No evidence for globally coherent warm and cold periods over the preindustrial Common Era.

Earth's climate history is often understood by breaking it down into constituent climatic epochs1. Over the Common Era (the past 2,000 years) these epochs, such as the Little Ice Age2-4, have been characterized as having occurred at the same time across extensive spatial scales5. Although the rapid global warming seen in observations over the past 150 years does show nearly global coherence6, the spatiotemporal coherence of climate epochs earlier in the Common Era has yet to be robustly tested. Here we use global palaeoclimate reconstructions for the past 2,000 years, and find no evidence for preindustrial globally coherent cold and warm epochs. In particular, we find that the coldest epoch of the last millennium-the putative Little Ice Age-is most likely to have experienced the coldest temperatures during the fifteenth century in the central and eastern Pacific Ocean, during the seventeenth century in northwestern Europe and southeastern North America, and during the mid-nineteenth century over most of the remaining regions. Furthermore, the spatial coherence that does exist over the preindustrial Common Era is consistent with the spatial coherence of stochastic climatic variability. This lack of spatiotemporal coherence indicates that preindustrial forcing was not sufficient to produce globally synchronous extreme temperatures at multidecadal and centennial timescales. By contrast, we find that the warmest period of the past two millennia occurred during the twentieth century for more than 98 per cent of the globe. This provides strong evidence that anthropogenic global warming is not only unparalleled in terms of absolute temperatures5, but also unprecedented in spatial consistency within the context of the past 2,000 years.

East Asian warm season temperature variations over the past two millennia.

East Asia has experienced strong warming since the 1960s accompanied by an increased frequency of heat waves and shrinking glaciers over the Tibetan Plateau and the Tien Shan. Here, we place the recent warmth in a long-term perspective by presenting a new spatially resolved warm-season (May-September) temperature reconstruction for the period 1-2000 CE using 59 multiproxy records from a wide range of East Asian regions. Our Bayesian Hierarchical Model (BHM) based reconstructions generally agree with earlier shorter regional temperature reconstructions but are more stable due to additional temperature sensitive proxies. We find a rather warm period during the first two centuries CE, followed by a multi-century long cooling period and again a warm interval covering the 900-1200 CE period (Medieval Climate Anomaly, MCA). The interval from 1450 to 1850 CE (Little Ice Age, LIA) was characterized by cooler conditions and the last 150 years are characterized by a continuous warming until recent times. Our results also suggest that the 1990s were likely the warmest decade in at least 1200 years. The comparison between an ensemble of climate model simulations and our summer reconstructions since 850 CE shows good agreement and an important role of internal variability and external forcing on multi-decadal time-scales.

Stochastic modelling of intermittency.

Recently, methods have been developed to model low-dimensional chaotic systems in terms of stochastic differential equations. We tested such methods in an electronic circuit experiment. We aimed to obtain reliable drift and diffusion coefficients even without a pronounced time-scale separation of the chaotic dynamics. By comparing the analytical solutions of the corresponding Fokker-Planck equation with experimental data, we show here that crisis-induced intermittency can be described in terms of a stochastic model which is dominated by state-space-dependent diffusion. Further on, we demonstrate and discuss some limits of these modelling approaches using numerical simulations. This enables us to state a criterion that can be used to decide whether a stochastic model will capture the essential features of a given time series.

Stochastic modeling of experimental chaotic time series.

Methods developed recently to obtain stochastic models of low-dimensional chaotic systems are tested in electronic circuit experiments. We demonstrate that reliable drift and diffusion coefficients can be obtained even when no excessive time scale separation occurs. Crisis induced intermittent motion can be described in terms of a stochastic model showing tunneling which is dominated by state space dependent diffusion. Analytical solutions of the corresponding Fokker-Planck equation are in excellent agreement with experimental data.