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A Scalable Approach for Variational Data Assimilation

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Abstract

Data assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state (the forecast). The DA is an inverse and ill posed problem usually used to handle a huge amount of data, so, it is a large and computationally expensive problem. Here we focus on scalable methods that makes DA applications feasible for a huge number of background data and observations. We present a scalable algorithm for solving variational DA which is highly parallel. We provide a mathematical formalization of this approach and we also study the performance of the resulted algorithm.

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Notes

  1. It was shown [28] that incremental 3D-Var is equivalent to a GaussNewton method [10] (i.e. an approximation to a Newton iteration, in which the second-order terms of the Hessian are neglected) applied to the full nonlinear regularization functional.

  2. The idea of using the L-BFGS method in variational data assimilation is not new because of its modest storage requirements and its high performance on large-scale unconstrained convex minimization [39, 46]. L-BFGS method is a Quasi–Newton method that can be viewed as extension of conjugate-gradient methods in which the addition of some modest storage serves to accelerate the convergence rate. The L-BFGS update formula generates the matrices approximating the Hessian using information from the last \(m\) Quasi-Newton iterations, where \(m\) is determined by the user (generally \(3 \le m \le 30\)). After having used the \(m\) vector storage locations for \(m\) quasi-Newton updates, the approximation of the Hessian matrix is updated by dropping the oldest information and replacing it by the newest information. Hence, time complexity of the L-BFGS increases linearly with the size of the \(m\) vectors [30].

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Authors and Affiliations

  1. Department of Mathematics and Applications, University of Naples Federico II, Naples, Italy

    Luisa D’Amore & Rossella Arcucci

  2. Istituto di Chimica e Tecnologia dei Polimeri, CNR, Naples, Italy

    Luisa Carracciuolo

  3. SPACI c/o Department of Mathematics and Applications, University of Naples Federico II, Naples, Italy

    Almerico Murli

Authors
  1. Luisa D’Amore
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  2. Rossella Arcucci
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  3. Luisa Carracciuolo
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  4. Almerico Murli
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Correspondence to Luisa D’Amore.

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D’Amore, L., Arcucci, R., Carracciuolo, L. et al. A Scalable Approach for Variational Data Assimilation. J Sci Comput 61, 239–257 (2014). https://doi.org/10.1007/s10915-014-9824-2

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  • DOI: https://doi.org/10.1007/s10915-014-9824-2

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