Statistical Modeling in Nonlinear Systems

The use of linear statistical methods in building climate prediction models is examined, particularly the use of anomalies. The author's perspective is that the climate system is a nonlinear interacting system, so the impact of modeling using anomalies rather than observed data directly is considered. With reference to the Lorenz system and a simple model for regime dependence, it is shown that anomalies impair our ability to reconstruct nonlinear dynamics. Some alternative approaches in the literature that offer an attractive way forward are explored, focusing on Bayesian hierarchical methods to construct so-called physical-statistical models. The author's view is that anomalies should be reserved in most cases as a tool for enhancing graphical representations of climate data. The exceptions are when the implicit assumptions underlying the use of anomalies are met or when an anomaly representation is physically motivated.