Understanding the Earth’s Energy Budget
Readers who follow climate science are probably aware of how sunlight initiates a complicated chain of thermal events. A well-known depiction of this is the old 1997 chart (above), which we’ll use here for the sake of visual clarity.
But let’s touch on some other considerations beforehand.
In all such depictions of the energy budget, the Earth is regarded as a theoretical “blackbody” whose temperature exactly corresponds to the light it absorbs. 390 watts per square meter (W/m²) of radiance, for instance, will stimulate a blackbody to reach 15° Celsius. This is not true for real bodies but does make it easy to calculate energy budget temperatures¹.
One more thing. Since the Earth is spherical, it has four times the surface area of a flat plate of the same diameter, so it is thought to be able to absorb only 25{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117} of the light it’s exposed to. To simplify budget presentations, then, its spherical surface is displayed as a flat plate and sunlight’s average intensity on this plate is cut down to 25{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117}. The actual sunlight reaching our vicinity has an intensity of about 1368 W/m². Now we can proceed.
Here I’ve superimposed the Celsius temperatures that are tied to several radiant fluxes, something you’ll never see in other energy budgets. These provide clues to the interactions.
As sunlight’s 342 travels down to the Earth, some of it is reflected by clouds and by the Earth’s surface itself. That’s a radiant loss for the surface. Another portion is intercepted by certain gases and tiny particles in the air, which this chart depicts.
The orange line is an index of the amount of solar radiation reaching the Earth’s surface. The closer it is to the blue line, the more surface irradiation occurs. By the same token, dips along this line represent surface losses; gases like H₂O and CO₂ and are responsible for much of that loss.
So the Earth’s averaged surface receives what remains of 342, i.e., 168 W/m², enough to raise its temperature to minus 40 degrees. That’s what it gains. This is countered by a loss, however, because a total of 102 W/m² (24 plus 78) are removed from the surface by nonradiative mechanisms.
Arithmetically, this leaves the surface’s energy with a piddling 66 watts per square meter and a consequent temperature of minus 88 degrees.
Minus 88 degrees on the Earth’s average surface? Yes. Watch how budgets work. If the surface is left with 66 W/m² after non-radiative losses, ask yourself what it needs in order to emit 390 W/m² – that is, what a blackbody would emit at 15°, which is regarded as the Earth’s average temperature. The answer is simple: It needs 324 W/m² more. And that’s exactly how it plays out in these budgets.
The result of this arithmetic is no happy coincidence. Indeed, it allows climate scientists to claim that the radiant tally is “balanced.”
To prove this point, let’s look at a detail of a more updated budget. But I must first call your attention to a modern feature: “Net absorbed.”
The idea here is that the oceans are overheating year by year but aren’t showing it yet in terms of temperature or radiation, so this extra 0.9 is sort of being tucked away for now. Okay, here it is.
Do you see? All the fluxes are different here but the same arithmetical trick of the trade is used. That 396 result means 16° this time. That isn’t the most important detail to observe however. No, the take-home lesson is how this numerical method controls the outcome.
Because look at the downwelling radiation from greenhouse gases. The temperature of the atmosphere must be at 2° in order to emit 324 W/m² to the surface. Hold that thought.
Recall that energy budgets are all about averages.
• Averaged sunlight all over the globe and throughout the year.
• Averaged reflections from clouds.
• Averaged absorption by the atmosphere.
• Averaged absorption by the surface.
• Averages fix all of these factors as a constant.
To review, the original 342 of sunlight becomes 235 by reflection, and then 168 due to atmospheric interception, leaving a constant 168 for the surface, which responds in kind, reaching a temperature of minus 40° and constantly radiating 168 W/m² itself.
How then shall we evaluate the 324 W/m² that’s constantly beaming down from greenhouse gases?
In this odd case the surface responds by emitting more than 324. The previous example demonstrated radiative equality: 168 stimulus, 168 response. Why not the same for back radiation, therefore?
What’s more, how can a 2° body warm a minus 88° body to 15 degrees?
Well, frankly it can’t. But as you’ve already seen, there’s a method to this madness. Climate scientists need to add 324 to 66 in order to get 390 (or whatever the goal demands), and so they do. Omitting the temperatures involved , of course, helps the trick immensely.
But still, if you believe that continuous radiation from a 2° body can heat a minus 88° body to 15 degrees, then bless your trusting heart. Maybe you should also try barbecuing your burgers on ice cubes.
Alan Siddons
Notes
¹ The blackbody formula states that (W/m² ÷ 0.0000000567)0.25 = temperature in Kelvin
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tom0mason
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“In all such depictions of the energy budget, the Earth is regarded as a theoretical “blackbody” whose temperature exactly corresponds to the light it absorbs. 390 watts per square meter (W/m²) of radiance, for instance, will stimulate a blackbody to reach 15° Celsius. This is not true for real bodies but does make it easy to calculate energy budget temperatures¹.“
Too right!
