The Earth's atmosphere-ocean dynamics is chaotic: its evolution is sensitive to small perturbations in initial conditions. This sensitivity limits our ability to predict the detailed evolution of weather; inevitable errors and uncertainties in the starting conditions of a weather forecast amplify through the forecast (Palmer, 2000). As well as uncertainty in initial conditions, such predictions are also degraded by errors and uncertainties in our ability to represent accurately the significant climate processes. In practice, detailed weather prediction is limited to about two weeks.
However, because of the more slowly varying components of the climate system, predictability of climate is not limited to the two week time-scale. Perhaps the most well-known and clear cut example of longer-term predictability is El Niño (see Section 7.6.5) which is predictable at least six months in advance. There is some evidence that aspects of the physical climate system are predictable on even longer time-scales (see Section 7.6). In practice, if natural decadal variability is partially sensitive to initial conditions, then projections of climate change for the 21st century will exhibit a similar sensitivity.
In order to be able to make reliable forecasts in the presence of both initial condition and model uncertainty, it is now becoming common to repeat the prediction many times from different perturbed initial states, and using different global models (from the stock of global models that exist in the world weather and climate modelling community). These so-called multi-model, multi-initial-condition ensembles are the optimal basis of probability forecasts (e.g., of a weather event, El Niño, or the state of the THC).
Estimating anthropogenic climate change on times much longer than the predictability time-scale of natural climate fluctuations does not, by definition, depend on the initial state. On these time-scales, the problem of predicting climate change is one of estimating changes in the probability distribution of climatic states (e.g., cyclonic/anticyclonic weather, El Niño, the THC, global mean temperature) as atmospheric composition is altered in some prescribed manner. Like the initial value problems mentioned above, estimates of such changes to the probability distribution of climate states must be evaluated using ensemble prediction techniques.
The number of ensemble members required to estimate reliably changes to the probability distribution of a given climatic phenomenon depends on the phenomenon in question. Estimating changes in the probability distribution of localised extreme weather events, which by their nature occur infrequently, may require very large ensembles with hundreds of members. Estimating changes in the probability distribution of large scale frequent events (e.g., the probability of above-average hemispheric mean temperature) requires much smaller ensembles.
An important question is whether a multi-model ensemble made by pooling the world climate community's stock of global models adequately spans the uncertainty in our ability to represent faithfully the evolution of climate. Since the members of this stock of models were not developed independently of one another, such an ensemble does not constitute an independent unbiased sampling of possible model formulations.
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