Advertisement

Initial Errors Growth in Chaotic Low-Dimensional Weather Prediction Model

Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 210)

Abstract

The growth of small errors in weather prediction is exponential. As an error becomes larger, the growth rate decreases and then stops with the magnitude of the error about at a value equal to the size of the average distance between two states chosen randomly.

This paper studies an error growth in a low-dimensional atmospheric model after the initial exponential divergence died away. We test cubic, quartic and logarithmic hypotheses by ensemble prediction method. Furthermore quadratic hypothesis that was suggested by Lorenz in 1969 is compared with the ensemble prediction method. The study shows that a small error growth is best modeled by the quadratic hypothesis. After the initial error exceeds about a half of the error saturation value, logarithmic approximation becomes superior.

Keywords

Chaos Atmosphere Prediction Error growth 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lorenz, E.N., Emanuel, K.A.: Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model. J. Atmos. Sci. 55, 399–414 (1998)CrossRefGoogle Scholar
  2. 2.
    Lorenz, E.N.: Designing Chaotic Models. J. Atmos. Sci. 62, 1574–1587 (2005)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Palmer, T., Hagegorn, R.: Predictability of Weather and Climate, 718 p. Cambridge University Press (2006)Google Scholar
  4. 4.
    Lorenz, E.N.: Atmospheric predictability as revealed by naturally occurring analogs. J. Atmos. Sci. 26, 636–646 (1969)CrossRefGoogle Scholar
  5. 5.
    Lorenz, E.N.: Predictability: A problem partly solved. In: Proc. Seminar on predictability, vol. 1, pp. 1–18. CMWF, Reading (1996); reprinted Palmer T., Hagegorn R.: Predictability of Weather and Climate, 718 p. Cambridge University Press (2006) Google Scholar
  6. 6.
    Sprott, J.C.: Chaos and Time-Series Analysis, 507p. Oxford University Press, New York (2003)Google Scholar
  7. 7.
    Trevisan, A.: Impact of transient error growth on global average predictability measures. J. Atmos. Sci. 50, 1016–1028 (1993)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Benzi, R., Carnevale, F.C.: A possible measure of local predictability. J. Atmos. Sci. 46, 3595–3598 (1989)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lorenz, E.N.: Atmospheric predictability experiments with a large numerical model. Tellus 34, 505–513 (1982)CrossRefGoogle Scholar
  10. 10.
    Bengtsson, L., Hodges, K.I.: A note on atmospheric predictability. Tellus 58A, 154–157 (2006)Google Scholar
  11. 11.
    Trevisan, A., Malguzzi, P., Fantini, M.: A note on Lorenz’s law for the growth of large and small errors in the atmosphere. J. Atmos. Sci. 49, 713–719 (1992)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Department of Meteorology and Environment Protection, Faculty of Mathematics and PhysicsCharles University in PraguePragueCzech Republic

Personalised recommendations