Conditioning of incremental variational data assimilation, with application to the Met Office system
By: S. A. Haben, A. S. Lawless and N. K. Nichols
References
-
Andersson
, E., Fisher, M., Munro, R.and McNally, A. 2000. Diagnosis of background errors for radiances and other observable quantities in a variational data assimilation scheme, and the explanation of a case of poor convergence. Q. J. R. Met. Soc. 126, 1455– 1472. -
Bannister
, R. 2008. A Review of forecast error covariance statistics in atmospheric variational data assimilation. II: modelling the forecast error covariance statistics. Q. J. R. Met. Soc. 134, 1971– 1996. -
Courtier
, P., Thepaut, J.-N.and Hollingsworth, A. 1994. A strategy for operational implementation of 4D-Var, using an incremental ap-proach. Q. J. R. Met. Soc. 120, 1367– 1387. -
Cullen
, M. J. P. 2003. Four-dimensional variational data assimilation: a new formulation of the background-error covariance matrix based on a potential voracity representation. Q. J. R. Met. Soc. 129, 2777– 2796. -
Dando
, M. L., Thorpe, A. J.and Eyre, J. R. 2007. The optimal density of atmospheric sounder observations in the Met Office NWP system. Q. J. R. Met. Soc. 133, 1933– 1943. -
Fisher
, M., Nocedal, J., Tremolet, Y.and Wright, S. J. 2009. Data as-similation in weather forecasting: a case study in PDE-constrained optimization. Optim. Eng. 10, 409– 426. -
Gauthier
, R, Charette, C., Fillion, L., Koclas, P.and Laroche, S. 1999. Implementation of a 3D variational data assimilation system at the Canadian Meteorological Centre. Part 1: the global analysis. Atmos.-Ocean, 103– 156. -
Gauthier
, P., Tanguay, M., Laroche, S., Pellerin, S.and Morneau, J. 2007. Extension of 3DVAR to 4DVAR: implementation of 4DVAR at the Meteorological Service of Canada. Mon. Wea. Re v. 135, 2339– 2354. -
Gauthier
, P.and Thepaut, J.-N. 2001. Impact of the digital filter as a weak constraint in the preoperational 4DVAR assimilation system of Meteo-France. Mon. Wea. Re v. 129, 2089– 2102. -
Golub
, G. H.and Van Loan, C. F. 1996. Matrix Computations , 3rd Edition, Johns Hopkins University Press, Baltimore, MD. -
Gratton
, S., Lawless, A. S.and Nichols, N. K., Baltimore, MD. Ap-proximate Gauss-Newton methods for non-linear least-squares prob-lems. SIAM J. Optim. 18, 106– 132. -
Haben
, S. A., Lawless, A. S.and Nichols, N. K. 2009. Conditioning of the 3DVAR data assimilation problem. Mathematics Report 3/2009, Department of Mathematics , University of Reading, U.K. Available from http://www.reading.ac.uk/maths/research/maths-report-series. aspx -
Haben
, S. A., Lawless, A. S.and Nichols, N. K. 2010. Conditioning and preconditioning of the variational data assimilation problem. Comput. Fluids, 252– 256. -
Healy
, S. B.and White, A. A. 2005. Use of discrete fourier transforms in the ldvar retrieval problem. Q. J. R. Met. Soc. 131, 63– 72. -
Huang
, X.-Y., Xiao, Q., Barker, D. M., Zhang, X., Michalakes, J.and co-authors. 2009. Four-dimensional variational data assimilation for WRF: formulation and preliminary results.. 137, 299- 314. -
Ingleby
, N. B. 2001. The statistical structure of forecast errors and its representation in The Met. Office Global 3-D Variational Data Assimilation Scheme. Q. J. R. Met. Soc. 127, 209– 231. -
Katz
, D., Lawless, A. S., Nichols, N. K., Cullen, M. J. P.and Bannis-ter, R. N. 2011. Correlations of control variables in variational data assimilation. Q. J. R. Met. Soc. 137, 620– 630. -
Lawless
, A. S., Gratton, S.and Nichols, N. K. 2005. An investigation of incremental 4D-Var using non-tangent linear models. Q. J. R. Met. Soc. 131, 459– 476. -
Lorene
, A. C. 1997. Development of an operational variational assimi-lation scheme. J. Met. Soc. Japan, 339– 346. -
Lorene
, A. C., Ballard, S. P., Bell, R. S., Ingleby, N. B., Andrews, P. L. E, and co-authors. 2000. The Met. Office global 3-dimensional variational data assimilation scheme. Q. J. R. Met. Soc. 126, 2991-301 2. -
Nocedal
, J.and Wright, S. J. 2006. Numerical Optimization, Springer, New York. -
Rabier
, E, Järvinen, H., Klinker, E., Mahfouf, J. F.and Simmons, A. 2000. The ECMWF operational implementation of four-dimensional variational assimilation. I: experimental results with simplified physics. Q. J. R. Met. Soc. 126, 1143– 1170. -
Rawlins
, F., Ballard, S. P., Bovis, K. J., Clayton, A. M., Li, D., and co-authors. 2007. The Met Office global four-dimensional vari-ational data assimilation scheme.. 133, 347- 362. -
Rodgers
, C. D. 2000. Inverse Methods for Atmospheric Sounding: The-ory and Practice, World Scientific, Singapore. -
Stewart
, L. M. 2010. Correlated Observation Errors in Data Assimilation, PhD Thesis , Department of Mathematics, University of Reading. -
Tremolet
, Y. 2007. Incremental 4D-Var convergence study. Tellus, 706– 718. -
Tshimanga
, J., Gratton, S., Weaver, A. T.and Sartenaer, A. 2008. Limited-memory preconditioners, with application to incremental four-dimensional variational data assimilation. Q. J. R. Met. Soc. 134, 751– 769. -
Yang
, W., Navon, I. M.and Courtier, P. 1996. A new Hessian pre-conditioning method applied to variational data assimilation experi-ments using NASA General Circulation Models. Mon. Wea. Re v. 124, 1000– 1017. -
Zupanski
, M. 1996. A preconditioning algorithm for four-dimensional variational data assimilation. Mon. Wea. Re v. 124, 2562– 2573.
DOI: https://doi.org/10.1111/j.1600-0870.2011.00527.x | Journal eISSN: 3035-9554
Language: English
Page range: 782 - 792
Submitted on: Jul 22, 2010
Accepted on: Mar 29, 2011
Published on: Jan 1, 2011
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services
© 2011 S. A. Haben, A. S. Lawless, N. K. Nichols, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.