Test models for filtering with superparameterization

Multiscale Modeling and Simulation

Volumn 11, Issue 1, 2013, Pages 282-308

  Harlim, John ^a   Majda, Andrew J ^b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

Data assimilation; Kalman filter; No scale separation; Superparameterization

Indexed keywords

CONTROLLABILITY CONDITION; CONVENTIONAL APPROACH; DATA ASSIMILATION; FAST NUMERICAL ALGORITHM; OBSERVATION NETWORKS; SCALE SEPARATION; STATISTICAL PREDICTION; SUPERPARAMETERIZATION;

ALGORITHMS; DYNAMICAL SYSTEMS; DYNAMICS; ERRORS; KALMAN FILTERS; PLASMA THEORY;

STOCHASTIC MODELS;

EID: 84875278546     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/120890594     Document Type: Article

References (31)

1. B.D. Anderson and J.B. Moore, Optimal Filtering, Prentice-Hall, Englewood Cliffs, NJ, 1979.
2. E. Castronovo, J. Harlim, and A.J. Majda, Mathematical test criteria for filtering complex systems: Plentiful observations, J. Comput. Phys., 227 (2008), pp. 3678-3714.
3. Daley, Atmospheric Data Analysis, Cambridge University Press, New York, 1991.
4. W. E, B. Engquist, X. Li, W. Ren, and E. Vanden-Eijnden, The heterogeneous multi-scale method: A review, Commun. Comput. Phys, 2 (2007), pp. 367-450.
5. W.W. Grabowski, Coupling cloud processes with the large-scale dynamics using the Cloud-Resolving Convection Parameterization (CRCP), J. Atmos. Sci., 58 (2001), pp. 978-996.
6. W.W. Grabowski and P.K. Smolarkiewicz, CRCP: A Cloud Resolving Convection Parameterization for modeling the tropical convecting atmosphere, Phys. D, 133 (1999), pp. 171-178.
7. I. Grooms and A.J. Majda, Stochastic superparameterization in a one-dimansional model for wave turbulence, Multiscale Model. Simul., submitted.
8. J. Harlim, Numerical strategies for filtering partially observed stiff stochastic differential equations, J. Comput. Phys., 230 (2011), pp. 744-762.
9. J. Harlim and A.J. Majda, Mathematical strategies for filtering complex systems: Regularly spaced sparse observations, J. Comput. Phys., 227 (2008), pp. 5304-5341.
10. J.O. Hinze, Turbulence, McGraw-Hill, New York, 1975.
11. B.R. Hunt, E.J. Kostelich, and I. Szunyogh, Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter, Phys. D, 230 (2007), pp. 112-126. (Pubitemid 46776911)
12. R.E. Kalman and R. Bucy, New results in linear filtering and prediction theory, Trans. ASME J. Basic Engrg., 83D (1961), pp. 95-108.
13. E.L. Kang and J. Harlim, Filtering partially observed multiscale systems with heterogeneous multiscale methods-based reduced climate models, MonthlyWeather Rev., 140 (2012), pp. 860-873.
14. C.L. Keppenne, Data assimilation into a primitive-equation model with a parallel ensemble Kalman filter, Monthly Weather Rev., 128 (2000), pp. 1971-1981. (Pubitemid 30464430)
15. A.R. Kerstein, A linear-eddy model of turbulent scalar transport and mixing, Combustion Sci. Technology, 60 (1988), pp. 391-421.
16. A.R. Kerstein, One-dimensional turbulence: Model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows, J. Fluid Mech., 392 (1999), pp. 277-334.
17. R. Khasminskii, On averaging principle for it stochastic differential equations, Kybernetika Chekhoslovakia, 4 (1968), pp. 260-279, (in Russian).
18. R. Klein and A.J. Majda, Systematic multiscale models for deep convection on mesoscales, Theo. Comp. Fluid Dyn., 20 (2006), pp. 525-551. (Pubitemid 44601473)
19. T.G. Kurtz, Semigroups of conditional shifts and approximations of Markov processes, Ann. Probab., 3 (1975), pp. 618-642.
20. A.J. Majda, Multiscale models with moisture and systematic strategies for superparameterization, J. Atmospheric Sci., 64 (2007), pp. 2726-2734.
21. A.J. Majda, Challenges in climate science and contemporary applied mathematics, Comm. Pure Appl. Math., 65 (2012), pp. 920-948.
22. A.J. Majda and M.J. Grote, Explicit off-line criteria for stable accurate time filtering of strongly unstable spatially extended systems, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 1124-1129. (Pubitemid 46183971)
23. A.J. Majda and M.J. Grote, Mathematical test models for superparametrization in anisotropic turbulence, Proc. Natl. Acad. Sci. USA, 2106 (2009), pp. 5470-5474.
24. A.J. Majda and J. Harlim, Filtering Complex Turbulent Systems, Cambridge University Press, Cambridge, UK, 2012.
25. A.J. Majda, J. Harlim, and B. Gershgorin, Mathematical strategies for filtering turbulent dynamical systems, Discrete Contin. Dyn. Syst. A, 27 (2010), pp. 441-486.
26. A.J. Majda and Y. Xing, New multi-scale models on mesoscales and squall lines., Commun. Math. Sci., 8 (2010), pp. 113-134.
27. A.S. Monin, A.M. Iaglom, and J.L. Lumley, Statistical fluid mechanics: Mechanics of turbulence, in Statistical Fluid Mechanics: Mechanics of Turbulence 2, MIT Press, Cambridge, MA, 1975.
28. G. Papanicolaou, Some probabilistic problems and methods in singular perturbations, Rocky Mountain J. Math., 6 (1976), pp. 653-673.
29. A.A.R. Townsend, The Structure of Turbulent Shear Flow, Cambridge Monogr. Mech. Appl. Math., Cambridge University Press, Cambridge, UK, 1980.
30. Y. Xing, A.J. Majda, and W.W. Grabowski, New efficient sparse space-time algorithms for superparameterization on mesoscales, Monthly Weather Rev., 137 (2009), pp. 4307-4323.
31. A.M. Yaglom, An Introduction to the Theory of Stationary Random Functions, Dover, New York, 2004.