Living with the butterfly effect: a seamless view of predictability
Buizza, Roberto ; Leutbecher, Martin ; Thorpe, Alan
Errors in numerical weather prediction grow from the smaller to the larger scales, and even if the initial-time errors are very small, they can eventually grow to affect the larger scales. The less faithful our model representation of the atmosphere is, the faster the error propagates and the sooner predictable signals coming from the initial conditions are lost. This destructive interaction between initial-time and model errors is a consequence of chaos in such predictions, as first noted by French mathematician Henri Poincaré in his book Science and Hypothesis (first published in 1902) and then developed by Lorenz in a series of landmark scientific papers (for example 1969a). It is often referred to as 'the butterfly effect' and quoted as the main reason why predicting the weather on particular days beyond two weeks is an extremely challenging, if not impossible, venture. However, ECMWF has been issuing operational monthly forecasts since 2004 and seasonal forecasts since 1997. They show that two weeks can be exceeded provided care is taken in defining the scales one wants to predict. Indeed, some parameters can be predicted with extremely high skill, and average accuracy measures indicate skill definitely beyond two weeks. Results published in a recent paper (Buizza & Leutbecher, 2015; hereafter BL15) and summarized in this article confirm earlier indications (see, e.g., Shukla 1998) that the 'forecast skill horizon', defined as the lead time when ensemble forecasts cease to be more skillful than a climatological distribution, is longer than two weeks. This conclusion can be reached if we follow a seamless approach to measure it for forecast fields with increasingly coarse spatial and temporal scales. Thanks to major advances in numerical weather prediction, for some weather parameters forecast skill horizons longer than two weeks are now achievable even on relatively fine scales. In other words, we have learned to live with the butterfly effect.
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