Fluctuation-Dissipation, Stochasticity, and Climate-Dependent Subgrid-Scale Parameterizations for Efficient Climate Models

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For several applications in climate modeling, e.g. paleoclimatology or climate sensitivity studies, there is need for an especially efficient atmosphere component. Low-order models, based on empirical orthogonal functions (EOFs) and using an empirical deterministic linear subgrid-scale (SGS) parameterization, compare well with general circulation models, so that they could be an interesting tool in this regard. A remaining problem has been the climate sensitivity of the empirical SGS parameterization. Two closely interrelated approaches shall be investigated to address this: (1) Recent work indicates that the fluctuation-dissipation theorem (FDT) has a potential for predicting the response of an empirical SGS parameterization to external perturbations, especially if the system which it is applied to has enough fast components. The barotropic vorticity equation used in that study allows only barotropic planetary waves. It is to therefore to be expected that in a more realistic setting the FDT strategy will be even more fruitful. Hence, and also on the path to successively increasing realism, it is planned to extend the FDT approach to low-order models of quasigeostrophic three-layer (QG3L) dynamics, allowing synoptic-scale baroclinic waves, with an empirical linear-stochastic (Ornstein-Uhlenbeck, OU) parameterization.(2) Even more based on first principles than the approach with an empirical OU parameterization is stochastic mode reduction (SMR). The explicit derivation of the effective fast-mode impact in SMR, with multiplicative noise and nonlinear deterministic terms supplementing the forcing and additive noise of an OU parameterization, is expected to yield more robust a model behavior in a perturbed climate than a direct, purely data-driven, OU parameterization of the SGS. As models developed by such methods tend to have a climate bias, however, and given the success of the empirical methods described above, it is intended to try and improve the performance of SMR low-order models by empirically modifying their deterministic forcing and linear dynamics. Once more in the QG3L context, the FDT shall be used for predicting the response of all empirical elements in the modified SMR models to external perturbations.The ultimate purpose of these efforts is an efficient atmospheric model, based on first principles as much as presumably possible at the present state of the art, and using the FDT for controlling the climate dependence of the remaining empirical elements.