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A COMPARISON OF EOF and REDUNDANCY ANALYSES FOR THE COUPLED ATMOSPHERE-OCEAN SYSTEM

A COMPARISON OF EOF and REDUNDANCY ANALYSES FOR THE COUPLED ATMOSPHERE-OCEAN SYSTEM. F. Bakalian 1 , H. Ritchie 1,2 , K. Thompson 1 , W. Merryfield 3 1 Dept. Of Oceanography, Dalhousie University, Halifax, NS 2 Meteorological Research Division, Environment Canada, Halifax, NS

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A COMPARISON OF EOF and REDUNDANCY ANALYSES FOR THE COUPLED ATMOSPHERE-OCEAN SYSTEM

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  1. A COMPARISON OF EOF and REDUNDANCY ANALYSES FOR THE COUPLED ATMOSPHERE-OCEAN SYSTEM F. Bakalian1, H. Ritchie1,2, K. Thompson1, W. Merryfield3 1Dept. Of Oceanography, Dalhousie University, Halifax, NS 2 Meteorological Research Division, Environment Canada, Halifax, NS 3Canadian Centre for Climate Modelling and Analysis, Victoria, BC

  2. Research objectives • Long-Term Research Goals: • Exploratory studies on joint assimilation into coupled models • Model background errors and observation errors for coupled system: εb and εo • Identify global covariance structures of coupled system • investigate lead-lag relations • error propagation across mediums • Explore new statistical techniques • Locate regions of possible interest

  3. Motivation for Redundancy Analysis • Limitation of coupled EOF analyses • Identify patterns that maximize variance in coupled SST and SLP fields … no directionality implied • Redundancy analysis => directionality • Set up a regression equation • Find pattern in one variable that best explains variance in other variable • carry out time-lagged analyses • Data assimilation:observation -- model

  4. The State Space Model Coupled Atmosphere-ocean state space model • Simplified representation of coupled atmosphere-ocean system • Model Parameters: • Diffusion (both media) • Advection (both media) • Coupling between overlying ocean / atmosphere cells • Eigenvector Analyses of state model output

  5. State Space Eigenvector Analysis

  6. State Space Time-Lagged Analyses

  7. State Space Model Results for weakly coupled systems • EOF eigenvector amplitudes approach zero for non-stochastically forced medium • de-coupling of the two media • over-representation of one medium • Explained variance in first mode is greater for RA than EOF • Time-lagged redundancy index is a powerful tool for determining directionality

  8. CCCma EOF Analysis(Mode 1)

  9. NCEP EOF Analysis(Mode 1)

  10. CCCma Redundancy Analysis(Mode 1)

  11. NCEP Redundancy Analysis(Mode 1)

  12. Time-lagged Explained Variances

  13. Time-lagged Redundancy Index

  14. Summary and Final Comments • Redundancy analysis provides a clearer, more consistent picture of the underlying physics than PCA analysis (coupled system) • agreement between NCEP and CCCma data • realistic physical processes identified • more variance explained by fewer modes • Time lagged Redundancy Index as a predictive tool => “force” - “response” patterns

  15. References • Johnson, R.A. and D.W. Wicheren, Applied Multivariate Statistical Analysis, Prentice-Hall Inc., 1988. • Storch, H.V. and F.W. Zwiers, Statistical Analysis in Climate Research, Cambridge U. Press, ISBN 0 521 45071 3, 1999. • Tyler, D.E., One the optimality of the simultaneous redundancy transformations, Psychometrika, 47 (1), 77-86, 1982 • Van Den Wollenberg, A.L., Redundancy analysis an alternative for canonical correlation analysis, Psychometrika, 42 (2), 207-219, 1977. • Wang, X.L. and F.W. Zwiers, Using Redundancy analysis to improve dynamical seasonal mean 500 hPa Geopotential forecasts, Int. J. Climatol., 21, 637-654, 2001.

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