Abstract
Abstract. A new framework is proposed for the evaluation of stochastic subgrid-scale parameterizations in the context of the Modular Arbitrary-Order Ocean-Atmosphere Model (MAOOAM), a coupled ocean–atmosphere model of intermediate complexity. Two physically based parameterizations are investigated – the first one based on the singular perturbation of Markov operators, also known as homogenization. The second one is a recently proposed parameterization based on Ruelle's response theory. The two parameterizations are implemented in a rigorous way, assuming however that the unresolved-scale relevant statistics are Gaussian. They are extensively tested for a low-order version known to exhibit low-frequency variability (LFV), and some preliminary results are obtained for an intermediate-order version. Several different configurations of the resolved–unresolved-scale separations are then considered. Both parameterizations show remarkable performances in correcting the impact of model errors, being even able to change the modality of the probability distributions. Their respective limitations are also discussed.
Highlights
Climate models are not perfect, as they cannot encompass the whole world in their description
It raises the question about the mechanism of this rather drastic modification: is it the noise that changes the dynamics or does the noise trigger and shift a bifurcation of the unresolved system, which induces the change in modality? To give some insight about this latter possibility, we considered the noLFV parameter set and increased the ocean– atmosphere wind stress coupling parameter d to 5 × 10−9
We have introduced a new framework to test different stochastic parameterization methods in the context of the ocean–atmosphere coupled model Modular Arbitrary-Order Ocean-Atmosphere Model (MAOOAM)
Summary
Climate models are not perfect, as they cannot encompass the whole world in their description. A revival of interest in stochastic parameterization methods for climate systems has occurred, due to the availability of new mathematical methods to perform the reduction of ordinary differential equations (ODEs) systems: either based on the conditional averaging (Kifer, 2001; Arnold, 2001; Arnold et al, 2003), on the singular perturbation theory of Markov processes (Majda et al, 2001) (MTV, Majda–Timofeyev–Vanden-Eijnden), on the conditional Markov chain (Crommelin and Vanden-Eijnden, 2008), or on Ruelle’s response theory (Wouters and Lucarini, 2012) and non-Markovian reduced stochastic equations (Chekroun et al, 2014, 2015) These methods have all in common a rigorous mathematical framework. One may ask the question of the influence of the fast atmospheric processes on the slower atmospheric modes as well as on the very slow ocean This problem was already addressed by the authors in Demaeyer and Vannitsem (2017) for a particular decomposition of the atmospheric modes based on the existence of an underlying invariant manifold.
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