Various multivariate statistical methods exist for analyzing covariance and isolating linear relationships between datasets, most of which use singular Value Decomposition (sVD) to maximize some quantity based on cross- covariance. In this study, Continuum Power CCA (CPCCA) is introduced as an extension of continuum power regression for isolating pairs of coupled patterns whose temporal variation maximizes the squared covariance between partially-whitened variables. similar to the whitening transformation, the partial whitening transformation acts to decorrelate individual variables, but only to a partial degree with the added benefit of pre-conditioning sample covariance matrices prior to inversion, providing a more accurate estimate of the population covariance. CPCCA is a unified approach in the sense that the full range of solutions bridges Canonical Correlation Analysis (CCA), Maximum Covariance Analysis (MCA), Redundancy Analysis (RDA) as well as Principal Component Regression (PCR). Recommended CPCCA solutions include a regularization for CCA, a variance bias correction for MCA, and a regularization for RDA. An objective parameter choice is offered for regularization based on the covariance estimate of Ledoit and Wolf (2004). Following this, CPCCA is applied to statistical downscaling of seasonal surface temperature and precipitation based on sea surface temperature and sea level pressure predicted by the APCC MME hindcast for various seasons and regions. Along with other pattern-based downscaling approaches, CPCCA improves the skill over MME output and tends to yield higher skill than Regularized CCA. however, the use of prior EoF truncation (Barnett and Preisendorfer 1987) for CCA tends to yield higher skill than either form of regularization.

1. INTRODUCTION

2. CONTINUUM POWER CCA

2.1 A generalized sVD procedure

2.2 Fix solutions and regularization

2.3 objective parameter choices for regularization

3. DATA DESCRIPTION AND DOWNSCALING METHODOLOGY

4. RESULTS

4. 1 December – February (DJF)

4.1.1 East Asian temperature based on Pacific SST

4.1.2 North American temperature based on Pacific SLP

4.1.3 La Plata Basin precipitation based on Indo-Pacific SLP

4.2 March – May (MAM)

4.2.1 Precipitation in NE Brazil based on Pacific-Atlantic SLP

4.3 June-July-August (JJA)

4.3.1 South China precipitation based on Indo-W. Pacific SLP

4.3.2 W. Maritime Continent precipitation based on Indo-W. Pacific SLP

4.3.3 Temperature over the Indian Subcontinent based on Indo-Pacific SLP

4.4 september-october-November (SON)

4.4.1 Australian temperature based on Indo-W. Pacific SST

4.4.2 Australian precipitation based on Indo-W. Pacific SST

5. SUMMARY AND CONCLUSIONS

REFERENCES