Water Vapor Feedback

Guest Post by Willis Eschenbach

Well, another productive ramble through the CERES dataset, which never ceases to surprise me. This time my eye was caught by a press release about a new (paywalled) study by Gordon et al. regarding the effect of water vapor on the climate:

From 2002 to 2009, an infrared sounder aboard NASA’s Aqua satellite measured the atmospheric concentration of water vapor. Combined with a radiative transfer model, Gordon et al. used these observations to determine the strength of the water vapor feedback. According to their calculations, atmospheric water vapor amplifies warming by 2.2 plus or minus 0.4 watts per square meter per degree Celsius. (See Notes for sources)

Hmmm, sez I, plus or minus 0.4 W/m2? I didn’t know if that was big or small, so I figured I’d take a look at what the CERES data said about water vapor. As the inimitable Ramanathan pointed out, the distribution of water vapor in the atmosphere is shown by the variations in the clear-sky atmospheric absorption of upwelling longwave.

Figure 1. Distribution of Atmospheric Water Vapor, as shown by absorption of upwelling surface longwave (LW) radiation, in watts per square metre (W/m2). In areas of increased water vapor, a larger amount of the upwelling radiation is absorbed in clear-sky conditions. Absorption is calculated as the upwelling surface longwave radiation minus the upwelling top-of-atmosphere (TOA) longwave radiation. The difference between the two is what is absorbed. Contours are at 10 W/m2 intervals.

As Ramanathan saw, there’s only one greenhouse gas (GHG) that shows that kind of spatial variability of absorption, and that’s water vapor. The rest of the GHGs are too well mixed and change too slowly to be responsible for the variation we see in atmospheric absorption of upwelling surface radiation.. OK, sez I, I can use that information to figure out the change in clear-sky absorption per degree of change in temperature. However, I wanted an answer in watts per square metre … and that brings up a curious problem. Figure 2 shows my first (unsuccessful) cut at an answer. I simply calculated the change in absorption (in W/m2) that results from a one-degree change in temperature.

Figure 2. Pattern of changes in clear-sky atmospheric absorption, per 1°C increase in temperature. This is the pattern after the removal of the monthly seasonal variations.

The problem with Figure 2 is that if there is a 1°C increase in temperature, we expect there to be an increase in watts absorbed even if there is absolutely no change in the absorption due to water vapor. In other words, at 1°C higher temperature we should get more absorption (in W/m2) even if water vapor is fixed, simply because at a higher temperature, more longwave is radiated upward by the surface. As a result, more upwelling longwave will be radiated will be absorbed. So I realized that Figure 2 was simply misleading me, because it includes both water vapor AND direct temperature effects.

But how much more radiation should we get from a surface temperature change of 1°C? I first considered using theoretical blackbody calculations. After some reflection, I realized that I didn’t have to use a theoretical answer, I could use the data. To do that, instead of average W/m2 of absorption, I calculated the average percentage of absorption for each gridcell, as shown in Figure 3.

Figure 3. As in Figure 1, showing the distribution of water vapor, but this time shown as the percentage of upwelling surface longwave radiation which is absorbed in clear-sky conditions. Contours are at intervals of 2%, highest contour is 40%. Contours omitted over the land for clarity.

This is an interesting plot in and of itself, because it shows the variations in the efficiency of the clear-sky atmospheric greenhouse effect in percent. It is similar to Figure 1, but not identical. Note that the clear-sky greenhouse effect in the tropics is 30-40%, while at the poles it is much smaller. Note also how Antarctica is very dry. You can also see the Gobi desert in China and the Atacama desert in Peru. Finally, remember this does not include the manifold effects of clouds, as it is measuring only the clear-sky greenhouse effect.

Back to the question of water vapor feedback, using percentages removes the direct radiative effect of the increase in temperature. So with that out of the way, I looked at the relationship between the percentage of absorption of upwelling LW, and the temperature. Figure 4 shows the average temperature and the average absorption of upwelling LW (%):

Figure 4. Scatterplot of 1°x1° gridcell average atmospheric absorption and average temperature. The green data points are land gridcells, and the blue points show ocean gridcells. N (number of observations) = 64,800.

