The Earth’s Energy Balance: Simple Overview


The idea behind an energy balance is the conservation of energy.  All the energy that enters a system (the Earth for instance) must go somewhere.  In the case of the Earth, most of the energy is leaving the Earth.  The small amount of energy that does not leave is used (absorbed).  For example plants use the suns energy to drive photosynthesis.  So for the Earth as a whole the energy balance looks like this.

Ein = Eout + Eabsorbed

Many papers cover this, but the most commonly cited one today is Trenberth, Fasullo, Kiehl, 2008 (FT08 hereafter).  That paper presents a detailed analysis of the Earth’s energy balance and compares it to others.  The overall summary of the energy balance is presented in a single graphic that shows the different energy transfers for the different parts of the Earth.  I will use the 2008 version although it is the 1997 that is more often seen.

The Inconvenient Skeptic

Trenberth, Fasullo, Kiehl, 2008

This is reasonably accurate, but it is also entirely misleading.  The two large energy flows named Surface Radiation and Back Radiation are different from all the others.  They are not measures of energy transfers, but of radiative flux (also called forcing).  As I have described before, there is a difference between energy transfers and radiative flux.  Two objects at the same temperature have zero net energy transfer and as a result, will not change temperature.  As the surface of the Earth and the atmosphere above have a small temperature difference (to be shown in a later article), there is little energy transfer between the two.

FT08 calls this energy transfer NET LW in table 2b on page 318.  That 63 W/m2 of NET energy is the only radiative energy available to cause a temperature change in the atmosphere.  The atmosphere cannot absorb all of that energy and a portion of that energy freely escapes the atmosphere.  That is the Atmospheric Window that has been assigned a value of 40 W/m2.  Since 40 of the 63 W/m2 escapes that leaves only 23 W/m2 from the surface that is absorbed by the atmosphere.

If the overall energy balance for the surface of the Earth is performed using only NET energy transfers, then the result would be as follows:

Ein = Eout + Eabsorbed

Solar Absorbed = Thermals + Evaporation + Radiative + Net Absorbed

161 W/m2 = 17 W/m2 + 80 W/m2 + 23 W/m2 + 40 W/m2 + 1 W/m2

This does properly balance in with the other portions of the overall energy balance.  The difference that this makes is it changes the apparent value of radiative transfer to the atmosphere.  The total energy transferred from the surface to the atmosphere is 120 W/m2.  That is 74.5% of the energy that the sun transfers to the surface of the Earth.  If the flux values used by FT08 are used, then the amount transferred from the surface to the atmosphere is 453 W/m2, which is 2.8 times the amount of energy that the surface absorbs from the sun.

From a practical point of view it is unreasonable that the surface of the Earth transfers more energy to the atmosphere than the sun transfers to the Earth.  That is really the main problem with the FT08 and any balance that uses radiative flux (forcing) instead of transfer of energy.  While the values for flux are reasonable, the idea behind their usage is not as they do not accurately describe the transfer of heat from the surface to the atmosphere.

That is why it is important to show only NET energy transfers in the Earth’s energy balance.  When the impact of CO2 is viewed as part of the NET energy transfers from the surface to the atmosphere, it is only 3% of the total.  That is one of the main reasons that the overall effect of CO2 changes are so limited.  Changes in CO2 concentration have a very, very small impact on that 3%.  That in turn has almost no impact on the global temperature.

If the NET energy values are substituted in for the flux values used in the FT08 graphic, here is what the graphic would look like (that is if I had any skill in photo editing).  The difference is enormous.  The fact is that Radiative Heat Transfer accounts for only 19% of the overall transfer of energy from the surface to the atmosphere.  This does nothing to diminish the overall Greenhouse Effect, because it does not diminish it.  The Earth and the atmosphere are warmer because of that energy transfer, but CO2 is only a small part of the picture.

The Inconvenient Skeptic

I will gladly re-post this picture is someone fixes and rescales it to the proper values.

Posted in Energy Balance and Radiative Heat Transfer by inconvenientskeptic on November 28th, 2010 at 1:40 pm.

22 comments

This post has 22 comments

  1. Hi,
    You state “The Earth and the atmosphere are warmer because of that [radiative] energy transfer” one-way from the Earth to the atmosphere. Why would the Earth be warmer by transferring energy to the atmosphere?

  2. inconvenientskeptic Nov 28th 2010

    Hi Hockey,

    There are two reasons that the surface is warmer. First is the atmosphere transfers energy to places where it isn’t. The tropics send energy to the mid-latitudes and the mid-latitudes send it to the polar regions. If the atmosphere wasn’t warm, that would not happen (ocean as well, but this is atmosphere specific).