If there were no life on earth such over-simplistic modeled idea may have a little merit.
However THIS planet has life! All of nature, and the expanding human population and all it needs to keep going — does all of that take no energy? Does that life not sequester solar energy into chemical bonds? Chemical bonds that may not be released for minutes, or hours, or centuries?
Can these ‘scientists’ not consider that as the sun’s energy is transferred to chemical bonds in all these lifeforms, and these structures built from simple chemistry, are NOT given-up to be re-radiated off the planet! Also it took energy (and arguably all of this energy was ultimately solar energy) to build the pyramids, and all towns and cities — old and new, when will all that re-radiate off the planet?
From the continual detritus that is building up on the ocean floors, to the formation of peat and coal today, solar energy does not all radiate away. The fossilized structures (even fossilized bacteria!) in rocks are evidence of sunlight changed into chemical bonds unreleased. Not re-radiated to space, and this process continues even now, every second of every day. The evidence is in the dirt under your feet!
This planet accumulates solar energy, not quickly — slowly but for a very long time, and it is stored in the chemical bonds in the structures that life builds.
That ‘energy balance’ model is gross BS.
Ultimately the balance will be, but ultimately is a very long time away, and nobody will be there to see it. For now nature’s life-force is winning the battle against entropy, life however has no care for entropy right now, it neither knows nor cares that ultimately entropy will win the war.
Solar energy to chemical bonds, overlooked by many so called scientists.
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Alan Siddons
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Here’s a related point, Tom0mason. A lot of people might suppose that a reflective object absorbs very little light and so it can’t get very hot by radiative heat transfer. But anybody who’s ever picked up a chrome wrench that’s been lying in the Sun knows different! To be sure, shiny metals absorb very little light. The thing is, though, their ability to radiate the little heat they do absorb is even more restricted. As a result, shiny metals reach a very high temperature under irradiation, far higher than the ultra-absorptive blackbody. This has to do with the absorptivity/emissivity ratios of real objects and substances. A theoretical blackbody is the only thing in the universe whose a/e ratio is exactly 1:1, which actually makes it the poorest model to use. So you’re correct: The radiation budget itself is based on a false premise.
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tom0mason
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Thank-you Alan Siddons,
yes that chrome wrench is a good example of how to undo simplistic thinking.
Rereading the piece again reminded me how truly dumb that model is. It’s static, a snapshot that somehow represents this spinning world, it’s seasonality, night and day and all it’s dynamic processes, ON AVERAGE(?).
And many thanks for seeing the point about the natural processes holding on to solar energy. I’ve had that argument so many times it hurts. All the sciency types want entropy winning with a simple equation. Nature unfortunately doesn’t always work with simple equations.
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Ed Bo
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Alan:
You say: “Here I’ve superimposed the Celsius temperatures that are tied to several radiant fluxes, something you’ll never see in other energy budgets.”
You don’t see it in other energy budgets because it’s WRONG! The SB equation expresses the maximum thermal radiation output as a function of temperature. You can include emissivity for real-world objects. Most actual solid and liquid objects have an emissivity of 0.95 or so at typical earth temperatures.
The temperature is calcuated by adding and subtracting ALL of the power inputs and outputs, many of which are temperature dependent, and using these to solve for temperature. But because these relationships are non-linear, you cannot ascribe a single temperature to a single mode of transfer. Your whole analysis is meaningless.
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Hans Schreuder
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Ed Bo, have you ever written an essay or paper so that we mere portals can marvel at your, obviously, superior knowledge and understanding of everything? If so, please submit it for publication so we may learn from you. If not, shut the f up with your supercilious comments that are, in the exact meaning of the word, meaningless.
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Ed Bo
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Hans — Just get a standard introductory thermodynamics or heat transfer textbook — physics or engineering (nothing to do with climate science if you don’t want). Everything I’ve said is laid out plainly in the early chapters. This stuff has been used successfully for over a century to design systems that really work.
Alan understands none of this. Yet he fancies himself an expert.
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Alan Siddons
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I’m getting a sense of how Ed Bo sees the world. It’s like looking through a paper towel tube and pretending it’s a telescope. Tunnel vision. For one thing, these budget charts do indeed use a blackbody model for their flattened Earth. Say that they assumed an emissivity of 0.95 throughout instead of 1. With a total of 235 W/m² of sunlight exciting the Earth’s components, then, the average temperature would be minus 16° instead of minus 18°. This contradicts the accepted temperature calculation. What’s more, once the magical impact of greenhouse gases raise the Earth’s 0.95 emissivity surface to 390 W/m², its temperature would be 19° instead of 15°. Another contradiction.
