For the statistical work we will initially use sea surface temperature
(SST) indices for two of the foremost D2M climate modes, the Atlantic
multidecadal oscillation (AMO) and the Pacific decadal oscillation
(PDO). The indices will be of two types: an annualized version based on
150 years of instrumental data (1856-2005); and annualized multi-century
indices of the oscillations reconstructed from tree rings in North
America and Europe, calibrated against the instrumental indices
[17,18].
To discourage unwanted short-interval occurrences, the time series are
first smoothed, the sample size is increased through Monte Carlo
resampling methods [19],
and the durations of positive and negative
climate regimes are estimated by the intervals between successive zero
crossings of the resampled series
(Figure 2). The empirical
distributions of sampled intervals are then fitted by a gamma
probability density function (pdf) and a Kolmogorov-Smirnov test is used
to determine the goodness of fit
(Figure 3). The random resampling and
fitting procedure is repeated many times to obtain stable means of the
distribution parameters. Finally, the estimated distributions are used
to determine the probability of future D2M regime shifts conditional on
the time elapsed since the last shifts, and the parameter spreads are
used to estimate the uncertainty of the probability projections.