The Role of Air–Sea Interaction in Controlling the Optimal Perturbations of Low-Frequency Tropical Coupled Ocean–Atmosphere Modes

Andrew M. Moore Program in 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
,
Jérôme Vialard European Centre for Medium-Range Weather Forecasts, Reading, Berkshire, United Kingdom; and LODYC, Unité Mixte de Recherche CNRS, Université Paris, Paris, France

Search for other papers by Jérôme Vialard in
Current site
Google Scholar
PubMed
Close
,
Anthony T. Weaver Centre Europeén de Recherche et de Formation Avancée en Calcul Scientifique, Toulouse, France

Search for other papers by Anthony T. Weaver in
Current site
Google Scholar
PubMed
Close
,
David L. T. Anderson European Centre for Medium-Range Weather Forecasts, Reading, Berkshire, United Kingdom

Search for other papers by David L. T. Anderson in
Current site
Google Scholar
PubMed
Close
,
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
, and
Jolie R. Johnson Program in Atmospheric and Oceanic Sciences, and Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado

Search for other papers by Jolie R. Johnson in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

In this paper the structure and dynamics of the optimal perturbations of tropical low-frequency coupled ocean–atmosphere oscillations relevant to El Niño–Southern Oscillation (ENSO) are explored. These optimal perturbations yield information about potential precursors for ENSO events, and about the fundamental dynamical processes that may control perturbation growth and limit the predictability of interannual variability. The present study uses a hierarchy of hybrid coupled models. Each model is configured for the tropical Pacific Ocean and shares a common ocean general circulation model. Three different atmospheric models are used: a statistical model, a dynamical model, and a combination of a dynamical model and boundary layer model. Each coupled model possesses a coupled ocean–atmosphere eigenmode oscillation with a period of the order of several years. The properties of these various eigenmodes and their corresponding adjoint eigenmodes are explored.

The optimal perturbations of each coupled model for two different perturbation growth norms are also examined, and their behavior can be understood in terms of the properties of the aforementioned eigenmode oscillations. It is found that the optimal perturbation spectrum of each coupled model is primarily dominated by one member. The dominant optimal perturbation evolves into the most unstable eigenmode of the system. The structure of the optimal perturbations of each model is found to be controlled by the dynamics of the atmospheric model and air–sea interaction processes. For the coupled model with a statistical atmosphere, the optimal perturbation center of action is spread across the entire tropical Pacific in the form of a dipole. For the coupled models that include deep atmospheric convection, the optimal perturbation center of action is primarily confined to the western Pacific warm pool. In addition, the degree of nonnormality of the eigenmodes is controlled by the atmospheric model dynamics. These findings are in general agreement with the results obtained from intermediate coupled models. In particular, the atmospheric models used here have also been used in intermediate coupled models that have been employed extensively in previous studies of the optimal perturbations of El Niño–Southern Oscillation. Thus, a direct comparison of the optimal perturbation behavior of those intermediate models and the optimal perturbations of the hybrid models used here can be made.

Corresponding author address: Dr. Andrew M. Moore, PAOS, University of Colorado, Campus Box 311, Boulder, CO 80309-0311. Email: andy@australis.colorado.edu

Abstract

In this paper the structure and dynamics of the optimal perturbations of tropical low-frequency coupled ocean–atmosphere oscillations relevant to El Niño–Southern Oscillation (ENSO) are explored. These optimal perturbations yield information about potential precursors for ENSO events, and about the fundamental dynamical processes that may control perturbation growth and limit the predictability of interannual variability. The present study uses a hierarchy of hybrid coupled models. Each model is configured for the tropical Pacific Ocean and shares a common ocean general circulation model. Three different atmospheric models are used: a statistical model, a dynamical model, and a combination of a dynamical model and boundary layer model. Each coupled model possesses a coupled ocean–atmosphere eigenmode oscillation with a period of the order of several years. The properties of these various eigenmodes and their corresponding adjoint eigenmodes are explored.

The optimal perturbations of each coupled model for two different perturbation growth norms are also examined, and their behavior can be understood in terms of the properties of the aforementioned eigenmode oscillations. It is found that the optimal perturbation spectrum of each coupled model is primarily dominated by one member. The dominant optimal perturbation evolves into the most unstable eigenmode of the system. The structure of the optimal perturbations of each model is found to be controlled by the dynamics of the atmospheric model and air–sea interaction processes. For the coupled model with a statistical atmosphere, the optimal perturbation center of action is spread across the entire tropical Pacific in the form of a dipole. For the coupled models that include deep atmospheric convection, the optimal perturbation center of action is primarily confined to the western Pacific warm pool. In addition, the degree of nonnormality of the eigenmodes is controlled by the atmospheric model dynamics. These findings are in general agreement with the results obtained from intermediate coupled models. In particular, the atmospheric models used here have also been used in intermediate coupled models that have been employed extensively in previous studies of the optimal perturbations of El Niño–Southern Oscillation. Thus, a direct comparison of the optimal perturbation behavior of those intermediate models and the optimal perturbations of the hybrid models used here can be made.

