Logarithmic Relation between the Initial Error and Predictability for the Barotropic Component of the Atmosphere.

Abstract

In this study, predictability for the barotropic component of the atmosphere is examined based on analog weather maps in the historical data. The limit of predictability P is defined as the time taken for the initial error to reach the climate noise level which is defined by one standard deviation from the long term mean of the fluctuation in the observed atmosphere. According to the quadratic error growth model by Lorenz (1982), the predictability P is expected to obey a logarithmic function rather than a linear function of the initial error. Although we searched 15, 667, 760 combinations of weather maps, there are no good analog pairs to investigate the error growth for a sufficiently small initial error. For this reason, model experiments were conducted to demonstrate that the quadratic error growth model is applicable to infer the behavior of a small error from the distribution of a large error. From the results of the model experiments, and the best analog pairs in the historical data, we estimated that the predictability for the real atmosphere increases about 6.3 days when the initial error energy is reduced to 1/10. Hence, we may extend the predictability for the barotropic component of the atmosphere if we can reduce the initial error in the vertical mean of the atmosphere.