Recent Applications in Representer-Based Variational Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 294

be computed during the minimization. The generalized conjugate residual (GCR)
algorithm provides these diagnostics, at the cost of some additional complexity
compared with the conjugate gradient algorithm, but it performs reliably when the
approximate adjoint of the model is used.
The analysis produced by any data assimilation system is always limited by
the quality of the prior covariance models for the background, model forcings,
and observations. In Sect. 12.3 it was shown how the posterior error analysis of
Desroziers and Ivanov ( 2001 ) could be applied to calibrate these covariance models
in variational data assimilation systems using representer-based solvers. Application
of these methods has been applied to diagnose the observation error in NAVDAS-
AR, which utilizes many sources of atmospheric data, each with unique error
characteristics.
Acknowledgements Zaron was sponsored by the National Science Foundation (NSF), award
OCE-0623540, with additional support from the Naval Research Laboratory, award N00173-08-
2-C015. Authors Chua, Xu, Baker, and Rosmond gratefully acknowledge the support of their
sponsors, the Naval Research Laboratory, the Office of Naval Research, and the PMW-120, under
program elements, 0602435N and 0603207N, respectively. Computational resources for Zaron
were provided by the National Center for Atmospheric Research, which is sponsored by NSF.
References
Bennett AF (1985) Array design by inverse methods. Prog Oceanogr 15:129-156
Bennett AF (1992) Inverse methods in physical oceanography, 1st edn. Cambridge University
Press, New York, 346p
Bennett AF (2002) Inverse modeling of the ocean and atmosphere. Cambridge University Press,
New York, 234p
Bennett AF, Thorburn MA (1992) The generalized inverse of a nonlinear quasigeostrophic ocean
circulation model. J Phys Oceanogr 22:213-230
Bennett AF, Chua BS, Harrison DE, McPhaden MJ (2000) Generalized inversion of tropical
atmosphere-ocean (TAO) data and a coupled model of the tropical ocean. Part II: the 1995-
96 La Ni na and 1997-98 El Ni no. J Climate 13:2770-2785
Bennett AF, Chua BS, Pflaum BL, Erwig M, Fu Z, Loft RD, Muccino JC (2008) The inverse ocean
modeling system. I: implementation. J Atmos Oceanic Technol 25:1608-1622
Chapnik B, Desroziers G, Rabier F, Talagrand O (2004) Properties and first application of an error-
statistics tuning method in variational assimilation. Q J R Meteorol Soc 130:2253-2275
Chapnik B, Desroziers G, Rabier F, Talagrand O (2006) Diagnosis and tuning of observational
error in quasi-operational data assimilation setting. Q J R Meteorol Soc 132:543-565
Chua B, Bennett AF (2001) An inverse ocean modeling system. Ocean Model 3:137-165
Cohn SE, Da Silva A, Guo J, Sienkiewicz M, Lamich D (1998) Assessing the effects of data
selection with the DAO physical-space statistical analysis system. Mon Weather Rev 126:2913-
2926
Courtier P (1997) Dual formulation of four-dimensional assimilation. Q J R Meteorol Soc
123:2449-2461
Courtier P, Thepaut J, Hollingsworth A (1994) A strategy for operational implementation of
4D-Var, using an incremental approach. Q J R Meteorol Soc 120:1367-1387
Daley R, Barker E (2001) NAVDAS: formulation and diagnostics. Mon Weather Rev 129:869-883