Corresponding author address: Dr. Andrew M. Moore, PAOS, University of Colorado, Campus Box 311, Boulder, CO 80309-0311. Email: andy@australis.colorado.edu

Save
  • Aiken, C. M., A. M. Moore, and J. H. Middleton, 2002: The nonnormality of coastal ocean flows around obstacles, and their response to stochastic forcing. J. Phys. Oceanogr., 32 , 29552974.

    • Search Google Scholar
    • Export Citation
  • Balmaseda, M. A., M. K. Davey, and D. L. T. Anderson, 1995: Decadal and seasonal dependence of ENSO predictive skill. J. Climate, 8 , 27052715.

    • Search Google Scholar
    • Export Citation
  • Barkmeijer, J., M. van Gijzen, and F. Bouttier, 1998: Singular vectors and estimates of the analysis-error covariance metric. Quart. J. Roy. Meteor. Soc., 124 , 16951713.

    • Search Google Scholar
    • Export Citation
  • Blumenthal, M. B., 1991: Predictability of a coupled ocean–atmosphere model. J. Climate, 4 , 766784.

  • Bretherton, C. S., C. Smith, and J. M. Wallace, 1992: An intercomparison of methods for finding coupled patterns in climate data. J. Climate, 5 , 541560.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., and T. N. Palmer, 1995: The singular-vector structure of the atmospheric global circulation. J. Atmos. Sci., 52 , 14341456.

    • Search Google Scholar
    • Export Citation
  • Chen, Y-Q., D. S. Battisti, T. N. Palmer, J. Barsugli, and E. S. Sarachik, 1997: A study of the predictability of tropical Pacific SST in a coupled atmosphere/ocean model using singular vector analysis: The role of the annual cycle and the ENSO cycle. Mon. Wea. Rev., 125 , 831845.

    • Search Google Scholar
    • Export Citation
  • Courant, R., and D. Hilbert, 1953: Methods of Mathematical Physics. Vol. I. Wiley Interscience, 559 pp.

  • Eckert, C., 1999: On predictability limits of ENSO. A study performed with a simplified model of the tropical Pacific ocean–atmosphere system. Rep. 55, 76 pp. [Available from Max Planck Institut für Meteorologie, Bundesstrasse 55 D-20146, Hamburg, Germany.].

    • Search Google Scholar
    • Export Citation
  • Fan, Y., M. R. Allen, D. L. T. Anderson, and M. A. Balmaseda, 2000: How predictability depends on the nature of uncertainty in initial conditions in a coupled model of ENSO. J. Climate, 13 , 32983313.

    • Search Google Scholar
    • Export Citation
  • Farrell, B. F., 1982: The initial growth of disturbances in baroclinic flow. J. Atmos. Sci., 39 , 16631686.

  • Farrell, B. F., 1984: Modal and nonmodal baroclinic waves. J. Atmos. Sci., 41 , 668673.

  • Farrell, B. F., 1985: Transient growth of damped baroclinic waves. J. Atmos. Sci., 42 , 27182727.

  • Farrell, B. F., 1988a: Optimal excitation of neutral Rossby waves. J. Atmos. Sci., 45 , 163172.

  • Farrell, B. F., 1988b: Optimal excitation of perturbations in viscous shear flow. Phys. Fluids, 31 , 20932102.

  • Farrell, B. F., 1989a: Optimal excitation of baroclinic waves. J. Atmos. Sci., 46 , 11931206.

  • Farrell, B. F., 1989b: Transient development in confluent and diffluent flow. J. Atmos. Sci., 46 , 32793288.

  • Farrell, B. F., and A. M. Moore, 1992: An adjoint method for obtaining the most rapidly growing perturbation to oceanic flows. J. Phys. Oceanogr., 22 , 338349.

    • Search Google Scholar
    • Export Citation
  • Farrell, B. F., and P. J. Ioannou, 1996: Generalized stability theory. Part I: Autonomous operators. J. Atmos. Sci., 53 , 20252040.

  • Farrell, B. F., and P. J. Ioannou, 1999: Perturbation growth and structure in time-dependent flows. J. Atmos. Sci., 56 , 36223639.

  • Frederiksen, J. S., 1982: A unified three-dimensional instability theory for the onset of blocking and cyclogenesis. J. Atmos. Sci., 39 , 969982.

