Gaussian quadrature 4D‐Var

A new incremental four‐dimensional variational (4D‐Var) data assimilation algorithm is introduced. The algorithm does not require the computationally expensive integrations with the nonlinear model in the outer loops. Nonlinearity is accounted for by modifying the linearization trajectory of the obs...

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Vydané v:Quarterly journal of the Royal Meteorological Society Ročník 139; číslo 675; s. 1462 - 1472
Hlavní autori: Stappers, R. J. J., Barkmeijer, J.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Chichester, UK John Wiley & Sons, Ltd 01.07.2013
Wiley
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Predmet:
Algorithms
Data collection
Earth, ocean, space
Evolution
Exact sciences and technology
External geophysics
fixed‐point iteration
Gaussian
Gauss–Newton
long window 4D‐Var
Mathematical analysis
Mathematical models
Meteorology
nonlinear least squares
Nonlinearity
observation impact
Operators
optimal linearization trajectories
Physics of the high neutral atmosphere
Quadratures
Studies
observation impact
Four dimensional calculations
Variational calculus
fixed-point iteration
long window 4D-Var
trajectory
Gauss-Newton
optimal linearization trajectories
Linearization
nonlinear least squares
ISSN:0035-9009, 1477-870X
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Shrnutí:A new incremental four‐dimensional variational (4D‐Var) data assimilation algorithm is introduced. The algorithm does not require the computationally expensive integrations with the nonlinear model in the outer loops. Nonlinearity is accounted for by modifying the linearization trajectory of the observation operator based on integrations with the tangent linear (TL) model. This allows us to update the linearization trajectory of the observation operator in the inner loops at negligible computational cost. As a result the distinction between inner and outer loops is no longer necessary. The key idea on which the proposed 4D‐Var method is based is that by using Gaussian quadrature it is possible to get an exact correspondence between the nonlinear time evolution of perturbations and the time evolution in the TL model. It is shown that J‐point Gaussian quadrature can be used to derive the exact adjoint‐based observation impact equations and furthermore that it is straightforward to account for the effect of multiple outer loops in these equations if the proposed 4D‐Var method is used. The method is illustrated using a three‐level quasi‐geostrophic model and the Lorenz (1996) model.
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ISSN:0035-9009
1477-870X
DOI:10.1002/qj.2056