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

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dc.contributor.authorKhouider, Boualem
dc.contributor.authorLeclerc, Etienne
dc.date.accessioned2020-07-06T16:46:17Z
dc.date.available2020-07-06T16:46:17Z
dc.date.copyright2019en_US
dc.date.issued2019
dc.description.abstractThe representation of clouds and organized tropical convection remains one of the biggest sources of uncertainties in climate and long‐term weather prediction models. Some of the most common cumulus parameterization schemes, namely, mass‐flux schemes, rely on the quasi‐equilibrium (QE) closure, which assumes that convection consumes the large‐scale instability and restores large‐scale equilibrium instantaneously. However, the QE hypothesis has been challenged both conceptually and in practice. Subsequently, the QE assumption was relaxed, and instead, prognostic equations for the cloud work function (CWF) and the cumulus kinetic energy (CKE) were derived and used. It was shown that even if the CWF kernel serves to damp the CWF, the prognostic system exhibits damped oscillations on a timescale of a few hours, giving parameterized‐cumulus‐clouds enough memory to interact with each other, with the environment, and with stratiform anvils in particular. Herein, we show that when cloud‐cloud interactions are reintroduced into the CWF‐CKE equations, the coupled system becomes unstable. Moreover, we couple the CWF‐CKE prognostic equations to dynamical equations for the cloud area fractions, based on the mean field limit of a stochastic multicloud model. Qualitative analysis and numerical simulations show that the CKE‐CWF‐cloud area fraction equations exhibit interesting dynamics including multiple equilibria, limit cycles, and chaotic behavior both when the large‐scale forcing is held fixed and when it oscillates with various frequencies. This is representative of cumulus convection variability, and its capability to transition between various regimes of organization at multiple scales and regimes of scattered convection, in an intermittent and chaotic fashion.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.description.sponsorshipThe research of B. K. is partially funded by a grant from the Natural Sciences and Engineering Research Council of Canada (NSERC). This research was conducted in the context of E. L.'s NSERC Undergraduate Student Research Award. No new data has been used during this research. We are grateful to Mitch Moncrieff and the two other anonymous referees for their thoughtful comments and suggestions that greatly helped improve this paper from its original submission.en_US
dc.identifier.citationKhouider, B. & Leclerc, E. (2019). Toward a Stochastic Relaxation for the Quasi- Equilibrium Theory of Cumulus Parameterization: Multicloud Instability, Multiple Equilibria, and Chaotic Dynamics. Journal of Advances in Modeling Earth Systems, 11(8), 2474-2502. https://doi.org/10.1029/2019MS001627.en_US
dc.identifier.urihttps://doi.org/10.1029/2019MS001627
dc.identifier.urihttp://hdl.handle.net/1828/11894
dc.language.isoenen_US
dc.publisherJournal of Advances in Modeling Earth Systemsen_US
dc.subjectcumulus parameterization
dc.subjectmass flux
dc.subjectprognostic closure
dc.subjectcloud area fraction
dc.subjectchaotic dynamics
dc.subjectmultiple equilibria
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleToward a Stochastic Relaxation for the Quasi-Equilibrium Theory of Cumulus Parameterization: Multicloud Instability, Multiple Equilibria, and Chaotic Dynamicsen_US
dc.typeArticleen_US

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