A Technique for Analyzing Optimal Relationships among Multiple Sets of Data Fields. Part H: A Reliability Case Study

Abstract

In Part I a multiple-set canonical correlation analysis (MCCA) was proposed to generalize the conventional two-set canonical correlation analysis. The MCCA seeks the optimal correlation among more than two data fields through a diagonalization of the product or the squared product of the correlation matrices between selected (desired) field pairs. In this study a specific case is used to empirically test the sensitivities of the MCCA technique. The case study uses an MCCA application of the 850-hPa meridional wind data over the tropical western Pacific to study tropical synoptic wave disturbances during summer. Successive 12-h meridional winds are used as the different data fields. The result shows that the method is stable with respect to sampling changes when the data contain significant signals of physical phenomenon and not stable when the data are random. The study also confirms the use of the largest residual correlation, or the largest cross-component correlation, as a preliminary significance test for the technique.