The atmospheric boundary layer and the "gray zone" of turbulence: a critical review

Recent increases in computing power mean that atmospheric models for numerical weather prediction are now able to operate at grid spacings of the order of a few hundred meters, comparable to the dominant turbulence length scales in the atmospheric boundary layer. As a result, models are starting to partially resolve the coherent overturning structures in the boundary layer. In this resolution regime, the so‐called boundary‐layer "gray zone", neither the techniques of high‐resolution atmospheric modeling (a few tens of meters resolution) nor those of traditional meteorological models (a few kilometers resolution) are appropriate because fundamental assumptions behind the parameterizations are violated. Nonetheless, model simulations in this regime may remain highly useful. In this paper, a newly‐formed gray‐zone boundary‐layer community lays the basis for parameterizing gray‐zone turbulence, identifies the challenges in high‐resolution atmospheric modeling and presents different gray‐zone boundary‐layer models. We discuss both the successful applications and the limitations of current parameterization approaches, and consider various issues in extending promising research approaches into use for numerical weather prediction. The ultimate goal of the research is the development of unified boundary‐layer parameterizations valid across all scales

A Binomial Stochastic Framework for Efficiently Modeling Discrete Statistics of Convective Populations

Understanding the coupling between convective clouds and the general circulation, as well as addressing the gray zone problem in convective parameterization, requires insight into the genesis and maintenance of spatial patterns in cumulus cloud populations. In this study, a simple toy model for recreating populations of interacting convective objects as distributed over a two‐dimensional Eulerian grid is formulated to this purpose. Key elements at the foundation of the model include i) a fully discrete formulation for capturing discrete behavior in convective properties at small population sample sizes, ii) object age‐dependence for representing life‐cycle effects, and iii) a prognostic number budget allowing for object interactions and co‐existence of multiple species. A primary goal is to optimize the computational efficiency of this system. To this purpose the object birth rate is represented stochastically through a spatially aware Bernoulli process. The same binomial stochastic operator is applied to horizontal advection of objects, conserving discreteness in object number. The applicability to atmospheric convection as well as behavior implied by the formulation is assessed. Various simple applications of the BiOMi model (Binomial Objects on Microgrids) are explored, suggesting that important convective behavior can be captured at low computational cost. This includes i) subsampling effects and associated powerlaw scaling in the convective gray zone, ii) stochastic predator‐prey behavior, iii) the downscale turbulent energy cascade, and iv) simple forms of spatial organization and convective memory. Consequences and opportunities for convective parameterization in next‐generation weather and climate models are discussed.Plain Language Summary: Convective clouds play a crucial role in Earth's climate. The way they interact with the atmospheric circulation is not well understood, and is associated with long‐standing problems in weather forecasting and climate prediction. Recent research has suggested that the spatial structure of these cloud fields is a key factor in this problem, and that improving our understanding of such convective cloud patterns is crucial for making progress. This study explores a new model framework for generating such cloud patterns, consisting of populations of convective objects on small grids. The objects are born in a random way, complete a life cycle, and can freely move around on the grid. They can also interact and form larger clusters, obeying certain rules of interaction. The way the objects behave and move around features some key innovations compared to previous ecosystem models of this kind. These are introduced to optimize the performance and reduce run time on a computer. Various experiments are conducted to explore the new model, illustrating that well‐known behavior of convective populations is reproduced. These tests also highlight opportunities created for improving convection in weather and climate models.Key Points: A scale‐aware stochastic number generator based on a Bernoulli process is applied to model object births and advection on Eulerian grids. Discreteness in object number is conserved, while an age dimension is included to represent object life cycle effects. Population subsampling effects in the convective gray zone are reproduced, while simple applications capture well‐known convective behavior.U.S. Department of Energy (DOE) http://dx.doi.org/10.13039/10000001

A Binomial Stochastic Framework for Efficiently Modeling Discrete Statistics of Convective Populations

Understanding the coupling between convective clouds and the general circulation, as well as addressing the gray zone problem in convective parameterization, requires insight into the genesis and maintenance of spatial patterns in cumulus cloud populations. In this study, a simple toy model for recreating populations of interacting convective objects as distributed over a two-dimensional Eulerian grid is formulated to this purpose. Key elements at the foundation of the model include i) a fully discrete formulation for capturing discrete behavior in convective properties at small population sample sizes, ii) object age-dependence for representing life-cycle effects, and iii) a prognostic number budget allowing for object interactions and co-existence of multiple species. A primary goal is to optimize the computational efficiency of this system. To this purpose the object birth rate is represented stochastically through a spatially aware Bernoulli process. The same binomial stochastic operator is applied to horizontal advection of objects, conserving discreteness in object number. The applicability to atmospheric convection as well as behavior implied by the formulation is assessed. Various simple applications of the BiOMi model (Binomial Objects on Microgrids) are explored, suggesting that important convective behavior can be captured at low computational cost. This includes i) subsampling effects and associated powerlaw scaling in the convective gray zone, ii) stochastic predator-prey behavior, iii) the downscale turbulent energy cascade, and iv) simple forms of spatial organization and convective memory. Consequences and opportunities for convective parameterization in next-generation weather and climate models are discussed

