ESRL/PSD Seminar Series

Abstracts

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The answer to this trillion-dollar question depends not just on the mean shift of the probability density function (PDF) of daily weather anomalies, but also on changes in the width and shape of the PDF. The PDFs of daily weather are generally not Gaussian and are therefore not characterized only by their mean and variance. One also has to account for their generally skewed and heavy-tailed character when assessing changes in tail probabilities. We are addressing this important issue using the longest global atmospheric circulation dataset currently available, an ensemble of 56 equally likely estimates of the global atmospheric state within observational error bounds generated for every six hours from 1871 to the present in the Twentieth Century Reanalysis (20CR) project, a major international effort led by CIRES and NOAA (Compo et al., QJRMS, 2011). Specifically, we are using the mean, variance, skewness, and kurtosis of the daily data to fit so-called SGS (stochastically generated skewed) PDFs (Sardeshmukh and Sura, J. Clim., 2009) to the histograms of the daily values, and then using the fitted PDFs to draw inferences about tail probabilities. We have initially focused on the PDFs of daily indices of four prominent modes of sea-level pressure variability: the North Atlantic Oscillation (NAO), the North Pacific Oscillation (NPO), the tropical Pacific Walker Circulation (PWC), and the Annular Antarctic Oscillation (AAO). We have fitted SGS distributions to the histograms of these indices separately in the first and second halves of the 136-year record (1874 to 1942 and 1943 to 2010) and assessed the statistical significance of any apparent changes in the PDFs through extensive Monte Carlo integrations with a “weather generator” model whose parameters are consistent with those of the fitted distributions.

Applying this rigorous significance-testing procedure, we find no significant change in the mean of the NAO and NPO, and a small but significant positive shift in the mean of PWC and AAO from the first to the second half of the 136-year period. For the PDF as a whole, we find no significant changes in the PDFs of the NAO and NPO. The small positive mean shifts of the PWC and AAO are associated with increased probabilities of large positive values and reduced probabilities of large negative values, but these changes are much smaller and statistically insignificant for extreme positive values, beyond about 2.5 standard deviations. Such results underscore the danger of drawing inferences about changes in extreme-value statistics merely from shifts of the mean. The extent to which these results are replicated in large ensembles of coupled climate model simulations (CMIP5) of the 1874 to 2010 period, as well as in uncoupled atmospheric model simulations (AMIP) of the period with prescribed observed SSTs and radiative forcings, will also be discussed in the talk.

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