Abstract
Abstract. A technique for estimating the age–depth relationship in an ice core and evaluating its uncertainty is presented. The age–depth relationship is determined by the accumulation of snow at the site of the ice core and the thinning process as a result of the deformation of ice layers. However, since neither the accumulation rate nor the thinning process is fully known, it is essential to incorporate observational information into a model that describes the accumulation and thinning processes. In the proposed technique, the age as a function of depth is estimated by making use of age markers and δ18O data. The age markers provide reliable age information at several depths. The data of δ18O are used as a proxy of the temperature for estimating the accumulation rate. The estimation is achieved using the particle Markov chain Monte Carlo (PMCMC) method, which is a combination of the sequential Monte Carlo (SMC) method and the Markov chain Monte Carlo method. In this hybrid method, the posterior distributions for the parameters in the models for the accumulation and thinning process are computed using the Metropolis method, in which the likelihood is obtained with the SMC method, and the posterior distribution for the age as a function of depth is obtained by collecting the samples generated by the SMC method with Metropolis iterations. The use of this PMCMC method enables us to estimate the age–depth relationship without assuming either linearity or Gaussianity. The performance of the proposed technique is demonstrated by applying it to ice core data from Dome Fuji in Antarctica.
Highlights
Ice cores provide vital information on the climatic and environmental changes over the past hundreds of thousands of years
Parrenin et al (2007) considered a glaciological process model that contains several uncertain parameters. They estimated the parameters for that model using the Bayesian approach and the Markov chain Monte Carlo (MCMC) method, they did not consider the errors in the glaciological process model in the estimation of the parameters
In order to verify the convergence of the sequential Monte Carlo (SMC) sampling, we repeated sampling from the marginal posterior distribution p(x0:Z|y1:Z) five times with different seeds and confirmed that there were no apparent differences between the results of the five trials. (The figures shown in this paper show the result of one of the five trials.) the estimate shown in Fig. 4 is considered reliable
Summary
Ice cores provide vital information on the climatic and environmental changes over the past hundreds of thousands of years. Many of the dating methods for determining the age–depth relationship rely on glaciological modeling. It is important to effectively make use of the information of age markers, which provides significant constraints on the age–depth relationship. Parrenin et al (2007) considered a glaciological process model that contains several uncertain parameters They estimated the parameters for that model using the Bayesian approach and the Markov chain Monte Carlo (MCMC) method, they did not consider the errors in the glaciological process model in the estimation of the parameters. The uncertainty of the estimate was evaluated in a Bayesian manner
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