Predictability in a changing climate

Abstract

The standard framework of predictability defines a variable to be unpredictable from a set of observations if it is independent of those observations. This definition requires comparing two distributions: a forecast distribution that is conditioned on observations, and a climatological distribution that is not. However, if the system is non-stationary because of externally forced climate changes, or is characterized by a climatological distribution that is much broader than the distribution of states over the recent past, then a rigorous application of this framework gives unsatisfying answers to reasonable questions about weather and climate predictability. This paper proposes generalizations of this framework that resolves these limitations and is consistent with the definition of independence. The first generalization, which was proposed effectively by Lorenz and Leith, is to distinguish initial-value predictability from forced predictability, where the latter is defined by time variations in the climatological distribution. This paper goes a step further by introducing a new measure, called total climate predictability, that can be decomposed into a sum of previously known measures of forced and initial-value predictability, namely relative entropy and mutual information. The second generalization, called generalized predictability, provides a new approach to filtering in such a way that processes with long time scales do not contribute to predictability. This generalization is important when the system’s climatological distribution is much broader than the range of climates experienced in the recent past. These concepts are illustrated using a simple model in which all aspects of predictability can be solved exactly.