# Convective initiation uncertainties without trigger or stochasticity: probabilistic description by the Liouville equation and Bayes' theorem

## Yano, Jun-Ichi ; Ouchtar, Eïda

Initiation of atmospheric moist convection is often so sudden and unexpected that it is often presumed that a special mechanism called a 'trigger' is required in a 'stochastic' manner. This article shows, in contrast, that sudden convective initiation can be induced solely by nonlinearity in the generation rate of kinetic energy by buoyancy, which is always present in a convective system. No additional special mechanism is required. Stochasticity is not an indispensable ingredient either. The article demonstrates these points by taking a convective energy-cycle system describing the evolution of a spectrum of convective mass fluxes truncated into a single deep convective mode. Though this system is highly conceptualized, it is realistic enough to adopt directly as a prognostic closure condition for mass-flux convection parametrization. By adopting a simple system containing only periodic solutions, furthermore, a simple, important point is made that the prediction uncertainty can grow without any randomness, chaos or irregularity in a given system. Even without any of those elements, the uncertainty for convective initiation increases with time, but associated with a periodic modulation following the convective cycle. These tendencies in the uncertainty growth are shown explicitly by time-integrating the probability of the convective system using the Liouville equation. Bayes' theorem leads further to the probability for the timing of convective initiation.

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