Editorial Type:
Article
Article Type:
Research Article

Stochastic Forcing of the North Atlantic Wind-Driven Ocean Circulation. Part II: An Analysis of the Dynamical Ocean Response Using Generalized Stability Theory

Kettyah C. Chhak Program in Atmospheric and Oceanic Sciences, and Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado

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Andrew M. Moore Program in Atmospheric and Oceanic Sciences, and Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado

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Ralph F. Milliff Colorado Research Associates, Boulder, Colorado

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Grant Branstator National Center for Atmospheric Research,* Boulder, Colorado

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William R. Holland National Center for Atmospheric Research,* Boulder, Colorado

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Michael Fisher European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom

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Print Publication:
01 Mar 2006
DOI:
https://doi.org/10.1175/JPO2853.1
Page(s):
316–334
Restricted access

Abstract

As discussed in Part I of this study, the magnitude of the stochastic component of wind stress forcing is comparable to that of the seasonal cycle and thus will likely have a significant influence on the ocean circulation. By forcing a quasigeostrophic model of the North Atlantic Ocean circulation with stochastic wind stress curl data from the NCAR CCM3, it was found in Part I that much of the stochastically induced variability in the ocean circulation is confined to the western boundary region and some major topographic features even though the stochastic forcing is basinwide. This can be attributed to effects of bathymetry and vorticity gradients in the basic state on the system eigenmodes. Using generalized stability theory (GST), it was found in Part I that transient growth due to the linear interference of nonnormal eigenmodes enhances the stochastically induced variance. In the present study, the GST analysis of Part I is extended and it is found that the patterns of wind stress curl that are most effective for inducing variability in the model have their largest projection on the most nonnormal eigenmodes of the system. These eigenmodes are confined primarily to the western boundary region and are composed of long Rossby wave packets that are Doppler shifted by the Gulf Stream to have eastward group velocity. Linear interference of these eigenmodes yields transient growth of stochastically induced perturbations, and it is this process that maintains the variance of the stochastically induced circulations. Analysis of the large-scale circulation also reveals that the system possesses a large number of degrees of freedom, which has significant implications for ocean prediction. Sensitivity studies show that the results and conclusions of this study are insensitive and robust to variations in model parameters and model configuration.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation

Corresponding author address: Dr. Kettyah C. Chhak, Program in Atmospheric and Oceanic Sciences, and Cooperative Institute for Research in Environmental Sciences, University of Colorado, Campus Box 311, Boulder, CO 80309-0311. Email: chhak@colorado.edu

Abstract

As discussed in Part I of this study, the magnitude of the stochastic component of wind stress forcing is comparable to that of the seasonal cycle and thus will likely have a significant influence on the ocean circulation. By forcing a quasigeostrophic model of the North Atlantic Ocean circulation with stochastic wind stress curl data from the NCAR CCM3, it was found in Part I that much of the stochastically induced variability in the ocean circulation is confined to the western boundary region and some major topographic features even though the stochastic forcing is basinwide. This can be attributed to effects of bathymetry and vorticity gradients in the basic state on the system eigenmodes. Using generalized stability theory (GST), it was found in Part I that transient growth due to the linear interference of nonnormal eigenmodes enhances the stochastically induced variance. In the present study, the GST analysis of Part I is extended and it is found that the patterns of wind stress curl that are most effective for inducing variability in the model have their largest projection on the most nonnormal eigenmodes of the system. These eigenmodes are confined primarily to the western boundary region and are composed of long Rossby wave packets that are Doppler shifted by the Gulf Stream to have eastward group velocity. Linear interference of these eigenmodes yields transient growth of stochastically induced perturbations, and it is this process that maintains the variance of the stochastically induced circulations. Analysis of the large-scale circulation also reveals that the system possesses a large number of degrees of freedom, which has significant implications for ocean prediction. Sensitivity studies show that the results and conclusions of this study are insensitive and robust to variations in model parameters and model configuration.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation

Corresponding author address: Dr. Kettyah C. Chhak, Program in Atmospheric and Oceanic Sciences, and Cooperative Institute for Research in Environmental Sciences, University of Colorado, Campus Box 311, Boulder, CO 80309-0311. Email: chhak@colorado.edu

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  • Aiken, C. M., A. M. Moore, and J. H. Middleton, 2002: Nonnormality of coastal ocean flows around obstacles, and their response to stochastic forcing. J. Phys. Oceanogr, 32 , 2955–2974.

