Multivariate projection of ocean surface data onto subsurface sections

A multivariate projection of ocean surface data onto subsurface fields is presented. The method is applied to the projection of sea surface height and sea surface temperature anomalies onto the three dimensional temperature field. The results are compared to the conventional univariate regression between sea surface height and the underlying temperature structure. The multivariate method clearly outperforms the univariate approach and succeeds in capturing the equatorial anomaly structures even during the early nineties, a period in which the:univariate projection encounters great difficulties. A multivariate scheme projects onto linear combinations of different vertical modes, depending on the contribution of each input variable. Thus, vertical patterns, different not only in amplitude but also in shape can be affected, as opposed to the univariate case. During the ENSO cycle two different vertical temperature modes become dominant. To address both:modes, two linearly independent variables are required. Therefore, the combination of SSH and SST contains additional information about the vertical temperature structure that cannot: be extracted from either sea surface height measurements, or sea surface temperature only. This is of relevance in:the context of ENSO predictions, and it may help to improve the initialization of ENSO forecast models.