• Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129 , 28842903.

  • Annan, J. D., 2004: On the orthogonality of bred vectors. Mon. Wea. Rev., 132 , 843849.

  • Ashwin, P., J. Buescu, and I. Stewart, 1994: Bubbling of attractors and synchronization of chaotic oscillators. Phys. Lett. A, 193 , 126139.

    • Search Google Scholar
    • Export Citation
  • Baek, S-J., B. R. Hunt, I. Szunyogh, A. Zimin, and E. Ott, 2004: Localized error bursts in estimating the state of spatiotemporal chaos. Chaos, 14 , 10421049.

    • Search Google Scholar
    • Export Citation
  • Bao, J-W., and R. Errico, 1997: An adjoint examination of a nudging method for data assimilation. Mon. Wea. Rev., 125 , 13551373.

  • Boccaletti, S., J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, 2002: The synchronization of chaotic systems. Phys. Rep., 366 , 1101.

    • Search Google Scholar
    • Export Citation
  • Brown, R., and N. Rulkov, 1997: Synchronization of chaotic systems: Tranverse stability of trajectories in invariant manifolds. Chaos, 7 , 395413.

    • Search Google Scholar
    • Export Citation
  • Corazza, M., and Coauthors, 2003: Use of the breeding technique to estimate the structure of the analysis “errors of the day.”. Nonlinear Processes Geophys., 10 , 111.

    • Search Google Scholar
    • Export Citation
  • Duane, G., and J. Tribbia, 2001: Synchronized chaos in geophysical fluid dynamics. Phys. Rev. Lett., 86 , 42984301.

  • Evans, E., N. Bhatti, J. Kinney, L. Pann, M. Peňa, S. C. Yang, E. Kalnay, and J. Hansen, 2004: RISE undergraduates find that regime changes in Lorenz’s model are predictable. Bull. Amer. Meteor. Soc., 85 , 521524.

    • Search Google Scholar
    • Export Citation
  • Hoke, J., and R. Anthes, 1976: The initialization of numerical weather models by a dynamic relaxation technique. Mon. Wea. Rev., 104 , 15511556.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., H. L. Mitchell, G. Pellerin, M. Buehner, M. Charron, L. Spacek, and B. Hansen, 2005: Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations. Mon. Wea. Rev., 133 , 604620.

    • Search Google Scholar
    • Export Citation
  • Junge, L., and U. Parlitz, 2001: Synchronization using dynamic coupling. Phys. Rev. E, 64 .doi:10.1103/PhysRevE.64.055204.

  • Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, 341 pp.

  • Kocarev, L., Z. Tasev, and U. Parlitz, 1997: Synchronizing spatiotemporal chaos of partial differential equations. Phys. Rev. Lett., 79 , 5154.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E., 1963: Deterministic non-periodic flow. J. Atmos. Sci., 20 , 130141.

  • Lui, Z., S. Chen, and B. Hu, 1999: Coupled synchronization of spatiotemporal chaos. Phys. Rev. E, 59 , 28172821.

  • Miller, R., M. Ghil, and F. Gauthiez, 1994: Advanced data assimilation in strongly nonlinear dynamical systems. J. Atmos. Sci., 51 , 10371056.

    • Search Google Scholar
    • Export Citation
  • Molteni, F., 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
  • Molteni, F., R. Buizza, T. Palmer, and T. Petroliagis, 1996: The new ECMWF ensemble prediction system: Methodology and validation. Quart. J. Roy. Meteor. Soc., 122 , 73119.

    • Search Google Scholar
    • Export Citation
  • Ott, E., and J. Sommerer, 1994: Blowout bifurcations: The occurrence of riddled basins and on–off intermittency. Phys. Lett. A, 188 , 3947.

    • Search Google Scholar
    • Export Citation
  • Pecora, L., and T. Carroll, 1990: Synchronization in chaotic systems. Phys. Rev. Lett., 64 , 821824.

  • Pecora, L., T. Carroll, G. Johnson, and D. Mar, 1997: Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos, 7 , 520543.

    • Search Google Scholar
    • Export Citation
  • Platt, N., E. A. Spiegel, and C. Tresser, 1993: On–off intermittency: A mechanism for bursting. Phys. Rev. Lett., 70 , 279282.

  • Pyragas, K., 1996: Weak and strong synchronization of chaos. Phys. Rev. E, 54 , R4508R4511.

  • Pyragas, K., 1997: Conditional Lyapunov exponents from time series. Phys. Rev. E, 56 , 51835188.

  • Rössler, O. E., 1976: An equation for continuous chaos. Phys. Lett., 57A , 397398.

  • Rulkov, N., M. Sushchik, L. Tsimring, and H. Abarbanel, 1995: Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E, 51 , 980994.

    • Search Google Scholar
    • Export Citation
  • So, P., E. Ott, and W. P. Dayawansa, 1994: Observing chaos: Deducing and tracking the state of a chaotic system from limited observations. Phys. Rev. E, 49 , 26502660.

    • Search Google Scholar
    • Export Citation
  • So, P., E. Barreto, K. Josic, E. Sander, and S. Schiff, 2002: Limits to the experimental detection of nonlinear synchrony. Phys. Rev. E, 65 .doi:10.1103/PhysRevE.65.046225.

    • Search Google Scholar
    • Export Citation
  • Stauffer, D. R., and N. L. Seaman, 1990: Use of four-dimensional data assimilation in a limited-area mesoscale model. Part I: Experiments with synoptic-scale data. Mon. Wea. Rev., 118 , 12501277.

