Abstract
The state-of-the-art data assimilation methods used today in operational weather prediction centers around the world can be classified as generalized one-way coupled impulsive synchronization. This classification permits the investigation of hybrid data assimilation methods, which combine dynamic error estimates of the system state with long time-averaged (climatological) error estimates, from a synchronization perspective. Illustrative results show how dynamically informed formulations of the coupling matrix (via an Ensemble Kalman Filter, EnKF) can lead to synchronization when observing networks are sparse and how hybrid methods can lead to synchronization when those dynamic formulations are inadequate (due to small ensemble sizes). A large-scale application with a global ocean general circulation model is also presented. Results indicate that the hybrid methods also have useful applications in generalized synchronization, in particular, for correcting systematic model errors.
Highlights
Data assimilation can broadly be defined as the mathematical discipline dedicated to the optimal reconciliation of a theoretical model with observed data—a primary application being state estimation of an imperfectly known dynamical system
We describe how data assimilation can be interpreted as a type of synchronization problem in which a modeled system is driven by observations of a natural system and extend this formalism to include the aforementioned hybrid data assimilation techniques
We examine the Lorenz (1996) model (L96) model with forcing term F 1⁄4 8.0 in its reduced dimension (m 1⁄4 6)
Summary
Data assimilation can broadly be defined as the mathematical discipline dedicated to the optimal reconciliation of a theoretical model with observed data—a primary application being state estimation of an imperfectly known dynamical system. At major operational weather forecasting centers around the world, hybrid data assimilation methods that combine a climatological (time-averaged) estimate of forecast errors with a dynamic (time-varying) estimate have been adopted as the primary approach for initializing numerical weather prediction (NWP) models. It has been suggested (Duane et al, 2006; Yang et al, 2006; Carrassi et al, 2008; and Abarbanel et al, 2010) that synchronization may be a useful mechanism to explore for applications to data assimilation.
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