A Bayesian Calibrated Deglacial History for the North American Ice Complex

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A Bayesian Calibrated Deglacial History for the
North American IceComplex

• Lev Tarasov, Radford Neal, and W. R. Peltier
• University of Toronto

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Outline

• Model
• Data
• Model Data Calibration methodology
• Some key results

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Glacial modelling challenges and issues
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Glacial Systems Model (GSM)
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Climate forcing

• LGM monthly temperature and precipitation from 6
  highest resolution PMIP runs
• Mean and top EOFS
• Total of 18 ensemble climate parameters

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Need constraints -gt DATA
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Deglacial margin chronology

• (Dyke, 2003)
• 36 time-slices
• /- 50 km uncertainty
• Margin buffer

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Relative sea-level (RSL) data
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VLBI and absolute gravity data
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Noisy data and non-linear system gt need
calibration and error bars
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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

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Large ensemble Bayesian calibration

• Bayesian neural network integrates over weight
  space

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It works!
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RSL results, best fit models
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LGM characteristics
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LGM comparisons
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Maximum NW ice thickness

• Green runs fail constraints
• Blue runs pass constraints
• Red runs are top 20 of blue runs

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Calibration favours fast flow
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Deglacial chronology
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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) -gt rational error bars

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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 gt added
  constraints

22
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)

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• 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

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NA LGM ice volume

• Best fits required low volumes given global
  constraints
• Possible indication of need for stronger Heinrich
  events

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• 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

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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)