A Linear Stochastic Model of Tropical Sea Surface Temperatures Related to El Niño

Climate Dynamics: Why Does Climate Vary

Volumn , Issue , 2013, Pages 65-77

  Penland, Cécile ^a  

^a EARTH SYSTEM RESEARCH LABORATORY   (United States)

Author keywords

Climatic changes; Convection (Meteorology); Dataanalysis; Dynamic meteorology; ElNi o; Linearinversemodeling; Multiscaleinteractions; Non normaldynamics; Ocean atmosphere interaction; Stochasticmodels

Indexed keywords

ATMOSPHERIC TEMPERATURE; DYNAMICAL SYSTEMS; LINEAR CONTROL SYSTEMS; METEOROLOGY; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; SUBMARINE GEOPHYSICS; SURFACE PROPERTIES; SURFACE WATERS; TROPICS;

CLIMATIC CHANGES; DATAANALYSIS; LINEARINVERSEMODELING; MULTISCALEINTERACTIONS; NON-NORMALDYNAMICS; OCEAN-ATMOSPHERE INTERACTIONS;

OCEANOGRAPHY;

EID: 84951266756     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1029/2008GM000814     Document Type: Chapter

References (80)

1. Alexander, M. (2010), Extratropical air-sea interaction, sea surface temperature variability, and the Pacific Decadal Oscillation, in Climate Dynamics: Why Does Climate Vary?, Geophys. Monogr. Ser., doi:10.1029/2008GM000794, this volume.
2. An, S.-I., and F.-F. Jin (2004), Nonlinearity and asymmetry of ENSO, J. Clim., 17, 2399-2412, doi:10.1175/1520-0442(2004) 017<2399:NAAOE>2.0.CO;2.
3. Barnett, T. P. (1977), The principal time and space scales of the Pacific trade wind fields, J. Atmos. Sci., 34, 221-236.
4. Barnett, T. P. (1983), Interaction of the monsoon and trade wind system at interannual time scales. Part I: The equatorial zone, Mon. Weather Rev., 111, 756-773.
5. Barnett, T. P. (1984), Interaction of the monsoon and trade wind system at interannual time scales. Part II: The tropical band, Mon. Weather Rev., 112, 2380-2387.
6. Barnston, A. G., and R. E. Livezey (1987), Classification, seasonality and persistence of low-frequency atmospheric circulation patterns, Mon. Weather Rev., 115, 1083-1126, doi:10.1175/1520-0493(1987)115<1083:CSAPOL>2.0.CO;2.
7. Battisti, D. S. (1988), Dynamics and thermodynamics of a warming event in a coupled tropical atmosphere-ocean model, J. Atmos. Sci., 45, 2889-2919, doi:10.1175/1520-0469(1988)045<2889:DATOAW>2.0.CO;2.
8. Battisti, D. S. (1989), On the role of off-equatorial oceanic Rossby waves during El Niño, J. Phys. Oceanogr., 19, 551-560, doi:10. 1175/1520-0485(1989)019<0551:OTROOE>2.0.CO;2.
9. Battisti, D. S., and A. C. Hirst (1989), Interannual variability in a tropical atmosphere-ocean model: Influence of the basic state, ocean geometry and nonlinearity, J. Atmos. Sci., 46, 1687-1712, doi:10.1175/1520-0469(1989)046<1687:IVIATA>2.0. CO;2.
10. Blanke, B., J. D. Neelin, and D. Gutzler (1997), Estimating the effect of stochastic wind stress forcing on ENSO irregularity, J. Clim., 10, 1473 - 1486, doi:10.1175/1520-0442(1997)010<1473:ETEOSW>2.0.CO;2.
11. Capotondi, A. (2010), El Niño-Southern Oscillation ocean dynamics: Simulation by coupled general circulation models, in Climate Dynamics: Why Does Climate Vary?, Geophys. Monogr. Ser., doi:10.1029/2008GM000796, this volume.
12. Chang, P. (1994), A study of the seasonal cycle of sea surface temperature in the tropical Pacific Ocean using reduced gravity models, J. Geophys. Res., 99, 7725-7741.
13. Chang, P., L. Ji, H. Li, and M. Flügel (1996), Chaotic dynamics versus stochastic processes in El Niño-Southern Oscillation in coupled ocean-atmosphere models, Physica D, 98, 301-320.
14. Covey, D. L., and S. Hastenrath (1978), The Pacific El Niño phenomenon and Atlantic circulation, Mon. Weather Rev., 106, 1280-1287, doi:10.1175/1520-0493(1978)106<1280:TPENPA >2.0.CO;2.