Investigating the Scale Adaptivity of a Size-Filtered Mass Flux Parameterization in the Gray Zone of Shallow Cumulus Convection

Abstract In this study, the scale adaptivity of a new parameterization scheme for shallow cumulus clouds in the gray zone is investigated. The eddy diffusivity/multiple mass flux [ED(MF)n] scheme is a bin-macrophysics scheme in which subgrid transport is formulated in terms of discretized size densities. While scale adaptivity in the ED component is achieved using a pragmatic blending approach, the MF component is filtered such that only the transport by plumes smaller than the grid size is maintained. For testing, ED(MF)n is implemented into a large-eddy simulation (LES) model, replacing the original subgrid scheme for turbulent transport. LES thus plays the role of a nonhydrostatic testing ground, which can be run at different resolutions to study the behavior of the parameterization scheme in the boundary layer gray zone. In this range, convective cumulus clouds are partially resolved. The authors find that for quasi-equilibrium marine subtropical conditions at high resolutions, the clouds and the turbulent transport are predominantly resolved by the LES. This partitioning changes toward coarser resolutions, with the representation of shallow cumulus clouds gradually becoming completely carried by the ED(MF)n. The way the partitioning changes with grid spacing matches the behavior diagnosed in coarse-grained LES fields, suggesting that some scale adaptivity is captured. Sensitivity studies show that the scale adaptivity of the ED closure is important and that the location of the gray zone is found to be moderately sensitive to some model constants.</jats:p

What determines the fate of rising parcels in a heterogeneous environment?

© 2016. The Authors. We investigate the potential impact of the local environment on rising parcels in a convective boundary layer. To this end, we use data from an LES simulation of a shallow convective cloud field to feed a parcel model with a range of different local environments, representative of the heterogeneous environment inside a shallow cumulus cloud layer. With this method we can study the statistics of an ensemble of rising parcels, but also the behavior of individual parcels. Through the use of a heterogeneous environment, the interactions between different parcels are indirectly represented. The method, despite its simplicity, allows closer investigation of mechanisms like parcel screening and buoyancy sorting that have frequently been proposed in cumulus parameterization. The relative importance of the entrainment formulation can be assessed, considering various classic entrainment formulations. We found that while the entrainment formulation does affect parcel behavior, the impact of the local environment is significantly more important in determining the eventual fate of the parcel. Using a constant entrainment rate can already explain much of the variation in termination heights seen in nature and LES. The more complex entrainment models then seem to act on top of this mechanism, creating second-order adaptations in the main distribution as established by the heterogeneity of the environment. A parcel budget analysis was performed for two limit cases, providing more insight into the impact of the local environment on parcel behavior. This revealed that parcel screening inside cumulus clouds can be effective in enabling parcels to reach greater heights

Size-Dependent Characteristics of Surface-Rooted Three-Dimensional Convective Objects in Continental Shallow Cumulus Simulations

A segmentation algorithm is applied to high resolution simulations of shallow continental convection to identify individual convective 3D objects within the convective boundary layer, in order to investigate which properties of the objects vary with the object width. The study analyses the geometry of the objects, along with their profiles of vertical velocity and total water, to assess various assumptions often used in spectral mass-flux convection schemes. The methodology of this paper is unique in that we use (a) a novel application of the watershed algorithm to detect individual objects in the constantly evolving continental boundary layer efficiently, and (b) an unprecedentedly large number of simulations being analyzed. In total, 26 days of LASSO simulations at the Atmospheric Radiation Measurement Southern Great Plains site are analyzed, yielding roughly one million objects. Plume-like surface-rooted objects are found to be omnipresent, the vertical extent of which is strongly dependent on the object width. The vertical velocity and moisture anomaly profiles of the widest objects are roughly consistent with the classic buoyancy-driven rising plume model. The kinematic and thermodynamic properties of the objects vary with object width. This width dependence is strongest above cloud base, but much weaker below. Finally the impact of neglecting the contribution of covariances to the vertical moisture flux, which is commonly used in mass-flux parameterizations, is investigated. The average effect of neglecting covariances increases linearly with object width, leading to a 20% flux underestimation for 2 km wide objects. Implications of the results for spectral convection scheme development are briefly discussed