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A tipping point is defined by the IPCC as a critical threshold beyond which a system reorganizes, often abruptly and/or irreversibly. Tipping points can be crossed solely by internal variation in the system or by approaching a bifurcation point where the current state loses stability and forces the system to move to another stable state. It is currently debated whether or not Dansgaard-Oeschger (DO) events, abrupt warmings occurring during the last glacial period, are noise-induced or caused by the system reaching a bifurcation point. It can be shown that before a bifurcation point is reached there are observable changes in the statistical properties of the state variable. These are known as early warning signals and include increased fluctuation and correlation time. To express this behaviour we propose a new model based on the well-known first order autoregressive process (AR), with modifications to the correlation parameter such that it depends linearly on time. In order to estimate the time evolution of the correlation parameter we adopt a hierarchical Bayesian modeling framework, from which Bayesian analysis can be performed using the methodology of integrated nested Laplace approximations. We then apply the model to segments of the oxygen isotope ratios from the Northern Greenland Ice Core Project record corresponding to 17 DO events. Early warning signals were detected and found statistically significant for a number of DO events, suggesting that such events could indeed be caused by approaching a bifurcation point. The methodology developed to perform the given early warning analyses can be applied more generally, and is publicly available as the R-package INLA.ews. [ABSTRACT FROM AUTHOR]

Paleoclimate proxy records have non-negligible uncertainties that arise from both the proxy measurement and the dating processes. Knowledge of the dating uncertainties is important for a rigorous propagation to further analyses; for example for identification and dating of stadial-interstadial transitions in Greenland ice core records during glacial intervals, for comparing the variability in different proxy archives, and for model-data comparisons in general. In this study we develop a statistical framework to quantify and propagate dating uncertainties in layer-counted proxy archives using the example of the Greenland Ice Core Chronology 2005 (GICC05). We express the number of layers per depth interval as the sum of a structured component that represents both underlying physical processes and biases in layer counting, described by a regression model, and a noise component that represents the fluctuations of the underlying physical processes, as well as unbiased counting errors. The age-depth relationship of the joint dating uncertainties can then be described by a multivariate Gaussian process from which realizations of the chronology can be sampled. We show how the effect of an unknown counting bias can be incorporated in our framework and present refined estimates of the occurrence times of Dansgaard-Oeschger events evidenced in Greenland ice cores together with a complete uncertainty quantification of these timings. [ABSTRACT FROM AUTHOR]

Reliable quantification of the global mean surface temperature (GMST) response to radiative forcing is essential for assessing the risk of dangerous anthropogenic climate change. We present the statistical foundations for an observation-based approach, using a stochastic linear-response model that is consistent with the long-range temporal dependence observed in global temperature variability. We have incorporated the model in a latent Gaussian modeling framework, which allows for the use of integrated nested Laplace approximations (INLAs) to perform full Bayesian analysis. As examples of applications, we estimate the GMST response to forcing from historical data and compute temperature trajectories under the Representative Concentration Pathways (RCPs) for future greenhouse gas forcing. For historic runs in the Model Intercomparison Project Phase 5 (CMIP5) ensemble, we estimate response functions and demonstrate that one can infer the transient climate response (TCR) from the instrumental temperature record. We illustrate the effect of long-range dependence by comparing the results with those obtained from a 1-box energy balance model. The software developed to perform the given analyses is publicly available as the R-package INLA.climate. [ABSTRACT FROM AUTHOR]

Understanding the global mean surface temperature response to radiative forcing is essentialto assess the risks of global climate change. We present the statistical methodology for arealistic stochastic model that includes forcing contributions and accounts for chaoticatmospheric dynamics. This is achieved by using a long-memory stochastic process to modelthe temporal dependence observed in global temperature variability. This implies thatinference on the resulting model becomes computationally challenging, which is resolved byintroducing an approximation for the long memory process. The resulting model isincorporated in a latent Gaussian modeling framework and Bayesian inference is obtainedusing the methodology of integrated nested Laplace approximations (INLA). As an exampleof application the model will be fitted to the historical runs of the Earth System Models(ESMs) in the CMIP5 ensemble. The resulting model parameters will be used toobtain estimates of the transient climate responses (TCRs), which are comparedto the responses that arise from the ESMs directly. Estimations of the TCR forinstrumental temperature data is also obtained using forcing from the different ESMs.The presented method is implemented within the R-package INLA.climate. [ABSTRACT FROM AUTHOR]