Editorial Type:
Article
Article Type:
Research Article

The Differences between the Optimal Perturbations of Coupled Models of ENSO

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
and
Richard Kleeman Courant Institute for 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:
15 Jan 2001
DOI:
https://doi.org/10.1175/1520-0442(2001)014<0138:TDBTOP>2.0.CO;2
Page(s):
138–163
Restricted access

Abstract

The optimal perturbations (singular vectors) of a dynamical coupled model, a hybrid coupled model, and a linear inverse model of ENSO are compared. The hybrid coupled model consists of a dynamical ocean model and a statistical atmospheric model. The dynamical ocean model is identical to that used in the dynamical coupled model, and the atmospheric model is a statistical model derived from long time series of the dynamical coupled model. The linear inverse model was also derived from long time series from the dynamical coupled model. Thus all three coupled models are very closely related and all produce similar ENSO oscillations. The dynamical model and hybrid model also possess similar levels of hindcast skill. However, the optimal perturbations of the tangent linear versions of each model are not the same. The hybrid and linear inverse models are unable to recover the SST structure of the optimal perturbations of the dynamical model. The SST structure of the dynamical coupled model is a result of nonnormality introduced by latent heating of the atmosphere by deep convection over the west Pacific warm pool. It is demonstrated that standard statistical techniques remove the effects of the latent heating on the nonnormality of the hybrid and linear inverse models essentially rendering them more normal than their dynamical model counterpart. When the statistical components of the hybrid coupled model and the linear inverse models were recomputed using SST anomalies that are appropriately scaled by the standard deviation of SST variability, nonnormality was reintroduced into these models and they recovered the optimal perturbation structure of the dynamical model. Even though the hybrid and linear inverse model with scaled SSTs can recover the large-scale features of the correct optimal structure, state space truncation means that the dynamics of the resulting optimal perturbations is not the same as that governing optimal perturbation growth in the dynamical model. The consequences of these results for observed estimates of optimal perturbations for ENSO are discussed.

Corresponding author address: Dr. Andrew Moore, University of Colorado, Campus Box 311, Boulder, CO 80309-0311.

Abstract

The optimal perturbations (singular vectors) of a dynamical coupled model, a hybrid coupled model, and a linear inverse model of ENSO are compared. The hybrid coupled model consists of a dynamical ocean model and a statistical atmospheric model. The dynamical ocean model is identical to that used in the dynamical coupled model, and the atmospheric model is a statistical model derived from long time series of the dynamical coupled model. The linear inverse model was also derived from long time series from the dynamical coupled model. Thus all three coupled models are very closely related and all produce similar ENSO oscillations. The dynamical model and hybrid model also possess similar levels of hindcast skill. However, the optimal perturbations of the tangent linear versions of each model are not the same. The hybrid and linear inverse models are unable to recover the SST structure of the optimal perturbations of the dynamical model. The SST structure of the dynamical coupled model is a result of nonnormality introduced by latent heating of the atmosphere by deep convection over the west Pacific warm pool. It is demonstrated that standard statistical techniques remove the effects of the latent heating on the nonnormality of the hybrid and linear inverse models essentially rendering them more normal than their dynamical model counterpart. When the statistical components of the hybrid coupled model and the linear inverse models were recomputed using SST anomalies that are appropriately scaled by the standard deviation of SST variability, nonnormality was reintroduced into these models and they recovered the optimal perturbation structure of the dynamical model. Even though the hybrid and linear inverse model with scaled SSTs can recover the large-scale features of the correct optimal structure, state space truncation means that the dynamics of the resulting optimal perturbations is not the same as that governing optimal perturbation growth in the dynamical model. The consequences of these results for observed estimates of optimal perturbations for ENSO are discussed.

Corresponding author address: Dr. Andrew Moore, University of Colorado, Campus Box 311, Boulder, CO 80309-0311.

Save
Cover Journal of Climate
Journal of Climate

  • Barnston, A. G., and Coauthors, 1994: Long-lead seasonal forecasts—Where do we stand? Bull. Amer. Meteor. Soc.,75, 2097–2114.

  • Battisti, D. S., 1988: Dynamics and thermodynamics of a warming event in a coupled tropical atmosphere–ocean model. J. Atmos. Sci.,45, 2889–2919.

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

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

  • 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.

  • Davey, M. K., S. Ineson, and M. A. Balmaseda, 1994: Simulation and hindcasts of tropical Pacific Ocean variability. Tellus,46A, 433–447.

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

  • Fan, Y., 1998: ENSO prediction and predictability in an intermediate coupled model. Ph.D. dissertation, University of Oxford, 241 pp. [Available from Dept. of Atmospheric, Oceanic, and Planetary Physics, University of Oxford, Parks Rd., Oxford OXl 3PU, United Kingdom.].

  • ——, 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.

