Abstract
In this article we develop further an algorithm for data assimilation based upon a shadowing refinement technique [de Leeuw et al., SIAM J. Appl. Dyn. Syst., 17 (2018), pp. 2446-2477] to take partial observations into account. Our method is based on a regularized Gauss-Newton method. We prove local convergence to the solution manifold and provide a lower bound on the algorithmic time step. We use numerical experiments with the Lorenz 63 and Lorenz 96 models to illustrate convergence of the algorithm and show that the results compare favorably with a variational technique-weak-constraint four-dimensional variational method-and a shadowing technique-pseudo-orbit data assimilation. Numerical experiments show that a preconditioner chosen based on a cost function allows the algorithm to find an orbit of the dynamical system in the vicinity of the true solution.
| Original language | English |
|---|---|
| Pages (from-to) | 879-902 |
| Number of pages | 24 |
| Journal | SIAM Journal on Applied Dynamical Systems |
| Volume | 21 |
| Issue number | 2 |
| Early online date | 11 Apr 2022 |
| DOIs | |
| Publication status | Published - Jun 2022 |
Bibliographical note
Funding Information:\ast Received by the editors October 31, 2018; accepted for publication (in revised form) by C. Topaz November 10, 2021; published electronically April 11, 2022. https://doi.org/10.1137/18M1223897 Funding: 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, PO Box 94079, 1090 GB Amsterdam, Netherlands ([email protected]). \ddagger VU Amsterdam, Department of Mathematics, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands ([email protected], https://math.vu.nl/\sim S.Dubinkina/).
Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics.
Funding
\ast Received by the editors October 31, 2018; accepted for publication (in revised form) by C. Topaz November 10, 2021; published electronically April 11, 2022. https://doi.org/10.1137/18M1223897 Funding: 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, PO Box 94079, 1090 GB Amsterdam, Netherlands ([email protected]). \ddagger VU Amsterdam, Department of Mathematics, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands ([email protected], https://math.vu.nl/\sim S.Dubinkina/).
Keywords
- data assimilation
- partial observations
- shadowing
- tangent space decomposition