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Small Error Dynamics and the Predictability of Atmospheric Flows

Brian F. FarrellDepartment of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts

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Abstract

Forecast reliability is known to be highly variable and this variability can be traced in part to differences in the innate predictability of atmospheric flow regimes. These differences in turn have traditionally been ascribed to variation in the growth rate of exponential instabilities supported by the flow. More recently, drawing on modern dynamical systems theory, the asymptotic divergence of trajectories in phase space of the nonlinear equations of motion has been cited to explain the observed loss of predictability. In this report it is shown that increase in error on synoptic forecast time scales is controlled by rapidly growing perturbations that are not of normal mode form. It is further noted that unpredictable regimes are not necessarily associated with larger exponential growth rates than are relatively more predictable regimes. Moreover, model problems illustrating baroclinic and barotropic dynamics suggest that asymptotic measures of divergence in phase space, while applicable in the limit of infinite time, may not be appropriate over time intervals addressed by present synoptic forecast.

Abstract

Forecast reliability is known to be highly variable and this variability can be traced in part to differences in the innate predictability of atmospheric flow regimes. These differences in turn have traditionally been ascribed to variation in the growth rate of exponential instabilities supported by the flow. More recently, drawing on modern dynamical systems theory, the asymptotic divergence of trajectories in phase space of the nonlinear equations of motion has been cited to explain the observed loss of predictability. In this report it is shown that increase in error on synoptic forecast time scales is controlled by rapidly growing perturbations that are not of normal mode form. It is further noted that unpredictable regimes are not necessarily associated with larger exponential growth rates than are relatively more predictable regimes. Moreover, model problems illustrating baroclinic and barotropic dynamics suggest that asymptotic measures of divergence in phase space, while applicable in the limit of infinite time, may not be appropriate over time intervals addressed by present synoptic forecast.

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