Data assimilation is uniquely challenging in weather forecasting due to the high dimensionality of the employed models and the nonlinearity of the governing equations. Although current operational schemes are used successfully, our understanding of their long-term error behavior is still incomplete. In this work, we study the error of some simple data assimilation schemes in the presence of unbounded (e.g., Gaussian) noise on a wide class of dissipative dynamical systems with certain properties, including the Lorenz models and the two-dimensional incompressible Navier-Stokes equations. We exploit the properties of the dynamics to derive analytic bounds on the long-term error for individual realizations of the noise in time. These bounds are proportional to the variance of the noise. Furthermore, we find that the error exhibits a form of stationary behavior, and in particular an accumulation of error does not occur. This improves on previous results in which either the noise was bounded or the error was considered in expectation only.

Almost sure error bounds for data assimilation in dissipative systems with unbounded observation noise

Kuna T.
2020

Abstract

Data assimilation is uniquely challenging in weather forecasting due to the high dimensionality of the employed models and the nonlinearity of the governing equations. Although current operational schemes are used successfully, our understanding of their long-term error behavior is still incomplete. In this work, we study the error of some simple data assimilation schemes in the presence of unbounded (e.g., Gaussian) noise on a wide class of dissipative dynamical systems with certain properties, including the Lorenz models and the two-dimensional incompressible Navier-Stokes equations. We exploit the properties of the dynamics to derive analytic bounds on the long-term error for individual realizations of the noise in time. These bounds are proportional to the variance of the noise. Furthermore, we find that the error exhibits a form of stationary behavior, and in particular an accumulation of error does not occur. This improves on previous results in which either the noise was bounded or the error was considered in expectation only.
File in questo prodotto:
File Dimensione Formato  
Oljaca_broecker_Kuna_Almost_sure_bounds_M116230-gg.pdf

non disponibili

Descrizione: PDF
Tipologia: Documento in Versione Editoriale
Licenza: Creative commons
Dimensione 883.08 kB
Formato Adobe PDF
883.08 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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: http://hdl.handle.net/11697/176632
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact