| What meaning does a glaciological reconstruction have without error
bars? I would submit none. Interpretation of model results requires
some combination of explicit and implicit uncertainty estimates. The
glaciological, climate, and Earth systems modelling communities have
been slow to incorporate, in any statistically self-consistent way,
the objective determination of model and data uncertainties into their
results. Though ensemble calculations offer a first step, the order
million or more point sampling required to even partially cover
glacial cycle model parametric uncertainties in the context of
reconstructing past ice sheet chronologies precludes standard ensemble
approaches.
I will present a Bayesian framework for model calibration based on a
combination of Bayesian artificial neural networks and Markov Chain
Monte Carlo (MCMC) sampling. The neural networks function as
statistical emulators of model response to parameter variation. The
calibration provides a posterior distribution for model parameters
(and thereby in our case modelled glacial histories) given
observational constraint data sets. This methodology explicitly
accounts for constraint data uncertainty and emulation uncertainty of
the neural networks along with a partial assessment of structural
uncertainty of the model. The methodology also permits the
incorporation of diverse and large sets of noisy constraint data into
the calibration procedure and has been applied in varied incarnations
to both General Circulation climate models and 3D glacial systems
models (GSMs).
As partial validation, I will show that Bayesian artificial neural
networks are effective and efficient emulators for GSM response, that
they permit computationally feasible MCMC sampling of GSM ensemble
parameters, and that therefore a full Bayesian calibration of a GSM is
approachable (limited by incomplete assessment of structural
uncertainty). To convey a concrete example, I will present relevant
algorithmic details and some results from a recently completed
calibration of a deglacial model for Eurasia. I will also summarize
ongoing efforts towards more completely quantifying structural
uncertainty, especially with respect to spatial-temporal correlations. |