Flexible paleoclimate age-depth models using an autoregressive gamma process

Abstract

Radiocarbon dating is routinely used in paleoecology to build chronolo- gies of lake and peat sediments, aiming at inferring a model that would relate the sediment depth with its age. We present a new approach for chronology building (called \Bacon) that has received enthusiastic attention by paleoecologists. Our methodology is based on controlling core accumulation rates using a gamma au- toregressive semiparametric model with an arbitrary number of subdivisions along the sediment. Using prior knowledge about accumulation rates is crucial and in- formative priors are routinely used. Since many sediment cores are currently ana- lyzed, using difierent data sets and prior distributions, a robust (adaptive) MCMC is very useful. We use the t-walk (Christen and Fox, 2010), a self adjusting, robust MCMC sampling algorithm, that works acceptably well in many situations. Out- liers are also addressed using a recent approach that considers a Student-t model for radiocarbon data. Two examples are presented here, that of a peat core and a core from a lake, and our results are compared with other approaches. Past climates and environments can be reconstructed from deposits such as ocean or lake sediments, ice sheets and peat bogs. Within a vertical sediment proflle (core), mea- surements of microfossils, macrofossils, isotopes and other variables at a range of depths serve as proxy estimates or \proxies of climate and environmental conditions when the sediment of those depths was deposited. It is crucial to establish reliable relationships between these depths and their ages. Age-depth relationships are used to study the evolution of climate/environmental proxies along sediment depth and therefore through time (e.g., Lowe and Walker 1997). Age-depth models are constructed in various ways. For sediment depths containing organic matter, and for ages younger than c. 50,000 years, radiocarbon dating is often used to create an age-depth model. Cores are divided into slices and some of these are radiocarbon dated. A curve is fltted to the radiocarbon data and interpolated to obtain an age estimate for every depth of the core. The flrst restriction to be considered is that age should be increasing monotonically with depth, because sediment can never have accumulated backwards in time (extraordinary events leading to mixed or reversed sediments are, most of the time, noticeable in the stratigraphy and therefore such cores are ruled out from further analyses). Moreover, cores may have missing sections, leading to ∞at parts in the age depth models.