    • Search Google Scholar
    • Export Citation

  • Aiken, C. M., A. M. Moore, and J. H. Middleton, 2003: Nonnormal perturbation growth in idealised island and headland wakes. Dyn. Atmos. Oceans, 37 , 171–195.

    • Search Google Scholar
    • Export Citation

  • Bai, Z., M. Fahey, and G. Golub, 1995: Some large matrix computation problems. J. Comput. Appl. Math, 74 , 71–89.

  • Blumental, M. B., 1991: Predictability of a coupled ocean-atmosphere model. J. Climate, 4 , 766–784.

  • Buizza, R., 1995: Optimal perturbation time evolution and sensitivity of ensemble prediction to perturbation amplitude. Quart. J. Roy. Meteor. Soc, 121 , 1705–1738.

    • Search Google Scholar
    • Export Citation

  • Buizza, R., 1997: Potential forecast skill of ensemble prediction and spread and skill distributions of ECMWF ensemble prediction system. Mon. Wea. Rev, 125 , 99–119.

    • 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 , 1434–1456.

    • Search Google Scholar
    • Export Citation

  • Buizza, R., J. Tribbia, F. Molteni, and T. N. Palmer, 1993: Computation of optimal unstable structures for a numerical weather prediction model. Tellus, 45A , 388–407.

    • 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 , 831–845.

    • Search Google Scholar
    • Export Citation

  • Chhak, K., 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 , 300–315.

    • Search Google Scholar
    • Export Citation

  • DelSole, T. M., 1996: Can quasigeostrophic turbulence be modeled stochastically? J. Atmos. Sci, 53 , 1617–1633.

  • DelSole, T. M., 1999: Stochastic models of shear-flow turbulence with enstrophy transfer to subgrid scales. J. Atmos. Sci, 56 , 3692–3703.

    • Search Google Scholar
    • Export Citation

  • DelSole, T. M., 2004: Stochastic models of quasigeostrophic turbulence. Surv. Geophys, 25 , 107–149.

  • DelSole, T. M., and A. Y. Hou, 1999: Empirical stochastic models for the dominant climate statistics of a general circulation model. Mon. Wea. Rev, 127 , 2533–2545.

    • Search Google Scholar
    • Export Citation

  • Dobrovolski, S. G., 2000: Stochastic Climate Theory. Springer, 282 pp.

  • Eckert, C., 1999: On predictability limits of ENSO. A study performed with a simplified model of the tropical Pacific ocean-atmosphere system. Examensarbeit, No. 55, 76 pp. [Available from Max Planck Institut für Meteorologie, Bundesstrasse, 55, D-20146 Hamburg, Germany.].

  • Ehrendorfer, M., and J. J. Tribbia, 1997: Optimal prediction of forecast error covariances through singular vectors. J. Atmos. Sci, 54 , 286–313.

    • Search Google Scholar
    • Export Citation

  • Errico, R. M., T. Vukićecić, and K. Raeder, 1993: Examination of the accuracy of a tangent linear model. Tellus, 45A , 462–477.

    • Search Google Scholar
    • Export Citation

  • Fan, Y., 1998: ENSO prediction and predictability in an intermediate coupled model. Ph.D. thesis, University of Oxford, 241 pp.

  • 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 , 3298–3313.

    • Search Google Scholar
    • Export Citation

  • Farrell, B. F., 1982a: The initial growth of disturbances in a baroclinic flow. J. Atmos. Sci, 39 , 1663–1686.

  • Farrell, B. F., 1982b: Pulse asymptotics of the Charney baroclinic instability problem. J. Atmos. Sci, 39 , 507–517.

