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Radiocarbon age-depth modelling II – Bayesian age-depth models Dr. Maarten Blaauw School of Geography, Archaeology and Palaeoecology Queens 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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Neff et al. Nature 2001 Oman d 18 O & d 14 C Oman stalagmite vs solar forcing, tuned U/Th dated

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Bond et al Science 14 C dated

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

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Itambi et al. Paleoceanography 2009Senegal Millennial-scale dust fluxes are synchronous with North Atlantic Heinrich stadials No dates

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Tzedakis et al. Geology 2004Greece Age model based on calibrated 14 C ages (circles), astronomical calibration (squares), and tuning to GISP2 chronology (diamonds)

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

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Blaauw, submitted (Quat. Sci. Rev.)

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Tuning Based on model: –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 14 C 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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Sanchez Goñi et al. Climate Dynamics 2002Alboran Sea Millennial-scale pollen changes synchronous with Greenland events Of course, because they were tuned (via SST)!!!

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Courtillot et al. (EPSL '07, 08) show Mangini et al's (EPSL '05) 18 O record with 14 C. "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 δ 18 O." 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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Blaauw et al 2010, JQS Independent support for tuning? WARNING ILLEGAL CURVES

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

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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 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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