Editorial Type:
Article
Article Type:
Research Article

A Comparison of the Influence of Additive and Multiplicative Stochastic Forcing on a Coupled Model of ENSO

Cristina L. Perez Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York

Search for other papers by Cristina L. Perez in
Current site
Google Scholar
PubMed Close
,
Andrew M. Moore Program in the Atmospheric and Oceanic Sciences, and Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado

Search for other papers by Andrew M. Moore in
Current site
Google Scholar
PubMed Close
,
Javier Zavala-Garay Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

Search for other papers by Javier Zavala-Garay in
Current site
Google Scholar
PubMed Close
, and
Richard Kleeman Courant Institute of Mathematical Sciences, New York University, New York, New York

Search for other papers by Richard Kleeman in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Dec 2005
DOI:
https://doi.org/10.1175/JCLI3596.1
Page(s):
5066–5085
Restricted access

Abstract

A currently popular idea is that El Niño–Southern Oscillation (ENSO) can be viewed as a linear deterministic system forced by noise representing processes with periods shorter than ENSO. Also, there is observational evidence to suggest that the Madden–Julian oscillation (MJO) acts to trigger and/or amplify the warm phase of ENSO in this way. The feedback of the slower process, ENSO, to higher-frequency atmospheric phenomena, of which a large part of the variability in the intraseasonal band is due to the MJO, has received little attention. This paper considers the hypothesis that the probability of an El Niño event is modified by high MJO activity and that, in turn, the MJO is regulated by ENSO activity. If this is indeed the case, then viewing ENSO as a low-frequency oscillation forced by additive stochastic noise would not present a complete picture.

This paper tests the above hypothesis using a stochastically forced intermediate coupled model by allowing ENSO to directly influence the stochastic forcing. The model response to a variety of stochastic forcing types is found to be sensitive to the type of forcing applied. When the model is operated beyond its intrinsic Hopf bifurcation, its probability distribution function (PDF) is fundamentally altered when the stochastic forcing is changed from additive to multiplicative. The model integration period also influences the shape of the PDF, which is also compared to the PDF derived from observations. It is found that multiplicative stochastic forcing reproduces some measures of the observations better than the additive stochastic forcing.

Corresponding author address: Cristina L. Perez, IRI/Lamont-Doherty Earth Observatory, Columbia University, 202 Monell Building, P.O. Box 1000, Palisades, NY 10964-8000. Email: cristina@iri.columbia.edu

Abstract

A currently popular idea is that El Niño–Southern Oscillation (ENSO) can be viewed as a linear deterministic system forced by noise representing processes with periods shorter than ENSO. Also, there is observational evidence to suggest that the Madden–Julian oscillation (MJO) acts to trigger and/or amplify the warm phase of ENSO in this way. The feedback of the slower process, ENSO, to higher-frequency atmospheric phenomena, of which a large part of the variability in the intraseasonal band is due to the MJO, has received little attention. This paper considers the hypothesis that the probability of an El Niño event is modified by high MJO activity and that, in turn, the MJO is regulated by ENSO activity. If this is indeed the case, then viewing ENSO as a low-frequency oscillation forced by additive stochastic noise would not present a complete picture.

This paper tests the above hypothesis using a stochastically forced intermediate coupled model by allowing ENSO to directly influence the stochastic forcing. The model response to a variety of stochastic forcing types is found to be sensitive to the type of forcing applied. When the model is operated beyond its intrinsic Hopf bifurcation, its probability distribution function (PDF) is fundamentally altered when the stochastic forcing is changed from additive to multiplicative. The model integration period also influences the shape of the PDF, which is also compared to the PDF derived from observations. It is found that multiplicative stochastic forcing reproduces some measures of the observations better than the additive stochastic forcing.

Corresponding author address: Cristina L. Perez, IRI/Lamont-Doherty Earth Observatory, Columbia University, 202 Monell Building, P.O. Box 1000, Palisades, NY 10964-8000. Email: cristina@iri.columbia.edu

Save
Cover Journal of Climate
Journal of Climate

  • Alexander, M. A., and C. Penland, 1996: Variability in a mixed layer ocean model driven by stochastic atmospheric forcing. J. Climate, 9 , 2424–2442.

