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This version is not peer-reviewed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)
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.
Keywords
3DVAR; data assimilation; cost function; Sylvester equation
Subject
Environmental and Earth Sciences, Oceanography
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (1)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
Commenter: Xuan Chen
Commenter's Conflict of Interests: Author
giving an example with more common situation.