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.