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Mathematical Modelling and Data Analysis

Department 8.4

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Title: Bayesian Glaciological Modelling to quantify uncertainties in ice core chronologies
Author(s): K. Klauenberg, P. G. Blackwell, C. E. Buck, R. Mulvaney, R. Röthlisberger and E. W. Wolff
Journal: Quaternary Science Reviews
Year: 2011
Volume: 30
Issue: 21-22
Pages: 2961--2975
DOI: 10.1016/j.quascirev.2011.03.008
ISSN: 02773791
Web URL: http://www.sciencedirect.com/science/article/pii/S0277379111000801
Keywords: (Dating) uncertainty,(Hierarchical) linear modelling,Accumulation model,Automatic weather station,Bayes,Bayesian approach,Dyer,Glaciological modelling,Ice core chronology,Layer counting,Likelihood,Posterior distribution,Prior information,Volcanic eruptions
Tags: 8.42
Abstract: Valuable information about the environment and climate of the past is preserved in ice cores which are drilled through ice sheets in polar and alpine regions. A pivotal part of interpreting the information held within the cores is to build ice core chronologies i.e. to relate time to depth. Existing dating methods can be categorised as follows: (1) layer counting using the seasonality in signals, (2) glaciological modelling describing processes such as snow accumulation and plastic deformation of ice, (3) comparison with other dated records, or (4) any combination of these. Conventionally, implementation of these approaches does not use statistical methods. In order to quantify dating uncertainties, in this paper we develop the approach of category (2) further. First, the sources of uncertainty involved in glaciological models are formalised. Feeding these into a statistical framework, that we call Bayesian Glaciological Modelling (BGM), allows us to demonstrate the effect that uncertainty in the glaciological model has on the chronology. BGM may also include additional information to constrain the resulting chronology, for example from layer counting or other dated records such as traces from volcanic eruptions. Our case study involves applying BGM to date an Antarctic ice core (a Dyer plateau core). Working through this example allows us to emphasise the importance of properly assessing uncertain elements in order to arrive at accurate chronologies, including valid dating uncertainties. Valid dating uncertainties, in turn, facilitate the interpretation of environmental and climatic conditions at the location of the ice core as well as the comparison and development of ice core chronologies from different locations.

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