Detecting Regimes in Temperature Time Series

In the field of climate prediction, regimes are used to model long-term cyclic trends. Although air pressure regimes have been discovered, there has been little exploration into the possibility of temperature regimes. This paper develops an approach to finding regimes in a temperature time series. First, the time series is reconstructed in a phase space. Then, a clustering algorithm is used to search the phase space for clusters. Finally, the number of transitions between these clusters is recorded. A low ratio between the number of transitions into the cluster and the number of points in the cluster indicates that a regime structure is present. Results are given for various temperature time series. INTRODUCTION The Earth’s climate is a complex system with an undetermined number of variables. Many long-term prediction models have been proposed, but most are based on the assumption that the earth’s climate is a linear system. The sentiment in the field of meteorology seems to be that linear models are accurate enough for prediction even though evidence has been uncovered that seems to indicate some nonlinear trends in the Earth’s climate (Palmer, 1993). However, there has not been much research on these nonlinear climatic trends, and these trends may provide insight into climate prediction. If regimes could be found in the earth’s climate, they could be used to help predict future climatic trends. One technique used to expose patterns in a nonlinear time series is to reconstruct the time series in a phase space (Povinelli, 1999). A phase space is constructed by creating a vector space [s(t) s(t) s(t) ... s(t) ] where n+1 is the embedding dimension and s(t) is a time delayed s(t) or a time series of a related system parameter. Appropriate time delays can be determined by various statistical methods such as autocorrelation or auto mutual information (Abarbanel, 1996, Kantz, 1997). An example of a non-linear system is the Lorenz system (Figure 1). The Lorenz system was developed to model atmospheric flow. The system is defined by three differential equations. dX = -aX + aY dY = -XZ + rX – Y dZ = XY – bZ (1) Two regimes, or states, are easily discernable in the Lorenz system. Once the system is in one regime, it tends to stay in that regime. The area between the two regimes