An Improved Formula to Describe Error Growth in Meteorological Models

Abstract

In meteorological models, the logistic growth law has been used traditionally to describe the error growth due to sensitivity to the initial conditions. A detailed analysis obtained from long range forecasting experiments using a GCM model, as well as from simulations based on a simple 3-variable model, has revealed significant deviations from the logistic law. A natural generalization is proposed, giving a law that has been used previously for the description of biological growth. A new characteristic parameter, which can be interpreted as a saturation rate for error growth, is identified. Further studies, based on a simple 3-variable model for different magnitudes of the initial error, reveal a more complex behaviour having a transient initial regime that is independent of the error magnitude, a regime of exponential growth, and a “deceleration regime”. The deceleration regime as defined here includes both the phases of linear and saturated error growth in time. For the case of large initial errors, the vanishing of the exponential regime, as a result of the coalescence of the initial and deceleration regimes, gives a continuous decrease in error growth rate with time, which can be well represented by the Gompertz growth law.