Predictability – a problem partly solved

Abstract

Ed Lorenz, pioneer of chaos theory, presented this work at an earlier ECMWF workshop on predictability. The paper, which has never been published externally, presents what is widely known as the Lorenz 1996 model. Ed was unable to come to the 2002 meeting, but we decided it would be proper to acknowledge Ed's unrivalled contribution to the field of weather and climate predictability by publishing his 1996 paper in this volume. The difference between the state that a system is assumed or predicted to possess, and the state that it actually possesses or will possess, constitutes the error in specifying or forecasting the state. We identify the rate at which an error will typically grow or decay, as the range of prediction increases, as the key factor in determining the extent to which a system is predictable. The long-term average factor by which an infinitesimal error will amplify or diminish, per unit time, is the leading Lyapunov number; its logarithm, denoted by λ 1 , is the leading Lyapunov exponent. Instantaneous growth rates can differ appreciably from the average. With the aid of some simple models, we describe situations where errors behave as would be expected from a knowledge of λ 1 , and other situations, particularly in the earliest and latest stages of growth, where their behaviour is systematically different. Slow growth in the latest stages may be especially relevant to the long-range predictability of the atmosphere.