On Lorenz's Law for the Growth of Large and Small Errors in the Atmosphere

Abstract

Lorenz's hypothesis of a quadratic law governing the growth of errors provides an estimate of small error growth in the atmosphere based on the knowledge of large error behavior. An atmospheric model whose simplicity allows for an independent estimate of small error growth was used to investigate the validity of Lorenz's hypothesis. Only errors that are initially infinitesimally small were found to follow Lorenz's law, while errors of large size exhibit higher growth rates. Nonetheless, the results lead to a substantial confirmation of the estimate, based on experimental data, of the doubling time for small errors given by Lorenz for the atmosphere.