    The 2nd reason isn’t directly caused by the transfer, but a two part step. Because the atmosphere is warm, the surface transfers much less energy upwards. That is because the surface and the atmosphere are near equilibrium temperature. If the atmosphere was much, much colder, the surface would transfer more energy to the atmosphere. So there is less energy transfer because the atmosphere is warm.

    Hope that helps.

  3. Look’s like the real scientists at NASA are calling you a liar:

    http://climate.nasa.gov/evidence/

  4. inconvenientskeptic Nov 28th 2010

    Boo,

    Ummmm.. That might convince someone without an actual science degree, but I have discussed each topic on this site in far more detail than the NASA site.

    Please keep comments on topic about the energy balance for this particular article. I have extensive articles about CO2 and the ice ages if you are interested in understanding the science of atmospheric CO2 levels.

  5. Regarding the 1st paragraph of your reply, I don’t see why re-distributing heat by the oceans/atmosphere would change the so-called “average” temperature of the planet.

    Also don’t understand why “slowing of cooling” is equated to warming, especially on a rotating planet that doesn’t have time to reach equilibrium.

  6. inconvenientskeptic Nov 28th 2010

    This past week the United States experienced a significant drop in temperature. The reason for that is Arctic air built up and moved south and cooled the a large part of the northern hemisphere down.

    The region where the Arctic air came from did not warm up, because it is getting little to no energy from the sun, but the movement of cold air caused the average temperature of North America to drop.

    Places where warm air builds up and moves has the reverse effect. The atmosphere reduces temperature gradients. That does have an effect on the average.

    As for the “slowing the cooling.” The most important aspect of the atmosphere causing the Earth to warmer is night time, not day time. The surface would cool very rapidly after sunset if the atmosphere did not limit the heat loss from the surface. That is why humid areas have less of a temperature drop than arid areas during the night. The atmosphere limits the temperature drop. It also limits the temperature increase during the daylight period.

    Equilibrium isn’t relevant to the energy balance. The energy the surface receives is always changing as is the temperature. Energy flows from higher temperature to lower temperature always. Since the changes are so constant a true equilibrium will not be reached, but that doesn’t matter.

    Without the atmosphere the surface would be losing energy at a much higher rate to space. That would rapidly cause dramatic temperature drop. Think going outside in -40 C weather in a swimsuit. You would cool off rapidly. With a parka, you do not cool off rapidly. That atmosphere acts exactly like the parka would for your body.

    Hope that helps.

  7. Glenn Tamblyn Nov 29th 2010

    LOL. This is a joke, right John.

    Although I thought this was were you were heading.

    This notion that those surface/atmosphere flows don’t really exist is totally completely and utterly dead wrong. Not only do they actually exist. They are observed, measured. Anyone can buy a cheap solarimeter and measure incoming energy from the Sun – 1000 W/M^2 at its peak, 184 average over the day and year. So too can you use Infra-Red measurement equipment to directly measure Back Radiation. Researchers have been doing that for decades. So much so they are even observing the changes in this flow and its spectrum due to changes in GH gas levels.

    So how can it be that one flow can be measured and is real, but the other flow can also be measured but it isn’t real? None of this English Language gymnastics about flows vs fluxes vs forcings.

    So your comment: “The two large energy flows named Surface Radiation and Back Radiation are different from all the others.”.

    !!TOTALLY AND MONUMENTALLY WRONG. THEY ARE EXACTLY THE SAME AS ALL THE OTHERS!!

    Now I’m sure you will now comment that each flow/flux/forcing exists but the NET EFFECT is what you describe – yes it is. But that isn’t the point. The point is you can’t look at just the NET flow but need to look at each individual component flow because each has its own characteristics and is influenced by different things.

    The howler in all this is the following paragraph:

    “That is why it is important to show only NET energy transfers in the Earth’s energy balance. When the impact of CO2 is viewed as part of the NET energy transfers from the surface to the atmosphere, it is only 3% of the total. That is one of the main reasons that the overall effect of CO2 changes are so limited. Changes in CO2 concentration have a very, very small impact on that 3%. That in turn has almost no impact on the global temperature”

    A totally wrong leap of bad Logic.

    You are now talking about CO2’s (you do like to keep it focused on just that rather than all GH gases) impact on the GH Effect and Temps. And yet you are equating them to the NET flow to the atmosphere.

    John, the balance of the NET flow has NO BEARING ON TEMPERATURE OR GH EFFECT WHATSOEVER!

    Thermals, Evapo-Transpiration and Surface Radiation WILL ALWAYS balance Incoming Solar, NO MATTER WHAT THE TEMPERATURE IS. THATS THE WHOLE POINT.

    Imagine a world 20 DegC warmer due to a massively increased GH Effect. In this warmer world, the thermal and ET parts may be larger but TH, ET & NET SR combined will still equal 161. But the two flows (Non-NET SR & BR) that you want to exclude (perhaps I should say ‘magic away) will be very much larger.

