Projected shadowing-based data assimilation

Bart De Leeuw; Svetlana Dubinkina; Jason Frank; Andrew Steyer; Xuemin Tu; Erik Van Vleck

doi:10.1137/17M1141163

Projected shadowing-based data assimilation

Bart De Leeuw^*
, Svetlana Dubinkina
, Jason Frank
, Andrew Steyer
, Xuemin Tu
, Erik Van Vleck

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by work on assimilation in the unstable subspace [Carrassi et al., Chaos, 18 (2008), 023112; Trevisan, D'Isidoro, and Talagrand, Q. J. R. Meteorol. Soc., 136 (2010), pp. 487-496; Palatella, Carrassi, and Trevisan, J. Phys. A, 46 (2013), 254020] and pseudo-orbit data assimilation [Judd and Smith, Phys. D, 151 (2001), pp. 125-141; Judd et al., J. Atmos. Sci., 65 (2008), pp. 1749-1772; Du and Smith, J. Atmos. Sci., 71 (2014), pp. 469-482]. The algorithm utilizes time dependent projections onto the nonstable subspace determined by employing computational techniques for Lyapunov exponents/vectors. The method is extended to parameter estimation without changing the problem dynamics and we address techniques for adapting the method when (as is commonly the case) observations are not available in the full model state space. We use a combination of analysis and numerical experiments (with the Lorenz 63 and Lorenz 96 models) to illustrate the efficacy of the techniques and show that the results compare favorably with other variational techniques.

Original language	English
Pages (from-to)	2446-2477
Number of pages	32
Journal	SIAM Journal on Applied Dynamical Systems
Volume	17
Issue number	4
DOIs	https://doi.org/10.1137/17M1141163
Publication status	Published - 1 Jan 2018
Externally published	Yes

Funding

\ast Received by the editors July 28, 2017; accepted for publication (in revised form) by E. Sander July 26, 2018; published electronically October 16, 2018. http://www.siam.org/journals/siads/17-4/M114116.html Funding: The work of the fourth and sixth authors was supported by NSF grant DMS-1419047. The work of the fifth author was supported by NSF grants DMS-1419069 and DMS-1723066. The work of the first author was partially supported by the research program Mathematics of Planet Earth 2014 EW project 657.014.001, which is financed by the Netherlands Organisation for Scientific Research (NWO). \dagger Centrum Wiskunde \& Informatica, P.O. Box 94079, 1090 GB Amsterdam, Netherlands ([email protected], [email protected]). \ddagger Utrecht University, Mathematical Insitute, P.O. Box 80010, 3508 TA Utrecht, Netherlands ([email protected]). \S University of Kansas, Department of Mathematics, Lawrence, KS 66405. Current address: Sandia National Laboratories, Albuquerque, NM 87185 ([email protected]). \P University of Kansas, Department of Mathematics, Lawrence, KS 66405 ([email protected], [email protected]).

Funders	Funder number
National Science Foundation	DMS-1419047, DMS-1419069, 1714195, 657.014.001, DMS-1723066
???publication-publication-funding-organisation-not-added???	657.014.001

Keywords

data assimilation
shadowing
synchronization
tangent space decomposition

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10.1137/17M1141163

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title = "Projected shadowing-based data assimilation",

abstract = "In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by work on assimilation in the unstable subspace [Carrassi et al., Chaos, 18 (2008), 023112; Trevisan, D'Isidoro, and Talagrand, Q. J. R. Meteorol. Soc., 136 (2010), pp. 487-496; Palatella, Carrassi, and Trevisan, J. Phys. A, 46 (2013), 254020] and pseudo-orbit data assimilation [Judd and Smith, Phys. D, 151 (2001), pp. 125-141; Judd et al., J. Atmos. Sci., 65 (2008), pp. 1749-1772; Du and Smith, J. Atmos. Sci., 71 (2014), pp. 469-482]. The algorithm utilizes time dependent projections onto the nonstable subspace determined by employing computational techniques for Lyapunov exponents/vectors. The method is extended to parameter estimation without changing the problem dynamics and we address techniques for adapting the method when (as is commonly the case) observations are not available in the full model state space. We use a combination of analysis and numerical experiments (with the Lorenz 63 and Lorenz 96 models) to illustrate the efficacy of the techniques and show that the results compare favorably with other variational techniques.",

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AU - Frank, Jason

AU - Steyer, Andrew

AU - Tu, Xuemin

AU - Van Vleck, Erik

PY - 2018/1/1

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N2 - In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by work on assimilation in the unstable subspace [Carrassi et al., Chaos, 18 (2008), 023112; Trevisan, D'Isidoro, and Talagrand, Q. J. R. Meteorol. Soc., 136 (2010), pp. 487-496; Palatella, Carrassi, and Trevisan, J. Phys. A, 46 (2013), 254020] and pseudo-orbit data assimilation [Judd and Smith, Phys. D, 151 (2001), pp. 125-141; Judd et al., J. Atmos. Sci., 65 (2008), pp. 1749-1772; Du and Smith, J. Atmos. Sci., 71 (2014), pp. 469-482]. The algorithm utilizes time dependent projections onto the nonstable subspace determined by employing computational techniques for Lyapunov exponents/vectors. The method is extended to parameter estimation without changing the problem dynamics and we address techniques for adapting the method when (as is commonly the case) observations are not available in the full model state space. We use a combination of analysis and numerical experiments (with the Lorenz 63 and Lorenz 96 models) to illustrate the efficacy of the techniques and show that the results compare favorably with other variational techniques.

AB - In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by work on assimilation in the unstable subspace [Carrassi et al., Chaos, 18 (2008), 023112; Trevisan, D'Isidoro, and Talagrand, Q. J. R. Meteorol. Soc., 136 (2010), pp. 487-496; Palatella, Carrassi, and Trevisan, J. Phys. A, 46 (2013), 254020] and pseudo-orbit data assimilation [Judd and Smith, Phys. D, 151 (2001), pp. 125-141; Judd et al., J. Atmos. Sci., 65 (2008), pp. 1749-1772; Du and Smith, J. Atmos. Sci., 71 (2014), pp. 469-482]. The algorithm utilizes time dependent projections onto the nonstable subspace determined by employing computational techniques for Lyapunov exponents/vectors. The method is extended to parameter estimation without changing the problem dynamics and we address techniques for adapting the method when (as is commonly the case) observations are not available in the full model state space. We use a combination of analysis and numerical experiments (with the Lorenz 63 and Lorenz 96 models) to illustrate the efficacy of the techniques and show that the results compare favorably with other variational techniques.

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Projected shadowing-based data assimilation

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