    • Search Google Scholar
    • Export Citation
  • Stauffer, D. R., N. L. Seaman, J. M. Fritsch, C. W. Porter, and J-W. Bao, 1994: Nonhydrostatic real-case forecasting of wintertime aviation-sensitive events using 4-km resolution and four-dimensional data assimilation. Preprints, Proc. Sixth Conf. on Mesoscale Processes, Portland, OR, Amer. Meteor. Soc., 435–438.

  • Strogatz, S., 2003: Sync: The Emerging Science of Spontaneous Order. Theia, 338 pp.

  • Toth, Z., and E. Kalnay, 1993: Ensemble forecasting at NMC: The generation of perturbations. Bull. Amer. Meteor. Soc., 74 , 23172330.

  • Toth, Z., and E. Kalnay, 1997: Ensemble forecasting at NCEP: The breeding method. Mon. Wea. Rev., 125 , 32973318.

  • Trevisan, A., and F. Uboldi, 2004: Assimilation of standard and targeted observations within the unstable subspace of the observation–analysis–forecast cycle system. J. Atmos. Sci., 61 , 103113.

    • Search Google Scholar
    • Export Citation
  • Zhong, G., K. Man, and K. Ko, 2001: Uncertainty in chaos synchronization. Int. J. Bifurcat. Chaos, 11 , 17231735.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 381 113 14
PDF Downloads 331 105 14

Data Assimilation as Synchronization of Truth and Model: Experiments with the Three-Variable Lorenz System

Shu-Chih YangDepartment of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland

Search for other papers by Shu-Chih Yang in
Current site
Google Scholar
PubMed
Close
,
Debra BakerDepartment of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland

Search for other papers by Debra Baker in
Current site
Google Scholar
PubMed
Close
,
Hong LiDepartment of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland

Search for other papers by Hong Li in
Current site
Google Scholar
PubMed
Close
,
Katy CordesGoucher College, Baltimore, Maryland

Search for other papers by Katy Cordes in
Current site
Google Scholar
PubMed
Close
,
Morgan HuffUniversity of Kansas, Lawrence, Kansas

Search for other papers by Morgan Huff in
Current site
Google Scholar
PubMed
Close
,
Geetika NagpalDepartment of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland

Search for other papers by Geetika Nagpal in
Current site
Google Scholar
PubMed
Close
,
Ena OkerekeMorgan State University, Baltimore, Maryland

Search for other papers by Ena Okereke in
Current site
Google Scholar
PubMed
Close
,
Josue Villafañe*Universidad Metropolitana de Puerto Rico, San Juan, Puerto Rico

Search for other papers by Josue Villafañe in
Current site
Google Scholar
PubMed
Close
,
Eugenia KalnayDepartment of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland

Search for other papers by Eugenia Kalnay in
Current site
Google Scholar
PubMed
Close
, and
Gregory S. DuaneNational Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Gregory S. Duane in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The potential use of chaos synchronization techniques in data assimilation for numerical weather prediction models is explored by coupling a Lorenz three-variable system that represents “truth” to another that represents “the model.” By adding realistic “noise” to observations of the master system, an optimal value of the coupling strength was clearly identifiable. Coupling only the y variable yielded the best results for a wide range of higher coupling strengths. Coupling along dynamically chosen directions identified by either singular or bred vectors could improve upon simpler chaos synchronization schemes. Generalized synchronization (with the parameter r of the slave system different from that of the master) could be easily achieved, as indicated by the synchronization of two identical slave systems coupled to the same master, but the slaves only provided partial information about regime changes in the master. A comparison with a standard data assimilation technique, three-dimensional variational analysis (3DVAR), demonstrated that this scheme is slightly more effective in producing an accurate analysis than the simpler synchronization scheme. Higher growth rates of bred vectors from both the master and the slave anticipated the location and size of error spikes in both 3DVAR and synchronization. With less frequent observations, synchronization using time-interpolated observational increments was competitive with 3DVAR. Adaptive synchronization, with a coupling parameter proportional to the bred vector growth rate, was successful in reducing episodes of large error growth. These results suggest that a hybrid chaos synchronization–data assimilation approach may provide an avenue to improve and extend the period for accurate weather prediction.

Corresponding author address: Gregory S. Duane, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. Email: gduane@ucar.edu

Abstract

The potential use of chaos synchronization techniques in data assimilation for numerical weather prediction models is explored by coupling a Lorenz three-variable system that represents “truth” to another that represents “the model.” By adding realistic “noise” to observations of the master system, an optimal value of the coupling strength was clearly identifiable. Coupling only the y variable yielded the best results for a wide range of higher coupling strengths. Coupling along dynamically chosen directions identified by either singular or bred vectors could improve upon simpler chaos synchronization schemes. Generalized synchronization (with the parameter r of the slave system different from that of the master) could be easily achieved, as indicated by the synchronization of two identical slave systems coupled to the same master, but the slaves only provided partial information about regime changes in the master. A comparison with a standard data assimilation technique, three-dimensional variational analysis (3DVAR), demonstrated that this scheme is slightly more effective in producing an accurate analysis than the simpler synchronization scheme. Higher growth rates of bred vectors from both the master and the slave anticipated the location and size of error spikes in both 3DVAR and synchronization. With less frequent observations, synchronization using time-interpolated observational increments was competitive with 3DVAR. Adaptive synchronization, with a coupling parameter proportional to the bred vector growth rate, was successful in reducing episodes of large error growth. These results suggest that a hybrid chaos synchronization–data assimilation approach may provide an avenue to improve and extend the period for accurate weather prediction.

Corresponding author address: Gregory S. Duane, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. Email: gduane@ucar.edu

Save