Climate Dynamics

, Volume 35, Issue 6, pp 995–1009 | Cite as

Assimilation of time-averaged observations in a quasi-geostrophic atmospheric jet model

  • Helga S. HuntleyEmail author
  • Gregory J. Hakim


The problem of reconstructing past climates from a sparse network of noisy time-averaged observations is considered with a novel ensemble Kalman filter approach. Results for a sparse network of 100 idealized observations for a quasi-geostrophic model of a jet interacting with a mountain reveal that, for a wide range of observation averaging times, analysis errors are reduced by about 50% relative to the control case without assimilation. Results are robust to changes to observational error, the number of observations, and an imperfect model. Specifically, analysis errors are reduced relative to the control case for observations having errors up to three times the climatological variance for a fixed 100-station network, and for networks consisting of ten or more stations when observational errors are fixed at one-third the climatological variance. In the limit of small numbers of observations, station location becomes critically important, motivating an optimally determined network. A network of fifteen optimally determined observations reduces analysis errors by 30% relative to the control, as compared to 50% for a randomly chosen network of 100 observations.


Data assimilation Paleoclimate Ensemble Kalman filter Atmospheric modeling 



We thank Ryan Torn for discussions on ensemble filtering, Jeff Anderson for helpful comments on an earlier version of the manuscript, and Angie Pendergrass for discussions on literature related to paleoclimate state estimation and for reviewing an earlier version of the paper. We also thank two anonymous reviewers, whose comments have made this a better paper. The first author was supported in part by a National Science Foundation VIGRE grant and the second author was supported by the following grants: National Oceanic and Atmospheric Administration CSTAR Grant NA17RJ1232, Office of Naval Research Grant N00014-06-1-0510, and National Science Foundation grants 0552004 and 0902500, awarded to the University of Washington.


  1. Ancell B, Hakim GJ (2007) Comparing adjoint- and ensemble-sensitivity analysis with applications to observation targeting. Mon Weather Rev 135:4117–4134CrossRefGoogle Scholar
  2. Anderson J, Anderson S (1999) A monte carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Mon Weather Rev 127(12):2741–2758CrossRefGoogle Scholar
  3. Anderson JL (2007) Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter. Phys D 230:99–111CrossRefGoogle Scholar
  4. Dirren S, Hakim GJ (2005) Toward the assimilation of time-averaged observations. Geophys Res Lett 32(4):L04804CrossRefGoogle Scholar
  5. Gaspari G, Cohn SE (1999) Construction of correlation functions in two and three dimensions. QJR Meteorol Soc 125:723–757CrossRefGoogle Scholar
  6. Hakim GJ (2000) Role of nonmodal growth and nonlinearity in cyclogenesis initial-value problems. J Atmos Sci 57(17):2951–2967CrossRefGoogle Scholar
  7. Hakim GJ, Torn RD (2008) Ensemble synoptic analysis: synoptic-dynamic meteorology and weather analysis and forecasting—a tribute to Fred Sanders, p 36Google Scholar
  8. Hoskins BJ, West NV (1979) Baroclinic waves and frontogenesis. Part II: uniform potential vorticity jet flows—cold and warm fronts. J Atmos Sci 36(9):1663–1680CrossRefGoogle Scholar
  9. Khare SP, Anderson JL (2006a) An examination of ensemble filter based adaptive observation methodologies. Tellus A 58:179–195CrossRefGoogle Scholar
  10. Khare SP, Anderson JL (2006b) A methodology for fixed observational network design: theory and application to a simulated global prediction system. Tellus A 58:523–537CrossRefGoogle Scholar
  11. Murphy JM (1988) The impact of ensemble forecasts on predictability. QJR Meteorol Soc 114:463–493CrossRefGoogle Scholar
  12. Torn RD, Hakim GJ (2008) Ensemble-based sensitivity analysis. Mon Weather Rev 136:663–677CrossRefGoogle Scholar
  13. Whitaker JS, Hamill TM (2002) Ensemble data assimilation without perturbed observations. Mon Weather Rev 130:1913–1924CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA
  2. 2.School of Marine Science and PolicyUniversity of DelawareNewarkUSA
  3. 3.Department of Atmospheric SciencesUniversity of WashingtonSeattleUSA

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