    • Search Google Scholar
    • Export Citation

  • Blanke, B., J. D. Neelin, and D. Gutzler, 1997: Estimating the effect of stochastic wind stress forcing on ENSO irregularity. J. Climate, 10 , 1473–1486.

    • Search Google Scholar
    • Export Citation

  • Bowman, A. W., and A. Azzalini, 1997: Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-Plus Illustrations. Oxford Statistical Science Series, Oxford University Press, 204 pp.

    • Search Google Scholar
    • Export Citation

  • Bretherton, C., C. Smith, and J. Wallace, 1992: An intercomparison of methods for finding coupled patterns in climate data. J. Climate, 5 , 541–560.

    • Search Google Scholar
    • Export Citation

  • Delcroix, T., G. Eldin, M. McPhaden, and A. Morliere, 1993: Effects of westerly wind bursts upon the western equatorial Pacific Ocean, February–April 1991. J. Geophys. Res., 98 , C9,. 16379–16385.

    • Search Google Scholar
    • Export Citation

  • DelSole, T., 2001: A theory for the forcing and dissipation in stochastic turbulence models. J. Atmos. Sci., 58 , 3762–3775.

  • DelSole, T., and A. Y. Hou, 1999: Empirical stochastic models for the dominant climate statistics of a general circulation model. J. Atmos. Sci., 56 , 3436–3456.

    • Search Google Scholar
    • Export Citation

  • Eckert, C., and M. Latif, 1997: Predictability of a stochastically forced hybrid coupled model of El Niño. J. Climate, 10 , 1488–1504.

    • Search Google Scholar
    • Export Citation

  • Ewald, B., C. Penland, and R. Temam, 2004: Accurate integration of stochastic climate models with application to El Niño. Mon. Wea. Rev., 132 , 154–164.

    • Search Google Scholar
    • Export Citation

  • Fedorov, A. V., S. L. Harper, S. G. Philander, B. Winter, and A. Wittenberg, 2003: How predictable is El Niño? Bull. Amer. Meteor. Soc., 84 , 911–919.

    • Search Google Scholar
    • Export Citation

  • Gardiner, C. W., 1985: Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences. 2d ed. Springer, 442 pp.

  • Harrison, D. E., and G. A. Vecchi, 1997: Westerly wind events on the tropical Pacific, 1986–95. J. Climate, 10 , 3131–3156.

  • Hasselmann, K., 1976: Stochastic climate models. Part I: Theory. Tellus, 28 , 473–485.

  • Hasselmann, K., 1988: PIPs and POPs: The reduction of complex dynamical systems using principal interaction and oscillation patterns. J. Geophys. Res., 93 , 11015–11021.

    • Search Google Scholar
    • Export Citation

  • Hendon, H., C. Zhang, and J. Glick, 1999: Interannual variation of the Madden–Julian oscillation during austral summer. J. Climate, 12 , 2538–2550.

    • Search Google Scholar
    • Export Citation

  • Horsthemke, W., and R. Lefever, 1984: Noise Induced Transitions: Theory and Applications in Physics, Chemistry and Biology. Springer-Verlag, 318 pp.

    • Search Google Scholar
    • Export Citation

  • Keen, R. A., 1987: Equatorial westerlies and the Southern Oscillation. Proceedings of the U.S. TOGA Western Pacific Air-Sea Interaction Workshop, University Corporation for Atmospheric Research, 121–140.

    • Search Google Scholar
    • Export Citation

  • Kessler, W., 2001: EOF representations of the Madden–Julian oscillation and its connection with ENSO. J. Climate, 14 , 3055–3061.

  • Kessler, W., and R. Kleeman, 2000: Rectification of the Madden–Julian oscillation into the ENSO cycle. J. Climate, 13 , 3560–3575.

  • Kessler, W., M. J. McPhaden, and K. M. Weickmann, 1995: Forcing of intraseasonal Kelvin waves in the equatorial Pacific. J. Geophys. Res., 100 , 10613–10631.

    • Search Google Scholar
    • Export Citation

  • Kleeman, R., 1989: A modeling study of the effect of the Andean mountains on the summertime circulation of tropical South America. J. Atmos. Sci., 46 , 3344–3362.

    • Search Google Scholar
    • Export Citation

  • Kleeman, R., 1993: On the dependence of hindcast skill on ocean thermodynamics in a coupled ocean–atmosphere model. J. Climate, 6 , 2012–2033.

