Is the Atmosphere Interesting? A Projection Pursuit Study of the Circulation in the Northern Hemisphere Winter

Abstract

The Northern Hemisphere winter circulation is probed for deviations from Gaussianity. A projection pursuit approach is applied that searches for directions in phase space that maximize an index of interest. Different indices gauging different aspects of non-Gaussianity such as flatness, bimodality, and multimodality are considered. The projection pursuit approach allows high-dimensional data spaces to be investigated and it therefore complements previous studies that usually have been confined to spaces of a few dimensions. Both stratospheric and tropospheric circulations are studied at daily, monthly, and annual time scales. The statistical significance of the results is considered by a Monte Carlo method where results from the atmospheric data are compared with results from Gaussian distributed surrogate data. The surrogate data are generated so that they have the same temporal structure as the original data. Careful considerations of the statistical significance are of particular importance in studies with exploratory methods such as projection pursuit. In the stratosphere the moderate evidence for bimodality in the interannual variability of extended winter means is confirmed. On monthly and daily time scales strong evidence for non-Gaussianity but no evidence for bi- or multimodality is found. In the troposphere only evidence for non-Gaussianity is found and mainly on the shortest time scales. Finally, recent arguments that principal components are prone to Gaussianity are discussed. It is shown that these arguments are based on erroneous use of the central limit theorem.