Probabilistic concepts in intermediate-complexity climate models: A snapshot attractor picture

Mátyás Herein, János Márfy, Gábor Drótos, T. Tél

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16 Citations (Scopus)


A time series resulting from a single initial condition is shown to be insufficient for quantifying the internal variability in a climate model, and thus one is unable to make meaningful climate projections based on it. The authors argue that the natural distribution, obtained from an ensemble of trajectories differing solely in their initial conditions, of the snapshot attractor corresponding to a particular forcing scenario should be determined in order to quantify internal variability and to characterize any instantaneous state of the system in the future. Furthermore, as a simple measure of internal variability of any particular variable of the model, the authors suggest using its instantaneous ensemble standard deviation. These points are illustrated with the intermediatecomplexity climate model Planet Simulator forced by a CO2 scenario, with a 40-member ensemble. In particular, the leveling off of the time dependence of any ensemble average is shown to provide a much clearer indication of reaching a steady state than any property of single time series. Shifts in ensemble averages are indicative of climate changes. The dynamical character of such changes is illustrated by hysteresis-like curves obtained by plotting the ensemble average surface temperature versus the CO2 concentration. The internal variability is found to be the most pronounced on small geographical scales. The traditionally used 30-yr temporal averages are shown to be considerably different from the corresponding ensemble averages. Finally, the North Atlantic Oscillation (NAO) index, related to the teleconnection paradigm, is also investigated. It is found that the NAO time series strongly differs in any individual realization from each other and from the ensemble average, and climatic trends can be extracted only from the latter.

Original languageEnglish
Pages (from-to)259-272
Number of pages14
JournalJournal of Climate
Issue number1
Publication statusPublished - 2016



  • Atm/Ocean Structure/Phenomena
  • Circulation/Dynamics
  • Climate change
  • Climate variability
  • Ensembles
  • Forcing
  • Models and modeling
  • Nonlinear dynamics
  • North Atlantic Oscillation
  • Physical meteorology and climatology

ASJC Scopus subject areas

  • Atmospheric Science

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