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An Optimization Algorithm for the Meteorological Data Assimilation Problem

In: Recent Progress in Computational and Applied PDES

Author

Listed:
  • Eva Eggeling

    (Fraunhofer-lnstitute for Algorithms and Scientific Computing (SCAI))

  • Shlomo Ta’asan

    (Carnegie Mellon University, Department of Mathematical Sciences)

Abstract

The aim of this paper is to present an efficient optimization algorithm for solving the meteorological data assimilation problem. In our study this inverse problem is formulated as a constrained optimization problem. An accurate model for the problem involves the Navier-Stokes equations and in certain cases the Euler equations. In order to understand diverse intricate aspects of the problem we have focused on the Euler case and formulated three model problems which aim at tackling some of the basic difficulties faced in the real problem. We study the effect of dissipation in finite difference schemes on the identifiability in the problem. Basically, dissipation will result in bad estimation far from the measurement locations due to loss of information as the waves propagate. We demonstrate results for several cases, including the advection equation and a wave equation. For this purpose we use different measurement types in terms of the location of the measurements, the amount and noise level of the data.

Suggested Citation

  • Eva Eggeling & Shlomo Ta’asan, 2002. "An Optimization Algorithm for the Meteorological Data Assimilation Problem," Springer Books, in: Tony F. Chan & Yunqing Huang & Tao Tang & Jinchao Xu & Long-An Ying (ed.), Recent Progress in Computational and Applied PDES, pages 171-181, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-0113-8_12
    DOI: 10.1007/978-1-4615-0113-8_12
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