    And the Surface Radiation component will be larger BECAUSE the Back Radiation component is larger. More back radiation needs to be compensated for by more surface radiation. To get more surface radiation you need to increase the temperature to generate it.

    To use an analogy, lets look at my train example from your earlier post.
    We have 2 freight marshalling yards at the top and bottom of a hill. 2 rail lines run down the hill & three lines run up the hill.
    – Down line 1 carries 161 wagons a day, a straight through run pulled by a Loco called Mr Sun.
    – Up line 1 carries 17 wagons a day pulled by a Loco called Mr Thermals.

    – Up line 2 carries 80 wagons a day pulled by a bigger Loco called Mr E-T.
    – And Up line 3 carries 396 wagons a day pulled by a giant Loco called Mr SR .

    – Finally Down line 2 carries 333 wagons a day, pulled by another giant Loco called Mr BR.

    The Dispatcher in the bottom yard – Mr Surface – is receiving 494 wagons a day and dispatching 493 wagons a day, his yard is slowly filling up, he needs to dispatch more.

    The Dispatcher in the Top yard – Mr GH Gases – is receiving 493 wagons a day from Mr Surface and dispatching 333 wagons a day back down. The difference is because he is also receiving and dispatching wagons to/from other yards as well
    .

    So Mr GH Gases receives 493 wagons up from Mr Surface and sends 333 of them straight back down. Thats not 3%.

    More like 67%!

    And Mr GH Gases has no impact on dispatching decisions in the bottom yard. They don’t coordinate or commmunicate with each other. Each dispatcher just runs their own yard, trying to get wagons out. So if Mr GH Gases is given a bigger workforce, he will simply get more wagons out, and Mr Surface will just have to cope by working faster, i.e. getting hotter.

    Trying to use NET energy flow as a basis for looking at the GH Effect is a total nonsense John.

  8. inconvenientskeptic Nov 29th 2010

    Glenn,

    I am curious why you agreed that two rocks at the same temperature have no NET energy transfer, so the temperature does not change.

    You also agreed that the cold ground does not result in warming of the hands, but the hands were losing energy to the ground.

    You also agreed that it is energy transferred from the fire that warms the hands.

    All of those are EXACTLY the same situation. In all of them, NET transfer is the only part that resulted in temperature change.

    Why is this different? Your last statement is:

    “Trying to use NET energy flow as a basis for looking at the GH Effect is a total nonsense.”

    In every other portion of FT08 the only energy shown is the NET transfer. Why is NET irrelevant for only one portion of the balance?

  9. Vanderborght Nov 29th 2010

    What seems to be lacking in the story, is the time lag element. It should be Watts per hour or second by the way, and the time lag between the reception of the energy by the planet and the radiation of energy by our planet back into space should be adressed. In the end, the planet is going to radiate all received energy back into space, but thanks to the effects of the atmosphere there’s a time lag. Imagin for instance that the sun stops shining form one second to the next. It would take some time for the earth to freeze, because of this time lag. I think this approach would be easier to understand by us readers. It’s this time lag wich is made larger by increasing amounts of greenhouse gasses and it’s this increasing time lag wich is warming up the atmosphere (a little). Seen from space, the earth should be ‘shining’ less, as less Watts an hour are being emitted into space (sattelites like CERES are in fact just checking this). It would take the earth longer than an hour to radiate back into space the amount of energy received in an hour.

  10. inconvenientskeptic Nov 29th 2010

    Vander,

    The next post will actually discuss the energy transfer and the impact over the course over one day.

    The Earth is in a steady state. As a result it should be ‘shining’ the same amount of energy all the time. So far CERES and ERBE agree that it is a steady ‘shine.’

    If the sun were to stop shining, then there would be a lag before the amount of energy leaving slowed down, but it would not take very long. Only a few days and the global temperature would be dropping quickly.

    In one day the entire atmosphere would drop about 2 °C. The next day the same. After a few days of that the change in temperature would start to slow down the rate of loss.

  11. Hmmm, let’s see. I can either believe the scientists at NASA or some poor guy that’s trying to win an argument with his wife. I guess your wife must be the smart one in the family.

  12. inconvenientskeptic Nov 29th 2010

    Boo,

    That is a bit ad hominem, but funny. I would hope that you believe no one and research everything on your own. That is what I did.

    You might have missed the part where I started out thinking that AGW was probably real, but an overstated threat.

  13. Joris Vanderborght Nov 29th 2010

    I agree that if the sun were to stop shining, the earth would cool pretty quickly, and that the rate of its energy loss would decrease over time. Didn’t you mean “then there would be a lag before the amount of energy in the atmosphere dropped,” in stead of “then there would be a lag before the amount of energy leaving slowed down,”. I also think your statement about the steady state of the planet and it causing the planet to shine the same amount of energy all the time is vulnarable (think of the variations of distance between the sun and the earth over a year). I would rephrase that.

