Premium
A singular vector perspective of 4D‐Var: Filtering and interpolation
Author(s) -
Johnson Christine,
Hoskins Brian J.,
Nichols Nancy K.
Publication year - 2005
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1256/qj.03.231
Subject(s) - data assimilation , interpolation (computer graphics) , a priori and a posteriori , mathematics , singular spectrum analysis , vector autoregression , state vector , perspective (graphical) , computer science , algorithm , econometrics , singular value decomposition , artificial intelligence , meteorology , geography , motion (physics) , philosophy , physics , epistemology , classical mechanics
Four‐dimensional variational data assimilation (4D‐Var) combines the information from a time sequence of observations with the model dynamics and a background state to produce an analysis. In this paper, a new mathematical insight into the behaviour of 4D‐Var is gained from an extension of concepts that are used to assess the qualitative information content of observations in satellite retrievals. It is shown that the 4D‐Var analysis increments can be written as a linear combination of the singular vectors of a matrix which is a function of both the observational and the forecast model systems. This formulation is used to consider the filtering and interpolating aspects of 4D‐Var using idealized case‐studies based on a simple model of baroclinic instability. The results of the 4D‐Var case‐studies exhibit the reconstruction of the state in unobserved regions as a consequence of the interpolation of observations through time. The results also exhibit the filtering of components with small spatial scales that correspond to noise, and the filtering of structures in unobserved regions. The singular vector perspective gives a very clear view of this filtering and interpolating by the 4D‐Var algorithm and shows that the appropriate specification of the a priori statistics is vital to extract the largest possible amount of useful information from the observations. Copyright © 2005 Royal Meteorological Society