    • Search Google Scholar
    • Export Citation

  • Kleeman, R., and S. B. Power, 1994: Limits to predictability in a coupled ocean-atmosphere model due to atmospheric noise. Tellus, 46A , 529–540.

    • Search Google Scholar
    • Export Citation

  • Kleeman, R., and A. Moore, 1997: A theory for the limitations of ENSO predictability due to stochastic atmospheric transients. J. Atmos. Sci., 54 , 753–767.

    • Search Google Scholar
    • Export Citation

  • Kleeman, R., M. Latif, and M. Flügel, 1992: A hybrid coupled tropical atmosphere ocean model: Sensitivities and hindcast skill. Max Planck Institut für Meteorologie Tech. Rep. 76, 37 pp.

  • Kleeman, R., A. M. Moore, and N. R. Smith, 1995: Assimilation of subsurface thermal data into a simple ocean model for the initialization of an intermediate tropical coupled ocean–atmosphere forecast model. Mon. Wea. Rev., 123 , 3103–3113.

    • Search Google Scholar
    • Export Citation

  • Lau, K. M., and P. Chan, 1986: The 40–50 day oscillation and the El Niño/Southern Oscillation: A new perspective. Bull. Amer. Meteor. Soc., 67 , 533–534.

    • Search Google Scholar
    • Export Citation

  • Lau, K. M., and P. Chan, 1988: Intraseasonal and interannual variations of tropical convection: A possible link between the 40–50 day oscillation and ENSO? J. Atmos. Sci., 45 , 506–521.

    • Search Google Scholar
    • Export Citation

  • Lau, K. M., and C-H. Sui, 1997: Mechanisms of short-term sea surface temperature regulation: Observations during TOGA COARE. J. Climate, 10 , 465–472.

    • Search Google Scholar
    • Export Citation

  • Lukas, R., 1987: On the role of western Pacific air-sea interaction in the El Niño/Southern Oscillation phenomenon. Proceedings of the U.S. TOGA Western Pacific Air-Sea Interaction Workshop, University Corporation for Atmospheric Research, 43–69.

    • Search Google Scholar
    • Export Citation

  • Madden, R., and P. Julian, 1994: Observations of the 40–50-day tropical oscillation: A review. Mon. Wea. Rev., 122 , 814–837.

  • McPhaden, M. J., and J. Picaut, 1990: El-Niño-southern oscillation displacements of the western equatorial Pacific warm pool. Science, 250 , 1385–1388.

    • Search Google Scholar
    • Export Citation

  • McPhaden, M. J., and Coauthors, 1998: The Tropical Ocean-Global Atmosphere observing system: A decade of progress. J. Geophys. Res., 103 , 14169–14240.

    • Search Google Scholar
    • Export Citation

  • Moore, A. M., and R. Kleeman, 1996: The dynamics of error growth and predictability in a coupled model of ENSO. Quart. J. Roy. Meteor. Soc., 122 , 1405–1446.

    • Search Google Scholar
    • Export Citation

  • Moore, A. M., and R. Kleeman, 1997a: The singular vectors of a coupled ocean-atmosphere model of ENSO. I. Thermodynamics, energetics and error growth. Quart. J. Roy. Meteor. Soc., 123 , 953–981.

    • Search Google Scholar
    • Export Citation

  • Moore, A. M., and R. Kleeman, 1997b: The singular vectors of a coupled ocean-atmosphere model of ENSO. II. Sensitivity studies and dynamical interpretation. Quart. J. Roy. Meteor. Soc., 123 , 983–1006.

    • Search Google Scholar
    • Export Citation

  • Moore, A. M., and R. Kleeman, 1999a: Stochastic forcing of ENSO by the intraseasonal oscillation. J. Climate, 12 , 1199–1220.

  • Moore, A. M., and R. Kleeman, 1999b: The nonnormal nature of El Niño and intraseasonal variability. J. Climate, 12 , 2965–2982.

  • Penland, C., 1996: A stochastic model of IndoPacific sea surface temperature anomalies. Physica D, 98 , 534–558.

  • Penland, C., and T. Magorian, 1993: Prediction of Niño-3 sea surface temperatures using linear inverse modeling. J. Climate, 6 , 1067–1076.

