Intercomparison of Circulation Similarity Measures

Abstract

Most circulation studies use the root-mean-square difference (RMSD) or correlation (COR) (or both) as a toot for comparing different (observed or forecast) circulation patterns. However, there are some other measures introduced into the literature (e.g., mean absolute error, rms vector error, S1 score) and one might easily construct other measures of circulation similarity. The question of the appropriate choice among possible similarity measures rarely arises. In this paper an objective intercomparison of nine different similarity measures (also called distance functions) is presented. The similarity measures were evaluated through the 7OO-hPa hemispheric analog forecasts obtained by them. In the indirect evaluation, the analogs to the base cases found by each individual distance function were checked whether they were identical with the best analogs (selected by all nine functions) to the circulation pattern that actually followed. The number of coincidences is an indication of the quality of the similarity measures and is found, both for daily and pentad data, to be largest for a dynamically oriented distance function that measure the difference between the gradient of height of two maps. For daily data, RMSD also appears to be significantly better than COR. However, in a direct assessment, where analog forecasts by each distance function were compared to the analysis fields using one of the distance functions to measure the difference, practically no performance differences were found among the functions that performed differently in the indirect evaluation. It should be noted that the results of both intercompaiison methods are, in a strict sense, valid only for forecast situations. For other purposes, other distance functions might be more appropriate. However, there are some indications that the similarity measure that performed best in the forecast experiments (difference in the gradient of height) remains superior in other applications, too.