Logarithmic relation between the initial error and predictability for the barotropic component of the atmosphere

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 fr om the long term mean of the fluctuation in the observed atmosphere. Accord ing to the quadratic error growth model by Lorenz (1982), the predictabilit y P is expected to obey a logarithmic function rather than a linear functio n of the initial error. Although we searched 15,667,760 combinations of wea ther maps, there are no good analog pairs to investigate the error growth f or a sufficiently small initial error. For this reason, model experiments w ere conducted to demonstrate that the quadratic error growth model is appli cable to infer the behavior of a small error from the distribution of a lar ge error. From the results of the model experiments, and the best analog pa irs in the historical data, we estimated that the predictability for the re al atmosphere increases about 6.3 days when the initial error energy is red uced to 1/10. Hence, we may extend the predictability for the barotropic co mponent of the atmosphere if we can reduce the initial error in the vertica l mean of the atmosphere.