Prediction Rules for Regime Changes and Length in a New Regime for the Lorenz Model

Abstract

Despite the widespread use of the Lorenz model as a conceptual model for predictability studies in meteorology, only Evans et al. seem to have studied the prediction of occurrence of regime changes and their duration. In this paper, simpler rules are presented for forecasting regime changes and their lengths, with near-perfect forecasting accuracy. It is found that when |x(t)| is greater than a critical value xc, the current regime will end after it completes the current orbit. Moreover, the length n of the new regime increases monotonically with the maximum value xm of |x(t)| in the previous regime. A best-fit cubic expression provides a very good estimate of n for the next regime, given xm for the previous regime. Similar forecasting rules are also obtained for regime changes in the forced Lorenz model. This model was introduced by Palmer and used as a conceptual model to explore the effects of sea surface temperature on seasonal mean rainfall. It was found that for the forced Lorenz model, the critical value xc changed linearly with the forcing parameter providing bias to one of the regimes. Similar regime prediction rules have been found in some other two-regime attractors. It seems these forecasting rules are a generic property of a large class of two-regime attractors. Although as a conceptual model, the Lorenz model cannot be taken very literally, these results suggest a relationship between magnitudes of maximum anomaly in one regime, for example, the active spell, and duration of the subsequent break spell.