Radiocarbon age-depth modelling
II – Bayesian age-depth models
Dr. Maarten Blaauw
School of Geography, Archaeology and Palaeoecology
Queen’s University Belfast
Northern Ireland
This lecture
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A biased introduction to tuning

Bayesian age-depth modelling
Tuning -- intro
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Advocated by famous scientists such as Shackleton
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Major (climate) events must have been
synchronous
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e.g. tephra, sediment layers separated by
valley/ocean
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Use events to tune/tie between proxy sites
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Produces 'rope&rubber-band' age-models
U/Th dated
Oman stalagmite vs solar
forcing, tuned
Neff et al. Nature 2001
Oman d18O & d14C
14C
Bond et al. 2001 Science
dated
No dates
“Millennial-scale pollen
changes are synchronous
with Greenland events”
Sanchez Goñi et al. Climate Dynamics 2002 Alboran Sea
No dates
“Millennial-scale dust
fluxes are synchronous
with North Atlantic
Heinrich stadials”
Itambi et al. Paleoceanography 2009
Senegal
Age model based on
calibrated 14C ages
(circles), astronomical
calibration (squares), and
tuning to GISP2
chronology (diamonds)
Tzedakis et al. Geology 2004
Greece
No dates (for this part)
Hughen et al. 2006
Cariaco Basin (Venezuela) tuned against Hulu Cave (China)
Blaauw, submitted (Quat. Sci. Rev.)
Tuning
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Based on “model”:
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Major local event must be expressed on large scale
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So should also be found back in other sites
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Event shapes can be used as ID (saw, tephra)
Events happened simultaneously
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So provide very precise tie-points for age-models!
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Use events to glue to famous well-dated archives
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Especially handy where 14C has problems (old, ocean)
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Between tie-points, assume linear accumulation
Now hold on...
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Isn't this circular reasoning?
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How precise are tie-points for age-models?
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Do independent data support tuning?
1) Circular reasoning
premise 1) God is not a liar (Hebrews 6:18)
premise 2) God wrote the Bible (Lk. 16:1, etc.)
premise 3) The Bible says that God exists (2 Cor. 1)
→ therefore, God exists
Circular reasoning in palaeoclimate
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Before dating, no robust time frames and thus much freedom to
speculate about chronologies and correlations. Few could resist
the urge to fit their results into existing framework, e.g. pollen
zones. Thus arose 'coherent myths' or 'reinforcement syndrome'
(Oldfield 2001 The Holocene)
•
von Post (1946) warned us about this
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Problems still exists, suck-in smear effect (Baillie 1991),
'precisely dated known event becomes associated with more
poorly dated events' (Bennett 2002 JQS)
“Millennial-scale pollen
changes synchronous
with Greenland events”
Of course, because
they were tuned (via
SST)!!!
Sanchez Goñi et al. Climate Dynamics 2002Alboran Sea
Courtillot et al. (EPSL '07, ‘08) show
Mangini et al's (EPSL '05) d18O record with
d14C. "The match can of course not be
perfect because of the uncertainties. If
solar variability played only a minor role in
the past two millennia, tuning could not
improve the correlation. The correlation
coefficient is only 0.6, and other forcing
factors have to be taken into account. It is
therefore not surprising that the tuned
curve should reveal the link between solar
activity and δ18O."
Bard and Delaygue (EPSL '08) comment:
"To prove correlations and make inferences
about solar forcing, only untuned records
[...] with their respective and independent
time scales, should be used.
???
2) How precise are tie-points?
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Depends on reliable event-IDing (order, shape, tephra)
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Resolution/noise: did we catch the event (start)?
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Multiple/different proxies: do they agree? (ice, ocean)
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How precisely dated is 'mother archive'? (rubber band)
•
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NGRIP: uncertainty thousands of years
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SPECMAP: c. 5,000 yr uncertainties
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Radiocarbon: errors stated more explicitly
Linear accumulation between tie-points
reasonable?
Are all climate events global?
Barber and Langdon 2007, Quat. Sci. Rev.
Charman et al. 2009, Quat. Sci. Rev.
Independent support for tuning?
WARNING
ILLEGAL CURVES
Blaauw et al 2010, JQS
Blaauw et al 2010, JQS
Blaauw et al 2010, JQS
Blaauw et al 2010, JQS
Know your resolution
Tuning
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With tuning dates become 'nuisance'
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Approach inherited from pre-dating period?
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Cannot use tuning for spatio-temporal patterns
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Keep time-scales independent+errors
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Assume non-synchroneity until proven false
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Stick with appropriate resolution (millennial/decadal)
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Our eyes/minds are eager to interpret patterns
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Use quantitative, objective methods (e.g. for tuning)
Bayesian age-modelling
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Bayes: combine data with prior information
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express everything in probabilities, not “black/white”
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MexCal: Christen, 1994. PhD thesis Nottingham
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BCal: Buck et al., 1999. Internet Archaeology 7
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OxCal: Bronk Ramsey, 2008. QSR 27:42-60
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Bpeat: Blaauw & Christen, 2005. Appl Stat 54: 805-816
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Prior information:
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chronological ordering dates in stratigraphy
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accumulation rate, ranges and variation; hiatuses
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outlying dates
Stratigraphic order dates
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Christen, 1994. Appl Stat 43:489-503
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Only accept iterations with correct order
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Reduces error ranges
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Removes outliers
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Hard to question
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Easy in Bcal / OxCal
Stratigraphic order dates
Blaauw and Heegaard, in press
Stratigraphic order dates
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Example: Marshall et al. 2007. Quat Res 68
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Large calibrated range of C14 dates
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Many ranges unlikely given other dates and acc.rate
Stratigraphic order dates
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Example: Marshall et al. 2007. Quat Res 68
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Large calibrated range of C14 dates
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Many ranges unlikely given other dates and acc.rate
Outlier analysis
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Why outliers?
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chance? About 1 in 20 dates are off...
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contamination?
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errors in labelling?
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real?
Outlier analysis: assign prior outlier probabilities
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e.g. 5% for good dates, 50% for unreliable material
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base on prior knowledge, NOT after seeing the dates!
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available in BCal, Bpeat, mexcal, not in OxCal
Wiggle-match dating
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Assume linear accumulation (Bpeat)
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age = a*depth + b
Wiggle-match dating
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Assume linear accumulation (Bpeat)

age = a*depth + b
Wiggle-match dating
Include additional information
prior
hiatus,
outlier
size
probabilities
prior outlier
probabilities
other dates:
tephra, pollen,
210Pb, U/Th, ...
Include additional information
p(date1)*p(date2)*p(date3)*p(date4)*p(date5) *
p(acc.rate1)*p(hiatus1)*p(acc.rate2)*p(acc.rate2)
MCMC process
Many parameters
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Get initial point estimate all parameters
Change values parameters one by one
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acc.rate, division depth and hiatus per section
outlier probability every date
within prior limits
repeat millions of times
Simulates true distribution parameters
Grey-scale ghost graphs
Age-depth modelling
Wohlfarth et al. JQS 2006
Order of events between archives
Timing between events
Buck and Bard 2007, Quat. Sci. Rev.
Meta-analysis Europe
Blaauw et al. in prep.