15. Ewald, B., C. Penland, and R. Temam (2004), Accurate integration of stochastic climate models with application to El Niño, Mon. Weather Rev., 132, 154-164, doi:10.1175/1520-0493(2004)132<0154:AIOSCM>2.0.CO;2.
16. Farrell, B. (1988), Optimal excitation of neutral Rossby waves, J. Atmos. Sci., 45, 163-172, doi:10.1175/1520-0469(1988)045 <0163:OEONRW>2.0.CO;2.
17. Farrell, B. F., and P. J. Ioannou (1996), Generalized stability theory. Part I: Autonomous operators, J. Atmos. Sci., 53, 2025-2040, doi:10.1175/1520-0469(1996)053<2025:GSTPIA>2.0.CO;2.
18. García, A. L., and C. Penland (1991), Fluctuating hydrodynamics and principal oscillation pattern analysis, J. Stat. Phys., 64, 1121-1132.
19. Godfrey, J. S. (1975), On Ocean Spindown I: A linear experiment, J. Phys. Oceanogr., 5, 399-409.
20. Hasselmann, K. (1976), Stochastic climate models, Tellus, 6, 473-485.
21. Hasselmann, K. (1988), PIPS and POPS: The reduction of complex dynamical systems using principal interaction and oscillation patterns, J. Geophys. Res., 93, 11,015-11,021.
22. Hirst, A. C. (1986), Unstable and damped equatorial modes in simple coupled ocean-atmosphere models, J. Atmos. Sci., 43, 606-632, doi:10.1175/1520-0469(1986)043<0606:UADEMI >2.0.CO;2.
23. Horel, J. D. (1984), Complex principal component analysis:Theory and examples, J. Clim. Appl. Meteorol., 23, 1660-1673.
24. Jin, F.-F., and J. D. Neelin (1993a), Modes of interannual tropical ocean-atmosphere interaction-A unified view. Part I: Numerical results, J. Atmos. Sci., 50, 3477-3503, doi:10.1175/1520-0469(1993)050<3477:MOITOI>2.0.CO;2.
25. Jin, F.-F., and J. D. Neelin (1993b), Modes of interannual tropical ocean-atmosphere interaction-A unified view. Part III: Analytical results in fully coupled cases, J. Atmos. Sci., 50, 3523-3540, doi:10.1175/1520-0469(1993)050<3523:MOITOI>2.0.CO;2.
26. Jin, F.-F., J. D. Neelin, and M. Ghil (1994), El Niño on the Devil's Staircase: Annual subharmonic steps to chaos, Science, 264, 70-72, doi:10.1126/science.264.5155.70.
27. Jin, F.-F., J. D. Neelin, and M. Ghil (1996), El Niño/Southern Oscillation and the annual cycle: Subharmonic frequencylocking and aperiodicity, Physica D, 98, 442-465.
28. Johnson, S. D., D. S. Battisti, and E. S. Sarachik (2000), Empirically derived Markov models and prediction of tropical Pacific sea surface temperature anomalies, J. Clim., 13, 3-17, doi:10. 1175/1520-0442(2000)013<0003:EDMMAP>2.0.CO;2.
29. Khasminskii, R. Z. (1966), A limit theorem for solutions of differential equations with random right hand side, Theory Probab. Appl., 11, 390-406.
30. Kleeman, R. (1993), On the dependence of hindcast skill on ocean thermodynamics in a coupled ocean-atmosphere model, J. Clim., 6, 2012 - 2033, doi:10.1175/1520-0442(1993)006<2012:OTDOHS>2.0.CO;2.
31. Kleeman, R., and A. M. Moore (1997), A theory for the limitation of ENSO predictability due to stochastic atmospheric transients, J. Atmos. Sci., 54, 753-767, doi:10.1175/1520-0469(1997)054 <0753:ATFTLO>2.0.CO;2.
32. Kohler, W., and G. Papanicolaou (1976), Chapter 4, in Wave Propagation and Underwater Acoustics, edited by, edited by J. B. Keller, and J.S. Papadakis, Lect. Notes Phys., 70, 153-223.
33. Kondrashov, D., S. Kravtsov, A.W. Robertson, and M. Ghil (2005), A hierarchy of data-based ENSO models, J. Clim., 18, 4425-4444, doi:10.1175/JCLI3567.1.
34. Legler, D. M. (1983), Empirical orthogonal function analysis of wind vectors over the tropical Pacific region, Bull. Am. Meteorol. Soc., 64, 234-241.
35. Lorenz, E. (1966), Deterministic non-periodic flow, J. Atmos. Sci., 20, 130-141.
36. Majda, A. J., I. Timofeyev, and E. Vanden Eijnden (1999), Models for stochastic climate prediction, Proc. Natl. Acad. Sci. U. S. A., 96, 14,687-14,691.
