Working Paper Article Version 2 This version is not peer-reviewed

A Preliminary Study on Dimension-Reduction Algorithm for Variational Methods in Three Dimensions

Version 1 : Received: 31 January 2018 / Approved: 1 February 2018 / Online: 1 February 2018 (14:37:58 CET)
Version 2 : Received: 5 December 2019 / Approved: 5 December 2019 / Online: 5 December 2019 (10:36:30 CET)

How to cite: Chen, X. A Preliminary Study on Dimension-Reduction Algorithm for Variational Methods in Three Dimensions. Preprints 2018, 2018010293 Chen, X. A Preliminary Study on Dimension-Reduction Algorithm for Variational Methods in Three Dimensions. Preprints 2018, 2018010293

Abstract

Three Dimensional Variational data assimilation or analysis (3DVAR) is one of most classical methods for providing the initial values for numerical models. In this method, the dimensions of the background error covariance and the observational error covariance matrices are large. Therefore, it is difficult to get the inverse of the covariance matrices and to reduce the orders of these matrices without information loss. With the use of the Sylvester Equation, on the basis of a new linear regression, a new cost function for 3DVAR was given. For the first-guess m×n field, there is an approximate 1−(m2+n2)/(mn×mn) reduction with m>1 & n>1 by using the cost function. The results of the numerical experiments show that the effect of this algorithm is no worse than that of the old cost function for 3DVAR.

Subject Areas

3DVAR; data assimilation; cost function; Sylvester equation

Comments (1)

Comment 1
Received: 5 December 2019
Commenter: Xuan Chen
Commenter's Conflict of Interests: Author
Comment: improving mathematical foundation; giving an example with more common situation.
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