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 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
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)