  • Farrell, B. F., 1984: Modal and non-modal baroclinic waves. J. Atmos. Sci, 41 , 668–673.

  • Farrell, B. F., 1985: Transient growth of damped baroclinic waves. J. Atmos. Sci, 42 , 2718–2727.

  • Farrell, B. F., 1988: Optimal excitation of neutral Rossby waves. J. Atmos. Sci, 45 , 163–172.

  • Farrell, B. F., 1989: Optimal excitation of baroclinic waves. J. Atmos. Sci, 46 , 1193–1206.

  • Farrell, B. F., 1990: Small error dynamics and the predictability of atmospheric flows. J. Atmos. Sci, 47 , 2409–2416.

  • Farrell, B. F., and P. Ioannou, 1993: Stochastic dynamics of baroclinic waves. J. Atmos. Sci, 50 , 4044–4057.

  • Farrell, B. F., and P. Ioannou, 1995: Stochastic dynamics of the midlatitude atmospheric jet. J. Atmos. Sci, 52 , 1642–1656.

  • Farrell, B. F., and P. Ioannou, 1996a: Generalized stability theory. Part I: Autonomous operators. J. Atmos. Sci, 53 , 2025–2039.

  • Farrell, B. F., and P. Ioannou, 1996b: Generalized stability theory. Part II: Nonautonomous operators. J. Atmos. Sci, 53 , 2041–2053.

    • Search Google Scholar
    • Export Citation

  • Farrell, B. F., and P. Ioannou, 1999: Perturbation growth and structure in time-dependent flows. J. Atmos. Sci, 56 , 3622–3639.

  • Ferranti, L., T. N. Palmer, F. Molteni, and E. Klinker, 1990: Tropical-extratropical interaction with the 30–60 day oscillation and its impact on medium and extended range prediction. J. Atmos. Sci, 47 , 2177–2199.

    • Search Google Scholar
    • Export Citation

  • Gardiner, C. W., 1985: Handbook of Stochastic Methods. Springer-Verlag, 442 pp.

  • Glover, K., 1984: All optimal Hankel-norm approximations of linear multivariable systems and their error bounds. Int. J. Control, 39 , 1115–1193.

    • Search Google Scholar
    • Export Citation

  • Golub, G., and C. van Loan, 1989: Matrix Computations. The Johns Hopkins University Press, 642 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 , 3885–3894.

    • Search Google Scholar
    • Export Citation

  • Johnson, S., 1999: Markov model studies of the El Niño Southern Oscillation. Ph.D. thesis, University of Washington, 131 pp.

  • Kleeman, R., and A. M. 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., and A. M. Moore, 1999: A new method for determining the reliability of dynamical ENSO predictions. Mon. Wea. Rev, 127 , 694–705.

    • Search Google Scholar
    • Export Citation

  • Kutzbach, J. E., 1967: Empirical eigenvectors of sea-level pressure, surface temperature, and precipitation complexes over North America. J. Appl. Meteor, 6 , 791–802.

    • Search Google Scholar
    • Export Citation

  • Lacarra, J. F., and O. Talagrand, 1988: Short-range evolution of small perturbations in a barotropic model. Tellus, 40A , 81–95.

  • Lorenz, E. N., 1965: A study of the predictability of 28-variable atmospheric model. Tellus, 17 , 321–333.

  • Milliff, R. F., W. G. Large, W. R. Holland, and J. C. McWilliams, 1996: The general circulation responses of high-resolution North Atlantic ocean models to synthetic scatterometer winds. J. Phys. Oceanogr, 26 , 1747–1768.

    • Search Google Scholar
    • Export Citation

  • Milliff, R. F., W. G. Large, J. Morzel, G. Danabasoglu, and T. Chin, 1999: Ocean general circulation model sensitivity to forcing from scatterometer winds. J. Geophys. Res, 104 , 11337–11358.

