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. Bakalian1, H. Ritchie1,2, K. Thompson1, W. Merryfield3

1Dept. Of Oceanography, Dalhousie University, Halifax, NS2 Meteorological Research Division, Environment Canada, Halifax, NS3Canadian Centre for Climate Modelling and Analysis, Victoria, BC

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

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

The 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

Coupled Atmosphere-ocean state space model

State Space Eigenvector Analysis

State Space Time-Lagged Analyses

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

CCCma EOF Analysis(Mode 1)

NCEP EOF Analysis(Mode 1)

CCCma Redundancy Analysis(Mode 1)

NCEP Redundancy Analysis(Mode 1)

Time-lagged Explained Variances

Time-lagged Redundancy Index

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

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.