Premium
The ECMWF implementation of three‐dimensional variational assimilation (3D‐Var). II: Structure functions
Author(s) -
Rabier F.,
McNally A.,
Andersson E.,
Courtier P.,
Undén P.,
Eyre J.,
Hollingsworth A.,
Bouttier F.
Publication year - 1998
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 - 10.1002/qj.49712455003
Subject(s) - geostrophic wind , data assimilation , range (aeronautics) , mathematics , horizontal and vertical , scale (ratio) , variable (mathematics) , meteorology , climatology , statistics , geology , geometry , physics , mathematical analysis , materials science , quantum mechanics , composite material
Structure functions for the 3D‐Var assimilation scheme of the European Centre for Medium‐Range Weather Forecasts are evaluated from statistics of the differences between two forecasts valid at the same time. Results compare satisfactorily with those reported in the existing literature. Non‐separability of the correlation functions is a pervasive feature. Accounting for non‐separability in 3D‐Var is necessary to reproduce geostrophic characteristics of the statistics, such as the increase of length‐scale with height for the horizontal correlation of the mass variable, sharper vertical correlations for wind than for mass and shorter horizontal length‐scales for temperature than for mass. In our non‐separable 3D‐Var, the vertical correlations vary with total wave‐number and the horizontal correlation functions vary with vertical level.