Murry Salby is doing a tour of the UK that is being promoted both by Bishop Hill and by ScottishSceptic. One of the ideas promoted by Salby is that the rise in atmospheric CO2 is natural and not anthropogenic. As pointed out by Tom Curtis, there are 10 lines of evidence why this is wrong. There are also other things presented by Salby, that are easily shown to be wrong. I’ve mentioned them before, so won’t go into detail here. However, it is now my view that claiming to be a skeptic while also considering that Salby’s ideas have merit are inconsistent positions. It is not difficult to show that his ideas are wrong.
What Murry Salby is largely suggesting is that the rise in atmospheric CO2 is natural. The biggest sink of CO2 is the ocean. The amount of CO2 that the ocean can absorb depends on temperature and so, one possibility, is that the rise in atmospheric CO2 is driven by the oceans releasing CO2 as temperatures increase. This is governed by Henry’s Law, so in an attempt to be skeptical, I thought I would investigate what Henry’s law can tell us. I should make clear though, that a week ago I knew of the existence of Henry’s Law and roughly what it related to, but not much more. So, what I present in this post could be nonsense and I’m more than happy to be corrected by those who know more than me. I’m simply presenting an attempt to be skeptical (investigate) what Henry’s Law can tell us about the relationship between temperature and atmospheric CO2 concentration.
So, Henry’s Law relates the concentration of a gas in a liquid to the partial pressure of the gas in the air above the liquid. The basic form of Henry’s Law is
where c is the concentration in the liquid (in moles/litre), p is the partial pressure of the gas in the atmosphere, and kH is Henry’s constant (in litres atm/mole). Henry’s constant is kHo = 29.41 L atm/mol, but this is at a temperature of 298.15K. The dependence on temperature is
So, if the temperature is 288K, then kH = 22.15 L atm/mol. If we consider pre-industrial times, then p = 280 ppm = 280 x 10-6 atm. From Henry’s law then, c = 1.26 x 10-5 mol/L. If we know the volume of the ocean involved, then we can determine the total mass of CO2 in that region of the ocean, given that 1 mole of CO2 is 44g.
Okay, so the above tells us the concentration in the layer of the ocean that was exchanging CO2 with the atmosphere in pre-industrial times. There are two things I would like to know. How do atmospheric concentrations change with temperature, and what happens if we increase the total amount of CO2 through our use of fossil fuels? Doing this requires two more assumptions. One relates to what happens to the CO2 in solution. The CO2 reacts with water to produce HCO3 and CO32-. Only about 0.5% is in the form of CO2 itself. Therefore, what I’ve assumed is that the total mass of carbon in the region of the ocean that exchanges CO2 with the atmosphere is 200 times greater than the mass of the dissolved CO2 determined using Henry’s Law.
The next thing to determine is what volume of the ocean is involved in exchanging CO22. From the calculation above, in pre-industrial times, the mass of CO2 in a litre was 1.26 x 10-5 x 0.044 kg = 5.54 x 10-7 kg. This is only 1/200 of the total (because of the HCO3 and CO32-), so the total mass is 0.00011 kg. The mass per m3 is then 0.11 kg. From what I’ve read, the mass of carbon in the surface layers of the ocean is about 1000 GTC = 3700 GTCO2. So, to determine the thickness of the layer, I can determine the total volume and then divide by the surface area of the oceans
So, the layer of the ocean that exchanges CO2 with the atmosphere is about 100m deep (at least that’s what I estimate). So, now we can determine how the atmospheric CO2 concentration should change with temperature. We’ve already calculated the mass in the ocean layer. The mass of CO2 in the atmosphere can be determined using 1ppm = 7.81 GtCO2 = 7.81 x 1012 kg. We now have the total mass (that must be conserved) involved in this process. I can vary Henry’s constant using the second equation in this post. All I’ve done then is write a short computer code that, for a given new temperature, varies the atmospheric concentration until the total mass at the new temperature matches the total mass at the old temperature (if anyone would like a copy of the code I wrote, I’ll happily email it to them. It is in Fortan though:-)). Although I calculate that layer thickness to be about 100m, I’ve also repeated the calculation for layer thicknesses of 500m, 1000m, and 3800m (essentially the entire ocean). The results I get are in the figure below.
The result suggests that if a 100m layer of ocean is exchanging CO2 with the atmosphere, then a 1oC rise in temperature should increase atmospheric CO2 concentrations by about 6ppm. This was a little surprising as I had thought that it was more like 20ppm per degree. So, maybe I’ve made a mistake or some of my assumptions are just too simple. However, even if I assume that the entire ocean is exchanging CO2 with the atmosphere, I only get a rise of 10ppm for a one degree rise in temperature. So, even if I’m wrong by a factor of 4, the most extreme possible case comes nowhere near producing a 120 ppm rise for a one degree increase in temperature (as would be required if Salby’s ideas have merit).
The other thing I considered was what the atmospheric CO2 concentration would be if we assume a one degree rise since pre-industrial times (I know it’s slightly less, but this is just a test), an increase in the total carbon content due to our use of fossil fuels (240ppm x 7.81GTCO2 = 1.87 x 1015 kg), and an ocean depth of 100m. If I do this calculation, I get that the atmospheric CO2 concentration should be 372 ppm. So, not quite what we actually observe, but pretty close.
What do I conclude from this?
- Maybe I’m completely wrong and don’t know what I’m talking about. Always a possibility given that I only started working on this a few days ago and have no actual experience in this field
- If I’m not completely wrong, then one can use this to estimate how much the atmospheric CO2 concentration should rise with increasing temperature. There appears to be no way that the 120ppm increase that has occurred since the mid 1800s could be natural. My most extreme estimate is that natural processes could only have produced a maximum rise of around 10 ppm. This does seem a little low, though, but to get 120 ppm per degree would require something to be very different from what we expect.
- If we consider how our emission of CO2 since pre-industrial times would have influenced the atmospheric CO2 concentrations, what I’ve done here suggests that it should have increased it by close to 100ppm. I know this is slightly less than what is actually observed, but it’s pretty close and this is, very clearly, a very simple calculation.
So, why have I done this? Well, partly it’s just fun to try something new. I think I understand Henry’s Law better than I did before. Now that I do, I can’t see any way that the rise in atmospheric CO2 could be natural. I can, however, now show that it is largely consistent with being anthropogenic. I also think I can now talk from a slightly stronger position when I discuss Salby’s ideas with others. I’m not just taking someone elses’s word it, I’ve actually done some calculations of my own. Of course, I do acknowledge that there is a chance that I’ve made some kind of embarrassing blunder or that some of my assumptions are wrong. That, however, is what the comments are for.