TABLE 2.1 Historical methods for evaluating predictability and their advantages and disadvantages.

Method and References



Physical System: Analytic closure (Leith, 1971)

Assuming that the atmosphere is governed by the laws of two-dimensional turbulence, a predictability limit can be estimated from the rate of error growth implied by the energy spectrum.

  • Estimates are rough due to numerous assumptions.

  • Assumptions are stringent (e.g., atmospheric flow is non-divergent and moist processes are not important for error).

  • Difficult to extend to other aspects of real atmosphere.

Model: (Lorenz, 1965; Tribbia and Baumhefner, 2004; Buizza, 1997; Kalnay, 2003)

Using a dynamical model, experiments are designed to answer: How long is it expected to take for two random draws from the analysis distribution for this model and observing system to become practically indistinguishable from two random draws from the model’s climatological distribution?

  • Predictability results are highly dependent on the quality of the model being used.

  • Predictability is a function of the uncertainty in analyses used as model initial conditions.

Observations: Observed Analogs (Lorenz, 1969a; Van den Dool, 1994; Van den Dool et al., 2003)

The observed divergence in time of analogs (i.e., similar observed atmospheric states) provides an estimate of forecast divergence.

  • Difficult to identify analogs and extrapolate the results to real atmosphere. Close analogs are not expected without a much longer observational record.

The studies listed in Table 2.1 demonstrate that for practical purposes (i.e., using available atmospheric observations and dynamical models), the limit for making skillful forecasts of mid-latitude weather systems is estimated to be approximately two weeks5, largely due to the sensitivity of forecasts to the atmospheric initial conditions (see Box 2.1)6. However, their focus on weather and the state of the atmosphere excludes processes that are valuable for climate prediction. For instance, many factors external to the atmosphere were ignored, such as incoming solar radiation and the state of the ocean, land, and cryosphere. Single events, such as a volcanic eruption, that might influence predictability were not considered; nor were long-term trends in the climate system, such as global warming. In addition, the models were unable to replicate many features internal to the atmosphere, including tropical cyclones, the Quasi-Biennial Oscillation (QBO), the Madden Julian Oscillation (MJO), atmospheric tides, and low frequency atmospheric patterns of variability like the Arctic and Antarctic Oscillations. These additional features are important for the impacts that they may have on the estimates of weather predictability, as well as for their influence on predictability on longer climate timescales.


 The limit also depends on the quantitative skill metric being used.


Model error also contributes to errors in weather prediction (e.g., Orrell et al., 2001).

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