A Bayesian Calibrated Deglacial History for the North American Ice

Complex

Lev Tarasov, Radford Neal, and W. R. PeltierUniversity 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)