| We use different annual temperature reconstructions (Moberg, Jones, Ammann) in order to
measure predictability of the temperature data. We use recurrence plot (RP) analysis, which is
suitable for short and non-stationary time series analysis. These plots show behavior of the
trajectory segments in a phase space, where we use time-delay embedding to reconstruct the
phase space from the scalar, temperature data. Namely, black dot is marked in the RP when
trajectory segment for time "i" comes close to trajectory segment for time "j". If there is no
recurrence of the trajectory for these times , white dot is marked in the RP instead.
Diagonal, horizontal, vertical lines and dots are typical patterns in an RP, and all of
them describe different dynamical regimes (chaotic, periodic, laminar, or random
behavior). For the purpose of our analysis, we define a measure for predictability Î,
which is an inverse of the mean diagonal line length in an RP. Diagonal lines in
an RP for the time series from the chaotic systems, measure for how long time
two trajectory segments run together, and Î, in this case, approximately measures
inverse Lyapunov exponent. On the other hand, Î for colored noises measures time
correlations (existence of the long memory in the data), and has the same function as
self-similarity exponent. Thus, Î is a measure for predictability and is more universal than
Lyapunov exponent or Hurst exponent, since it can be applied to both dynamical or
stochastic systems. Î is, further, used in temperature analysis, and preliminary results
indicate higher predictability in temperature data around big temperature changes
(Maunder minimum, around 1940, or around green-house effect which occurs now). |