studying uncertainty in palaeoclimate reconstruction supranet suprmodels supr software
DESCRIPTION
Studying Uncertainty in Palaeoclimate Reconstruction SUPRaNet SUPRModels SUPR software. Brian Huntley, Andrew Parnell Caitlin Buck, James Sweeney and many others Science Foundation Ireland Leverhulm Trust. Result: one pollen core in Ireland. Mean Temp of Coldest Month. - PowerPoint PPT PresentationTRANSCRIPT
Studying Uncertainty in Palaeoclimate Reconstruction
SUPRaNet SUPRModels
SUPR softwareBrian Huntley, Andrew Parnell
Caitlin Buck, James Sweeney and many others
Science Foundation Ireland Leverhulm Trust
Result: one pollen core in Ireland
95% of plausible scenarios have at least one “100 year +ve change”
> 5 oC
Mean Temp of Coldest Month
Climate over 100,000 yearsGreenland Ice Core
10,000 year intervals
Oxygen isotope – proxy for Greenland tempMedian smooth.
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Age
Past 23000 years
The long summer
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Age
Past 23000 years
Climate over 100,000 yearsGreenland Ice Core
10,000 year intervalsThe long summer
Int Panel on Climate Change WG1 2007“During the last glacial period, abrupt regional warmings (probably up to 16◦C within decades over Greenland) occurred repeatedly over the North Atlantic region”
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Climate over 15,000 yearsGreenland Ice Core
Younger Dryas
Transition
Holocene
Ice dynamics?Ocean dynamics?
What’s the probability of abrupt climate change?
Modelling Philosophy
Climate is – • Latent space-time stoch process C(s,t)• All measurements are
– Indirect, incomplete, with error– ‘Regionalised’ relative to some ‘support’
• Uncertainty – Prob (Event)– Event needs explicitly defined function of C(s,t)
Proxy Data Collection
Oak tree GISP ice Sediment PollenThanks to Vincent Garreta
coresamples
mult. counts by taxa
Pollen
Data
Data Issues
• Pollen 150 slices– 28 taxa (not species); many counts zero– Calibrated with modern data 8000 locations
• 14C 5 dates – worst uncertainties ± 2000 years
• Climate `smoothness’– GISP data 100,000 years, as published
Model Issues
• Climate - Sedimentation - Veg responselatent processes
– Climate smooth (almost everywhere)– Sedimentation non decreasing– Veg response smooth
• Data generating process– Pollen – superimposed pres/abs & abundance– 14C - Bcal
• Priors - Algorithms …….
SUPR-ambitions
• Principles– All sources of uncertainty– Models and modules– Communication
• Scientist to scientist• to others
• Software Bclim • Future
SUPR tech stuff•non-linear•non-Gaussian•multi-proxy•space-time•incl rapid change•dating uncertainty•mechanistic system models•fully Bayesian•fast software
Modelling Approach• Latent processes
– With defined stochastic properties– Involving explicit priors
• Conditional on ‘values’ of process(es)– Explicit stochastic models of – Forward Data Generating Processes– Combined via conditional independence– System Model
Modelling Approach• Modular Algorithms
– Sample paths, ensembles– Monte Carlo– Marginalisation to well defined random vars and
events
Progress in Modelling Uncertainty
• Statistical models– Partially observed space-time
stochastic processes– Bayesian inference
• Monte Carlo methods– Sample paths– Thinning , integrating
• Communication– Supplementary materials
ModelledUncertaintyDoes it change? In time? In space?
SUPR Info
• Proxy data: typically cores– Multiple proxies, cores; multivariate counts– Known location(s) in (2D) space– Known depths – unknown dates, some 14C data– Calibration data – modern, imperfect
• System theory– Uniformitarian Hyp– Climate ‘smoothness’; Sedimention Rates ≥ 0– Proxy Data Generating Processes
Chronology example
Bchron Models
• Sedimentation a latent process– Rates ≥ 0, piecewise const– Depth vs Time - piece-wise linear– Random change points (Poisson Process)– Random variation in rates (based on Gamma dist)
• 14C Calibration curve latent process– ‘Smooth’ – in sense of Gaussian Process (Bcal)
• 14C Lab data generation process– Gaussian errors
Bchron Algorithm
Posterior – via Monte Carlo Samples • Entire depth/time histories, jointly
– Generate random piece-wise linear ‘curves’– Retain only those that are ‘consistent’ with model
of data generating system
• Inference– Key Parameter; shape par in Gamma dist– How much COULD rates vary?
