Detecting abrupt climate changes on different time scales

Two concepts are introduced for detecting abrupt climate changes. In the first case, the sampling frequency of climate data is high as compared to the frequency of climate events examined. The method is based on a separation of trend and noise in the data and is applicable to any dataset that satisfies some mild smoothness and statistical dependence conditions for the trend and the noise, respectively. We say that an abrupt change occurs when the first derivative of the trend function has a discontinuity and the task is to identify such points. The technique is applied to Northern Hemisphere temperature data from 1850 to 2009, Northern Hemisphere temperature data from proxy data, a.d. 200–1995 and Holocene δ18O values going back to 11,700 years BP. Several abrupt changes are detected that are, among other things, beneficial for determining the Medieval Warm Period, Little Ice Age and Holocene Climate Optimum. In the second case, the sampling frequency is low relative to the frequency of climate events studied. A typical example includes Dansgaard–Oeschger events. The methodology used here is based on a refinement of autoregressive conditional heteroscedastic models. The key element of this approach is the volatility that characterises the time-varying variance, and abrupt changes are defined by high volatilities. The technique applied to δ18O values going back to 122,950 years BP is suitable for identifying DO events. These two approaches for the two cases are closely related despite the fact that at first glance, they seem quite different.