A note on linear prediction of large chaotic systems

Abstract: Reliable prediction of large chaotic sytems in the short to middle time range is of interest in a number of fields, including climate, ecology, seismology, and economics. In this paper, results from chaos theory, and statistical theory are combined to suggest rulse for building linear predictive models of chaotic systems. The rules are tested on a problems identified as hard in the climate literature, interseasonal to interannual prediction of regional seasonal precipitation. In a test of prediction the method yields third season ahead predictions in 4 regions over 5 seasons which beat the NOAA climate prediction centers half season predictions for the same region and seasons. In a test using dimensionless climate patterns to infer parameters of the climate system, remarkably accurate estimates of increase in average global surface air temperature are produced.