Sensitivity and out-of-sample error in continuous time data assimilation

Quarterly Journal of the Royal Meteorological Society

Volumn 138, Issue 664, 2012, Pages 785-801

  Bröcker, Jochen ^a   Szendro, Ivan G ^b  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^b UNIVERSITY OF COLOGNE   (Germany)

Author keywords

Best linear unbiased estimator; Out of sample error; Sensitivity; Synchronization; Variational data assimilation

Indexed keywords

BEST LINEAR UNBIASED ESTIMATOR; CONTINUOUS TIME; DATA ASSIMILATION; DYNAMICAL MODEL; MODEL EQUATIONS; MODEL STATE; NEWTONIANS; NUMERICAL EXAMPLE; OPERATIONAL CONDITIONS; SENSITIVITY; VARIATIONAL DATA ASSIMILATION;

METEOROLOGY; SYNCHRONIZATION;

EXTRATERRESTRIAL ATMOSPHERES;

DATA ASSIMILATION; ERROR ANALYSIS; NUMERICAL MODEL; PERTURBATION; SENSITIVITY ANALYSIS; SYNCHRONY; WEATHER FORECASTING;

EID: 84859777434     PISSN: 00359009     EISSN: 1477870X     Source Type: Journal    
DOI: 10.1002/qj.940     Document Type: Article

References (23)

1. Apte A, Jones C, Stuart A, Voss J. 2008. Data assimilation: mathematical and statistical perspectives. Int. J. Numer. Meth. Fl. 56: 1033-1046.
2. Åström KJ. 2006. Introduction to Stochastic Control Theory. Dover, New York.
3. Boccaletti S, Kurths J, Osipov G, Valladares DL, Zhou CS. 2002. The synchronization of chaotic systems. Phys. Rep. 366: 1-101.
4. Bröcker J. 2010. On variational data assimilation in continuous time. Q. J. R. Meteorol. Soc. 136: 1906-1919.
5. Cardinali C, Pezzulli S, Andersson E. 2004. Influence-matrix diagnostic of a data assimilation system. Q. J. R. Meteorol. Soc. 130: 2767-2786.
6. Courtier P, Talagrand O. 1987. Variational assimilation of meteorological observations with the adjoint vorticity equation II. Numerical results. Q. J. R. Meteorol. Soc. 113: 1329-1347.
7. Derber J. 1989. A variational continuous assimilation technique. Mon. Weather Rev. 117: 2437-2446.
8. Hastie T, Tibshirani R, Friedman J. 2001. The Elements of Statistical Learning (1st edn). Springer: New York.
9. Jazwinsky AH. 1970. Stochastic Processes and Filtering Theory. Mathematics in Science and Engineering, Vol. 64. Academic Press: New York.
10. Judd K. 2008. Forecasting with imperfect models, dynamically constrained inverse problems, and gradient descent algorithms. Physica D 237: 216-232.
11. Kierzenka J, Shampine LF. 2001. A BVP solver based on residual control and the Matlab PSE. ACM Trans. Math. Software 27: 299-316.
12. Le Dimet FX, Talagrand O. 1986. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A 38: 97-110.
13. Liu J, Kalnay E. 2008. Estimating observation impact without adjoint model in an ensemble Kalman filter. Q. J. R. Meteorol. Soc. 134: 1327-1335.
14. Liu J, Kalnay E, Miyoshi T, Cardinali C. 2009. Analysis sensitivity calculation in an ensemble Kalman filter. Q. J. R. Meteorol. Soc. 135: 1842-1851.
15. Lorenz EN. 1963. Deterministic nonperiodic flow. J. Atmos. Sci. 20: 130-141.
16. Lorenz E. 1996. Predictability: a problem partly solved. In Proceedings of the Seminar on Predictability, European Centre for Medium-Range Weather Forecasts, Reading, UK; 1-18.
17. Nijmeirer H, Mareels IMY. 1997. An observer looks at synchronization. IEE transactions on circuits and systems I: fundemental theory 44: 882-890.
18. Parlitz U, Kocarev L. 1999. Synchronization of chaotic systems. In Handbook of Chaos Control, Schuster H (ed.). Wiley-VCH: Weinheim; 271-303.
19. Pereyra V. 1979. PASVA3: An Adaptive Finite Difference Fortran Program for First Order Nonlinear, Ordinary Boundary Problems. Springer: Berlin; 40-66.
20. Sage A. 1968. Optimum Systems Control. Prentice-Hall: Englewood Cliffs, NJ.
21. Seaman N. 1990. Newtonian nudging: a four-dimensional approach to data assimilation. In Mesoscale Data Assimilation: 1990 Summer Colloquium, Advanced Study Program. National Center for Atmospheric Research: Boulder, CO; 263-277.
22. Szendro IG, Rodríguez MA, López JM. 2009. On the problem of data assimilation by means of synchronization. J. Geophys. Res. 114: D20109, DOI: 10.1029/2009JD012411.
23. Zeitouni O, Dembo A. 1987. A maximum a posteriori estimator for trajectories of diffusion processes. Stochastics 20: 221.