Age-depth modelling part 1
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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. R. Stats and graphing software Many user-provided modules Free, open-source Open R and type:

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Age-depth modelling part 1

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Age depth modelling part 1

Age-depth modelling part 1

0 random walk proxy simulations

1 Calibration of 14C dates

2 Basic 14C age-depth modelling

  • Schedule flexible and interactive!

  • Focus on uncertainty


Age depth modelling part 1

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


Age depth modelling part 1

Random walk simulations

Checkhttp://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()


Age depth modelling part 1

Introduction – 14C decay

  • Atm. 12C (99%), 13C (1%), 14C (10-12)

  • 14C decays exponentially with time

  • Cease metabolism -> clock starts ticking

  • Measure ratio 14C/C to estimate age fossil


Age depth modelling part 1

Calibrate – 14C age errors

  • Counting uncertainty AMS

    • Counting time (normal vs high-precision dates)

    • Sample size (larger = more 14C 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


Age depth modelling part 1

14C dating


Age depth modelling part 1

Bull’s Eye- Precise and Accurate


Age depth modelling part 1

Precise but inaccurate


Age depth modelling part 1

Accurate (on average) but imprecise


Age depth modelling part 1

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?


Age depth modelling part 1

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


Age depth modelling part 1

14C calibration


Age depth modelling part 1

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+sd2)


Age depth modelling part 1

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!


Age depth modelling part 1

Calibration, the equations

  • Calibration curve provides 14C ages µ for calendar years θ, µ(θ)

  • 14C measurement y ~ N(mean, sd)

  • Calibrate: find probability of y for θ

    N( µ(θ) , σ ), where σ2 = sd2 + σ(θ)2

    for sufficiently wide range of θ


Age depth modelling part 1

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?


Age depth modelling part 1

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


Age depth modelling part 1

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) )


Age depth modelling part 1

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)


Age depth modelling part 1

2. clam, calibrating

  • Type calibrate()

  • This calibrated 14C 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


Age depth modelling part 1

Feedback please

  • What was for you the best way to understand 14C calibration? Why?

    • Dedicated software (OxCal, Calib, clam)

    • Draw by hand

    • Animations

    • Equations


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