Saturday, December 29, 2018

Eli Explains It All: Or Why Just About Everybunny Gets Energy Thermal Energy Transfer Between the Surface and the Atmosphere Wrong

Everybunny who has been hanging about the Climateball Court for the Christmas Dinner Playoffs has heard the bit about how heat transfer from the surface to the atmosphere by radiation is small compared to that by convection.

Eli posted an elegant explanation of why that was, well to be nice, complete bollocks, but thinking about it again the Bunny has come up with a simple one that you could explain even to your obstreperous uncle next big family dinner.  Well.....maybe.

Perhaps we start with the usual figure

and the usual argument, that the heat flow into the atmosphere by evaporation and sensible heat is 104 W/m2 is massive while radiation only accounts for 398 - 342 W/m2 which is a minuscule 56 W/m2.  Limited sarcasm about minuscule.

There is a major problem with this.

It assumes that there is a difference between thermal energy that has entered the atmosphere from evaporation and sensible heat and thermal energy that entered the atmosphere by radiation.  


Let Eli reduce this to jelly beans.

If three bunnies put black jelly beans into a well shaken jar can anybunny tell Eli which one donated the black jelly bean he took out and is munching on?


David B. Benson said...

But I don't like jelly beans.

EliRabett said...

Chocolate covered raisins?

Pieter Zijlstra said...

Thanks Eli. A nice one!

Now anybody can notice that the atmosphere is in between anything.

It is the atmosphere! Of course!

Jan Galkowski said...

It's difficult to understand why Heat has no hair is so difficult to understand. But, well, it did receive 65 comments, including some Apparent Believers in the fundamental logical inconsistency of Physics. And I, poor me, thought that the Ultraviolet Catastrophe I learned in frosh college Physics was relegated to the dustbin long ago ....

Nevermind that we build things which actually work based upon these same assumptions and wouldn't if they were wrong. A reader might be holding one of these right now, in fact.

All the best for your continued explanations and wish you happiness, health, and continued good spirits. Your writing is a joy.

Snape said...

In the post "Heat has no hair" you wrote, "The total amount of thermal energy leaving the surface is ~502 W/m2 with 398 of them coming from radiation and 104 from a combination of evaporation and sensible heat."

I think that's misleading. The 398 w/m2 is one-way.. I assume we don't know the actual value for evaporation or the one-way conduction/convection value, but together they would be much greater than 104 w/m2.

Hence the total thermal energy leaving the surface would be a lot more than 502 w/m2.

EliRabett said...

Snape, nope. The TOTAL leaving the surface is on average 502 W/m2. The point about this post and that is you can't tell the source of the thermal energy in the atmosphere once it gets up there. It's all black jelly beans, and that means you can't tell the source of the back radiation or the radiation to space other than proportionally allocating it.


The decline of the Oval Office dates to the removal of the Presidental Jelly Bean Jar.

Eli is on the same page as President Reagan, who so favored the liquorice beans in the herman Goelitz mix that the White house ran through 720 bags a month.

The blueberry ones were great too.

Snape said...

I like the jelly bean analogy, but ended up reading the earlier comment as well.
Consider, for example, when warm air moves up from the Gulf of Mexico into the Midwest, where the ground might still be frozen. The air is a heat source for the colder surface via conduction/convection. The same sort of thing is happening at different locations and times all over the planet.

The opposite is of course happening as well, and to a greater extent - where a warmer surface heats the atmosphere above by conduction/convection.

From what I can tell the energy budget chart only gives the net result of those two fluxes. Sort of like if it had only shown a radiative flux of 56 w/m2 and left out the two much larger contributing factors (398 - 342).

Jan Galkowski said...


Unless and until there's a physical argument why effects depend upon the maximum instantaneous excursion from the net result of those two fluxes, there's no point to the (your?) observation. The amount of excursion in any subsystem also depends upon the time window over which accounting is done, so the instantaneous excursion could be, and most likely to be, much smaller than the one observed over an entire year, say. That's because it's just improbable that a year's excursion would be allocated to a short time window, with the rest of the year seeing essentially nothing.

