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

• Published in: Journal of advances in modeling earth systems 2021-03, Vol.13 (3), p.n/a
• Main Authors: Neggers, Roel A. J., Griewank, Philipp J.
• Format: Article
• Language: English
• Subjects: Advection; Age; Atmospheric convection; binomial sampling; Climate models; Clouds; Convective clouds; Cumulus clouds; Eddy kinetic energy; Efficiency; General circulation; gray zone; Horizontal advection; INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; microgrids; Modelling; object interactions; Parameterization; Physics; Population; population modeling; Predators; Prey; Scaling; Spacetime; Statistical methods; Stochastic processes; Turbulent energy
• ISSN: 1942-2466; 1942-2466
• DOI: 10.1029/2020MS002229

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