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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.

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studying uncertainty in palaeoclimate reconstruction supranet suprmodels supr software

Studying Uncertainty in Palaeoclimate ReconstructionSUPRaNet SUPRModelsSUPR software

Brian Huntley, Andrew Parnell

Caitlin Buck, James Sweeney and many others

Science Foundation Ireland Leverhulm Trust

slide2

Result: one pollen core in Ireland

Mean Temp of Coldest Month

95% of plausible scenarios have at least one

“100 year +ve change”

> 5 oC

climate over 100 000 years greenland ice core
Climate over 100,000 yearsGreenland Ice Core

10,000 year intervals

The long summer

Past 23000 years

Oxygen isotope – proxy for Greenland temp

Median smooth.

climate over 100 000 years greenland ice core1
Climate over 100,000 yearsGreenland Ice Core

10,000 year intervals

The long summer

Past 23000 years

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”

climate over 15 000 years greenland ice core
Climate over 15,000 yearsGreenland Ice Core

Younger Dryas

Holocene

What’s the probability of abrupt climate change?

Ice dynamics?

Ocean dynamics?

Transition

modelling philosophy
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
Proxy Data Collection

Oak tree

GISP ice

Sediment

Pollen

Thanks to Vincent Garreta

pollen

samples

mult. counts by taxa

Pollen

core

data issues
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
Model Issues
  • Climate - Sedimentation - Veg response

latent 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
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
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 approach1
Modelling Approach
  • Modular Algorithms
    • Sample paths, ensembles
    • Monte Carlo
    • Marginalisation to well defined random vars and events
progress in modelling uncertainty
Progress in Modelling Uncertainty

Modelled

Uncertainty

Does it change?

In time? In space?

  • Statistical models
    • Partially observed space-time stochastic processes
    • Bayesian inference
  • Monte Carlo methods
    • Sample paths
    • Thinning , integrating
  • Communication
    • Supplementary materials
supr info
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
bchron models
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
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?
bivariate gamma renewal process
Bivariate Gamma Renewal Process

Comp Poisson Gamma wrt x; x incs exponential

Comp Poisson Gamma wrt y; y incs exponential

compound poisson gamma process
Compound Poisson Gamma Process

We take y= 1 for access to CPG

and x> 2 for continuity wrt x

Slope

= Exp / Gamma

= Exp x InvGamma

infinite var

if x> 2

modelling with bivariate gamma renewal process
Modelling with Bivariate Gamma Renewal Process

Data assumed to be subset of renewal points

Implicitly  not small

Marginalised wrt renewal pts

Indep increments process

Stochastic interpolation by simulation

new y

unknown x

stochastic interpolation
Stochastic Interpolation

Monotone piece-wise linear CPG Process

Unit Square

stochastic interpolation1
Stochastic Interpolation

Monotone piece-wise linear CPG Process

stochastic interpolation2
Stochastic Interpolation

Monotone piece-wise linear CPG Process

stochastic interpolation3
Stochastic Interpolation

Monotone piece-wise linear CPG Process

stochastic interpolation4
Stochastic Interpolation

Monotone piece-wise linear CPG Process

stochastic interpolation5
Stochastic Interpolation

Monotone piece-wise linear CPG Process

stochastic interpolation6
Stochastic Interpolation

Known age

Known

Depths

Calendar age

Known age

Density

time slice transfer function via modern training data
Time-Slice “Transfer-Function”via Modern Training Data

Glendalough

Hypothesis

Modern analogue

Climate at

Glendalough 8,000 yearsBP

“like”

Somewhere right now

The present is a model for the past

calibration
Calibration

Modern

(c, y ) pairs

In space

Eg dendro

Two time series

Much c data missing

Eg pollen

One time series

All c data missing

c(t) y(t)

c(t) y(t)

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Over-lapping time series

Space for time substitution

calibration model
Calibration Model

Simple model of Pollen Data Generating Process

  • ‘Response’ y depends smoothly on climc
  • Two aspects Presence/Absence

Rel abundance if present

Taxa not species

Egyi=0 probq(c)

yi~Poisson (λ(c)) prob 1-q(c)

Thus obsyi=0, yi=1 very diff implications

one slice at a time
One-slice-at-a time
  • Slice j has count vector yj, depth dj
  • Whence – separately - π(cj| yj) and π(tj| dj)

Response Chron

module module

slide35

Uncertainty one-layer-at-a-time

Here showing 10 of 150 layers

Pollen => Uncertain Climate

Depth => Uncertain depth

But monotonicity

slide37

Uncertainty jointly

Many potential climate histories are

Consistent with ‘one-at-a-time

Jointly inconsistent with Climate Theory

Refine/subsample

coherent histories
Coherent Histories

One-slice-at-a-time samples =>

{c(t1), c(t2),……c(tn)}

coherent histories1
Coherent Histories

One-slice-at-a-time samples =>

{c(t1), c(t2),……c(tn)}

coherent histories2
Coherent Histories

One-slice-at-a-time samples =>

{c(t1), c(t2),……c(tn)}

coherent histories3
Coherent Histories

One-slice-at-a-time samples =>

{c(t1), c(t2),……c(tn)}

climate property
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
mtco reconstruction
MTCO Reconstruction

Marginal

time-slice:

may not be unimodal

Jointly, century resolution, allowing for temporal uncertainty

One layer at a time, showing temporal uncertainty

rapid change in gdd5
Rapid Change in GDD5

Identify 100 yr period with

greatest change

One history

rapid change in gdd51
Rapid Change in GDD5

Identify 100 yr period with

greatest change

One history

rapid change in gdd52
Rapid Change in GDD5

1000 histories

Identify 100 yr period with

greatest change

Study uncertainty in

non linear functionals of past climate

slide52

Result: one pollen core in Ireland

Mean Temp of Coldest Month

95% of plausible scenarios have at least one 100 year +ve change > 5 oC

communication
Communication
  • Scientist to scientist
  • Exeter Workshop
    • Data Sets
    • With Uncertainty
      • Associated with what precise support?
modelling approach2
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