Quantifying uncertainty for predictions with model error in non-Gaussian systems with intermittency

Nonlinearity

Volumn 25, Issue 9, 2012, Pages 2543-2578

  Branicki, Michal ^a   Majda, Andrew J ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84865527649     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/25/9/2543     Document Type: Article

References (53)

1. Abramov R V, Majda A J and Kleeman R 2005 Information theory and predictability for low-frequency variability J. Atmos. Sci. 62 65-87 (Pubitemid 40195743)
2. Akaike H 1974 A new look at the statistical model identification IEEE Trans. Autom. Control 19 716-23
3. Alexander M A, Matrosova L, Penland C, Scott J D and Chang P 2008 Forecasting Pacific SSTs: linear inverse model predictions of the PDO J. Climate 21 385-402 (Pubitemid 351395652)
4. Branicki M, Gershgorin B and Majda A J 2012 Filtering skill for turbulent signals for a suite of nonlinear and linear kalman filters J. Comput. Phys. 231 1462-98
5. Branstator G and Teng H 2010 Two limits of initial-value decadal predictability in a CGCM J. Climate 23 6292-311
6. Burnham K and Anderson D 2002 Model Selection and Multimodel Inference: a Practical Information-Theoretic Approach (New York: Springer Science)
7. DelSole T 2004 Predictability and information theory: I: Measures of predictability J. Atmos. Sci. 61 2425-40
8. DelSole T 2004 Stochastic model of quasigeostrophic turbulence Surv. Geophys. 25 107-49 (Pubitemid 38783891)
9. DelSole T 2005 Predictability and information theory: II. Imperfect models J. Atmos. Sci. 62 3368-81 (Pubitemid 41601738)
10. DelSole T and Shukla J 2010 Model fidelity versus skill in seasonal forecasting J. Climate 23 4794-806
11. Emanuel K A, Wyngaard J C, McWilliams J C, Randall D A and Yung Y L 2005 Improving the Scientific Foundation for Atmosphere-Land-Ocean Simulations (Washington, DC: National Academic)
12. Epstein E S 1969 Stochastic dynamic predictions Tellus 21 739-59
13. Gardiner C 2010 Stochastic Methods: A Handbook for the Natural and Social Sciences (Springer Series in Synergetics) 4th edn (Berlin: Springer)
14. Gershgorin B, Harlim J and Majda A J 2010 Improving filtering and prediction of spatially extended turbulent systems with model errors through stochastic parameter estimation J. Comput. Phys. 229 32-57
15. Gershgorin B, Harlim J and Majda A J 2010 Test models for improving filtering with model errors through stochastic parameter estimation J. Comput. Phys. 229 1-31
16. Gershgorin B and Majda A J 2010 A test model for fluctuation-dissipation theorems with time-periodic statistics Physica D 239 1741-57
17. Gershgorin B and Majda A J 2012 Quantifying uncertainty for climate change and long range forecasting scenarios with model errors: I. Gaussian models J. Climate 25 4523-48
18. Gershgorin B and Majda A J 2008 A nonlinear test model for filtering slow-fast systems Commun. Math. Sci. 6 611-49
19. Gershgorin B and Majda A J 2009 Filtering a nonlinear slow-fast system with strong fast forcing Commun. Math. Sci. 8 67-92
20. Giannakis D and Majda A J 2012 Quantifying the predictive skill in long-range forecasting: I. Coarse-grained predictions in a simple ocean model J. Climate 25 1793-813
21. Giannakis D and Majda A J 2012 Quantifying the predictive skill in long-range forecasting: II. Model error in coarse-grained Markov models with application to ocean-circulation regimes J. Climate 25 1814-26
22. Gritsun A and Branstator G 2007 Climate response using a three-dimensional operator based on the fluctuation-dissipation theorem J. Atmos. Sci. 64 2558-75 (Pubitemid 47233151)
23. Gritsun A, Branstator G and Majda A J 2008 Climate response of linear and quadratic functionals using the fluctuation-dissipation theorem J. Atmos. Sci. 65 2824-41
24. Hairer M and Majda A J 2010 A simple framework to justify linear response theory Nonlinearity 23 909-22
25. Jazwinski A H 1970 Stochastic Processes and Filtering Theory (New York: Academic)
26. Jia L and DelSole T 2011 Diagnosis of multi-year predictability on continental scales J. Climate 24 5108-24
