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Abstract
In this paper, taking the Lorenz system as an example, we compare the influences of the arithmetic
mean and the geometric mean on measuring the global and local average error growth. The results show
that the geometric mean error (GME) has a smoother growth than the arithmetic mean error (AME) for
the global average error growth, and the GME is directly related to the maximal Lyapunov exponent, but
the AME is not, as already noted by Krishnamurthy in 1993. Besides these, the GME is shown to be more
appropriate than the AME in measuring the mean error growth in terms of the probability distribution
of errors. The physical meanings of the saturation levels of the AME and the GME are also shown to be
different. However, there is no obvious difference between the local average error growth with the arithmetic
mean and the geometric mean, indicating that the choices of the AME or the GME have no influence on the
measure of local average predictability.
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Citation
DING Ruiqiang, LI Jianping. 2011: Comparisons of Two Ensemble Mean Methods in Measuring the Average Error Growth and the Predictability. Journal of Meteorological Research, 25(4): 395-404.
DING Ruiqiang, LI Jianping. 2011: Comparisons of Two Ensemble Mean Methods in Measuring the Average Error Growth and the Predictability. Journal of Meteorological Research, 25(4): 395-404.
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DING Ruiqiang, LI Jianping. 2011: Comparisons of Two Ensemble Mean Methods in Measuring the Average Error Growth and the Predictability. Journal of Meteorological Research, 25(4): 395-404.
DING Ruiqiang, LI Jianping. 2011: Comparisons of Two Ensemble Mean Methods in Measuring the Average Error Growth and the Predictability. Journal of Meteorological Research, 25(4): 395-404.
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