A New Stochastic Model for the Boundary Layer Clouds and Stratocumulus Phase Transition Regimes: Open Cells, Closed Cells, and Convective Rolls

Abstract

Adequate forecasting, nowcasting, and parameterization of fog and low clouds is still challenging despite being the focus of intensive research for a long time. Stratocumulus clouds have the ability to self‐organize into a variety of topological structures, including closed and open convection cells, convection rolls, and scattered cumulus. A lot is known about the large‐scale conditions in which shallow clouds and fog develop and decay. However, because of the various complex interactions with the environment, transitions between these various cloud regimes are hard to capture in numerical models. Recent work viewed these cloud regimes as the equilibrium states of phase transition in a stochastic model. Here we build on this idea to propose a new stochastic model based on the lattice particles‐Ising model of statistical mechanics, bringing in important improvements by allowing, for example, multiple equilibria and for direct feedback onto the large‐scale dynamics. Idealized numerical simulations demonstrate that the new model reproduces qualitatively the observed regimes of stratocumulus when the external forcing is varied. The new model forms a metastable dynamical system where transitions between extreme regimes occur dynamically, that is, within the same numerical simulation, for a large range of fixed parameter values, and sometimes lead to the co‐occurrence of mixed states with pockets of closed cells and open cells intercepted by regions of scattered cloudiness, resembling the emergence of convection rolls in nature. This is believed to be a step forward in improving the parameterization of shallow clouds in climate models.

Toward a Stochastic Relaxation for the Quasi‐Equilibrium Theory of Cumulus Parameterization: Multicloud Instability, Multiple Equilibria, and Chaotic Dynamics

“…As expected from the mean field CAF model (Khouider & Bihlo, 2018;Majda & Khouider, 2002), the cases U 0 = 7 and U 0 = 8 present regimes of multiple equilibria. In the first case, the system begins with a single equilibrium that is near = 0 and transitions to a regime with three equilibrium points when F is roughly between 6 and 7.5, to a regime with again a single equilibrium but near = 1.…”

“…Simple algebra shows that the equilibrium solutions of satisfy where C , D , E are positive constants that depend on the parameters F , J , γ , and H . Because is + ∞ at σ =0 and −1 at σ =1, there is a positive, odd, number of solutions to this equation that are easily computed using a root‐finding numerical technique (Khouider & Bihlo, ; Majda & Khouider, ).…”

“…where C, D, E are positive constants that depend on the parameters F, J, , and H. Because ( ) is +∞ at = 0 and −1 at = 1, there is a positive, odd, number of solutions to this equation that are easily computed using a root-finding numerical technique (Khouider & Bihlo, 2018;Majda & Khouider, 2002).…”

Shallow-cloud impact on climate and uncertainty: A simple stochastic model

“…As background, phase transitions are seen in a variety of contexts in statistical physics, such as magnetism (with two phases-spin-up and spin-down) and water (with three phases-solid, liquid, and gas) [44]. It has been proposed that shallow clouds may also exhibit phase transitions, where the two phases could be open-cell and closed-cell stratocumulus phases, and/or cloudy and non-cloudy phases as indicated by cloud fraction [22,38]. Other possible phase transitions related to deep convection have also been proposed and investigated in some detail [1,18,19,28,30,39,40].…”

Parallelizing a serial code: open–source module, EZ Parallel 1.0, and geophysics examples

“…The EZP software should be useful for several different scenarios. For example, simulations of idealized models are commonly used, such as quasi-geostrophic (QG) models for the atmosphere or ocean (e.g., Thompson and Young, 2007;Edwards et al, 2020a, b), stochastic models of cloud patterns (e.g., Hottovy and Stechmann, 2015;Ahmed and Neelin, 2019;Khouider and Bihlo, 2019), tropical circulation models (e.g., Neelin and Zeng, 2000;Lin and Neelin, 2002;Khouider and Majda, 2005;Lin, 2009), and coupled ocean-atmosphere models for El Niño-Southern Oscillation (ENSO) (e.g., Zebiak and Cane, 1987;Xie and Jin, 2018;Thual et al, 2016Thual et al, , 2019, to name only a few examples. Such idealized models have typically been simulated using serial codes, in large part due to the large time and effort required to parallelize a serial code.…”