27. Kleeman R 2002 Measuring dynamical prediction utility using relative entropy J. Atmos. Sci. 59 2057-72 (Pubitemid 34817275)
28. Kullback S and Leibler R 1951 On information and sufficiency Ann. Math. Stat. 22 79-86
29. Leith C E 1975 Climate response and fluctuation dissipation J. Atmos. Sci. 32 2022-25
30. Lorenz E N 1963 Deterministic nonperiodic flow J. Atmos. Sci. 20 130-41
31. Lorenz E N 1968 A study of predictability of a 28-variable atmospheric model Tellus 17 321-33
32. Lorenz E N 1969 The predictability of a flow which possesses many scales of motion Tellus 21 289-307
33. Majda A J 2000 Real world turbulence and modern applied mathematics Mathematics: Frontiers and Perspectives 2000 (International Mathematical Union) (Providence, RI: American Mathematical Society) pp 137-51
34. Majda A J 2012 Challenges in climate science and contemporary applied mathematics Commun. Pure Appl. Math. 65 920-48
35. Majda A J, Abramov R V and Grote M J 2005 Information Theory and Stochastics for Multiscale Nonlinear Systems (CRM Monograph Series vol 25) (Providence, RI: Americal Mathematical Society)
36. Majda A J and Branicki M 2012 Lessons in uncertainty quantification for turbulent dynamical systems Discrete Contin. Dyn Syst. 32 3133-231
37. Majda A J and Gershgorin B 2010 Quantifying uncertainty in climate change science through empirical information theory Proc. Natl Acad. Sci. 107 14958-63
38. Majda A J and Gershgorin B 2011 Improving model fidelity and sensitivity for complex systems through empirical information theory Proc. Natl. Acad. Sci. 108 10044-49
39. Majda A J and Gershgorin B 2011 Link between statistical equilibrium fidelity and forecasting skill for complex systems with model error Proc. Natl Acad. Sci. 108 12599-604
40. Majda A J, Kleeman R and Cai D 2002 A mathematical framework for predictability through relative entropy Methods Appl. Anal. 9 425-44
41. Majda A J and Wang X 2006 Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows (Cambridge: Cambridge University Press)
42. Majda A J and Wang X 2010 Linear response theory for statistical ensembles in complex systems with time-periodic forcing Commun. Math. Sci. 8 145-72
43. Majda A J, Abramov R V and Grote M J 2005 Information Theory and Stochastics for Multiscale Nonlinear Systems (CRM Monograph Series vol 25) (Providence, RI: American Mathematical Society)
44. Majda A J, Harlim J and Gershgorin B 2010 Mathematical strategies for filtering turbulent dynamical systems Discrete Contin. Dyn. Syst. 27 441-86
45. Neelin J D, Munnich M, Su H, Meyerson J E and Holloway C E 2006 Tropical drying trends in global warming models and observations Proc Natl Acad Sci USA 103 6110-15
46. Oksendal B K 2010 Stochastic Differential Equations: An Introduction with Applications (Berlin: Springer)
47. Palmer T 2001 A nonlinear dynamical perspective on model error: a proposal for nonlocal stochastic dynamic parameterizations in weather and climate prediction models Quart J. R. Meteor. Soc. 127 279-303
48. Penland C 2007 Stochastic linear models of nonlinear geosystems Nonlinear Dynamics in Geosystems (New York: Springer)
49. Penland C 2010 A linear stochastic model of sea surface temperatures Climate Dynamics: Why does Climate Vary? (Geophysical Monograph 189) (Washington, DC: The American Geophysical Union)
50. Penland C and Sardeshmukh P D 1995 The optimal growth of tropical sea surface temperature anomalies J. Climate 8 1999-2024 (Pubitemid 26472943)
51. Randall D A 2007 Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge: Cambridge University Press) chapter 8 pp 589-662 (Climate models and their evaluation)
52. Teng H and Branstator G 2010 Initial-value predictability of prominent modes of North Pacific subsurface temperature in a CGCM Climate Dyn. 36 1813-34
53. Winkler C R, Newman M and Sardeshmukh P D 2001 A linear model of wintertime low-frequency variability: I. Formulation and forecast skill J. Climate 14 4474-94 (Pubitemid 34143801)