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High Dimensional Dataset Compression Using Principal Components

Until recently, computational power was insufficient to diagonalize 
atmospheric datasets of order 108 - 109 elements. Eigenanalysis of tens of thousands of variables now can achieve 
massive data compression for spatial fields with strong correlation properties. Application 
of eigenanalysis to 26,394 variable dimensions, for three severe weather 
datasets (tornado, hail and wind) retains 9 - 11 principal 
components explaining 42% - 52% of the variability. Rotated principal 
components (RPCs) detect localized coherent data variance structures for each 
outbreak type and are related to standardized anomalies of the meteorological 
fields. Our analyses of the RPC loadings and scores show that these graphical 
displays can efficiently reduce and interpret large datasets. Data is 
analyzed 24 hours prior to severe weather as a forecasting aid. RPC loadings of 
sea-level pressure fields show different morphology loadings for each outbreak 
type. Analysis of low level moisture and temperature RPCs suggests moisture 
fields for hail and wind which are more related than for tornado outbreaks. 
Consequently, these patterns can identify precursors of severe weather and 
discriminate between tornadic and non-tornadic outbreaks.