2014, Rehfeld, K., Kurths, J.

Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not measurable and not suitable for the comparison of many data sets at a time, the latter introduces interpolation bias, and both face difficulties if the underlying dependencies are nonlinear. In this paper we investigate similarity estimators that could be suitable for the quantitative investigation of dependencies in irregular and age-uncertain time series. We compare the Gaussian-kernel-based cross-correlation (gXCF, Rehfeld et al., 2011) and mutual information (gMI, Rehfeld et al., 2013) against their interpolation-based counterparts and the new event synchronization function (ESF). We test the efficiency of the methods in estimating coupling strength and coupling lag numerically, using ensembles of synthetic stalagmites with short, autocorrelated, linear and nonlinearly coupled proxy time series, and in the application to real stalagmite time series. In the linear test case, coupling strength increases are identified consistently for all estimators, while in the nonlinear test case the correlation-based approaches fail. The lag at which the time series are coupled is identified correctly as the maximum of the similarity functions in around 60–55% (in the linear case) to 53–42% (for the nonlinear processes) of the cases when the dating of the synthetic stalagmite is perfectly precise. If the age uncertainty increases beyond 5% of the time series length, however, the true coupling lag is not identified more often than the others for which the similarity function was estimated. Age uncertainty contributes up to half of the uncertainty in the similarity estimation process. Time series irregularity contributes less, particularly for the adapted Gaussian-kernel-based estimators and the event synchronization function. The introduced link strength concept summarizes the hypothesis test results and balances the individual strengths of the estimators: while gXCF is particularly suitable for short and irregular time series, gMI and the ESF can identify nonlinear dependencies. ESF could, in particular, be suitable to study extreme event dynamics in paleoclimate records. Programs to analyze paleoclimatic time series for significant dependencies are included in a freely available software toolbox.

2017, Nauels, Alexander, Meinshausen, Malte, Mengel, Matthias, Lorbacher, Katja, Wigley, Tom M.L.

Sea level rise (SLR) is one of the major impacts of global warming; it will threaten coastal populations, infrastructure, and ecosystems around the globe in coming centuries. Well-constrained sea level projections are needed to estimate future losses from SLR and benefits of climate protection and adaptation. Process-based models that are designed to resolve the underlying physics of individual sea level drivers form the basis for state-of-the-art sea level projections. However, associated computational costs allow for only a small number of simulations based on selected scenarios that often vary for different sea level components. This approach does not sufficiently support sea level impact science and climate policy analysis, which require a sea level projection methodology that is flexible with regard to the climate scenario yet comprehensive and bound by the physical constraints provided by process-based models. To fill this gap, we present a sea level model that emulates global-mean long-term process-based model projections for all major sea level components. Thermal expansion estimates are calculated with the hemispheric upwelling-diffusion ocean component of the simple carbon-cycle climate model MAGICC, which has been updated and calibrated against CMIP5 ocean temperature profiles and thermal expansion data. Global glacier contributions are estimated based on a parameterization constrained by transient and equilibrium process-based projections. Sea level contribution estimates for Greenland and Antarctic ice sheets are derived from surface mass balance and solid ice discharge parameterizations reproducing current output from ice-sheet models. The land water storage component replicates recent hydrological modeling results. For 2100, we project 0.35 to 0.56m (66% range) total SLR based on the RCP2.6 scenario, 0.45 to 0.67m for RCP4.5, 0.46 to 0.71m for RCP6.0, and 0.65 to 0.97m for RCP8.5. These projections lie within the range of the latest IPCC SLR estimates. SLR projections for 2300 yield median responses of 1.02m for RCP2.6, 1.76m for RCP4.5, 2.38m for RCP6.0, and 4.73m for RCP8.5. The MAGICC sea level model provides a flexible and efficient platform for the analysis of major scenario, model, and climate uncertainties underlying long-term SLR projections. It can be used as a tool to directly investigate the SLR implications of different mitigation pathways and may also serve as input for regional SLR assessments via component-wise sea level pattern scaling.

2012, Breitenbach, S.F.M., Rehfeld, K., Goswami, B., Baldin, J.U.L., Ridley, H.E., Kennett, D.J., Prufer, K.M., Aquino, V.V., Asmerom, Y., Polyak, V.J., Cheng, H., Kurths, J., Marwan, N.

Reliable age models are fundamental for any palaeoclimate reconstruction. Available interpolation procedures between age control points are often inadequately reported, and very few translate age uncertainties to proxy uncertainties. Most available modeling algorithms do not allow incorporation of layer counted intervals to improve the confidence limits of the age model in question. We present a framework that allows detection and interactive handling of age reversals and hiatuses, depth-age modeling, and proxy-record reconstruction. Monte Carlo simulation and a translation procedure are used to assign a precise time scale to climate proxies and to translate dating uncertainties to uncertainties in the proxy values. The presented framework allows integration of incremental relative dating information to improve the final age model. The free software package COPRA1.0 facilitates easy interactive usage.