Circulation Patterns in Phase Space: A Multinormal Distribution?

In this paper daily wintertime extratropical Northern Hemisphere (NH) circulation analogs are studied. First the analog forecasts are compared to various common benchmark methods such as random or persistence forecasts and the climate mean as a forecast. In line with earlier work, it is concluded that beyond a few days lead time the analogs offer no advantage over any of these benchmark methods. The same is true for derivative analogs (where only the time derivative of the analogs is used and added to the base case), although they perform considerably better than the traditional analogs on the first time step(s). Even though the circulation analogs have no extended-range forecast capability, they nevertheless offer a convenient way of studying the gross structure of the phase space of circulation patterns. A thorough study of the root-mean-square distances (rmsd) between the best circulation analogs, considered as an indicator for the relative frequency in the phase space, has been performed. It was shown that in a phase-average sense, when the density characteristics are considered only as a function of distance from the climate mean, the distribution of circulation patterns is statistically indistinguishable from a multinormal distribution. This simple but previously unobserved fact has a series of consequences, some of which are presented here. First, since the density of the distribution of circulation patterns is increasing with decreasing distance from the climate mean, the best analog to a particular circulation pattern is more likely to be closer to the climate mean than the base case. A second observation is that the persistence of the flow increases with decreasing distance from the climate mean. A double stratification of the analogs according to their initial difference and the persistence of the flow showed no enhanced predictability in persistent cases; the forecast error depends only on the initial error of the analogs. This is an indication that the higher numerical forecast skill in persistent cases (reported in earlier studies) may be related to the fact that those cases are relatively close to the climate mean, where even random forecasts have smaller rms error. A third point is that analog predictability does not depend on the initial flow's distance from the climate mean either. The phase-average multinormality of the wintertime extratropical NH circulation phase space discussed in this study does not rule out the possibility of a fine structure with several local maxima (multiple equilibria) embedded in the overall gross structure of approximate normality. Indeed, a refined methodology revealing the existence of such “dense” areas will be reported in a later paper.