Articles | Volume 11, issue 3
Technical note
24 Mar 2015
Technical note |  | 24 Mar 2015

Technical Note: Probabilistically constraining proxy age–depth models within a Bayesian hierarchical reconstruction model

J. P. Werner and M. P. Tingley

Abstract. Reconstructions of the late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurements of tree rings, ice cores, and varved lake sediments. Considerable advances could be achieved if time-uncertain proxies were able to be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors.

Current approaches for accounting for time uncertainty are generally limited to repeating the reconstruction using each one of an ensemble of age models, thereby inflating the final estimated uncertainty – in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space–time covariance structure of the climate to re-weight the possible age models. Here, we demonstrate how Bayesian hierarchical climate reconstruction models can be augmented to account for time-uncertain proxies. Critically, although a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age model probabilities decreases uncertainty in the resulting reconstructions, as compared with the current de facto standard of sampling over all age models, provided there is sufficient information from other data sources in the spatial region of the time-uncertain proxy. This approach can readily be generalized to non-layer-counted proxies, such as those derived from marine sediments.

Short summary
We present a Bayesian approach to simultaneously constrain the age models associated with time-uncertain proxies and inferring past climate in space and time. For the sake of exposition, the discussion focuses on annually resolved climate archives, such as varved lakes, corals, and tree rings, with dating by layer counting. Numerical experiments show that updating the probabilities associated with an ensemble of possible age models reduces uncertainty in the inferred climate.