Preventing Catastrophic Filter Divergence Using Adaptive Additive Inflation for Baroclinic Turbulence

Yoonsang Lee, Andrew J. Majda and Di Qi*
Courant Institute

Ensemble based filtering methods have proved to be indispensable tools in science and engineering as they allow computationally cheap, low dimensional ensemble state approximation for extremely high dimensional turbulent dynamical systems. One important issue hindering the applications of the standard ensemble filtering methods to high-dimensional systems is the prevalence of catastrophic filter divergence, which frequently drives the filter predictions to infinity. Adaptive additive inflation combined with localized is introduced to stabilize the ensemble methods and improve the filtering skills. Two-layer quasi-geostrophic equations which are classical idealized models for geophysical turbulence are proposed here as test models to check the catastrophic filter divergence. Both a coarse-grained ocean code, which ignores the small-scale parameterization, and stochastic superparameterization (SP), which is a seamless multi- scale method developed for large-scale models without scale-gap between the resolved and unresolved scales, are applied to generate large-scale model forecasts with a spatial resolution 48 × 48 compared with the full DNS resolution 256 × 256. The methods are tested in various dynamical regimes in the ocean, and catastrophic filter divergence is reported for the standard filter case without inflation. Using both the ocean code and stochastic superparameterization, various kinds of model inflation with or without model localization are compared. It shows that proper adaptive additive inflation can effectively stabilize the ensemble methods uniformly without catastrophic filter divergence in all the regimes. Furthermore, stochastic superparameterization achieves accurate filtering skills with localization while the ocean code performs poor even with localization.

*Preference: Poster