We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method. © 2008 American Institute of Physics.

Carrassi A., Ghil M., Trevisan A., Uboldi F. (2008). Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system. CHAOS, 18(2), 023112-N/A [10.1063/1.2909862].

Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system

Carrassi A.;
2008

Abstract

We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method. © 2008 American Institute of Physics.
2008
Carrassi A., Ghil M., Trevisan A., Uboldi F. (2008). Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system. CHAOS, 18(2), 023112-N/A [10.1063/1.2909862].
Carrassi A.; Ghil M.; Trevisan A.; Uboldi F.
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/841458
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? 0
  • Scopus 42
  • ???jsp.display-item.citation.isi??? 40
social impact