Recent insights into the spatial organization of atmospheric convection have emphasized the importance of its correct representation in Earth System Models (ESM). This study explores new opportunities created when combining a thermal population model on a horizontal microgrid with a decentralized vertical transport model. To this purpose the recently proposed BiOMi population model (Binomials on Microgrids) is used. BiOMi mimicks a population of independent but interacting convective thermals, with their birth, movement and life cycle described as Bernoulli processes. Simple rules of interaction are introduced to reflect observed physical behavior in single cumulus clouds, such as pulsating growth and environmental deformation. Under these rules, thermals can congregate and form longer-lived coherent clusters or chains that resemble cumulus clouds. The formation and evolution of these clusters is a form of self-organization that retains convective memory. Through an online clustering method the microgrid is coupled to a spectral EDMF convection scheme, providing the cluster size distribution it needs as input. This way, the inherently 3D structure of organized convection can in principle be captured in reduced but efficient form. The system is fully decentralized in that central top-down bulk closures are avoided. The main science objective of this study is to provide proof of concept of decentralized frameworks of this kind. To this purpose the BiOMi-EDMF scheme as implemented in the DALES circulation model is tested for various LASSO cases of shallow convection at the ARM SGP site. We find that the scheme achieves stable and realistic diurnal quasi-equilibria (as shown in the figure), and that the associated self-organizing patterns on the microgrid are realistic. Impacts of spatial organization and convective memory on the parameterized transport will be investigated.

A clustering method is applied to high resolution simulations of shallow continental convection to investigate the size dependence of coherent structures in the convective boundary layer. The study analyses the geometry of the clusters, along with their profiles of vertical velocity and total water. The main science goal is to assess various assumptions often used in spectral mass-flux convection schemes. Novel aspects of the study methodology include i) a newly developed clustering algorithm, and ii) an unprecedentedly large number of simulations being analysed. In total 26 days of LASSO simulations at the ARM-SGP site are analyzed, yielding roughly one million individual clusters. Plume-like surface-rooted coherent convective clusters are found to be omnipresent, the depth of which is strongly dependent on cluster size. The largest clusters carry vertical structures that are roughly consistent with the classic buoyancy-driven rising plume model, while smaller clusters feature considerable variation in top height. The cluster area is found to strongly vary with height and size, with small clusters losing mass and large clusters gaining mass below cloud base. Similar size dependence is detected in kinematic and thermodynamic properties, being strongest above cloud base but much weaker below. Finally the efficiency of the top-hat approach in flux parameterization is investigated, found to be 80-85 \% including a weak but well-defined dependence on cluster size. Implications of the results for spectral convection scheme development are briefly discussed.

Understanding cloud-circulation coupling in the Trade wind regions, as well as addressing the grey 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 binary behavior at small population sample sizes, ii) object demographics 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. Implied behavior of the formulation is assessed, illustrating that typical powerlaw scaling in the internal variability of subsampled convective populations as found in previous LES studies is reproduced. Various simple applications of the BiOMi model (Binomial Objects on Microgrids) are explored, suggesting that well-known phenomena from nature can be captured at low computational cost. These include i) subsampling effects in the convective grey zone, ii) stochastic predator-prey behavior, iii) the down-scale 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.

Multi-plume convection schemes based on discretized size densities can be easily made scale-aware by size filtering the parametrized plumes to fit the model resolution. Combined with their capability to smoothly transition from shallow to deep convection while being both numerically robust and computationally viable, these bin macrophysics models are well suited to the needs of high resolution NWP and regional climate modeling. One such approach is the ED(MF)n scheme which has previously been evaluated in a single column model against maritime cumulus LES. In this presentation we will confront the ED(MF)n scheme with long-term Doppler lidar observations of shallow cumulus days from the ARM-SGP site in Oklahoma. To do so the ED(MF)n scheme is implemented and tested in a non-hydrostatic model on a microgrid of 8x8 or 16x16 gridpoints. By using a ~10 km resolution this system behaves as a collection of weakly interacting single column models. We will compare the modeled relationship of vertical velocity to plume size against the relationship found in both the Doppler lidar observations and the LASSO LES run routinely at the ARM-SGP site. Next we examine which effect the assumed cloud-size distribution and entrainment as a function of plume size have on the resulting vertical transport.

In this study a spectral model for convective transport is coupled to a thermal population on a horizontal microgrid, with the goal of exploring new ways of representing impacts of spatial organization in cumulus cloud fields. The thermals are considered the smallest building block of convection, with thermal life cycle and movement represented through binomial functions. Thermals interact through two simple rules, reflecting pulsating growth and environmental deformation. Long-lived thermal clusters thus form on the microgrid, exhibiting scale growth and spacing that represent simple forms of spatial organization and memory. Size distributions of cluster number are diagnosed from the microgrid through an online clustering algorithm, and provided as input to a spectral multi-plume Eddy-Diffusivity Mass Flux (EDMF) scheme. This yields a decentralized transport system, with the thermal clusters acting as independent but interacting nodes that carry information about spatial structure. The main objectives of this study are i) to seek proof of concept of this approach, and ii) to gain insight into impacts of spatial organization on convective transport. Single-column model experiments demonstrate satisfactory skill in reproducing two observed cases of continental shallow convection at the ARM SGP site. Metrics expressing self-organization and spatial organization match well with large-eddy simulation results. We find that in this coupled system, spatial organization impacts convective transport primarily through the scale break in the size distribution of cluster number. The rooting of saturated plumes in the subcloud mixed layer plays a key role in this process.