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 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 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 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 desert- elevation 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 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 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 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)