Late stages of initial errors growth in weather prediction with use of low-dimensional atmospheric model
Abstract
The growth of small errors in weather prediction is exponential. As an error becomes larger, the growth rate should diminish.
Finally, all systematic growth should stop, and the magnitude of the error should oscillate about a value equal to the magnitude of the distance between two states chosen randomly. The aim of this paper is study of error growth in low-dimensional atmospheric model after the initial exponential divergence died away.
For this purpose we test several hypotheses (cubic, quartic, logarithmic) by ensemble prediction method. Also quadratic hypothesis that was introduced by Lorenz in 1969 is compared with the ensemble prediction method.
The study shows that a small error growth is best modeled by quadratic hypothesis. After the initial error exceed a half of average value of variables than logarithmic approximation is better.