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Bivariate Gamma Renewal Process
Comp Poisson Gamma wrt x; x incs exponentialComp Poisson Gamma wrt y; y incs exponential
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Compound Poisson Gamma Process
We take y = 1 for access to CPGand x > 2 for continuity wrt x
Slope = Exp / Gamma= Exp x InvGamma infinite var if x > 2
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Modelling with Bivariate Gamma Renewal Process
Data assumed to be subset of renewal pointsImplicitly not smallMarginalised wrt renewal ptsIndep increments processStochastic interpolation by simulation
new y
unknown x
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Stochastic Interpolation
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Monotone piece-wise linear CPG Process
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Stochastic Interpolation
Monotone piece-wise linear CPG Process
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Stochastic Interpolation
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Stochastic Interpolation
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Stochastic Interpolation
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Stochastic Interpolation
Density
Known Depths
Known age
Known age
Calendar age
Data
Glendalough
Time-Slice “Transfer-Function”via Modern Training Data
Hypothesis
Modern analogue
Climate at
Glendalough 8,000 yearsBP
“like”
Somewhere right now
The present is a model for the past
Calibration
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c(t)y(t)
Modern (c, y ) pairsIn space
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c(t)y(t)
Eg dendroTwo time seriesMuch c data missing
Eg pollenOne time seriesAll c data missing
Space for time
substitution
Over-lapping time series
Calibration Model
Simple model of Pollen Data Generating Process• ‘Response’ y depends smoothly on clim c• Two aspects Presence/Absence
Rel abundance if presentTaxa not species
Eg yi=0 prob q(c)yi~Poisson (λ(c)) prob 1-q(c)
Thus obs yi=0, yi=1 very diff implications
One-slice-at-a time
• Slice j has count vector yj, depth dj
• Whence – separately - π(cj| yj) and π(tj| dj)
Response Chronmodule module
Uncertainty one-layer-at-a-time
Pollen => Uncertain ClimateDepth => Uncertain depth
But monotonicity
Here showing 10 of 150 layers
Uncertainty one-layer-at-a-time
Uncertainty jointly
Many potential climate histories areConsistent with ‘one-at-a-timeJointly inconsistent with Climate TheoryRefine/subsample
Coherent Histories
One-slice-at-a-time samples => {c(t1), c(t2),……c(tn)}
Coherent Histories
One-slice-at-a-time samples => {c(t1), c(t2),……c(tn)}
Coherent Histories
One-slice-at-a-time samples => {c(t1), c(t2),……c(tn)}
Coherent Histories
One-slice-at-a-time samples => {c(t1), c(t2),……c(tn)}
GISP series (20 years)
Climate property?
Non-overlapping (20 year?) averages are such that first differences are:
• adequately modelled as independent• inadequately modelled by Normal dist• adequately modelled by Normal Inv Gaussian
– Closed form pdf– Infinitely divisible– Easily simulated, scale mixture of Gaussian dist
One joint (coherent) history
One joint (coherent) history
One joint (coherent) history
One joint (coherent) history
MTCO Reconstruction
One layer at a time, showing temporal uncertainty
Jointly, century resolution, allowing for temporal uncertainty
Marginaltime-slice:may not be unimodal
Rapid Change in GDD5
Identify 100 yr period with greatest change
One history
Rapid Change in GDD5
One history
Identify 100 yr period with greatest change
Rapid Change in GDD5
Study uncertainty in non linear functionals of past climate
1000 histories
Identify 100 yr period with greatest change
Result: one pollen core in Ireland
95% of plausible scenarios have at least one 100 year +ve change > 5 oC
Mean Temp of Coldest Month
Communication• Scientist to scientist• Exeter Workshop
– Data Sets– With Uncertainty
• Associated with what precise support?
Modelling Approach• Latent processes
– With defined stochastic properties– Involving explicit priors
• Conditional on ‘values’ of process(es)– Explicit stochastic models of – Forward Data Generating Processes– Combined via conditional independence
• Modular Algorithms– Sample paths, ensembles– Monte Carlo– Marginalisation to well defined random vars and events