    • Search Google Scholar
    • Export Citation

  • Penland, C., and L. Matrasova, 1994: A balance condition for stochastic numerical models with application to El Niño–Southern Oscillation. J. Climate, 7 , 1352–1372.

    • Search Google Scholar
    • Export Citation

  • Penland, C., and P. Sardeshmukh, 1995: The optimal growth of tropical sea surface temperature anomalies. J. Climate, 8 , 1999–2024.

  • Perez, C., 2003: Simulating the interaction between intraseasonal and interannual variability in the tropical Pacific with a coupled system of nonlinear ordinary differential equations. Ph.D. thesis, University of Colorado, 229 pp.

  • Reynolds, R. W., and T. M. Smith, 1995: A high-resolution global sea surface temperature climatology. J. Climate, 8 , 1571–1583.

  • Sardeshmukh, P. D., C. Penland, and M. Newman, 2001: Rossby waves in a stochastically fluctuating medium. Stochastic Climate Models, P. Imkeller and J.-S. von Storch, Eds., Vol. 49, Progress in Probability, Birkhäuser Verlag, 369–383.

    • Search Google Scholar
    • Export Citation

  • Sardeshmukh, P. D., C. Penland, and M. Newman, 2003: Drifts induced by multiplicative red noise with application to climate. Europhys. Lett., 63 , 498–504.

    • Search Google Scholar
    • Export Citation

  • Schopf, P., and M. Suarez, 1988: Vacillations in a coupled ocean–atmosphere model. J. Atmos. Sci., 45 , 549–566.

  • Slingo, J., D. Rowell, K. Sperber, and F. Nortley, 1999: On the predictability of the interannual behavior of the Madden-Julian Oscillation and its relationship with El Niño. Quart. J. Roy. Meteor. Soc., 125 , 583–609.

    • Search Google Scholar
    • Export Citation

  • Sura, P., 2002: Noise-induced transitions in a barotropic β-plane channel. J. Atmos. Sci., 59 , 97–110.

  • Sura, P., 2003: Stochastic analysis of Southern and Pacific Ocean sea surface winds. J. Atmos. Sci., 60 , 654–666.

  • Thompson, C., and D. S. Battisti, 2000a: A linear stochastic dynamical model of ENSO. Part I: Model development. J. Climate, 13 , 2818–2832.

    • Search Google Scholar
    • Export Citation

  • Thompson, C., and D. S. Battisti, 2000b: A linear stochastic dynamical model of ENSO. Part II: Analysis. J. Climate, 14 , 445–466.

  • Wainer, I., and P. Webster, 1996: Monsoon/El Niño-Southern Oscillation relationships in a simple coupled ocean-atmosphere model. J. Geophys. Res., 101 , 25599–25614.

    • Search Google Scholar
    • Export Citation

  • Wang, B., and X. Xie, 1998: Coupled modes of the warm pool climate system. Part I: The role of air–sea interaction in maintaining Madden–Julian oscillation. J. Climate, 11 , 2116–2135.

    • Search Google Scholar
    • Export Citation

  • Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences. Academic Press, 467 pp.

  • Young, H. D., 1962: Statistical Treatment of Experimental Data. McGraw-Hill, Inc., 172 pp.

  • Yu, L., R. A. Weller, and W. T. Liu, 2003: Case analysis of a role of ENSO in regulating the generation of westerly wind bursts in the Western Equatorial Pacific. J. Geophys. Res., 108 .3128, doi:10.1029/2002JC001498.

    • Search Google Scholar
    • Export Citation

  • Zavala-Garay, J., A. M. Moore, C. L. Perez, and R. Kleeman, 2003: The response of a coupled model of ENSO to observed estimates of stochastic forcing. J. Climate, 16 , 2827–2842.

    • Search Google Scholar
    • Export Citation

  • Zebiak, S. E., and M. A. Cane, 1987: A model El Niño–Southern Oscillation. Mon. Wea. Rev., 115 , 2262–2278.

  • Zhang, C. D., 2001: Intraseasonal perturbations in sea surface temperatures of the equatorial eastern pacific and their association with the Madden–Julian oscillation. J. Climate, 14 , 1309–1322.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1006 445 66
PDF Downloads 417 85 26