layers ◽  
Numerical Models ◽  
Potential Temperature ◽  
Grid Size ◽  
Gray Zone ◽  
Subgrid Scale ◽  
Convective Boundary ◽  
Bottom Up ◽  
Large Eddy ◽  
Convective Boundary Layers

Abstract The gray zone of a physical process in numerical models is defined as the range of model resolution in which the process is partly resolved by model dynamics and partly parameterized. In this study, the authors examine the grid-size dependencies of resolved and parameterized vertical transports in convective boundary layers (CBLs) for horizontal grid scales including the gray zone. To assess how stability alters the dependencies on grid size, four CBLs with different surface heating and geostrophic winds are considered. For this purpose, reference data for grid-scale (GS) and subgrid-scale (SGS) fields are constructed for 50–4000-m mesh sizes by filtering 25-m large-eddy simulation (LES) data. As relative importance of shear increases, the ratio of resolved turbulent kinetic energy increases for a given grid spacing. Vertical transports of potential temperature, momentum, and a bottom-up diffusion passive scalar behave in a similar fashion. The effects of stability are related to the horizontal scale of coherent large-eddy structures that change in the different stability. The subgrid-scale vertical transport of heat and the bottom-up scalar are divided into a nonlocal mixing owing to the coherent structures and remaining local mixing. The separate treatment of the nonlocal and local transports shows that the grid-size dependency of the SGS nonlocal flux and its sensitivity to stability predominantly determine the dependency of total (nonlocal plus local) SGS transport.

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

2007 ◽  
Vol 64 (4) ◽  
pp. 1230-1248 ◽  
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.

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

2011 ◽  
Vol 68 (7) ◽  
pp. 1526-1540 ◽  
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.

Subcloud and Cloud-Base Latent Heat Fluxes during Shallow Cumulus Convection

2019 ◽  
Vol 77 (3) ◽  
pp. 1081-1100 ◽  
Author(s):  
Neil P. Lareau
Keyword(s):  
Boundary Layer ◽  
Water Vapor ◽  
Latent Heat ◽  
Surface Fluxes ◽  
Heat Fluxes ◽  
Cloud Base ◽  
Cumulus Convection ◽  
Mixing Ratio ◽  
Convective Boundary ◽  
Water Vapor Mixing Ratio

Abstract Doppler and Raman lidar observations of vertical velocity and water vapor mixing ratio are used to probe the physics and statistics of subcloud and cloud-base latent heat fluxes during cumulus convection at the ARM Southern Great Plains (SGP) site in Oklahoma, United States. The statistical results show that latent heat fluxes increase with height from the surface up to ~0.8Zi (where Zi is the convective boundary layer depth) and then decrease to ~0 at Zi. Peak fluxes aloft exceeding 500 W m−2 are associated with periods of increased cumulus cloud cover and stronger jumps in the mean humidity profile. These entrainment fluxes are much larger than the surface fluxes, indicating substantial drying over the 0–0.8Zi layer accompanied by moistening aloft as the CBL deepens over the diurnal cycle. We also show that the boundary layer humidity budget is approximately closed by computing the flux divergence across the 0–0.8Zi layer. Composite subcloud velocity and water vapor anomalies show that clouds are linked to coherent updraft and moisture plumes. The moisture anomaly is Gaussian, most pronounced above 0.8Zi and systematically wider than the velocity anomaly, which has a narrow central updraft flanked by downdrafts. This size and shape disparity results in downdrafts characterized by a high water vapor mixing ratio and thus a broad joint probability density function (JPDF) of velocity and mixing ratio in the upper CBL. We also show that cloud-base latent heat fluxes can be both positive and negative and that the instantaneous positive fluxes can be very large (~10 000 W m−2). However, since cloud fraction tends to be small, the net impact of these fluxes remains modest.

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