Is There Evidence of Multiple Equilibria in Planetary Wave Amplitude Statistics?

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Abstract
Results obtained by Hansen and Sutera concerning the occurrence of bimodal probability density functions (PDFs) in a wave amplitude index (WAI) calculated from large-scale atmospheric flow data are re-examined. The PDFs are found to be highly sensitive to changes in the parameters used to calculate the WAI. The excessive sensitivity is suggestive of an insufficient number of degrees of freedom in the PDFs. The Monte Carlo test used by Hansen and Sutera to establish the statistical significance of their PDFs is reexamined, with emphasis on their attempt to compensate for the interdependence between neighboring data points in their time series of the WAI. Their random samples contained only one (independent) data point for each 4.5 data points in the WAI time series. It is shown that in order to generate PDFs with the same degree of smoothing as the WAI PDF, they should have simultaneously reduced the smoothing parameter in the maximum penalized likelihood (MPL) algorithm by the same factor. When this scaling factor is properly taken into account, more than half of the randomly generated samples exhibit multimodality: hence, the occurrence of bimodality in the PDFs calculated from the WAI data does not appear to be statistically significant. It is estimated that in order to distinguish between samples drawn from populations with a degree of bimodality comparable to that reported in the WAI data and samples drawn from a Gaussian population, a period of record of at least 150 years would be needed.