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

  • ——, and P. J. Ioannou, 1996a: Generalized stability theory. Part I: Autonomous operators. J. Atmos. Sci.,53, 2025–2040.

  • ——, and ——, 1996b: Generalized stability theory. Part II: Non-autonomous operators. J. Atmos. Sci.,53, 2041–2053.

  • ——, and ——, 1999: Perturbation growth and structure in time-dependent flows. J. Atmos. Sci.,56, 3622–3639.

  • Godfrey, J. S., R. A. Houze Jr., R. H. Johnson, R. Lukas, J. L. Redelsperger, A. Sumi, and R. Weller, 1998: Coupled ocean–atmosphere response experiment (COARE): An interim report. J. Geophys. Res.,103, 14 395–14 450.

  • Goswami, B. N., and J. Shukla, 1991: Predictability of a coupled ocean–atmosphere model. J. Climate,4, 3–22.

  • Graham, N., and T. P. Barnett, 1987: Observations of sea surface temperature and convection over tropical oceans. Science,238, 657–659.

  • 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.

  • Hoerling, M. P., A. Kumar, and M. Zhong, 1997: El Niño, La Niña, and the nonlinearity of their teleconnections. J. Climate,10, 1769–1786.

  • Kerr, R. A., 1999: Does a glode-girdling disturbance jigger El Niño? Science,285, 322–323.

  • 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.

  • ——, 1991: A simple model of the atmospheric response to ENSO sea surface temperature anomalies. J. Atmos. Sci.,48, 3–18.

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

  • ——, 1994: Forecasts of tropical Pacific SST using a low-order coupled ocean–atmosphere dynamical model. NOAA Experimental Long-Lead Forecast Bulletin (since June 1994). [Available online at http://nic.fb4.noaa.gov/products/predictions/experimental/bulletin/index.html.].

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

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

  • ——, M. Latif, and M. Flügel, 1992: A hybrid tropical atmosphere ocean model: Sensitivities and hindcast skill. Max-Planck-Institut für Meteorologie Rep. 76, 37 pp. [Available from Max-Planck-Institut für Meteorologie, Bundesstr. 55, D-20146 Hamburg, Germany.].

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

  • Latif, M., T. P. Barnett, M. A. Cane, M. Fügel, N. E. Graham, H. von Storch, J.-S. Xu, and S. E. Zebiak, 1994: A review of ENSO prediction studies. Climate Dyn.,9, 167–179.

  • Lau, K.-M., 1985: Elements of a stochastic dynamical theory of the long-term variability of the El Niño–Southern Oscillation. J. Atmos. Sci.,42, 1552–1558.

  • Mayer, D. A., and R. H. Weisberg, 1998: El Niño–Southern Oscillation-related ocean–atmosphere coupling in the western tropical Pacific. J. Geophys. Res.,103, 18 635–18 648.

  • McPhaden, M. J., 1999: Genesis and evolution of the 1997–98 El Niño. Science,283, 950–954.

  • 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.

  • ——, and ——, 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.

  • ——, and ——, 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.

  • ——, and ——, 1998: Skill assessment for ENSO using ensemble prediction. Quart. J. Roy. Meteor. Soc.,124, 557–584.

  • ——, and ——, 1999a: Stochastic forcing of ENSO by the intraseasonal oscillation. J. Climate,12, 1199–1220.

  • ——, and ——, 1999b: The non-normal nature of El Niño and intraseasonal variability. J. Climate,12, 2965–2982.

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

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

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

  • Picaut, J., M. Ioualalen, C. Menkes, T. Delcroix, and M. J. McPhaden, 1996: Mechanisms of the zonal displacements of the Pacific warm pool: Implications for ENSO. Science,274, 1486–1489.

  • Syu, H.-H., J. D. Neelin, and D. S. Gutzler, 1995: Seasonal and interannual variability in a hybrid coupled GCM. J. Climate,8, 2121–2143.

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

  • ——, and D. S. Battisti, 2001: A linear stochastic dynamical model of ENSO. Part II: Analysis. J. Climate,14, 445–466.

  • Wang, C., R. H. Weisberg, and J. I. Virmani, 1999: Western Pacific interannual variability associated with the El Niño–Southern Oscillation. J. Geophys. Res.,104, 5131–5149.

  • Webster, P. J., 1995: The annual cycle and the predictability of the tropical coupled ocean–atmosphere system. Meteor. Atmos. Phys.,56, 33–55.

  • 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.

  • ——, ——, and ——, 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.

  • ——, ——, and ——, 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.

  • ——, A. Leetmaa, and M. Ji, 2000: ENSO prediction with Markov models: The impact of sea level. J. Climate,13, 849–871.

  • Zebiak, S. E., 1986: Atmospheric convergence feedback of a simple model for El Niño. Mon. Wea. Rev.,114, 1263–1271.

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

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 575 358 49
PDF Downloads 97 29 5