The Role of Ocean Dynamics in the Optimal Growth of Tropical SST Anomalies

Laure Zanna Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts

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Patrick Heimbach Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts

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Andrew M. Moore Ocean Sciences Department, University of California, Santa Cruz, Santa Cruz, California

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Eli Tziperman Department of Earth and Planetary Sciences, and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts

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Abstract

The role of ocean dynamics in optimally exciting interannual variability of tropical sea surface temperature (SST) anomalies is investigated using an idealized-geometry ocean general circulation model. Initial temperature and salinity perturbations leading to an optimal growth of tropical SST anomalies, typically arising from the nonnormal dynamics, are evaluated. The structure of the optimal perturbations is characterized by relatively strong deep salinity anomalies near the western boundary generating a transient amplification of equatorial SST anomalies in less than four years.

The associated growth mechanism is linked to the excitation of coastal and equatorial Kelvin waves near the western boundary following a rapid geostrophic adjustment owing to the optimal initial temperature and salinity perturbations. The results suggest that the nonnormality of the ocean dynamics may efficiently create large tropical SST variability on interannual time scales in the Atlantic without the participation of air–sea processes or the meridional overturning circulation. An optimal deep initial salinity perturbation of 0.1 ppt located near the western boundary can result in a tropical SST anomaly of approximately 0.45°C after nearly four years, assuming the dynamics are linear. Possible mechanisms for exciting such deep perturbations are discussed. While this study is motivated by tropical Atlantic SST variability, its relevance to other basins is not excluded.

The optimal initial conditions leading to the tropical SST anomalies’ growth are obtained by solving a generalized eigenvalue problem. The evaluation of the optimals is achieved by using the Massachusetts Institute of Technology general circulation model (MITgcm) tangent linear and adjoint models as well the the Arnoldi Package (ARPACK) software for solving large-scale eigenvalue problems.

Corresponding author address: Laure Zanna, Atmospheric, Oceanic and Planetary Physics, Dept. of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom. Email: laure.zanna@earth.ox.ac.uk

Abstract

The role of ocean dynamics in optimally exciting interannual variability of tropical sea surface temperature (SST) anomalies is investigated using an idealized-geometry ocean general circulation model. Initial temperature and salinity perturbations leading to an optimal growth of tropical SST anomalies, typically arising from the nonnormal dynamics, are evaluated. The structure of the optimal perturbations is characterized by relatively strong deep salinity anomalies near the western boundary generating a transient amplification of equatorial SST anomalies in less than four years.

The associated growth mechanism is linked to the excitation of coastal and equatorial Kelvin waves near the western boundary following a rapid geostrophic adjustment owing to the optimal initial temperature and salinity perturbations. The results suggest that the nonnormality of the ocean dynamics may efficiently create large tropical SST variability on interannual time scales in the Atlantic without the participation of air–sea processes or the meridional overturning circulation. An optimal deep initial salinity perturbation of 0.1 ppt located near the western boundary can result in a tropical SST anomaly of approximately 0.45°C after nearly four years, assuming the dynamics are linear. Possible mechanisms for exciting such deep perturbations are discussed. While this study is motivated by tropical Atlantic SST variability, its relevance to other basins is not excluded.

The optimal initial conditions leading to the tropical SST anomalies’ growth are obtained by solving a generalized eigenvalue problem. The evaluation of the optimals is achieved by using the Massachusetts Institute of Technology general circulation model (MITgcm) tangent linear and adjoint models as well the the Arnoldi Package (ARPACK) software for solving large-scale eigenvalue problems.

Corresponding author address: Laure Zanna, Atmospheric, Oceanic and Planetary Physics, Dept. of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom. Email: laure.zanna@earth.ox.ac.uk

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  • Adcroft, A., 1995: Numerical algorithms for use in a dynamical model of the ocean. Ph.D. thesis, Imperial College, 116 pp.

