On the use of multivariate statistics to validate global climate models

The goal of the present research was to investigate the low frequency modes of variability in the observed atmosphere and compare those to the counterpart modes in a Global Climate Model (GCM). As a means to accomplish this, a multivariate statistical technique introduced for the first time to the atmospheric sciences, orthogonal Procrustes Target Analysis (PTA) was applied. A four dimensional analysis of the low frequency variability of observed geopotential height at 700 and 200hPa for the Northern Hemisphere in the National Meteorological Center's (NMC) final analysis data set for the winters and summers of 1970 to 1988 was investigated. This was compared to the low frequency variability in counterpart analyses using the European Center for Medium Range Weather Forecasting numerical model modified by the Max Planck Institut fur Meteorologie for global climate modeling. The model used, known as ECHAM2, specified observed values of sea-surface temperature and sea-ice extent for 1970 to 1988.The low frequency variability was analyzed with Rotated Principal Component (RPC) Analysis and orthogonal PTA. The RPCA was used to remove noise variance from the observed and GCM data sets and served as a set of basis vectors in a much lower dimensionality (15 PCs winter, 14 PCs summer). The PTA technique brought the model and observed data subspaces as close together as possible, which allowed quantitative assessment of how closely the observed low frequency modes matched the ones in the model space. The orthogonal PTA technique was applied to the ECHAM2 simulated data to examine how similar the subspace spanned by 15 winter PCs or 14 summer PCs was to the corresponding observational data subspaces. The most striking results were that a single multivariate statistical procedure (orthogonal PTA) applied to each PC improved the observation-ECHAM2 matches for individual FCs and replaced individually testing 3954 gridpoints for each PC in the domain. This improvement, over matching Varimax rotated sets of observation-ECHAM2 geopotential RPCs, was from 23 percent (Varimax) to 41 percent (orthogonal PTA) variance overlap for the subspaces in summer, and from 41 percent (Varimax) to 60.8 percent (orthogonal PTA) variance overlap for the subspaces in winter.The physical insights gained by using orthogonal PTA were better delineated in the model subspace as many of the low frequency modes of variation found in the observational subspace were found in the ECHAM2 model. These were compared to modes depicted in Barnston and Livezey (1987), who had previously identified in their 700hPa observational data set and designated the winter modes as: "Subtropical Zonal", "Eastern Atlantic", "Pacific/North American", "North Atlantic Oscillation", "West Pacific Oscillation", patterns to name a few. The summer orthogonal PTA confirmed that the ECHAM2 model subspace contained many of the following low frequency modes which matched to observation subspace which Barnston and Livezey (1987) referred to as: "Pacific Transition", "Asian Summer", "Northern Asian", "North Atlantic Oscillation", "Eurasian Type 1", and "Subtropical Zonal", to name a few. Moreover, the leading summer mode of variation which the subspace ECHAM2 and the observation analyses shared was similar to the Ward et al. (1994) "Tropical Wide Pattern". (Abstract shortened by UMI.)U of I OnlyETDs are only available to UIUC Users without author permissio