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An important question of climate science is the effect of a changing climate on the long term statistical properties of the atmosphere and ocean dynamics. Mathematically speaking, the question is whether and how statistical quantities of the dynamics (e.g. correlations, averages, variabilities etc) react to changes in the external forcing of the system.A (stochastic or deterministic) dynamical system is said to exhibit linear response if the statistical quantities describing the long term behaviour of the system depend differentiably on the relevant parameter (i.e. the forcing), and therefore a small change in the forcing will result in a small and proportional change of the statistical quantity. A methodology to establish response theory for a class of nonlinear stochastic partial differential equations has recently been provided in [1]. This contribution will discuss the ``ingredients'' necessary for this methodology on an intuitive level. In particular, the required mathematical properties of the system are related to their physical counterparts. The results are applied to stochastic single-layer and two-layer quasi-geostrophic models which are popular in the geosciences to study atmosphere and ocean dynamics.[1] G. Carigi, T. Kuna and J. Bröcker, Linear and fractional response for nonlinear dissipative SPDEs, arXiv, doi = 10.48550/ARXIV.2210.12129, 2022. |