  • Adcroft, A., C. N. Hill, and J. C. Marshall, 1999: A new treatment of the Coriolis terms in C-grid models at both high and low resolutions. Mon. Wea. Rev., 127 , 19281936.

    • Search Google Scholar
    • Export Citation
  • Bugnion, V., C. Hill, and P. H. Stone, 2006: An adjoint analysis of the meridional overturning circulation in an ocean model. J. Climate, 19 , 37323750.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., 1995: Optimal perturbation time evolution and sensitivity of ensemble prediction to perturbation amplitude. Quart. J. Roy. Meteor. Soc., 121 , 17051738.

    • 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
  • Carton, J. A., X. H. Cao, B. S. Giese, and A. M. Dasilva, 1996: Decadal and interannual SST variability in the tropical Atlantic Ocean. J. Phys. Oceanogr., 26 , 11651175.

    • Search Google Scholar
    • Export Citation
  • Chang, P., L. Ji, and H. Li, 1997: A decadal climate variation in the tropical Atlantic Ocean from thermodynamic air-sea interactions. Nature, 385 , 516518.

    • Search Google Scholar
    • Export Citation
  • Chang, P., R. Saravanan, L. Ji, and G. C. Hegerl, 2000: The effect of local sea surface temperatures on atmospheric circulation over the tropical Atlantic sector. J. Climate, 13 , 21952216.

    • Search Google Scholar
    • Export Citation
  • Chang, P., L. Ji, and R. Saravanan, 2001: A hybrid coupled model study of tropical Atlantic variability. J. Climate, 14 , 361390.

  • Chhak, K. C., A. M. Moore, R. F. Milliff, G. Branstator, W. R. Holland, and M. Fisher, 2006: Stochastic forcing of the North Atlantic wind-driven ocean circulation. Part I: A diagnostic analysis of the ocean response to stochastic forcing. J. Phys. Oceanogr., 36 , 300315.

    • Search Google Scholar
    • Export Citation
  • Dengler, M., F. A. Schott, C. Eden, P. Brandt, J. Fischer, and R. J. Zantopp, 2004: Break-up of the Atlantic deep western boundary current into eddies at 8 degrees S. Nature, 432 , 10181020.

    • Search Google Scholar
    • Export Citation
  • Dukowicz, J. K., and R. D. Smith, 1994: Implicit free-surface method for the Bryan-Cox-Semtner ocean model. J. Geophys. Res., 99 , (C4). 79918014.

    • Search Google Scholar
    • Export Citation
  • Enfield, D. B., and D. A. Mayer, 1997: Tropical Atlantic sea surface temperature variability and its relation to El Niño-Southern Oscillation. J. Geophys. Res., 102 , (C1). 929945.

    • Search Google Scholar
    • Export Citation
  • Farrell, B., 1988: Optimal excitation of neutral Rossby waves. J. Atmos. Sci., 45 , 163172.

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

  • Farrell, B., and P. J. Ioannou, 1996: Generalized stability theory. Part I: Autonomous operators. J. Atmos. Sci., 53 , 20252040.

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

  • Forget, G., and C. Wunsch, 2007: Estimated global hydrographic variability. J. Phys. Oceanogr., 37 , 19972008.

  • Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20 , 150155.

  • Giering, R., and T. Kaminski, 1998: Recipes for adjoint code construction. ACM Trans. Math. Software, 24 , 437474.

  • Golub, G. H., and C. F. Van Loan, 1989: Matrix Computations. 2nd ed. The Johns Hopkins University Press, 642 pp.

  • Heimbach, P., C. Hill, and R. Giering, 2005: An efficient exact adjoint of the parallel MIT general circulation model, generated via automatic differentiation. Future Gener. Comput. Syst., 21 , 13561371.

    • Search Google Scholar
    • Export Citation
  • Hsieh, W. W., M. K. Davey, and R. C. Wajsowicz, 1983: The free Kelvin wave in finite-difference numerical models. J. Phys. Oceanogr., 13 , 13831397.

