final_program_abstracts[1]

11 IMSC Session Program
Uncertainties in palaeoclimate reconstruction – sampling
ensembles for the younger dryas
Tuesday - Plenary Session 3
John Haslett
Palaeoclimate reconstruction involves the joint use of multiple sources of uncertain
data to make joint inference on the stochastic space-time system that is the palaeoclimate.
Current methodologies are crude but fast; the literature on uncertainty is
completely undeveloped. In a proof-of-concept paper, Haslett et al (2006) proposed
an ambitious Bayesian formulation for pollen-based reconstruction, illustrated by a
single core that covered the past 15,000 years. More recently, SUPRAnet authors
(2010) have discussed a larger framework, arguing that multi-proxy space-time
reconstructions can be cast as Bayesian inversion of forward process models.
Algorithms are the practical challenge; that proposed in Haslett et al was completely
infeasible in practice. We report here on the overall framework and on considerable
progress with the algorithms.
The overall framework sees a multivariate space-time stochastic process C = C (s, t) -
defined everywhere in a continuous region of space-time. This drives other systems
such as vegetation V = V (s, t) which in turn drive proxy-deposition in archive systems
A and ultimately generate data Y – of which we have a single instance y. Archive
systems - eg sedimentation - have their own dynamics and other inputs; these include
absorption and subsequent decay of radio-carbon.
We propose a joint model F for the data generating system. Viewed as computer code
F is simply a network of input-output sub-models, with external inputs such as known
forcing and numerical values for some system parameters – jointly X - and with very
many stochastic outputs - being proxy data Y , as well as the states of the many subsystems.
It may also be viewed as implicitly specifying the joint likelihood. Then the
posterior probability distribution is π (C | Y = y), for the palaeoclimate given the data,
is proportional to F (y | C, X, Θ) π (C) π (Θ) (these latter being priors) marginalised
with respect both to such states and the internal system parameters Θ. Palaeoclimate
reconstruction - with due allowance for the many uncertainties - is achieved by
sampling ensembles from the posterior. Post- processing these permits focus on
specific aspects of the palaeoclimate. There are of course many practical challenges to
such a broad framework.
We illustrate the general framework and the challenges with modular algorithms,
replacing and extending those in Haslett et al (2006). These can be seen as sampling
climate ensembles that are probabilistically consistent with sediment based proxies of
uncertain date. We focus on the Younger Dryas, the rapid changes in which provide a
demanding test.
Haslett, J et al (2006) Bayesian Palaeoclimate Reconstruction, Journal of the Royal
Statistical Society (A)169, 395-430
SUPRAnet project (2010) Studying Uncertainty in Palaeoclimate Reconstruction: a
Framework for Research; in draft, March 2010
Abstracts 86