Initial Errors Growth in Chaotic Low-Dimensional Weather Prediction Model

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.