    • Search Google Scholar
    • Export Citation
  • Galanti, E., E. Tziperman, M. Harrison, A. Rosati, R. Giering, and Z. Sirkes, 2002: The equatorial thermocline outcropping—A seasonal control on the tropical Pacific ocean–atmosphere instability strength. J. Climate, 15 , 27212739.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1980: Simple solutions for heat-induced tropical circulation. Quart. J. Roy. Meteor. Soc., 106 , 447462.

  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Hartmann, D. L., R. Buizza, and T. N. Palmer, 1995: Singular vectors: the effect of spatial scale on linear growth of disturbances. J. Atmos. Sci., 52 , 38853894.

    • Search Google Scholar
    • Export Citation
  • 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 , 34773503.

    • Search Google Scholar
    • Export Citation
  • 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 , 35233540.

    • Search Google Scholar
    • Export Citation
  • Kleeman, R., 1991: A simple model of the atmospheric response to ENSO sea surface temperature anomalies. J. Atmos. Sci., 48 , 318.

  • Kleeman, R., 1993: On the dependence of hindcast skill on ocean thermodynamics in a coupled ocean–atmosphere model. J. Climate, 6 , 20122033.

    • Search Google Scholar
    • Export Citation
  • Kleeman, R., and S. B. Power, 1995: A simple atmospheric model for the surface heat flux of the ocean. J. Phys. Oceanogr., 25 , 92105.

    • Search Google Scholar
    • Export Citation
  • Kleeman, R., J. P. McCreary, and B. A. Klinger, 1999: A mechanism for the decadal variation of ENSO. Geophys. Res. Lett., 26 , 1743.

  • Latif, M., and A. Villwock, 1990: Interannual variability in the tropical Pacific as simulated in coupled ocean–atmosphere models. J. Mar. Systems, 1 , 5160.

    • Search Google Scholar
    • Export Citation
  • Latif, M., and M. Flügel, 1991: An investigation of short range climate predictability in the tropical Pacific. J. Geophys. Res., 96 , 26612673.

    • Search Google Scholar
    • Export Citation
  • Lau, K-M., and P. H. Chan, 1985: Aspects of the 40–50 day oscillation during the northern winter as inferred from outgoing longwave radiation. Mon. Wea. Rev., 113 , 18891909.

    • Search Google Scholar
    • Export Citation
  • Lau, K-M., and P. H. Chan, 1986: The 40–50 day oscillation and the El Nino/Southern Oscilation: A new perspective. Bull. Amer. Met. Soc., 67 , 533534.

    • Search Google Scholar
    • Export Citation
  • Lau, K-M., and P. H. Chan, 1988: Intraseasonal and interannual variations of tropical convection: A possible link between 40–50 day oscillation and ENSO? J. Atmos. Sci., 45 , 506521.

    • Search Google Scholar
    • Export Citation
  • Lehoucq, R. B., D. C. Sorensen, and C. Yaug, 1997: ARPACK Users' Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. Rice University, 140 pp.

    • Search Google Scholar
    • Export Citation
  • Levitus, S., 1982: Climatological atlas of the world ocean. NOAA Prof. Paper 13, U.S. Government Printing Office, 173 pp.

  • Macías, J., D. Stephenson, L. Terray, M. Balmaseda, and D. L. T. Anderson, 1996: ENSO and seasonal variability in a hybrid coupled model of the tropical Pacific. Annales Geophysicae, 14 , C. 647.

    • Search Google Scholar
    • Export Citation
  • Madec, G., P. Delecluse, M. Imbard, and C. Levy, 1998: OPA 8.1 Ocean General Circulation Model Reference Manual. Institut Pierre Simon Laplace des Sciences l'Environnement Global, LODYC, Universite Pierre et Marie Curie, 91 pp.

    • Search Google Scholar
    • Export Citation
  • McPhaden, M. J., 1999: Genesis and evolution of the 1997–98 El Niño. Science, 283 , 950954.

  • Molteni, F., R. Mureau, and T. N. Palmer, 1993: Predictability and finite time instability of the northern winter circulation. Quart. J. Roy. Meteor. Soc., 119 , 269298.

    • Search Google Scholar
    • Export Citation
  • Moore, A. M., and B. F. Farrell, 1993: Rapid perturbation growth on spatially and temporally varying oceanic flows determined using an adjoint method: Application to the Gulf Stream. J. Phys. Oceanogr., 23 , 16821702.

    • 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 , 14051446.

    • Search Google Scholar
    • Export Citation
  • Moore, A. M., and R. Kleeman, 1997a: The singular vectors of a coupled ocean–atmosphere model of ENSO. Part I: Thermodynamics, energetics and error growth. Quart. J. Roy. Meteor. Soc., 123 , 953981.

