National Oceanic and
Atmospheric Administration
United States Department of Commerce


 

FY 1983

Data Intercomparison Theory—Vol. III, S-phase and T-phase tests for spatial pattern and temporal evolution

Preisendorfer, R.W., and C.D. Mobley

NOAA Tech. Memo ERL PMEL-40, NTIS: PB83-182329, 120 pp (1982)


This is the third of a series of five reports on some new techniques in data intercomparison theory, devised particularly with observed and model climate data sets in mind. In this study we derive a set of statistics which describe differences in spatial patterns and temporal evolutions of data sets. These are derived from the SHAPE statistic of the second study. It is shown that SHAPE and its derivates are all of a correlational nature, thereby permitting immediate statistical significance tests using existing tables. However, it is also shown that correlation-type statistics, especially in multivariate settings, are limited in their ability to discern differences in spatial and temporal patterns of data sets. Two multiparameter tests (the S-Phase and T-Phase) are devised to remedy this limitation and their properties are given a preliminary examination. The S-Phase test is based on the canonic rotation angles between the singular value decomposition. The T-Phase test is based on the canonic correlation angles between the temporal (principal component) frames of two data sets under the same type of decomposition. These multiparameter tests, unfortunately, are difficult to interpret, even though they appear to perform well under realistic data conditions. Further multiparameter tests are devised and outlined with research programs suggested for future study. The five general procedures of the second study of the series (IOP, EOP, APP, PPP, CIP) are potential sources of reference distributions for the new multiparameter statistics.




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