Yes, there are a lot of dynamics all over the planet. But the deep insight of modern Physics, which began, incidentally, in the late 18th century with people like Lagrange and, later, with Hamilton, in the 19th century, is that the net energy considerations are independent of the paths the system takes. This is a very powerful idea. Yeah, and, sure, there are plenty of non-conservative forces at work, but these don't help, they just produce additional heat energy, worsening matters in the direction of global warming, not lessening them.

Being able to account for things in the manny of jelly beans is a lot of what Physics in modernity is about. No, you can't follow the trajectory of any one CO2 molecule or of one photon. But that doesn't render one helpless. You follow and observe the quantities you can, and these give explanatory and predictive power.

In this world, time-averaged quantities have a lot of capability for explanation. This may not be true of baseball scores, even if those have their own sense and means of explanation. And it doesn't mean there aren't mysteries to be pursued, such as what exactly happens and how in boundary layers like that of the ocean and atmosphere, and to what degree oceanic eddies and turbulence and atmospheric storms contribute to energy and gaseous exchanges. These are research topics.

But these are also a far cry from the composite pictures which you seem to be challenging here. Why? What moves you? If you are interested, which I suspect you are, why not probe into the mechanisms deeper? Why not learn the maths and physics?

It's fascinating stuff. I'll never learn it all in my entire life, and, yet, that never discourages me from trying.

Snape said...

Trenberth's diagram uses the term "thermals" instead of sensible heat, which is easier for me to understand:

It shows thermals heating the atmosphere at a rate of 17 w/m2. I then imagined the atmosphere with no greenhouse would it cool itself if it were always being heated by conduction/convection but unable to effectively radiate to space?

Well, at night, the surface would cool radiatively (very quickly) and become much colder than the air above. The air above would then cool itself by heating the colder surface below. In that way a steady global average would be runaway warming. Conduction downwards on one part of the planet, conduction upwards on the other.

It occurred to me that the same sort of thing might be happening in the real world. Conduction up in some places, down in others, with the net result being 17 w/m2 up.

If I'm right, then a more detailed version of Trenberth's diagram might show something like this:

Thermals down: 43 w/m2
Thermals up: 60 w/m2

And we would need to calculate the net (17 w/m2 upwards) just like we do with the radiative fluxes in his diagram.

CapitalistImperialistPig said...

Are the jelly beans on the blue plate or the green plate?

I think that there are a few subtleties worth mentioning even though they don't invalidate your core argument:

If the atmosphere lacked radiative opacity, there wouldn't be a temperature gradient in the atmosphere and convection wouldn't happen. Also, while radiative transfer in the relevant bands is well described in the diffusion approximation, that is less clear for convection.

Jan Galkowski said...


It's hard to know what you are blathering about without diagrams... It spunds like you are imposing choices between two dichotomies, opacity for one, and "radiative diffusion' vs gaseous convection for the other. As both are misleading, leaving out adiabatic cooling for example -- which I can only imagine is your purpose -- they should be disregarded by readers. The are atmospheres, not an atmosphere, that is, there are atmospheric layers, and each exchanges within and betwen. Since radiation is severely range limited, convection is present, but only where atmosphere is sufficiently enhanced with water vapor. That"s hard in regions where it freezes out. Why? Because adiabatic cooling drives temperature below zero Celsius. By the time atmosphere gets thin enough for radiation to become a factor it"s cold. This structure persists whether greenhouse gases are present greater or not, up to obviously a point. The effect of such additional GHGs is to raise the height of the radiative Blackbody balance point. That means, working backwards down the atmosphere, that the temperature at surface must be higher, so warming. What's opacity got to do with it?

Jan Galkowski said...

On the atmospheric layers things, yes, that a conceptual approximation ... In fact, adiabatic temperature, if you will, is a continuous function of average pressure ("geopotential pressure"?) which is a function of geopotential altitude, although there are hiccups at places like zero Celsius.

