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We review some recent methods of subgrid-scale parameterization used in the context of climate modeling. These methods are developed to take into account (subgrid) processes playing an important role in the correct representation of the atmospheric and climate variability. We illustrate these methods on a simple stochastic triad system relevant for the atmospheric and climate dynamics, and we show in particular that the stability properties of the underlying dynamics of the subgrid processes has a considerable impact on their performances.
A stochastic subgrid-scale parameterization based on the Ruelles response theory and proposed in Wouters and Lucarini [2012] is tested in the context of a low-order coupled ocean-atmosphere model for which a part of the atmospheric modes are consider
A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead to instab
Quantifying how distinguishable two stochastic processes are lies at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and ease of u
Global climate models represent small-scale processes such as clouds and convection using quasi-empirical models known as parameterizations, and these parameterizations are a leading cause of uncertainty in climate projections. A promising alternativ
Recently, a variational approach has been introduced for the paradigmatic Kardar--Parisi--Zhang (KPZ) equation. Here we review that approach, together with the functional Taylor expansion that the KPZ nonequilibrium potential (NEP) admits. Such expan