37. Matsuno, T. (1966), Quasi-geostrophic motions in equatorial areas, J. Meteorol. Soc. Jpn., 2, 25-43.
38. McWilliams, J. C., and P. R. Gent (1978), A coupled air and sea model for the tropical Pacific, J. Atmos. Sci., 35, 962-989, doi:10.1175/1520-0469(1978)035<0962:ACAASM>2.0.CO;2.
39. Neelin, J. D. (1990), A hybrid general circulation model for El Niño studies, J. Atmos. Sci., 47, 674-693, doi:10.1175/1520-0469 (1990)047<0674:AHCGCM>2.0.CO;2.
40. Neelin, J. D., and F.-F. Jin (1993), Modes of interannual tropical ocean-atmosphere interaction-A unified view. Part II: Analytical results in the weak-coupling limit, J. Atmos. Sci., 50, 3504-3522, doi:10.1175/1520-0469(1993)050<3504:MOITOI>2.0.CO;2.
41. Newman, M., P. D. Sardeshmukh, and C. Penland (2008), How important is air-sea coupling in ENSO and MJO evolution?, J. Clim., 22, 2958-2977, doi:10.1175/2008JCLI2659.1.
42. North, G. R. (1984), Empirical orthogonal functions and normal modes, J. Atmos. Sci., 41, 879-887, doi:10.1175/1520-0469 (1984)041<0879:EOFANM>2.0.CO;2.
43. Papanicolaou, G., and W. Kohler (1974), Asymptotic theory of mixing stochastic ordinary differential equations, Commun. Pure Appl. Math., 27, 641-668.
44. Penland, C. (1985), Acoustic normal mode propagation through a three-dimensional internal wave field, J. Acoust. Soc. Am., 78, 1356-1365.
45. Penland, C. (1989), Random forcing and forecasting using principal oscillation pattern analysis, Mon. Weather Rev., 117, 2165-2185.
46. Penland, C. (1996), A stochastic model of IndoPacific sea surface temperature anomalies, Physica D, 98, 534-558.
47. Penland, C. (2007), Stochastic linear models of nonlinear geosystems, in Nonlinear Dynamics in Geosciences, edited by A. A. Tsonis, and J. B. Elsner, 604 pp., Springer, Berlin.
48. Penland, C., and M. Ghil (1993), Forecasting Northern Hemisphere 700mb geopotential height anomalies using empirical normal modes, Mon. Weather Rev., 121, 2355-2371.
49. Penland, C., and T. Magorian (1993), Prediction of Niño 3 seasurface temperature anomalies using linear inverse modeling, J. Clim., 6, 1067-1075.
50. Penland, C., and L. Matrosova (1998), Prediction of tropical Atlantic sea surface temperatures using linear inverse modeling, J. Clim., 11, 483-496.
51. Penland, C., and L. Matrosova (2001), Expected and actual errors of Linear Inverse Modeling forecasts, Mon. Weather Rev., 129, 1740-1745.
52. Penland, C., and L. Matrosova (2006), Studies of El Niño and interdecadal variability in tropical sea surface temperatures using a nonnormal filter, J. Clim., 19, 5796-5815.
53. Penland, C., and P. D. Sardeshmukh (1995a), Error and sensitivity analysis of geophysical systems, J. Clim., 8, 1988-1998.
54. Penland, C., and P. D. Sardeshmukh (1995b), The optimal growth of tropical sea surface temperature anomalies, J. Clim., 8, 1999-2024.
55. Penland, C., M. Flügel, and P. Chang (2000), The identification of dynamical regimes in an intermediate coupled oceanatmosphere model, J. Clim., 13, 2105-2115.
56. Penland, C., D.-Z. Sun, A. Capotondi, and D. J. Vimont (2010), A brief introduction to El Niño and La Niña, in Climate Dynamics:Why Does Climate Vary?, Geophys. Monogr. Ser., doi:10.1029/2008GM000846, this volume.
57. Philander, S. G. (1990), in El Niño, La Niña, and the Southern Oscillation, Int. Geophys. Ser., vol. 46, 293 pp., Academic, San Diego, Calif.
58. Rasmussen, E. M., and T. H. Carpenter (1982), Variations in tropical sea surface temperature and surface wind fields associated with the Southern Oscillation, Mon. Weather Rev., 110, 354-384.
59. Rümelin, W. (1982), Numerical treatment of stochastic differential equations, SIAM J. Numer. Anal., 19, 604-613.
