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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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slide1
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
slide2
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

slide3
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()

slide4
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
slide5
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
slide10
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?
slide14
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)

slide15
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!
slide16
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

slide17
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?
slide18
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
slide19
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) )
slide20
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)
slide21
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
slide22
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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