Why Daniel Pangburn is Wrong

(c) 2024 by Barton Paul Levenson

Daniel Pangburn is a heat power engineer (boy, so many of these guys are engineers) who has been active as a global warming denier for many years. His constant refrain is that water vapor has increased much faster than carbon dioxide, therefore carbon dioxide is not responsible for global warming. He thinks increased irrigation is the culprit.

Of course this makes no sense at all, since global warming turned up sharply around 1975 and irrigation did not. In any case, more water vapor added to the atmosphere doesn't stay there. Water vapor is a volatile in Earth's atmosphere. The cycle of evaporation, precipitation, condensation (which we all learned about in our elementary school science classes) lasts 8.9 days on average (van der Ent and Tuinenburg 2017). Double water vapor tomorrow, and the excess will be almost all gone in less than a month. Humanity simply can't do very much to alter the level of water vapor in the atmosphere.

Except, that is, for altering the ambient temperature. The Clausius-Clapeyron law, discovered in the 19th century by Rudolf Clausius (of entropy fame) and Émile Clapeyron, states that the saturation vapor level of a volatile chemical is set by the ambient temperature. In mathematical terms, it reads:

Here p is the saturation vapor pressure, T is the absolute temperature, ∂s is the difference in specific entropy between the phases (here liquid and gas), ∂v is the difference in specific volume (reciprocal density) between the two phases, and L is the latent heat of conversion between the two phases. It is very difficult to solve this differential equation numerically, so physical chemists normally use approximations such as the August-Roche-Magnus equation:

where e_s is the saturation vapor pressure of water and T the temperature, not in kelvins as is usual in the physical sciences, but in Celsius (0°C is freezing, 100°C is boiling). 611.2 is a reference pressure in pascals (Pa). So you can tell the saturation vapor pressure if you know the temperature.

However, the ambient water vapor pressure is usually lower than the saturation vapor pressure. A simple equation for it is:

where RH is the relative humidity. Since on a global scale RH is relatively stable, it's relatively easy to predict the airborne water vapor burden for any given temperature.

Dan Pangburn isn't having it. He insists water vapor has been growing much faster than predicted by the Clausius-Clapeyron relation. (How that would work physically, he doesn't explain.) He's enamored of the "facts" that water vapor has been increasing five times faster than carbon dioxide, and that it is, by his reckoning, 34% higher than it should be.

Let's just examine that.

Mr. Pangburn very kindly directed me to a NASA web site which lists satellite-derived TPW:

NASA TPW time series

TPW stands for Total Precipitable Water, a measure of how high the liquid water on the ground would be if the whole atmospheric column above a unit area were suddenly liquefied and fell on the ground. Figures are listed monthly. I took the liberty of taking annual averages, and here they are for all the full years available, which happen to be 1988 through 2023:

The site actually lists TPW anomalies, which are the level above a standard average for that month. I derived absolute figures by adding 24.9 to each anomaly. If anyone can find the actual figures NASA used and wants to correct the list, please go ahead, but it should make very little difference. The last column are the NASA GISTEMP temperature anomalies for the years listed. We have a total of N = 36 data points, enough for a statistically significant sample.

Let's examine the data. From 1988 to 2023, TPW increased by 7.6%, or about 0.2% per year. If we use the August-Roche-Magnus formula, adding 14.0 to the temperature anomalies to find T in degrees Celsius, we find that saturation vapor pressure increaesd from 1,636 Pa to 1,720, an increase of only 5.1%, or 0.14% per year. The water vapor is a whopping 49% higher than it should be! Oh, my ears and whiskers!

Or that would be the case if we made the greenhorn mistake of dividing the last year figure by the first year figure to find the rate of increase. What we should do is a linear regression against time to find the average rate of increase. The regression line is TPW = -58.528 + 0.041739 Year (r² 0.73, SEE 0.272, p < 3.5 x 10^-11). The predicted increase using the figures on the regression line is 6.0%, or 0.16% per year.

There are some problems with the TPW series NASA lists. It's from satellite data which only covers latitudes 60° North to 60° South, or 86.6% of the globe. Not much different from full coverage? Ah, but there's a catch. Water vapor is greatest at the tropics and lowest at the poles, so this series leaves out the driest 13.3% of the Earth's surface.

If we recompute TPW using an estimate of 0 for latitudes 60+° to 90° (not far from the truth), the increase becomes 6.6% (annual rate 0.18%). The coefficient on the year term is 0.03775, with a 95% confidence interval of 0.02847 to 0.04382. So the observed rate of increase is anywhere from 5.0 to 8.2% (0.14-0.22% per year). The error bars overlap the observed increase. Thus we can't say that the observed increase of 7.6% is statistically different from the predicted rate of 6.6%. And Mr. Pangburn's conclusion that water vapor is increasing faster than it should be is wrong.

Reference:

van der Ent, R.J., Tuinenburg, O.A. 2017. The residence time of water in the atmosphere revisited. Hydrol. Earth Syst. Sci. 21, 779-790.