A sequential Bayesian approach for the estimation of the age–depth relationship of the Dome Fuji ice core

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 δ 18 O data. The age markers provide reliable age information at several depths. The data of δ 18 O 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.

Fractionation of O<sub>2</sub>∕N<sub>2</sub> and Ar∕N<sub>2</sub> in the Antarctic ice sheet during bubble formation and bubble–clathrate hydrate transition from precise gas measurements of the Dome Fuji ice core

“…After transporting to Japan, the samples had been stored at −50 • C at the Institute for Low Temperature Science, Hokkaido University (until 2009), and the National Institute of Polar Research (NIPR, 2009-present). Within the DF ice core, 105-450 m is bubbly ice, 450-1200 m is the BCTZ, and below 1200 m is bubblefree ice (Narita et al, 1999;Ohno et al, 2004).…”

“…The model is run for 100 kyr with the time step of ∼ 12 d to simulate the diffusive relaxation of the initial concentration variations and thus the composition of clathrate hydrates. To account for the actual ice sheet conditions, the box heights are gradually reduced according to the thinning function (Nakano et al, 2016) and age scale of the ice core (Kawamura et al, 2007) (Fig. A2).…”

“…Another obstacle to understanding the close-off fractionation lies in the transformation of bubbles to clathrate hydrates. In the bubble-clathrate hydrate transition zone (BCTZ: e.g., 450-1200 m at Dome Fuji (Narita et al, 1999), extreme gas fractionations on the order of several hundreds of ‰ can occur between individual bubbles and clathrate hydrates due to lower dissociation pressure and larger permeation coefficient of O 2 relative to N 2 (e.g., Chazallon et al, 1998;Ikeda-Fukazawa et al, 2001). The microscopic gas fractionation, combined with the post-coring gas-loss fractionation, creates high variabilities of δO 2 /N 2 and δAr/N 2 from gas measurements in the BCTZ (Bender, 2002;Kawamura et al, 2007;Kobashi et al, 2008;Lüthi et al, 2010;Shackleton et al, 2019).…”

Fractionation of O<sub>2</sub>/N<sub>2</sub> and Ar/N<sub>2</sub> in the Antarctic ice sheet during bubble formation and bubble-clathrate hydrate transition from precise gas measurements of the Dome Fuji ice core

“…6), and initial total air content is constant over the model domain. Borehole temperature profile (T) (Buizert et al, 2021) and thinning function (Nakano et al, 2016) were used to simulate the evolution of layer thickness and temperature of the model domain (Fig. A2).…”

“…Figure A2: Thinning function (red,Nakano et al, 2016), temperature (blue,Buizert et al, 2021) and age (black,Kawamura et al, 2007) in the ice sheet at Dome Fuji used for the diffusion model. Grey shading indicates the depth range of the model run.…”