Presentation on theme: "Radiocarbon age-depth modelling II – Bayesian age-depth models"— Presentation transcript:
1 Radiocarbon age-depth modelling II – Bayesian age-depth models Dr. Maarten BlaauwSchool of Geography, Archaeology and PalaeoecologyQueen’s University BelfastNorthern Ireland
2 This lecture A biased introduction to tuning Bayesian age-depth modelling
3 Tuning -- intro Advocated by famous scientists such as Shackleton Major (climate) events must have been synchronouse.g. tephra, sediment layers separated by valley/oceanUse events to tune/tie between proxy sitesProduces 'rope&rubber-band' age-models
4 Oman stalagmite vs solar forcing, tuned U/Th datedOman stalagmite vs solar forcing, tunedNeff et al. Nature Oman d18O & d14C
11 Tuning Based on “model”: Events happened simultaneously Major local event must be expressed on large scaleSo should also be found back in other sitesEvent shapes can be used as ID (saw, tephra)Events happened simultaneouslySo provide very precise tie-points for age-models!Use events to glue to famous well-dated archivesEspecially handy where 14C has problems (old, ocean)Between tie-points, assume linear accumulation
12 Now hold on... Isn't this circular reasoning? How precise are tie-points for age-models?Do independent data support tuning?
13 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
14 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 thisProblems still exists, suck-in smear effect (Baillie 1991), 'precisely dated known event becomes associated with more poorly dated events' (Bennett 2002 JQS)
15 “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
16 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.???
17 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 yearsSPECMAP: c. 5,000 yr uncertaintiesRadiocarbon: errors stated more explicitlyLinear accumulation between tie-points reasonable?
25 Tuning With tuning dates become 'nuisance' Approach inherited from pre-dating period?Cannot use tuning for spatio-temporal patternsKeep time-scales independent+errorsAssume non-synchroneity until proven falseStick with appropriate resolution (millennial/decadal)Our eyes/minds are eager to interpret patternsUse quantitative, objective methods (e.g. for tuning)
26 Bayesian age-modelling Bayes: combine data with prior informationexpress everything in probabilities, not “black/white”MexCal: Christen, PhD thesis NottinghamBCal: Buck et al., Internet Archaeology 7OxCal: Bronk Ramsey, QSR 27:42-60Bpeat: Blaauw & Christen, Appl Stat 54:Prior information:chronological ordering dates in stratigraphyaccumulation rate, ranges and variation; hiatusesoutlying dates
27 Stratigraphic order dates Christen, Appl Stat 43:Only accept iterations with correct orderReduces error rangesRemoves outliersHard to questionEasy in Bcal / OxCal
28 Stratigraphic order dates Blaauw and Heegaard, in press
29 Stratigraphic order dates Example: Marshall et al Quat Res 68Large calibrated range of C14 datesMany ranges unlikely given other dates and acc.rate
30 Stratigraphic order dates Example: Marshall et al Quat Res 68Large calibrated range of C14 datesMany ranges unlikely given other dates and acc.rate
31 Outlier analysis Why outliers? chance? About 1 in 20 dates are off...contamination?errors in labelling?real?Outlier analysis: assign prior outlier probabilitiese.g. 5% for good dates, 50% for unreliable materialbase on prior knowledge, NOT after seeing the dates!available in BCal, Bpeat, mexcal, not in OxCal
32 Wiggle-match dating Assume linear accumulation (Bpeat) age = a*depth + b
33 Wiggle-match dating Assume linear accumulation (Bpeat) age = a*depth + b
35 Include additional information prior outlierprobabilitieshiatus, sizeprior outlierprobabilitiesother dates:tephra, pollen,210Pb, U/Th, ...
36 Include additional information p(date1)*p(date2)*p(date3)*p(date4)*p(date5) *p(acc.rate1)*p(hiatus1)*p(acc.rate2)*p(acc.rate2)
37 MCMC process Many parameters Get initial point estimate all parameters acc.rate, division depth and hiatus per sectionoutlier probability every dateGet initial point estimate all parametersChange values parameters one by onewithin prior limitsrepeat millions of timesSimulates true distribution parameters