<p>Most layer-counting based paleoclimate proxy records have non-negligible uncertainties that arise from both the proxy measurement and the dating processes. Proper knowledge of the dating uncertainties in paleoclimatic ice core records is important for a rigorous propagation to further analyses; for example for identification and dating of stadial-interstadial transitions during glacial intervals, for model-data comparisons in general, or to provide a complete uncertainty quantification of early warning signals. We develop a statistical model that incorporates the dating uncertainties of the Greenland Ice Core Chronology 2005 (GICC05), which includes the uncertainty associated with layer counting. We express the number of layers per depth interval as the sum of a structural component that represents both underlying physical processes and biases in layer counting, described by a linear regression model, and a noise component that represents the internal variation of the underlying physical processes, as well as residual counting errors. We find the residual components to be described well by a Gaussian white noise process that appear to be largely uncorrelated, allowing us to represent the dating uncertainties using a multivariate Gaussian process. This means that we can easily produce simulations as well as incorporate tie-points from other proxy records to match the GICC05 time scale to other chronologies. Moreover, this multivariate Gaussian process exhibits Markov properties which grants a substantial gain in computational efficiency.</p>
Multivariate Gaussian Process Emulators With Nonseparable Covariance Structures
