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**Radiocarbon age-depth modelling II – Bayesian age-depth models**

Dr. Maarten Blaauw School of Geography, Archaeology and Palaeoecology Queen’s University Belfast Northern Ireland

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**This lecture A biased introduction to tuning**

Bayesian age-depth modelling

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**Tuning -- intro Advocated by famous scientists such as Shackleton**

Major (climate) events must have been synchronous e.g. tephra, sediment layers separated by valley/ocean Use events to tune/tie between proxy sites Produces 'rope&rubber-band' age-models

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**Oman stalagmite vs solar forcing, tuned**

U/Th dated Oman stalagmite vs solar forcing, tuned Neff et al. Nature Oman d18O & d14C

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14C dated Bond et al Science

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**“Millennial-scale pollen changes are synchronous **

No dates “Millennial-scale pollen changes are synchronous with Greenland events” Sanchez Goñi et al. Climate Dynamics 2002 Alboran Sea

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**“Millennial-scale dust fluxes are synchronous with North Atlantic **

No dates “Millennial-scale dust fluxes are synchronous with North Atlantic Heinrich stadials” Itambi et al. Paleoceanography Senegal

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Age model based on calibrated 14C ages (circles), astronomical calibration (squares), and tuning to GISP2 chronology (diamonds) Tzedakis et al. Geology Greece

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**Cariaco Basin (Venezuela) tuned against Hulu Cave (China)**

No dates (for this part) Hughen et al. 2006 Cariaco Basin (Venezuela) tuned against Hulu Cave (China)

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**Blaauw, submitted (Quat. Sci. Rev.)**

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**Tuning Based on “model”: Events happened simultaneously**

Major local event must be expressed on large scale So should also be found back in other sites Event shapes can be used as ID (saw, tephra) Events happened simultaneously So provide very precise tie-points for age-models! Use events to glue to famous well-dated archives Especially handy where 14C has problems (old, ocean) Between tie-points, assume linear accumulation

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**Now hold on... Isn't this circular reasoning?**

How precise are tie-points for age-models? Do independent data support tuning?

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**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

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**Circular reasoning in palaeoclimate**

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 Problems still exists, suck-in smear effect (Baillie 1991), 'precisely dated known event becomes associated with more poorly dated events' (Bennett 2002 JQS)

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**“Millennial-scale pollen changes synchronous with Greenland events” **

Of course, because they were tuned (via SST)!!! Sanchez Goñi et al. Climate Dynamics 2002 Alboran Sea

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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. ???

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**2) How precise are tie-points?**

Depends on reliable event-IDing (order, shape, tephra) Resolution/noise: did we catch the event (start)? Multiple/different proxies: do they agree? (ice, ocean) How precisely dated is 'mother archive'? (rubber band) NGRIP: uncertainty thousands of years SPECMAP: c. 5,000 yr uncertainties Radiocarbon: errors stated more explicitly Linear accumulation between tie-points reasonable?

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**Are all climate events global?**

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**Barber and Langdon 2007, Quat. Sci. Rev.**

Charman et al. 2009, Quat. Sci. Rev.

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**Independent support for tuning?**

WARNING ILLEGAL CURVES Blaauw et al 2010, JQS

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Blaauw et al 2010, JQS

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Blaauw et al 2010, JQS

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Blaauw et al 2010, JQS

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Know your resolution

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**Tuning With tuning dates become 'nuisance'**

Approach inherited from pre-dating period? Cannot use tuning for spatio-temporal patterns Keep time-scales independent+errors Assume non-synchroneity until proven false Stick with appropriate resolution (millennial/decadal) Our eyes/minds are eager to interpret patterns Use quantitative, objective methods (e.g. for tuning)

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**Bayesian age-modelling**

Bayes: combine data with prior information express everything in probabilities, not “black/white” MexCal: Christen, PhD thesis Nottingham BCal: Buck et al., Internet Archaeology 7 OxCal: Bronk Ramsey, QSR 27:42-60 Bpeat: Blaauw & Christen, Appl Stat 54: Prior information: chronological ordering dates in stratigraphy accumulation rate, ranges and variation; hiatuses outlying dates

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**Stratigraphic order dates**

Christen, Appl Stat 43: Only accept iterations with correct order Reduces error ranges Removes outliers Hard to question Easy in Bcal / OxCal

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**Stratigraphic order dates**

Blaauw and Heegaard, in press

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**Stratigraphic order dates**

Example: Marshall et al Quat Res 68 Large calibrated range of C14 dates Many ranges unlikely given other dates and acc.rate

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**Stratigraphic order dates**

Example: Marshall et al Quat Res 68 Large calibrated range of C14 dates Many ranges unlikely given other dates and acc.rate

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**Outlier analysis Why outliers?**

chance? About 1 in 20 dates are off... contamination? errors in labelling? real? Outlier analysis: assign prior outlier probabilities e.g. 5% for good dates, 50% for unreliable material base on prior knowledge, NOT after seeing the dates! available in BCal, Bpeat, mexcal, not in OxCal

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**Wiggle-match dating Assume linear accumulation (Bpeat)**

age = a*depth + b

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**Wiggle-match dating Assume linear accumulation (Bpeat)**

age = a*depth + b

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Wiggle-match dating

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**Include additional information**

prior outlier probabilities hiatus, size prior outlier probabilities other dates: tephra, pollen, 210Pb, U/Th, ...

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**Include additional information**

p(date1)*p(date2)*p(date3)*p(date4)*p(date5) * p(acc.rate1)*p(hiatus1)*p(acc.rate2)*p(acc.rate2)

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**MCMC process Many parameters Get initial point estimate all parameters**

acc.rate, division depth and hiatus per section outlier probability every date Get initial point estimate all parameters Change values parameters one by one within prior limits repeat millions of times Simulates true distribution parameters

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**Grey-scale ghost graphs**

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Age-depth modelling Wohlfarth et al. JQS 2006

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**Order of events between archives**

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Timing between events Buck and Bard 2007, Quat. Sci. Rev.

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Meta-analysis Europe Blaauw et al. in prep.

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