h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I have been looking at some data for isotopes ratios, which is shown in parts per million. However several times the isotopes are described as being -5 ppm. How exactly does that work, does it mean 1 part per 5 million? Or is it a exaggerated way of saying there is nothing there?

How is the data measured? The measurement technique may produce negative numbers. What are the error bars on the measurement?

For example, if I were making a spectroscopic measurement, there is inevitably a background subtraction required - i.e. you need to take into account any background radiation/results and remove that. Sometimes though there is a dip in your measured result (due to noise), and when you subtract what you think is the background, you end up with a negative result.

You can identify the above by looking at the error bars (or scatter) in the data. If it is just a negative blip due to noise, your above result would be something like -5 ppm with error bars of 5 or 10 ppm (so that the result of "0" is within the error bar).

It is the ratio of C12 and C13 in carbonat rocks. I just have some graphs, without any error bars. The way they talk about it, the negative values seem to be expected.

As I understand it, the standard amount of C13 in CO2 that enters ocean water is -5 to -7 ppm. So already there it shows up.

I've just had a quick look round t'interweb and it seems that sometimes what is listed isn't the C13/C12 ratio directly but the difference between the C13/C12 ratio in a sample of whatever (eg Ocean Water, plants, rocks, etc) and a standard C13/C12 ratio. This would easily lead to a negative or positive ratio if the measured sample ratio is different to the standard ratio.

I thought so at first, but I got the impression the standard rate was already those -5 to -7.

Yes this is puzzling.

I've found a site with a graph of Atmospheric Carbon Dioxide - C13 isotope concentration and the figure is shown ranging from about -7 ppm to about -9, with the -7 at the top as you would expect for a negative number. And this is the note that comes with the graph:

Id 249
Description Atmospheric Carbon Dioxide - C13 isotope concentration
Group Weather
Unit of Measure per mil
Allowed Range -20 to 20

So it can be positive or negative.

'...the isotopes are described as being -5 ppm. How exactly does that work, does it mean 1 part per 5 million?

No, this means that there are 5 atoms of a specific isotope per miilion total atoms. (I guess the hyphen shouldn't be there )

No, the hyphen is quite clearly a minus sign.

The C13 ratio should be expressed "per mil" Its talking about the deviation from some standard C12/C13 ratio.

Probably I am grossly oversimplifying, possibly even wrong, but anyway:

Plants take CO2 into their leaves via their stomata. They then go on to photosynthesize, and produce sugars from the CO2.
C13 atoms are bigger than C12 atoms, so C13O2 molecules are a bit bulkier than C12O2 molecules...
This means the plant uptake of C13 containing CO2 is slower than the uptake of C12 containing CO2.
Because there are lots of plants, the effect adds up - more plants means total atmospheric CO2 C12/C13 ratio gets smaller - conc of C13 stays roughly the same, but conc C12 goes down.

Now, go look at the annual CO2 levels graph - they vary annually as all the plants are photosynthesising crazily away in the summer/spring, and dying in the autumn/winter (the effects of northernhemisphere/southern hemisphere summer/winter do not cancel out, due to southern hemisphere being mainy just loads of water - if you want plants, look to the north (hey I did say I was oversimplifying slightly)).

So in the summer, the atmospheric CO2 C12/C13 ration is smaller than the in the winter. Now, because its changing all the time, they don't compare the atmospheric CO2 12/13 ratios to one another, but instead to some carbon they found in an ancient fossil. The ratio R of C12/C13 in this lump of rock is always Rstd = 0.011238.

Now we look at ratio in atmospheric CO2, which we call Ratm.

Then we express the changing ratio in terms of the standard with the following:

change in ratio = (Ratm / Rstd - 1 ) * 1000 per mil.

This number is expected to be negative, due to the smaller Ratm, which is in turn due to the pesky plants mentioned above, who are too lazy to take up all the heavier C13 atoms.

So if it says the concentration of C13 in atmospheric CO2 is -7 per mil that gives us the following:

-7 / 1000 = - 0.007
-0.007+1 = 0.993
0.993* Rstd = 0.993 * 0.011238 = 0.011159334

This then is the C12/C13 ratio in atmospheric CO2.

If the total concentration of CO2 is 400ppm, then the total C13CO2 concentration is 4.4637336 ppm.

Does that make sense?

vp

I actually found out why it was - numbers, just didn´t have time to get back on here. Essentially it was due to the found amount having the standard amount subtracted from it. Also per mil it turns out means per thousand, not per million. Kind of confusing.

Thats what I said. Kind of. Its a x/(x+dx) - 1 type thing rather than a straight forward subtraction though, so be careful in interpreting your data.

Per mill Test: ‰

Yay, it works