Abstract. In this study we investigate how to use sample data, generated by a fully resolved multiscale model, to construct stochastic representations of unresolved scales in reduced models. We explore three methods to model these stochastic representations. They employ empirical distributions, conditional Markov chains and conditioned Ornstein-Uhlenbeck processes, respectively. The Kac-Zwanzig heat bath model is used as a prototype model to illustrate the methods. We demonstrate that all tested strategies reproduce the dynamics of the resolved model variables accurately. Furthermore, we show that the computational cost of the reduced model is several orders of magnitude lower than that of the fully resolved model.
Abstract:In this study we investigate a covariate-based stochastic approach to parameterize unresolved turbulent processes within a standard model of the idealised, wind-driven ocean circulation. We focus on vertical instead of horizontal coarse-graining, such that we avoid the subtle di culties of horizontal coarsegraining. The corresponding eddy forcing is uniquely de ned and has a clear physical interpretation related to baroclinic instability. We propose to emulate the baroclinic eddy forcing by sampling from the conditional probability distribution functions of the eddy forcing obtained from the baroclinic reference model data. These conditional probability distribution functions are approximated here by sampling uniformly from discrete reference values. We analyze in detail the di erent performances of the stochastic parameterization dependent on whether the eddy forcing is conditioned on a suitable ow-dependent covariate or on a timelagged covariate or on both. The results demonstrate that our non-Gaussian, non-linear methodology is able to accurately reproduce the rst four statistical moments and spatial/temporal correlations of the stream function, energetics, and enstrophy of the reference baroclinic model.
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