Recently, Roger’s ClimateSci posted a blog entitled “Science Of Climate Change By Tim Curtin” which introduces a recent paper by Curtin .
The Curtin  paper discusses – amongst other topics – the potential impact of “anthropogenic water vapor” on climate. Anthropogenic water vapor refers to
“water vapour produced by the combustion of hydrocarbon fuels, both by direct creation of water vapour in the combustion process (18 GtH2O per year.), and by the much larger volume of steam created by the power generation process.”
The paper then goes on to claim that this additional water vapour has a signficicant impact in climate.
Now, as I am always on the lookout for unusual or new findings this paper caught my attention, also because in the past I had done some back-of-the-envelope calculations about how much water vapour (H2O) was released by combustion processes. Which is a lot, don’t get me wrong, but my further calculations back then suggested that the impact on the global climate was marginal. Since Curtin  comes to a different conclusion, I was puzzled how that could be. Given that Curtin  is a long paper with lots of information and calculations it took a little bit of time to figure things out, but in the end I think I understand what the culprit of the Curtin  calculation is and also where – as far as I am concerned right now – a mistake is made.
I mailed Roger my comments and he graciously offered to post it as a weblog and ask Tim Curtin for a response.
So, here we go: where do I think the Curtis  calculation goes astray.
The first question that comes up is how much the addition of anthropogenic H2O by combustion adds to the global amount of H2O. Here follows the calculation I did several years back:
– Curtin  mentiones 17.5 Gtons of anthropogenic H2O (= 1.75 10^16 g) for 2008-2009 (don’t know if that is for one of two years, but for the sake of argument let’s assume it is one year).
– Per unit area (area of Earth’s surface = 5.1 10^14 sq.metre) this becomes approximately 34 grams over one year
– The total amount of atmospheric H2O – global average – per unit area is about 25 mm, or 2.5 kg/sq.metre or 2500 g/sq.metre, which to good approximation is entirely located in the troposphere. Just for reference, one mm of rainfall equals on liter water per sq.metre.
– The residence time of tropospheric H2O is about 10 days, so the 2500 g/sq.metre is renewed every 10 days
– The contribution of anthropogenic H2O per 10 day per unit area then becomes ~ 1 gram (34 grams times 10 days / 365 days)
– The 1 gram is what should be compared to the 2500 g/sq.metre that is already present, which thus is a change in H2O by 0.04 %
Thus, the amount of anthropogenic H2O added with continiuous anthropogenic H2O emissions leads to a continuous change of H2O by 1 gram or ~ 0.04 % of the total amount of tropospheric H2O. That is the number to keep in mind, as explained next.
The Curtin paper goes on to refer to Pierrhumbert et al.  in the following calculation (halfway page 12 of Curtin ):
“But using the first Pierrehumbert et al. figure above, the radiative forcing (RF) from this addition to [H2O] is 50 per cent higher than that of increased atmospheric CO2. According to the IPCC [Forster and Ramaswamy 2007], the radiative forcing per GtCO2 is 0.0019 Watts/sq.metre, so that changes in [H2O] is 0.0028 W/sq.metre.”
This 50% is actually stated in Pierrehumbert et al.  as follows:
“…one finds that each doubling of water vapor reduces OLR by about 6 W/m2 (Pierrehumbert 1999). This is about 50% greater than the sensitivity of OLR to CO2.”
But what should be mentioned here as well is the sentence in Pierrehumbert  before the statement above:
“… The logarithmic effect of water vapor is somewhat more difficult to cleanly quantify than is the case for well mixed greenhouse gases like CO2, but if one adopts a base-case vertical distribution and changes water vapor by multiplying this specific humidity profile by an altitude independent factor, one finds that each doubling of water vapor reduces OLR by about 6W/m2 [Pierrehumbert 1999]. This is about 50% greater than the sensitivity of OLR to CO2.”
So this 50% is only valid for the case where the amount of humidity THROUGHOUT the troposphere is doubled. Pierrehumbert  wants to estimate how a doubling of CO2 compares to a doubling of H2O, but does not provide a value for similar changes in absolute amounts of H2O and CO2. This is important, because the amount of atmospheric H2O – typically a few % near the surface – is much larger than the absolute amount of CO2 – about 0.039 %. The radiative forcing of for example methane is much larger than that of CO2, but one should consider that the concentrations of methane are currently much smaller than that of CO2, and the residence time of CH4 is also much shorter. This already indicates that care should be taken when comparing the radiative forcings of atmosheric gases wich very much different concenrtations and residence times. And the absolute amounts of astmospheric CO2 and H2O also differ greatly.
For calculating the radiative effect of anthropogenic H2O using Pierrehumberts  number the relative change in total atmospheric H2O due to anthropogenic H2O should be used. The radiative forcing of anthropogenic H2O actually being 0.04% of the 6 W/sq.metre from Pierrehumbert , which really is close to negligible (0.0024 W/sq.metre). Even an order of magnitude more anthropogenic H2O still results in a very small radiative forcing.
Hence, where I think Curtis  makes a mistake is comparing the absolute change in anthropogenic H2O to the absolute change in anthropogenic CO2 for calculating its radiative effect, where instead the radiative effect of anthropogenic H2O should be calculated from the relative change in atmospheric H2O due to a change in anthropogenic H2O. The change in absolute amounts of anthropogenic H2O is quite similar to the change in absolute amount of (anthropogenic) CO2, but the change in the absolute amount of anthropogenic H2O is very small compared to the absolute amount of H2O. Hence, my much smaller estimate of its radiative effect.
Obviously such “back-of-the-envelope” calculations have limited use. The atmospheric H2O cycle is rather complex as Roger has pointed out on many occasions on this blog, and the radiative forcing of H2O is assumed to be mainly related to what happens in the upper troposphere – where H2O concentrations are orders of magnitudes smaller than at the surface. But then estimating the effect of anthropogenic H2O should include all the processes relevant to the hydrological cycle, which basically means full 3-D climate modelling.
For the moment I don’t see how such a relatively small increase in atmospheric water vapor could have such a large effect as claimed in Curtis , but feel free to comment.