As you can see, the relationship between surface temperature and percentage of absorption is surprisingly linear. It is also the same over the land and the ocean, which is not true of all variables. The slope of the trend line (gold dashed line in Figure 4) is the change in percentage of absorption per degree of change in temperature. The graph shows a ~ 0.4% increase in absorption per °C of warming.

Finally, to convert this percentage change in absorption to a global average water vapor feedback in watts per square metre per °C, we simply need to multiply the average upwelling longwave (~ 399 W/m2) times 0.443%, which is the change in percentage per degree C. This gives us a value for the change in absorption of 1.8 ± .001 W/m2 per degree C.

Finally, recall what the authors said above, that “atmospheric water vapor amplifies warming by 2.2 plus or minus 0.4 watts per square meter per degree Celsius.” That means that the CERES data does not disagree with the conclusions of the authors above. However, it is quite a bit smaller—the Gordon et al. value is about 20% larger than the CERES value.

Which one seems more solid? I’d say the CERES data, for a couple of reasons. First, because the trend is so linear and is stable over such a wide range. Second, because the uncertainty in the trend is so small. That indicates to me that it is a real phenomenon with the indicated strength, a 1.8 W/m2 increase in absorbed TOA radiation.

Finally, according to Gordon et al. there is both a short-term and a long-term effect. They say

By forcing a radiative transfer model with the observed distribution of water vapor, we can understand the effect that the water vapor has on the TOA irradiance. Combining information on how global mean surface temperature affects the total atmospheric moisture content, we provide an estimate of the feedback that water vapor exerts in our climate system. Using our technique, we calculate a short-term water vapor feedback of 2.2 W m–2 K–1. The errors associated with this calculation, associated primarily with the shortness of our observational time series, suggest that the long-term water vapor feedback lies between 1.9 and 2.8 W m-2 K–1.

So … which one is being measured in this type of analysis? I would argue that the gridcells in each case represent the steady-state, after all readjustments and including all long-term effects. As a result, I think that we are measuring the long-term water-vapor feedback.

That’s the latest news from CERES, the gift that keeps on giving.

Best to all,

w.

NOTES:

Ut Solet

If you disagree with something I (or anyone) says, please quote my words exactly. I can defend my own words, or admit their errors, and I’m happy to do so as needed. I can’t defend your (mis)understanding of my words. If you quote what I said, we can all be clear just what it is that you think is incorrect.

Data and Paper

Press Release here.

Paywalled paper: An observationally based constraint on the water-vapor feedback, Gordon et al., JGR Atmospheres

R Code: CERES Water Vapor (zipped folder 750 mb)

CERES Data: CERES TOA (220 Mb) and CERES Surface (115 Mb)

[UPDATE]

An alert reader noted that I had simplified the actual solution, saying:

Since one of the feedbacks is T^4 it would probably come out as T^3 in a percentage plot and this curve has strong upwards curvature.

To which I replied:

Not really, although you are correct that expressing it as a percentage removes most of the dependence on temperature, but not quite all of the dependence on temperature. As a result, as you point out the derivative would not be a straight line. Here’s the math. The absorption as a percentage, as noted above, is

(S- TOA)/S

with S being upwelling surface LW and TOA upwelling LW.

This simplifies to

1 – TOA/S

But as you point out, S, the surface upwelling LW, is related to temperature by the Stefan-Boltzmann equation, viz

S = sigma T⁴

where S is surface upwelling LW, sigma is the Stefan Boltzmann constant, and T is temperature. (As is usual in such calculations I’ve assumed the surface LW emissivity is 1. It makes no significant difference to the results.)

In addition, the TOA upwelling longwave varies linearly with T. This was a surprise to me. One of the interesting parts of the CERES dataset investigation is seeing who varies linearly with temperature, and who varies linearly with W/m2. In this case TOA can be well expressed (to a first order) as a linear function of T of the form mT+b.

This means that (again to a first order) I am taking the derivative of

1 – (m T + b) / (sigma T⁴)

which solves to

(4 b + 3 m T)/(sigma T⁵)

Over the range of interest, this graphs out as

Recall that my straight-line estimate was 0.44% per degree, the average of the values shown above. In fact, the more nuanced analysis the commenter suggested shows that it varies between about 0.38% and 0.5% per degree.