Minute Earth and Phil Plait (Bad Astronomer) Get Clouds Wrong (NOW FIXED AT MINUTE EARTH!)

I like both Minute Earth and Phil Plait’s column at slate.com. They are both great ways to communicate science to the public. That’s why writing this post is upsetting to me.

At about 0:50 into the video, it says this about a rising bubble of air: “In fact, the more water vapor it collects before lift off the lighter it gets.”

Phil follows up with this paragraph:

There were two parts in that video that I want to emphasize. One was just why clouds are buoyant; it’s for the same reason a helium balloon is. At a given temperature, a volume of a gas will have the same number of atoms or molecules in it no matter what those atoms or molecules are. Helium atoms have way less mass than oxygen and nitrogen, so it weighs less, so up it goes. And it’s the same for humid air!

Although true, the video and Phil’s interpretation leaves the viewer with the impression that the cause of the rising bubble is the moisture inside. The problem is that the difference between the mass of moist air versus dry air occurs as explained, but that’s not the reason why the bubble moves up (is buoyant).

The bubble moves upward because it is more buoyant than the surroundings because of temperature differences, not because of moisture differences. This is easily determined by calculating what meteorologists call the virtual potential temperature, basically a measure of density of the air. You can change the water vapor content of the air quite a bit to get just a small change in density, but even a small change in air temperature will yield a much larger difference in density.

My point is that the changes in density due to moisture changes are small compared to changes in density due to temperature changes.

Perhaps the best way to explain is to show the differences in density explicitly.

I found this calculator online: http://www.gribble.org/cycling/air_density.html

The graphs that the gribble site show indicate that the air density changes more for changes in temperature than for dewpoint temperature (a measure of water vapor in the air). So, if I wanted to lower the density of air (increase its buoyancy relative to surrounding air), it would be better to increase its temperature than increase its moisture content.

We can enter some numbers so that you can see them in action. Use their default values of air temperature of 15°C and air pressure of 1018 hPa. Specifically, an increase in dewpoint temperature of 5°C (51% relative humidity) to 10°C (72% relative humidity) leads to a density drop from 1.2268 to 1.2251 kg/m3 (drop of 0.0017 kg/m3).

(Relative humidities calculated here: http://andrew.rsmas.miami.edu/bmcnoldy/Humidity.html)

With a dewpoint temperature of 10°C and pressure of 1018 hPa, an increase in temperature from 10°C to 15°C leads to a drop in density from 1.2468 kg/m3 to 1.225 kg/m3 (a drop of 0.0217 kg/m3, which is an order of magnitude greater than for the moisture increase).

So, the changes in temperature lead to much greater changes in air density than changes in moisture content. This is implicit in the virtual temperature equation (approximation) of
T_v = T + w/6, (http://en.wikipedia.org/wiki/Virtual_temperature)
where T_v is virtual temperature in degrees C, T is air temperature in degrees C, and w is the mixing ratio in g/kg.

Mixing ratios are commonly about 5–10 g/kg, with 20 g/kg being an extreme value (over the corn fields of Iowa during the summer when transpiration is high). So, even with an extreme value of mixing ratio, you’re only getting about 3°C of added buoyancy due to all of its moisture content, which is small compared to the 5–10°C changes in temperature yielding buoyancy differences routinely. Those changes in buoyancy (density) are simply not very sensitive to the amount of moisture in the atmosphere. It is much easier to change the buoyancy of air by heating it up than it is by evaporating more moisture into the air.

That’s why hot-air balloonists heat their air instead of adding moisture. They get more bang for the buck with temperature. The moisture content is much less important to changes in buoyancy. And, the temperature differences leading to differences in air density is the primary reason why warm air rises to form clouds.

Epilogue: I exchanged an email with Phil, but he did not correct his article. Minute Earth did not respond to my tweet. Neither have corrected their error.

Update (28 July): Minute Earth has responded via tweet.

Update (29 July): Minute Earth added an annotation to the video. Thank you, Minute Earth for engaging in this discussion and making the change!