    • Search Google Scholar
    • Export Citation
  • Jackett, D. R., and T. J. Mcdougall, 1995: Minimal adjustment of hydrographic profiles to achieve static stability. J. Atmos. Oceanic Technol., 12 , 381389.

    • Search Google Scholar
    • Export Citation
  • Jochum, M., P. Malanotte-rizzoli, and A. Busalacchi, 2004: Tropical instability waves in the Atlantic Ocean. Ocean Modell., 7 , (1–2). 145163.

    • Search Google Scholar
    • Export Citation
  • Lagerloef, G., G. Mitchum, R. Lukas, and P. Niiler, 1999: Tropical Pacific near-surface current estimates from altimeter, wind and drifter data. J. Geophys. Res., 104 , 313326.

    • Search Google Scholar
    • Export Citation
  • Lehoucq, R., D. Sorensen, and C. Yang, 1998: ARPACK users’ guide: Solution of large scale eigenvalue problems with implicitly restarted Arnoldi methods. Rice University Tech. Rep., 140 pp.

    • Search Google Scholar
    • Export Citation
  • Lohmann, G., and J. Schneider, 1999: Dynamics and predictability of Stommel’s box model. A phase-space perspective with implications for decadal climate variability. Tellus, 51A , 326336.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1982: Atmospheric predictability experiments with a large numerical model. Tellus, 34 , 505513.

  • Marotzke, J., 1990: Instabilities and multiple equilibria of the thermohaline circulation. Ph.D. thesis, Berlin Instit Meereskunde, 126 pp.

  • Marotzke, J., R. Giering, K. Q. Zhang, D. Stammer, C. Hill, and T. Lee, 1999: Construction of the adjoint MIT ocean general circulation model and application to Atlantic heat transport sensitivity. J. Geophys. Res., 104 , (C12). 2952929547.

    • Search Google Scholar
    • Export Citation
  • Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, 1997a: A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102 , (C3). 57535766.

    • Search Google Scholar
    • Export Citation
  • Marshall, J., C. Hill, L. Perelman, and A. Adcroft, 1997b: Hydrostatic, quasi-hydrostatic and nonhydrostatic ocean modeling. J. Geophys. Res., 102 , (C3). 57335752.

    • Search Google Scholar
    • Export Citation
  • Marshall, J., and Coauthors, 2001: North Atlantic climate variability: Phenomena, impacts and mechanisms. Int. J. Climatol., 21 , 18631898.

    • Search Google Scholar
    • Export Citation
  • Moore, A. M., 1999: Wind-induced variability of ocean gyres. Dyn. Atmos. Oceans, 29 , (2–4). 335364.

  • Moore, A. M., and R. Kleeman, 1997: The singular vectors of a coupled ocean-atmosphere model of ENSO. I: thermodynamics, energetics and error growth. Quart. J. Roy. Meteor. Soc., 123 , 953981.

    • Search Google Scholar
    • Export Citation
  • Moore, A. M., J. Vialard, A. T. Weaver, D. L. T. Anderson, R. Kleeman, and J. R. Johnson, 2003: The role of air–sea interaction in controlling the optimal perturbations of low-frequency tropical coupled ocean–atmosphere modes. J. Climate, 16 , 951968.

    • Search Google Scholar
    • Export Citation
  • Moore, A. M., H. G. Arango, E. Di Lorenzo, B. D. Cornuelle, A. J. Miller, and D. J. Neilson, 2004: A comprehensive ocean prediction and analysis system based on the tangent linear and adjoint of a regional ocean model. Ocean Modell., 7 , (1–2). 227258.

    • Search Google Scholar
    • Export Citation
  • Ng, M. K. F., and W. W. Hsieh, 1994: The equatorial Kelvin wave in finite-difference models. J. Geophys. Res., 99 , (C7). 1417314185.

