Data Intercomparison Theory. III. S-Phase and T-Phase Tests for Spatial Pattern and Temporal Evolution

摘要

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. Further multiparameter tests are devised and outlined with research programs suggested for future study.