So I repeat my observation: Just as a blackbody absorption of 168 W/m² induces a temperature of minus 40°, an absorption of 324 W/m² induces a temperature of 2°, and certainly not 15°. These energy budget charts are ultimately self-contradictory as well, then. And they are self-contradictory precisely because of the arithmetical game that I outlined.
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Ed Bo
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Alan:
I see no temperatures on the K-T diagram you show — except for the ones you (incorrectly) added. If you bothered to read the paper(s) associated with the diagram, you would understand the ACTUAL measurements used to derive the numbers shown on the diagram. Are these numbers exact? No, but they are close enough to show the principles involved.
You say: “an absorption of 324 W/m² induces a temperature of 2°, and certainly not 15°.” If you actually understood the principle of conservation of energy (1st LoT), you would understand that you can (and MUST) add energy transfers, just as “conservation of money” means that you must add money transfers to/from multiple sources in balancing your checkbook. (There is no “conservation of temperature” principle, so whatever you are trying to do with the temperature values is meaningless.)
So the earth surface’s present temperature level can be explained by the SUM of the solar input AND the atmospheric input. It cannot be explained by either one alone.
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Alan Siddons
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Wrong again, Mr Bo. Anyone I correspond with will tell you that I regard myself merely as a climate science researcher. I do own the opinion, though, than many climate science “experts” could benefit from doing research themselves. Much of the climate science field is full of a confirmation bias so high that it rises to the level of delusion.
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Ed Bo
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But when you completely lack the mathematical and scientific background to even start the analysis correctly (as is true for you), all you are doing is providing fodder for the alarmists to say that skeptics don’t understand science at all (which in your case would be true).
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Alan Siddons
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I want to comment again on what Tom0mason has remarked, his idea being that lifeforms take solar energy and build proteins from it, which other lifeforms incorporate by predation and other means — and this building cycle just goes on and on without fully giving back the radiant energy they’ve exploited. That’s a very abbreviated description, I admit!
Well, there’s a physical analogy to such a cycle which was touched on in A Greenhouse Effect on the Moon.
http://ilovemycarbondioxide.com/pdf/Greenhouse_Effect_on_the_Moon.pdf
It turns out that the Moon never quite recovers from the solar irradiance it absorbs during its nearly two week day. On the nightside its temperature plummets for nearly two weeks, of course, but never as much as a blackbody would, as shown by a NASA study. At its lowest temperature just before dawn, the Sun begins heating it again and the cycle repeats. What this means is that the Moon has a permanent, ongoing reserve of thermal energy. Indeed, other researchers have concluded that if the Sun were “turned off” suddenly, it would take about 1000 years for the Moon to fully discharge this stored energy. Once again, a blackbody is a lousy model for real bodies.
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Ed Bo
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Once again, you don’t have the foggiest notion what you are talking about. The reason the moon’s surface doesn’t go completely down to the 3K of deep space during its two-week “night” is the non-zero thermal capacitance of the surface. Non-unity emissivity is not a factor.
At a temperature of 70K (often seen on the nighttime surface), a blackbody would radiate
Q = 1.0 * 5.67×10^-8 * (70^4) = 1.36 W/m^2
At a realistic emissivity of 0.95, the surface would radiate
Q = 0.95 * 5.67×10^-8 * (70^4) = 1.29 W/m^2
In either case, the power output is so low that any temperature decrease is incredibly slow. It has nothing to do with the surface not being an ideal blackbody.
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Peter Champness
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“One more thing. Since the Earth is spherical, it has four times the surface area of a flat plate of the same diameter, so it is thought to be able to absorb only 25% of the light it’s exposed to. To simplify budget presentations, then, its spherical surface is displayed as a flat plate and sunlight’s average intensity on this plate is cut down to 25%. The actual sunlight reaching our vicinity has an intensity of about 1368 W/m². Now we can proceed.”
Is that Fair?
The Earth is exposed to the radiation it is exposed to, ie the flat plate area (Pi R^2).
The radiative Area for outgoing radiation is the whole sphere (4piR^2),
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Alan Siddons
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Of course it’s fair, Peter. I’m merely explaining to readers that 1368 on a sphere is equivalent to 342 on a flat plate. Some folks might not understand that upfront.
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jerry krause
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Hi Alan,
When you state: “Some folks might not understand that upfront.” Your reasoning is simply of something that does not exist. Peter’s point seems to be that the earth surface can never be equivalent to a flat plate. It is the surface of a near sphere rotating in space and the direct radiation on its surface at any one moment varies from the maximum value of 1368 W/m² (reduced by the atmosphere’s albedo at that moment) to zero (actually twilight) at its limb. That’s the real system one must be dealing with and one cannot simplify it by pretending some artificial model. That’s what is not fair.
Have a good day, Jerry
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