Science in China Series D: Earth Sciences

, Volume 52, Issue 2, pp 279–286

An explicit four-dimensional variational data assimilation method based on the proper orthogonal decomposition: Theoretics and evaluation

Article

DOI: 10.1007/s11430-009-0012-4

Cite this article as:
Tian, X. & Xie, Z. Sci. China Ser. D-Earth Sci. (2009) 52: 279. doi:10.1007/s11430-009-0012-4
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Abstract

The proper orthogonal decomposition (POD) method is used to construct a set of basis functions for spanning the ensemble of data in a certain least squares optimal sense. Compared with the singular value decomposition (SVD), the POD basis functions can capture more energy in the forecast ensemble space and can represent its spatial structure and temporal evolution more effectively. After the analysis variables are expressed by a truncated expansion of the POD basis vectors in the ensemble space, the control variables appear explicitly in the cost function, so that the adjoint model, which is used to derive the gradient of the cost function with respect to the control variables, is no longer needed. The application of this new technique significantly simplifies the data assimilation process. Several assimilation experiments show that this POD-based explicit four-dimensional variational data assimilation method performs much better than the usual ensemble Kalman filter method on both enhancing the assimilation precision and reducing the computation cost. It is also better than the SVD-based explicit four-dimensional assimilation method, especially when the forecast model is not perfect and the forecast error comes from both the noise of the initial filed and the uncertainty of the forecast model.

Keywords

POD data assimilation 4DVAR explicit method 

Copyright information

© Science in China Press and Springer-Verlag GmbH 2009

Authors and Affiliations

  1. 1.Institute of Atmospheric PhysicsChinese Academy of SciencesBeijingChina

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