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I'm looking for a cheap non-invasive ways to approximate the age of a tree (a birch). Measuring the radius pops up in the mind as the first alternative. How would one do that? Measure at multiple defined heights?

I'm hoping that I could get some kind of confidence interval for the approximation, so that the data could be used in a scientific publication.

Or is there any reliable DIY radiocarbon dating technique?

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    $\begingroup$ I'd take a look here: arborilogical.com/tree-articles/how-to-age-a-tree $\endgroup$ – CKM Feb 12 '15 at 23:21
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    $\begingroup$ It's going to depend very strongly on species. I have some cottonwoods which I know were planted in the mid-60s, and which are about 4 feet thick at the base. (Some of the annual growth rings are almost an inch wide.) OTOH, some of the mountain mahogany I have for firewood is much older, yet only around 6 inches thick. $\endgroup$ – jamesqf Feb 12 '15 at 23:27
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    $\begingroup$ Radiocarbon dating won't work. For a start the tree needs to be dead, which since you're not using the rings I'm assuming it isn't. Also the atomic testing in the 20th century completely messed up the level of C14 in the atmosphere, so radiocarbon dating can't be used for anything that didn't die 70 years ago or more. $\endgroup$ – Rob Mackinnon Feb 17 '15 at 16:43
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    $\begingroup$ @RobMackinnon But it looks like the C-14 from bombs has been utilized in other tests. And as far as OP's original question goes, C-14 dating would not be a cheap way to do it, and you couldn't do it yourself. The uncertainty in the measurements also means that C-14 is only good for approximate age, and may be off by around 100 years, which is a lot compared to the lifespan of most trees. Dating based on bomb carbon might actually be better for recent objects. $\endgroup$ – user137 Feb 22 '15 at 17:08
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The radius of tree is not a good measure of the tree age, the most efficient technique to know the age of a tree is with dendrochronological methods, this is the less invasive technique. However, knowing very well the dynamics of growth of each species you can infer the age, check out this study:

Jan Lukaszkiewicz and Marek Kosmala. 2008. Determining the Age of Streetside Trees with Diameter at Breast Height-based Multifactorial Model (note this is a direct link to a pdf)

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A tried and true method is to measure the diameter of the tree (which plays into your radius idea). Measurements are taken at "breast height" (~4.3ft, 1.3m from the ground). You can purchase a 'diameter tape' or 'girth tape' which consists of pre-calculated measurements, this way you will not have to measure circumference and derive diameter from this measurement. Breast height has been a consistent standard measurement over time, despite where a tree may begin to buttress, or flare out at the base. Below is an image detailing atypical tree measurements.

enter image description here

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    $\begingroup$ This does not deal with age correlations at all, and does not answer the question. $\endgroup$ – fileunderwater Feb 17 '15 at 19:16
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    $\begingroup$ Can you add references to your answer and change it in a way it actually answers the question? $\endgroup$ – Chris Feb 19 '15 at 6:54

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