    • Search Google Scholar
    • Export Citation

  • Milliff, R. F., J. Morzel, D. Chelton, and M. H. Freilich, 2004: Wind stress curl and wind stress divergence biases from rain effects on QSCAT surface wind retrievals. J. Atmos. Oceanic Technol, 21 , 1216–1231.

    • Search Google Scholar
    • Export Citation

  • 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 , 269–298.

    • Search Google Scholar
    • Export Citation

  • Molteni, F., R. Buizza, T. N. Palmer, and T. Petroliagis, 1996: The ECMWF ensemble prediction system: Methodology and validation. Quart. J. Roy. Meteor. Soc, 122 , 73–120.

    • Search Google Scholar
    • Export Citation

  • Moore, A. M., 1999: Wind-induced variability of ocean gyres. Dyn. Atmos. Oceans, 29 , 335–364.

  • 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. Part 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. Part II: Sensitivity studies and dynamical significance. Quart. J. Roy. Meteor. Soc, 123 , 983–1006.

    • Search Google Scholar
    • Export Citation

  • Moore, A. M., and R. Kleeman, 1998: Skill assessment for ENSO using ensemble prediction. Quart. J. Roy. Meteor. Soc, 124 , 557–584.

    • Search Google Scholar
    • Export Citation

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

    • Search Google Scholar
    • Export Citation

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

  • Moore, A. M., and R. Kleeman, 2001: The differences between the optimal perturbations of coupled models of ENSO. J. Climate, 14 , 138–163.

    • 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 , 2681–2705.

    • 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 , 951–962.

    • Search Google Scholar
    • Export Citation

  • Moore, B., 1981: Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Trans. Auto. Control, AC-26 , 17–31.

    • Search Google Scholar
    • Export Citation

  • Mureau, R., F. Molteni, and T. N. Palmer, 1993: Ensemble prediction using dynamically conditioned perturbations. Quart. J. Roy. Meteor. Soc, 119 , 299–323.

    • Search Google Scholar
    • Export Citation

  • Palmer, T., 1996: Predictability of the atmosphere and oceans: From days to decades. Decadal Climate Variability: Dynamics and Predictability, D. L. T. Anderson and J. Willebrand, Eds., Springer, 83–155.

    • Search Google Scholar
    • Export Citation

  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. Springer-Verlag, 710 pp.

  • Penland, C., 1989: Random forcing and forecasting using principal oscillation pattern analysis. Mon. Wea. Rev, 117 , 2165–2185.

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

  • Penland, C., and P. D. Sardeshmukh, 1995a: Error and sensitivity analysis of geophysical eigensystems. J. Climate, 8 , 1988–1998.

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

    • Search Google Scholar
    • Export Citation

  • Tang, Y., R. Kleeman, and A. Moore, 2005: Reliability of ENSO dynamical predictions. J. Atmos. Sci, 62 , 1770–1791.

  • Thompson, C. J., 1998: Initial conditions for optimal growth in a coupled ocean–atmosphere model of ENSO. J. Atmos. Sci, 55 , 537–557.

    • Search Google Scholar
    • Export Citation

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

  • Willebrand, J., S. G. H. Philander, and R. C. Pacanowski, 1980: The oceanic response to large-scale atmospheric disturbances. J. Phys. Oceanogr, 10 , 411–429.

    • Search Google Scholar
    • Export Citation

  • 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 , 512–528.

    • 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 , 2043–2056.

    • Search Google Scholar
    • Export Citation

  • Xue, Y., M. A. Cane, S. E. Zebiak, and T. N. Palmer, 1997b: Predictability of a coupled model of ENSO using singular vector analysis. Part II: Optimal growth and forecast skill. Mon. Wea. Rev, 125 , 2057–2073.

    • Search Google Scholar
    • Export Citation

  • Xue, Y., A. Leetmaa, and M. Ji, 1999: Impact of sea level on predictability of ENSO: A study with Markov models. Preprints, Second Hayes Symp. on Seasonal to Interannual Climate Variability—The 1997/1998 ENSO Cycle, Dallas, TX, Amer. Meteor. Soc., 81–84.

  • 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
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