And, yes, there are things which can drive convection without water vapor involved, but latent heat in water is the Big Deal. Convection can be driven by, for example, differences in geopotential pressure (again, assuming that's really a word) on the same isotherm. This is lateral convection.

Also I left out saying the balance at top of atmosphere is because during day there is incoming radiation as well as outgoing. That's "diffused" too.

And, by the way, Eli weighed in on adiabatic lapse rate a long time ago, close to when I still had hair.

Snape said...

If you hold your hand an inch above a candle you'll need to quickly move it away. Hold your hand an inch to the side - no problem. That demonstrates convection. Hot air rises.

I assume the experiment would work even if the atmosphere lacked water vapor or Co2.

Snape said...

With that in mind, I should change my earlier, "thermals down" to thermals

A cold day in Kansas and then a southerly wind warms things up.

Snape said...

As always, I'm learning as I go: mechanical convection:

"At night, eddies generated by the wind transport relatively cold air upward from the ground and warmer air downward from higher up. In effect, eddies mix the lowest layers of the atmosphere."

CapitalistImperialistPig said...

@Jan G - Without atmospheric opacity - absorption - IR radiation from the ground would pass directly out into space.

CapitalistImperialistPig said...

This is a quibble of sorts, but latent heat is actually rather hairy, as it doesn't release its heat into the atmosphere until it condenses. Similar considerations mean that convection also carries some hair until it mixes thoroughly with the surrounding atmosphere. Radiation also carries its own hair because of the frequency dependence of absorption.

Jan Galkowski said...


Time averaging fixes those things. There are enough broad bands in atmosphere from molecules which love to be energized by heat that radiation's hair isn't a problem: It's automatically well-manicured.

This argument doesn't fix deep ocean heat imbalances which are rather long-lived, too bad for us. Indeed, to me, the ocean store and the atmospheric concentration of CO2, and naturally, the meaningful things which add to or subtract from the latter, are, to me, the Big Factors which predict climate. There are things which are less important, something which Luckwarmers and people like Curry seem to forget.

Oh, and to be fair, the same can be said of some progressive environmentalists who seek, now, to fix income inequality and social injustice while fixing climate. Of course, that's just my opinion ....

CapitalistImperialistPig said...

@Snape - convection depends on temperature difference. Candles with produce a convective plume unless atmospheric temperature is greater than the flame. In the absence of radiation, convection would increase the atmospheric temperature without limit - fortunately that can't happen because radiation does happen.

Snape said...

I was considering an atmosphere without radiative gasses (just Nitrogen and Oxygen). The surface would get really hot in the sun, really cold at night. The air above would simply follow along. Apparently, though, if the poles were cold enough, the atmosphere above would lose its buoyancy and settle to the ground as a puddle of liquid n2/o2. All conjecture, of course.

As an aside, I've been learning about climate science as a hobby and one of the first questions I had was, "what keeps the atmosphere from falling to the ground?" Surprisingly complicated! I still only half understand it.
Regarding the candle, the hot air rises not just because of the temperature difference, but also of course due to gravity (less dense). That's why the convection is upwards instead of sideways.

Jan Galkowski said...


I highly recommend:

(a) Principles of Planetary Climate as a teaching text, with exercises.
(b) If curious, The Warming Papers to see the history of climate science and global warming.
(c) With "(b)", the American Institute of Physics (AIP) has an excellent set of pages.
(d) The American Chemical Society has a bunch of references and good links (e.g., to AAAS) on climate change, the science, and how how long U.S. government has officially known:

Snape said...

Thanks for the links.

CapitalistImperialistPig said...

@Jan G - Yep. That's why I called it a quibble, not a critique.

@Snape - I heartily recommend the Princeton Climate Primers:

I have read most of them and they are quite good semi-technical accounts of most aspects of climate, and easier reading than Pierrehumbert's excellent textbook recommended by Jan G.