Intensive Variability Extraction

Abstract

A modified version of the principal component analysis (PCA) is introduced by reconsidering statistical degrees of freedom inspatial dimensions based on spatial auto-correlations. In the conventionalPCA, data points that represent equal areas are assumedto have equal amount of information. In our new method, theintensive variability extraction (IVE), data points correlated withless other data points are weighted more before performing PCA.Hence, variability with independent information is emphasized,even if the variability is confined to small areas.Sea surface temperature (SST) data at each grid in the tropicsare shown to have fewer spatial statistical degrees of freedom thanthat in the extratropics. Tropical SSTs exhibit covariability withlarge areas, because oceanic equatorial waves and atmosphericgravity waves share temperature information with surroundingareas. As to the extratropics, grids along the western boundariesof oceanic basins are more independent than those in the east,following dynamical requirement of the Earth’s rotation.Using IVE, climate modes that involve interscale covariabilityare extracted. IVE performed for the Pan-Pacific SSTs extracts thePacific Decadal Oscillation assuming the aforementioned a prioridynamical expectation. Using extratropical SSTs, it is demonstratedthat IVE detects synchronicity of small-scale variabilitybetween distant narrow regions