  • Pedlosky, J., 1979: Geophysical Fluid Dynamics. 1st ed. Springer, 624 pp.

  • Penland, C., 1996: A stochastic model of IndoPacific sea surface temperature anomalies. Physica D, 98 , (2–4). 534558.

  • Penland, C., and P. D. Sardeshmukh, 1995: The optimal growth of tropical sea surface temperature anomalies. J. Climate, 8 , 19992024.

  • Penland, C., and L. Matrosova, 1998: Prediction of tropical Atlantic sea surface temperatures using linear inverse modeling. J. Climate, 11 , 483496.

    • Search Google Scholar
    • Export Citation
  • Redi, M. H., 1982: Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12 , 11541158.

  • Saji, N. H., B. N. Goswani, P. N. Vinayachandran, and T. Yamagata, 1999: A dipole mode in the tropical Indian Ocean. Nature, 401 , 360363.

    • Search Google Scholar
    • Export Citation
  • Seo, H., M. Jochum, R. Murtugudde, and A. J. Miller, 2006: Effect of ocean mesoscale variability on the mean state of tropical Atlantic climate. Geophys. Res. Lett., 33 , L09606. doi:10.1029/2005GL025651.

    • Search Google Scholar
    • Export Citation
  • Sevellec, F., M. B. Jelloul, and T. Huck, 2007: Optimal surface salinity perturbations influencing the thermohaline circulation. J. Phys. Oceanogr., 37 , 27892808.

    • Search Google Scholar
    • Export Citation
  • Stommel, H., and A. B. Arons, 1960a: On the abyssal circulation of the World Ocean—I. Stationary planetary flow patterns on a sphere. Deep-Sea Res., 6 , 140154.

    • Search Google Scholar
    • Export Citation
  • Stommel, H., and A. B. Arons, 1960b: On the abyssal circulation of the World Ocean—II. An idealized model of the circulation pattern and amplitude in oceanic basins. Deep-Sea Res., 6 , 217233.

    • Search Google Scholar
    • Export Citation
  • Trefethen, L. N., A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, 1993: Hydrodynamic stability without eigenvalues. Science, 261 , 578584.

    • Search Google Scholar
    • Export Citation
  • Tziperman, E., and P. J. Ioannou, 2002: Transient growth and optimal excitation of thermohaline variability. J. Phys. Oceanogr., 32 , 34273435.

    • Search Google Scholar
    • Export Citation
  • Wajsowicz, R. C., and A. E. Gill, 1986: Adjustment of the ocean under buoyancy forces. Part I: The role of Kelvin waves. J. Phys. Oceanogr., 16 , 20972114.

    • Search Google Scholar
    • Export Citation
  • Weaver, A. J., and E. S. Sarachik, 1990: On the importance of vertical resolution in certain ocean general circulation models. J. Phys. Oceanogr., 20 , 600609.

    • Search Google Scholar
    • Export Citation
  • Xie, S-P., and J. Carton, 2004: Tropical Atlantic variability: Patterns, mechanisms, and impacts. Earth’s Climate: The Ocean–Atmosphere Interaction, Geophys. Monogr., Vol. 147, Amer. Geophys. Union, 121–142.

    • Search Google Scholar
    • Export Citation
  • Zanna, L., 2009: Optimal excitation of Atlantic Ocean variability and implications for predictability. Ph.D. thesis, Harvard University, 177 pp.

  • Zanna, L., and E. Tziperman, 2005: Nonnormal amplification of the thermohaline circulation. J. Phys. Oceanogr., 35 , 15931605.

  • Zanna, L., and E. Tziperman, 2008: Optimal surface excitation of the thermohaline circulation. J. Phys. Oceanogr., 38 , 18201830.

  • Zebiak, S. E., 1993: Air–sea interaction in the equatorial Atlantic region. J. Climate, 6 , 15671568.

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