A Bayesian Calibrated Deglacial History for the North ...

A Bayesian Calibrated Deglacial History for the North ...

A Bayesian Calibrated Deglacial History for the North American Ice Complex Lev Tarasov, Radford Neal, and W. R. Peltier University of Toronto Outline

Model Data Model + Data: Calibration methodology Some key results Glacial modelling challenges and issues Glacial Systems Model (GSM)

Climate forcing LGM monthly temperature and precipitation from 6 highest resolution PMIP runs

Mean and top EOFS Total of 18 ensemble climate parameters Need constraints -> DATA Deglacial margin chronology

(Dyke, 2003) 36 time-slices +/- 50 km uncertainty Margin buffer Relative sea-level (RSL) data

VLBI and absolute gravity data Noisy data and non-linear system => need calibration and error bars Bayesian calibration Sample over posterior probability distribution for the ensemble parameters given fits to observational data using Markov Chain

Monte Carlo (MCMC) methods Sampling also subject to additional volume and ice thickness constraints

Large ensemble Bayesian calibration Bayesian neural network integrates over weight space It works! RSL results, best fit models

LGM characteristics LGM comparisons Maximum NW ice thickness Green runs fail constraints

Blue runs pass constraints Red runs are top 20% of blue runs Calibration favours fast flow Deglacial chronology Summary Glaciological results

Large Keewatin ice dome Multi-domed structure due to geographically restricted fast

flows Need strong ice calving and/or extensive ice-shelves in the Arctic to fit RSL data Need thin time-average Hudson Bay ice to fit RSL data Bayesian calibration method links data and physics (model) -> rational error bars Issues and challenges

Choice of ensemble parameters Error model for RSL data

Noisy and likely site biased Error model allows for site scaling and time-shifting Heavy-tailed error model to limit influence of outliers Neural network

Parameter set ended up being extended with time as troublesome regions were identified Method could easily handle more parameters, so best to try to cover deglacial phase space from the start Challenge of identifying appropriate priors for each parameter Non-trivial to find appropriate configuration Neural network for RSL was most complex: multi-layered and separate clusters for site location and time

Training takes a long time, predictions can be weak for distant regions MCMC sampling Can get stuck in local minima Unphysical solutions cropped up => added constraints RSL data redundancy

Fairly close correspondence between fit to full RSL data set and fit to reduced 313 datapoint calibration data set (only the last 50 runs have been calibrated against the whole data set) RSL data fits

Data-points should generally provide lower envelope of

true RSL history Black: best overall fit with full constraints Red: best overall fit to 313 data set and geodetic data with full constraints Green: best fit to just 313 RSL data,

no constraints Blue: best fit to just full RSL data, no constraints NA LGM ice volume Best fits required low volumes given global constraints

Possible indication of need for stronger Heinrich events Critical RSL site: SE Hudson Bay

Fitting this site required very strong regional desertelevation effect (ie low value) and therefore thin and warm ice core Atmospheric reorganization or weak Heinrich events?

Thin core results in low ice volumes Summary Bayesian calibration

Glaciological results

It works but is a non-trivial exercise Need to ensure that parameter space is large enough Phase space of model deglacial history must be quite bumpy Tricky to define complete error bars Calibration had tendency to find wacky(?) solutions Large Keewatin ice dome Multi-domed structure due to geographically restricted fast flows Need strong ice calving and/or extensive ice-shelves in the arctic to fit RSL data

Need thin time-average Hudson Bay ice to fit RSL data Future work: Faster (more diffusive computational kernal) ice-flow Addition of hydrological constraints and other data (especially to better constrain south-central and NW sectors)

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