All age-depth models are wrong

all models are wrong, but some are useful. George E. P. Box

Age-depth modelling is a crucial aspect of almost every palaeoecological study. Without a good chronology, it is impossible to relate events in different proxy archives. But how good are the models? This question is rarely possible to answer with real data – we don’t know what the true age-depth relationship is, so we cannot compare the model with truth. But with simulated radiocarbon dates, we can compare the output of the model with reality. This was the objective of Telford et al (2004) ‘All age-depth models are wrong: but how badly?’

In this paper, I used the varve chronology from Holzmaar as the true age-depth relationship. I created age-depth models based on different numbers of simulated radiocarbon dates, and compared the resulting models to the truth. With few dates, no method performed very well – errors were substantial – but linear interpolation is as good as any. With many dates, spline models performed best. Subsequent work has shown that mixed effect modelling also performs well, as does OxCal’s p_sequence model when there are many dates (the p_sequence model has better treatment of outliers. OxCal is a powerful tool, capacity for phases and sequences. These features are probably of more benefit archaeologists more that most palaeoecologists).

How many dates are required? This depends on the questions being asked of the model. If the model is required to differentiate the early and late Holocene on a core with ~constant sedimentation rate, rather few dates are needed. Conversely, if we want to identify the 8.2 ka event in a core with variable sedimentation rate, a high dating density is required.

I usually calibrate my dates in OxCal, and then fit the model with either linear interpolation (approx()) or a mixed effect model (essentially a spline; Heegaard et al, 2005) in R. I have code to automate sending dates to OxCal and reading the output files. I’ve recently had a look at Maarten Blauuw’s CLAM. I do like the procedure and the graphics, but I don’t like the restrictions the code puts on my workflow. Having to have data files in a particular format in a particular directory reminds me too much of using 1990s DOS software.

Blaauw & Heegaard’s (2012) chapter in Tracking Environmental Change Using Lake Sediments 5: Data Handling and Numerical Techniques (Birks et al) is probably the best resource for palaeoecologists.

About richard telford

Ecologist with interests in quantitative methods and palaeoenvironments
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4 Responses to All age-depth models are wrong

  1. thanks for your post!

    all age models are wrong. to some degree, all observations ever made of anything are wrong. from a certain point of view (obi wan kenobi, 1977). 😉

    data have relations, not relationships. 😉

    there is no such thing as a radiocarbon date. an example of a date is jan 4, 1314. radiocarbon age determinations do not result in dates, but ages. (however one could say “radiocarbon date range,” but that is rare if not nonexistent. so it is much easier and more correct to say radiocarbon age) many people make this mistake, sometimes incorrectly forced by their journal editor. 😉

    i am glad you and i agree that we like oxcal and p_sequence (and dislike the disruption of workflow with other data systems, tho i am not a programmer like you; i would love if oxcal worked nicely with excel…)

    on a final note, there is no truth. ( 😉 peace and blessings.

    • My dictionary (Chambers) defines as date as “the time of an event”, amongst other definitions. There is no specification as to either the precision, so both 4th January 1314 and 2217 are dates, nor the accuracy of a date.

      To argue that there is no such thing as a radiocarbon date is to argue than none of the multitude of dating technique used in geology generate dates. I don’t find that a useful argument. Date (verb and noun) has been defined in it’s geological sense by decades of usage, and, at least in English, it is how words are used that define what they mean. “Radiocarbon date range” is clearly misleading – it appears to refer to a span of time rather than the uncertainty in a date. I would also disagree that age should be used instead of date. The words have different meanings: the age of a tree increments by one year every year, the date on which it germinated is fixed. Clearly for most geological usage the difference is immaterial (though I do know a bad joke about a dinosaur being 100 million and seven years old), but for palaeolimnology work on sediment from recent decades, date and age and not interchangeable.

  2. Pingback: Radiocarbon calibration – Keenan (2012) | Musings on Quantitative Palaeoecology

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