Calculating 95% Confidence Interval for Laacher Sea Tephra's Age

[Andre]

So there is that wide spread layer of Volcanic ash, known as the Laacher Sea Tephra which is widely used as a dating marker but how old is it, itself?

All with 95% confidence interval:

K-Ar dating gives: 12,900 +/- 560 years before present
A carbon date of the last tree ring of an ash burried tree gives: 12,985 +/- 75 years before present
Counting individual annual sediment layers in a lake finds 12,880 +/- 120 years before present
A so called multi proxy trick combining all kind of techniques gives: 12,859 +/- 116 years

The only common time frame of all these is 12,910 to 12,975 years but the average value is 12.906 years. How would you calculate a statistically acceptable 95% confidence interval?

Thanks

 

[Hurkyl]

19,985 +/- 75

Typo?

How would you calculate a statistically acceptable 95% confidence interval?

Are the errors statistically independent? Are they roughly normally distributed? Do you know the distribution of the errors?

 

[Andre]

Typo?

Yes I corrected it

Are the errors statistically independent? Are they roughly normally distributed? Do you know the distribution of the errors?

Note that this ash layer is known as the Laacher See Tephra (LST) The Ar dating of 12,900 +/- 560 years before present is from (http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V61-3Y45G94-3B&_user=10&_coverDate=06%2F30%2F1995&_rdoc=15&_fmt=summary&_orig=browse&_srch=doc-info(%23toc%235801%231995%23998669998%23147982%23FLP%23display%23Volume)&_cdi=5801&_sort=d&_docanchor=&_ct=19&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=f333bca05724f63cd776ffa297082856


No more information than that but I have the publication on request. I guess a normal distribution with standard deviation? Certainly that dating technique is independent of the other

The 12,880 +/- 120 counted annual sediment layers (varves) is from Brauer et al 1999. For the Meerfelder maar and with volcanic ash correlated Holzmaar lakes a continuous record was obtained and this technique is certainly independent. They did not use other dating technique to wiggle match their results. They assume a counting error of 1% (stdev?) which should lead to 12,880 +/- 129, but okay. Layer counting can be compromised by not recognized discontinuities (dry lake for a certain period) but this is unlikely. I got the records from both the Meerfelder maar and those of Lake Gosciaz in Poland, the only two known lake records with continuous 'varving' throughout the Younger Dryas. I checked the duration of that period on 1126 annual varves in the former and 1124 in the latter, giving confidence that the 1% error is rather conservative. Also looks like a normal distribution, I would think.

About the carbon dated trees, http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBC-4RM89DF-3&_user=10&_coverDate=01%2F31%2F2008&_alid=699030562&_rdoc=1&_fmt=summary&_orig=search&_cdi=5923&_sort=d&_docanchor=&view=c&_ct=2&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=ca59a2d78233425dd548f8bfef8dd6ce state:

Perhaps the most reliable is the radiocarbon age of 11,063 +/- 12 conventional radiocarbon years BP, based on radiocarbon age measurements of the outer rings of trees from ~60 km from the eruptive centre that were buried by the LST (Friedrich et al., 1999). Since the publication of INCAL 04 (Reimer et al., 2004) the calibrated age for the LST from these trees is now 13,060–12,910 cal BP (95% confidence),

The process of carbon dating and subsequent calibration is rather complex and introduces a plethora of (little) error ranges. Moreover it's not independent. See for instance the calibration curve INTCAL04 being composed of matching chronologies. Take for instance dataset 15, annual sediment laminations on the floor of the Cariaco basin near the coast of Venezuala, which only starts some 6000 years ago, which meant that the initial stage was matched with a tree ring dendrochronology (German pines).

Finally the multi proxy trick combining all kind of techniques in another lake (Soppensee) giving: 12,859 +/- 116 years is also from Blockley et al 2008.

Plotting the age depth models for Soppensee (Fig. 5) and indicating the positions
of the LST, along with the biozone boundaries (see Ammann and Lotter, 1989), show that the revised Soppensee chronology performs well in predicting the age of the LST, giving an age of 12,975–12,743 cal BP, taking the combined age estimates of the two models (P_Sequence by depth and by varve spacing) deemed to be the most reliable age models.

Those models match calibrated carbon dates with varve counting since the lamination is discontinue, So it's not independent, the common factor being the carbon date calibration, that ties it to the tree ring carbon dating, but not the other two.

I admit that this thread looks like it should go in the Earth forums but it's really about the proper statistics getting a trustworthy estimate date of the volcanic eruption, combining independent assymetric data.





References:

Blockley S.P.E, C. Bronk Ramsey, C.S. Lane, A.F. Lotter, 2008 Improved age modelling approaches as exemplified by the revised chronology for the Central European varved lake Soppensee,Quaternary Science Reviews 27 (2008) 61–71

van den Bogaard, P., Schmincke, H.U., 1985. Laacher see Tephra—a widespread isochronous Late Quaternary tephra layer in central and Northern Europe. Geological Society of America Bulletin 96, 1554–1571.

Brauer, A., Endres, C., Negendank, J.F.W., 1999a. Lateglacial calendar year chronology based on annually laminated sediments from Lake Meerfelder Maar, Germany. Quaternary International 61, 17–25.

Friedrich, M., Kromer, B., Spurk, H., Hofmann, J., Kaiser, K.F., 1999; Paleo-environment and radiocarbon calibration as derived from Lateglacial/Early Holocene tree-ring chronologies. Quaternary International 61, 27–39.

 

[HallsofIvy]

I used to data a volcano- very exhausting!

 

[Andre]

Right, time flies like an arrow, fruit flies like bananas

 

[HallsofIvy]

And I thought I was being silly!

 

[Andre]

Well, I did not invent that, but it's hilarious how you can play with language.

Meanwhile I think I may have a useful (or not) -self made- solution for the problem. I intend to calculate yearly probabilities in a normal distribution for each of the individual dating results and then multiply those four probabilities for each year. I figure that a maximum will show up when all four distributions are optimum. or not?

 

[Andre]

See attached Excel sheet

So what I did,

Assuming that all four given distributions are normal and independent (not completely) and the error range is 95% or two sigma then the standard deviation should be half the error range.

so I calculated the normal distribution values for each year and muliplied them with a constant factor in column F to bring the cumulative summation value to 1 in column g.

Column J-K are tricks to locate the year with average value and the year with the 97.5% value to calculate the 95% confidence interval.

Result: 12,932 +/- 27.5 (stddev) years, giving a 95% confidence range 0f 12,987-12,877

Would this be reasonable?

Obviously I'm unhappy with the "14C" series which is interdependent with the "SS" (Soppensee) chronology not lining up with the other two high resolution series.

If you want to play with the input numbers, (B1 to E2) you'd also have to change the multiplication constant. Avoiding the circular calculation, you have to put the value 1 (one) in field H1, make the calculation and then transfer the value of H2 to H1 manually and calculate again.

 

[HallsofIvy]

Thank God someone has gotten back to the topic. My apologies. I just couldn't help myself!