Prediction is an effort to retain from an initial time into the future as much information about the state of a dynamical system as possible. It is well known that in chaotic systems, if the initial information about the state of the system is incomplete, eventually all information is lost due to the exponential divergence of initially nearby trajectory segments. The limit of initial value related predictability can then be defined as the lead time where a forecast with a perfect model loses skill (i.e., its error reaches a predefined value). Initial value related predictability can be defined both for the atmosphere - “weather predictability” on the time scale of hours or days, and the coupled atmosphere - ocean - land surface (AOL) system - often referred to as “climate predictability”, on the time scale of months to decades. The limit of predictability is of course a function of the error level in the estimate of the state of the system at initial time. It is understood that with any given level of initial error, the time limit of predictability is finite. Whether predictability is also bounded in a sense that reducing initial errors beyond a certain threshold may not yield further extension of the forecast period with useful skill is an open question.
Besides its initial value related definition, climate predictability has another interpretation, referring to the “prediction” of the climatic equilibrium of a dynamical system under a set of external forcing, such as the atmosphere’s long term response to a predefined lower boundary condition, or the coupled AOL system’s response to changes in the concentration of greenhouse gases. Unlike initial value related predictability, equilibrium predictability, however, is not related to forecasting in time. Yet for the lack of a better approach, climate equilibrium is customarily assessed via averaging all states from extended integrations of atmospheric or coupled numerical forecast models. Are there more direct and more economical ways to predict the response of dynamical systems to changes in their external forcing? Additional related research topics include the initialization of imperfect models, the study of the independent degrees of freedom in atmospheric dynamics, and the development of a variance prediction model or a statistical weather generator.
Chaotic error growth; Butterfly effect; Limits of predictability; Ensemble forecasting; Targeted observations; Model related forecast errors; Climatic equilibrium
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