This study addresses two questions: 1) whether there are local density maxima and minima in the Northern Hemisphere extratropical wintertime circulation phase space and 2) if so, what the preferred circulation types are. All investigations are based on the null hypothesis that the statistical distribution of circulation patterns in the phase space is a multinormal distribution. If this is a good approximation (as it was shown in a phase-average sense in earlier studies) and the assumed independent variables have equal variance, then the theoretical distribution of circulation patterns can be uniquely described by the (climatological) mean, a single standard deviation, and the number of independent variables (dimension). Having the estimates of all these variables, the local density of the actual circulation data can be easily compared to the theoretical expectation of a multinormal distribution. With randomly generated multinormal samples the significance of such discrepancies can also be tested.
The results at the 1% significance level show that out of the 273 circulation maps investigated in the phase space there are 28(15) that have a higher (lower) local density than that expected from a multinormal distribution. Moreover, the high number of local discrepancies is a statistically clear indication that the circulation data sample cannot come from a symmetric, fully multinormal distribution (global significance). The positive deviation from normal density properties in certain areas of the phase space (preferred maps) is offset by opposite sign deviations in other areas (unpreferred maps), ensuring multinormality only in a phase-average sense. This is clear evidence for the existence of multiple flow regimes in the hemispheric circulation.
As to the second question, the preferred and unpreferred circulation maps were found to cluster around 6 and 5 distinct area of the phase space, respectively. The average of the preferred or unpreferred circulation maps for each cluster was interpreted as an estimate of local density maximum or minimum areas in the phase space. Large changes in the database and the statistical methods made little change in the estimates (especially for local maxima).
The advantages and innovations of the above analysis were the following. 1) The phase space was studied in its full dimensionality. 2) Based on the appropriate null hypothesis (multinormality), the results were presented with a clear determination of statistical significance. 3) Due to the statistically significant results of the local density analysis, the possibility of a physical interpretation of clustering results (preferred circulation types) is guaranteed. A relationship between local maximum points and various boundary conditions is suspected. 4) Lacunar areas or unpreferred types that are theoretically as interesting as the preferred ones have been identified for the first time in the circulation phase space.