Articles | Volume 25, issue 3
Nonlin. Processes Geophys., 25, 633–648, 2018

Special issue: Numerical modeling, predictability and data assimilation in...

Nonlin. Processes Geophys., 25, 633–648, 2018

Research article 04 Sep 2018

Research article | 04 Sep 2018

Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error

Colin Grudzien et al.

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Cited articles

Barreira, L. and Pesin, Y.: Lyapunov Exponents and Smooth Ergodic Theory, Student Mathematical Library, American Mathematical Society, 38–40, 2002.
Benettin, G., Galgani, L., Giorgilli, A., and Strelcyn, J.: Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Part 1: Theory, Meccanica, 15, 9–20, 1980.
Bocquet, M.: Ensemble Kalman filtering without the intrinsic need for inflation, Nonlin. Processes Geophys., 18, 735–750,, 2011.
Bocquet, M. and Carrassi, A.: Four-dimensional ensemble variational data assimilation and the unstable subspace, Tellus A, 69, 1304 504, 2017.
Bocquet, M. and Sakov, P.: Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems, Nonlin. Processes Geophys., 19, 383–399,, 2012.
Short summary
Using the framework Lyapunov vectors, we analyze the asymptotic properties of ensemble based Kalman filters and how these are influenced by dynamical chaos, especially in the context of random model errors and small ensemble sizes. Particularly, we show a novel derivation of the evolution of forecast uncertainty for ensemble-based Kalman filters with weakly-nonlinear error growth, and discuss its impact for filter design in geophysical models.