60. Sardeshmukh, P. D., and P. Sura (2009), Reconciling non-Gaussian climate statistics with linear dynamics, J. Clim., 22, 1193-1207, doi:10.1175/2008JCLI2358.1.
61. Sardeshmukh, P. D., C. Penland, and M. Newman (2001), Rossby waves in a fluctuating medium, in Stochastic Climate Models, Progr. Probab., vol. 49, edited by P. Imkeller and J.-S. von Storch, pp. 369-384. Birkhaueser, Basel.
62. Schopf, P. S., and M. J. Suarez (1988), Vacillations in a coupled ocean-atmosphere model, J. Atmos. Sci., 45, 549-566, doi:10. 1175/1520-0469(1988)045<0549:VIACOM>2.0.CO;2.
63. Schopf, P. S., and M. J. Suarez (1990), Ocean wave dynamics and the time scale of ENSO, J. Phys. Oceanogr., 20, 629-645, doi:10.1175/1520-0485(1990)020<0629:OWDATT>2.0.CO;2.
64. Suarez, M. J., and P. S. Schopf (1988), A delayed-action oscillator for ENSO, J. Atmos. Sci., 45, 3283-3287, doi:10.1175/1520-0469(1988)045<3283:ADAOFE>2.0.CO;2.
65. Sun, D.-Z. (2010), The diabatic and nonlinear aspects of the El Niño-Southern Oscillation: Implications for its past and future behavior, in Climate Dynamics: Why Does Climate Vary?, Geophys. Monogr. Ser., doi:10.1029/2009GM000865, this volume.
66. Sura, P., and P. D. Sardeshmukh (2008), A global view of non-Gaussian SST variability, J. Phys. Oceanogr., 38, 639-647, doi:10.1175/2007JPO3761.1.
67. Sura, P., M. Newman, C. Penland, and P. D. Sardeshmukh (2005), Multiplicative noise and non-Gaussianity: A paradigm for atmospheric regimes?, J. Atmos. Sci., 62, 1391-1409.
68. Thompson, C. J., and D. S. Battisti (2000), A linear stochastic dynamical model of ENSO. Part I: Model development, J. Clim., 13, 2818 - 2832, doi:10.1175/1520-0442(2000)013<2818:ALSDMO>2.0.CO;2.
69. Thompson, C. J., and D. S. Battisti (2001), A linear stochastic dynamical model of ENSO. Part II: Analysis, J. Clim., 14, 445-466, doi:10.1175/1520-0442(2001)014<0445:ALSDMO>2.0. CO;2.
70. Thompson, J. B. (1969), An Introduction to Statistical Communications Theory, 663 pp., John Wiley, New York.
71. Trefethen, L. N., and M. Embree (2005), Spectra and Pseudospectra:The Behavior of Nonnormal Matrices and Operators, 606 pp., Princeton Univ. Press, Princeton, N. J.
72. Tziperman, E., L. Stone, M. A. Cane, and H. Jarosh (1994), El-Niño chaos-Overlapping of resonances between the seasonal cycle and the Pacific ocean-atmosphere oscillator, Science, 264, 72-74.
73. Von Storch, H., T. Bruns, I. Fischer-Bruns, and K. Hasselmann (1988), Principal oscillation pattern analysis of the 30-day to 60-day oscillation in a general circulation model equatorial troposphere, J. Geophys. Res., 93, 11,022-11,036.
74. Weare, B. C., A. R. Navato, and R. E. Newell (1976), Empirical orthogonal analysis of Pacific sea surface temperatures, J. Phys. Oceanogr., 6, 671-678.
75. Whitaker, J. S., and P. D. Sardeshmukh (1998), A linear theory of extratropical synoptic eddy statistics, J. Atmos. Sci., 55, 1336-1353, doi:10.1175/1520-0469(1998)055<1336:TIOTAC>2.0.CO;2.
76. Wong, E., and M. Zakai (1965), On the convergence of ordinary integrals to stochastic integrals, Ann. Math. Stat., 36, 1560-1564.
77. Woodruff, S., S. Lubker, K. Wolter, S. Worley, and J. Elms (1993), Comprehensive Ocean-Atmosphere Data Set (COADS) Release 1a: 1980-92, Earth Syst. Monit., 4, 1-8.
78. Xu, J.-S., and H. von Storch (1990), Predicting the state of the Southern Oscillation using principal oscillation pattern analysis, J. Clim., 3, 1316-1329, doi:10.1175/1520-0442(1990)003 <1316:PTSOTS>2.0.CO;2.
79. Xue, Y., A. Leetmaa, and M. Ji (2000), ENSO prediction with Markov models: The impact of sea level, J. Clim., 13, 849-871, doi:10.1175/1520-0442(2000)013<0849:EPWMMT>2.0.CO;2.
80. Zebiak, S. E., and M. A. Cane (1987), A model El Niño-Southern Oscillation, Mon. Weather Rev., 114, 1263-1271.