K parameter, low sedimentation rate

[Carley Crann]

Dear Dr. Bronk Ramsey,

In an earlier comment, I saw that you suggested the k parameter should vary between 1 and 10 when the units are set to cm. We are studying lakes in the subarctic - arctic where accumulation rates can be as low as 60 - 80 years/cm. When I set the k parameter this high (code attached), the model is very rigid and the agreement index is painfully low, yet all of our radiocarbon dates are from bulk sediment so I am not looking for perfection. When I lower the k parameter, my concern is that the model runs similar to linear interpolation between each dated horizon (connect-the-dots) and I'm not keen on that because (1) we've dated bulk sediment and (2) it creates some shifts in the model that don't show up in any of the other proxy data. Could you provide some insight on the situation?

Also, I would like to try out the new, flexible method for setting the k parameter that you presented at the Radiocarbon conference. I jotted this down form your slide:

P_Sequence("",1,0,U(-2,2))

Could you explain the "U(-2,2))" portion of the code and how this is meant to work?

Many thanks,

Carley

PS: thank you for setting up this discussion group. It has been helpful to read the previous Q&A.

[Christopher Ramsey]

Yes - that is probably too high for any sediment. The particle size may be very small, and sedimentation very low but there is still likely to be variability in sedimentation on a centennial level.

This may be a case where an average of different k values would help.

P_Sequence("",1,0,U(-2,2))

is what I suggested for cm depth scales. The third parameter after the name, here U(-2,2), gives the prior for log_10(k/k_0) where k_0 is 1. So in this case it allows k to take any value from 0.01 to 100. In practice the value chosen will depend on the degree to which the data suggest a uniform deposition rate.

The other parameter that you might want (relating to your later question) is the second parameter after the name - currently set to 0. This defines the number of interpolated points per unit length throughout the core. So for a core in cm you might set this to 1 to get an output every cm - or 0.5 to get an output every 2cm etc. This stops the model from producing join-the-dots type output - though if k is low the uncertainty between points becomes high.

In this case I think you want something like:

P_Sequence("",1,1,U(-2,2))

This gives a range of k values - but with an approximately normal distribution (log_10(k) ~ N(-0.3,0.15)) suggesting that a k value of less than 1 is most appropriate for this sequence - assuming the dates are an accurate reflection of the age of the sediments (a possible problem with bulk dates).

Best wishes

Christopher

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[Carley Crann]

Thank you for the quick response.

I think I have mistaken the k parameter for the accumulation rate because it was defined as "increments per unit length" (Bronk Ramsey 2008). At high latitudes the increments of deposition are annual, related to spring melt of snow and ice. So, if on average it takes 70 increments (years) to accumulate 1 cm of sediment, I presumed that k should be set to 70.

However, taking your comments into consideration and re-reading the chapter on the k parameter in Bronk Ramsey (2008), I think I better understand the effect of the k parameter. Since deposition is likely not to be perfectly uniform, the k parameter is a modelling parameter that divides each unit of length into increments that vary in thickness. If I were to divide 1 cm into 70 increments, the increments would be very tiny and there would be little variability between them, hence a rigid age-depth model. In reality, although on average it may take 70 years to deposit 1 cm, it is unlikely that every year we had the exact same deposition. ie one increment may represent 20 years of deposition, while another may represent 10 years of deposition and this goes on for approximately 70 years to make 1 cm.