A method for extracting coupled patterns of predictable and chaotic components in pairs of climate variables

Abstract

The development of seasonal climate forecast schemes, whether statistical or dynamical, is predicated on an understanding of the sources of predictive skill as well as the sources of uncertainty in the variability of relevant climate variables. The seasonal mean of many climate variables can be thought of as consisting of two components; one that is related to slowly varying boundary, or external, forcings on the climate system (for example, sea surface temperatures, sea-ice coverage and greenhouse gas concentration) and from slowly varying (interannual to supra-annual) internal atmospheric variability; the second one related to intraseasonal (month to month) variability. The former is generally considered as being potentially predictable, in that the forcings are themselves potentially predictable. The latter is related to meteorological phenomena that vary significantly within the season (for example, storms and atmospheric blocking, or intraseasonal variability associated with the Madden-Julian Oscillation) and is essentially unpredictable, or chaotic. Important climate variables (the predictands), such as seasonal mean temperatures and seasonal mean rainfall, are largely related to local or hemispheric seasonal mean pressure fields (that is, the atmospheric circulation). Hence, a knowledge of the spatial patterns that relate the potentially predictable component of the seasonal mean pressure fields to that of the predictand should help us to understand the meteorological phenomena associated with forecast skill. Conversely, the identification of the spatial patterns that relate the intraseasonal component of the pressure field to that of the predictand should help us to understand the meteorological phenomena mainly responsible for the uncertainty in forecast skill, at the long range (interannual or longer). In this paper, we propose a method for estimating the interannual cross-covariance matrices associated with the predictable and unpredictable components of a pair of climate variables. The method uses monthly mean time series of the climate variables. From the predictable and unpredictable cross-covariance matrices, and using a singular value decomposition analysis technique, it is possible to construct coupled patterns of the predictable and chaotic components of covariability of the pair of climate variables. The method is applied to observed Australian and New Zealand surface air temperature, and the global mean sea level pressure field.