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This paper contains the latest installment of the authors' project ondeveloping ensemble based data assimilation methodology for high dimensionalfluid dynamics models. The algorithm presented here is a particle filter thatcombines model reduction, tempering, jittering, and nudging. The methodology istested on a two-layer quasi-geostrophic model for a $\beta$-plane channel flowwith $O(10^6)$ degrees of freedom out of which only a minute fraction arenoisily observed. The model is reduced by following the stochastic variationalapproach for geophysical fluid dynamics introduced in Holm (Proc Roy Soc A,2015) as a framework for deriving stochastic parametrisations for unresolvedscales. The reduction is substantial: the computations are done only for$O(10^4)$ degrees of freedom. We introduce a stochastic time-stepping schemefor the two-layer model and prove its consistency in time. Then, we analyze theeffect of the different procedures (tempering combined with jittering andnudging) on the performance of the data assimilation procedure using thereduced model, as well as how the dimension of the observational data (thenumber of "weather stations") and the data assimilation step affect theaccuracy and uncertainty of the results.

Data assimilation for a quasi-geostrophic model with circulation-preserving stochastic transport noise