    • Search Google Scholar
    • Export Citation
  • Moore, A. M., and R. Kleeman, 1997b: The singular vectors of a coupled ocean–atmosphere model of ENSO. Part II: Sensitivity studies and dynamical significance. Quart. J. Roy. Meteor. Soc., 123 , 9831006.

    • Search Google Scholar
    • Export Citation
  • Moore, A. M., and A. J. Mariano, 1999: The dynamics of error growth and predictability in a model of the Gulf Stream. Part I: Singular vector analysis. J. Phys. Oceanogr., 29 , 158176.

    • Search Google Scholar
    • Export Citation
  • Moore, A. M., and A. J. Mariano, 2001: The differences between the optimal perturbations of coupled models of ENSO. J. Climate, 14 , 138163.

    • Search Google Scholar
    • Export Citation
  • Moore, A. M., C. L. Perez, and J. Zavala-Garay, 2002: A non-normal view of the wind-driven ocean circulation. J. Phys. Oceanogr., 32 , 26812705.

    • Search Google Scholar
    • Export Citation
  • 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 , 35043522.

    • Search Google Scholar
    • Export Citation
  • Palmer, T. N., and D. L. T. Anderson, 1994: Prospects for seasonal forecasting. Quart. J. Roy. Meteor. Soc., 120 , 755793.

  • Pedlosky, J., 1979: Geophysical Fluid Dynamics. Springer-Verlag, 710 pp.

  • Reynolds, R. W., and T. M. Smith, 1994: Improved global sea surface temperature analysis. J. Climate, 7 , 929948.

  • Simmons, A. J., and B. J. Hoskins, 1976: Baroclinic instability on the sphere: Normal modes of the primitive and quasigeostrophic equations. J. Atmos. Sci., 33 , 14541477.

    • Search Google Scholar
    • Export Citation
  • Syu, H-H., J. D. Neelin, and D. S. Gutzler, 1995: Seasonal and interannual variability in a hybrid coupled GCM. J. Climate, 8 , 21212143.

    • Search Google Scholar
    • Export Citation
  • Thompson, C. J., 1998: Initial conditions for optimal growth in a coupled ocean–atmosphere model of ENSO. J. Atmos. Sci., 55 , 537557.

    • Search Google Scholar
    • Export Citation
  • Vialard, J., and P. Delecluse, 1998a: An OGCM study for the TOGA decade. Part I: Role of salinity in the physics of the western Pacific fresh pool. J. Phys. Oceanogr., 28 , 10711088.

    • Search Google Scholar
    • Export Citation
  • Vialard, J., and P. Delecluse, 1998b: An OGCM study for the TOGA decade. Part II: Barrier layer formation and variability. J. Phys. Oceanogr., 28 , 10891106.

    • Search Google Scholar
    • Export Citation
  • Vialard, J., C. Menkes, J-P. Boulanger, P. Delecluse, E. Guilyardi, and M. J. McPhaden, 2001: A model study of oceanic mechanisms affecting equatorial Pacific sea surface temperature during the 1997–98 El Niño. J. Phys. Oceanogr., 31 , 16491675.

    • Search Google Scholar
    • Export Citation
  • Vialard, J., A. T. Weaver, and P. Delecluse, 2003: Three- and four-dimensional variational assimilation with a general circulation model of the tropical Pacific Ocean. Part II: Physical validation. Mon. Wea. Rev., in press.

    • Search Google Scholar
    • Export Citation
  • Weaver, A. T., J. Vialard, and D. L. T. Anderson, 2003: Three- and four-dimensional variational assimilation with a general circulation model of the tropical Pacific Ocean. Part I: Formulation, internal diagnostics, and consistency checks. Mon. Wea. Rev., in press.

    • Search Google Scholar
    • Export Citation
  • Webster, P. J., 1972: Response of the tropical atmosphere to local steady forcing. Mon. Wea. Rev., 100 , 518541.

  • Xue, Y., M. A. Cane, S. E. Zebiak, and M. B. Blumenthal, 1994: On the prediction of ENSO: A study with a low order Markov model. Tellus, 46A , 512528.

    • Search Google Scholar
    • Export Citation
  • Xue, Y., M. A. Cane, and S. E. Zebiak, 1997a: Predictability of a coupled model of ENSO using singular vector analysis. Part I: Optimal growth in seasonal background and ENSO cycles. Mon. Wea. Rev., 125 , 20432056.

    • Search Google Scholar
    • Export Citation
  • Xue, Y., M. A. Cane, and S. E. Zebiak, 1997b: Predictability of a coupled model of ENSO using singular vector analysis. Part II: Optimal growth and forecast skill. Mon. Wea. Rev., 125 , 20572073.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 196 38 4
PDF Downloads 73 30 6