1. Age-depth modelling part 1 0 random walk proxy simulations 1 Calibration of 14 C dates 2 Basic 14 C age-depth modelling Schedule flexible and interactive! Focus on uncertainty

2. R Stats and graphing software Many user-provided modules Free, open-source Open R and type: plot(1:10, 11:20) x <- 1:10 ; y <- 11:20 ; plot(x, y, type='l') Case sensitive Previous commands: use up cursor

3. Random walk simulations Check http://chrono.qub.ac.uk/blaauw/Random.R in browser Open R and load the link: Source ( url( 'http://chrono.qub.ac.uk/blaauw/Random.R' ) ) RandomEnv() RandomEnv(nforc=2, nprox=5) RandomProx()

4. Introduction – 14 C decay Atm. 12 C (99%), 13 C (1%), 14 C (10 -12 ) 14 C decays exponentially with time Cease metabolism -> clock starts ticking Measure ratio 14 C/C to estimate age fossil

5. Calibrate – 14 C age errors Counting uncertainty AMS  Counting time (normal vs high-precision dates)  Sample size (larger = more 14 C atoms)  Drift machine (need to correct, standards) Preparation samples  Pretreatment, chemical & graphitisation  Material-dependent (e.g. trees, bone, coral)  Lab-specific Every measurement will be bit different Errors assumed to have Normal distribution

6. 14 C dating

7. Bull’s Eye- Precise and Accurate

8. Precise but inaccurate

9. Accurate (on average) but imprecise

10. An alternative to the normal model Christen and Perez 2009, Radiocarbon Spread of dates often beyond expected Reported errors are estimates Propose an error multiplier, gamma Results in t student distribution No need for outlier modelling?

12. http:///www.chrono.qub.ac.uk/blaauw/

13. 14 C calibration

14. Calibrate - methods Probability preferred over intercept  Less sensible to small changes in mean  Resulting cal.ranges make more sense Procedure probability method:  What is prob. of cal.year x, given the date?  Calculate this prob. for all cal.ages Combine errors date and cal.curve √(  2 +sd 2 )

15. Calibrate - methods Multimodal distributions  Which of the peaks most likely (Calib %)?  How report date? 1 or 2 sd sd range mean±sd mode weighted mean (Telford et al. ‘05 Holocene) why not plot the entire distribution!

16. Calibration, the equations Calibration curve provides 14 C ages µ for calendar years θ, µ(θ) 14 C measurement y ~ N(mean, sd) Calibrate: find probability of y for θ N( µ(θ), σ ), where σ 2 = sd 2 + σ(θ) 2 for sufficiently wide range of θ

17. Calibrate - DIY A) Using eyes/hands on handout paper  Imagine invisible arbitrary second axes for probs  Try to avoid using intercept  Try “cosmic schwung”, not mm precision  Don’t go from C14 to calBP! What is prob x cal BP?  Calibrated ranges?

18. 1. clam... R R works in “workspace” Remember where you work(ed)! Change working dir via File > Change Dir Or permanently using Desktop Icon (right- click, properties, start in) Change R to your Clam workspace

19. 1. Calibrating DIY Define years: yr <- 1:1000 A date: y <- 230; sdev <- 70 Prob. for each yr: prob < - dnorm(yr, y, sdev) plot(yr, prob, type=‘l’) But we should calibrate: cc <- read.table(“IntCal09.14C”, header=TRUE) cc[1:10,] prob <- dnorm(cc[,2], y, sqrt(sdev^2+cc[,3]^2)) plot(cc[,1], prob, type='l', xlim=c(0, 1000) )

20. Calibrate - DIY clam (Blaauw, in press Quat Geochr)  Open R (via desktop icon or Start menu)  Change working directory to clam dir  Type: source(''clam.R'') [enter]  Type: calibrate(130, 35)

21. 2. clam, calibrating Type calibrate() This calibrated 14 C date of 2450 +- 50 BP Type calibrate(130, 30) Type calibrate(130, 30, sdev=1) Try calibrating other dates, e.g., old ones All clam code is open source, you can read the code to see/follow what it does

22. Feedback please What was for you the best way to understand 14 C calibration? Why? – Dedicated software (OxCal, Calib, clam) – Draw by hand – Animations – Equations