    But I am still worried about the slow accumulation of energy in the atmosphere due to this time lag, we at least all agree upon. Even an extremely small lag would cause the amount of energy stored in the atmosphere to grow slowly over time (if the radiation of the sun remains identical). Its the ‘delta’ (the lag) in the equation that does it. The fact is that our atmosphere doesn’t warm up endlessly, even though the time lag exists. Something prevents the atmosphere, wich has been receiving energy of the sun for billions of years, to reach such a high energy state. This can only be explained by talking about feedback mechanisms wich react to the amount of energy stored in the atmosphere. These feedback mechanisms should alter the atmosphere in such a way that it is able to lose more of its energy into space and/or prevent sunlight from warming the atmosphere further.

    These feedbacks and their complex relations make me sceptical about our ability to predict what effects our greenhouse gas emissions have on the climate.

    Sorry for my English by the way.

  14. I, too, would hope that you believe no one but after skimming your first chapter I can see that is not the case.

    I apologize if my previous comment came across as a personal attack. That was not my intent.

  15. inconvenientskeptic Nov 29th 2010

    Joris,

    Your English is fine. 🙂

    The atmosphere doesn’t hold enough energy to worry about. Dropping the temperature of the entire atmosphere by 33 °C is the same energy that dropping 36 m of the oceans by 3 °C. As others have pointed out, the energy is stored in the oceans. Accumulation of energy would take place in the oceans and not the atmosphere.

    There is also very little time lag in the atmosphere. It only takes a few hours for the effect of the sun to make a substantial difference, much like it only takes a few hours for it to cool down after the sun sets.

    The atmosphere responds very quickly to change. There is lots of evidence that response to changes is very quick. In the US after September 11th, the difference between min and max temp changed right away due to the absence of planes flying. It was an immediate response.

    There is little reason to believe that there is much of a time lag for the atmosphere. If the full effect for increased CO2 is in effect now, then projections based on a time lag are meaningless.

  16. Richard111 Nov 29th 2010

    That 161W/m^2 of radiation to the surface, that would put the surface temperature at -43C !!! To get to +15C we need 392W/m^2.
    I’m doing something wrong again. (sigh)

  17. inconvenientskeptic Nov 29th 2010

    Richard,

    The 161 W/m2 is the amount of energy that the surface absorbs from the sun. The solar constant is 1364 W/m2. Since the Earth absorbs π*r^2, but the energy is spread over the SA of a sphere (4π*r^2) the average energy to for the Earth is 1/4th the area of a circle with the Earth’s radius.

    That is the 341.3 W/m2. Since the Earth reflects some and the atmosphere absorbs some only 161 W/m2 reaches the ground.

    The 392 W/m2 is correct for the flux leaving the Earth’s surface. FT08 did a slightly more complex calculation where they divided the Earth into bands and determined the flux from the ranges. They got a few more W/m2 as a result. There is a little section on it in the FT08 paper I have linked.

  18. Richard111 Nov 30th 2010

    341.3 W/m2 incoming at TOA and “”392 W/m2 is correct for the flux leaving the Earth’s surface””. ???

    I’ll go read some more. 🙂

  19. Glenn Tamblyn Dec 3rd 2010

    John

    Firstly, you are totally wrong with your first claim that the BR and SR flows are ‘different’ from all the others because they are ‘forcings’. I disagreed with you when you raised this in your previous post, describing it as gobbledeegook which it is. You have not given a single reference for where this terminology of ‘forcing’ comes from since it absolutely IS NOT how the term is used in Climate Science. I can only assume it is your own invention.

    BR and SR are flows just like every other arrow on the diagram. Measured and observed. To suggest otherwise is un-physical.

    You use the following language to describe your claim “The two large energy flows named Surface Radiation and Back Radiation are different from all the others. They are not measures of energy transfers, but of radiative flux (also called forcing). ”

    Your language is quite confusing, drawing arbitrary distinctions that do not actually exist. So to clarify.

    Every arrow on the diagram is an Energy Flow (or flux). Energy flowing from an A to a B via some process. They are all identical in that they are all energy flows, even though the mechanism of each flow may differ. They are ALL energy transfers!

    Then for any given location on the diagram, surface, atmosphere etc, you can calculate the NET Energy Transfer being the sum of the magnitude and direction of all the relevent individual Energy Transfers.

    So your calculation of the NET Energy Transfer from the Surface to the Atmosphere is rather arbitrary. The actual NET transfer is actually 120 not 23 – Thermals and E-T are Energy Transfers as well. And simply comparing SR against BR isn’t valid on its own since some of the energy coming down as BR originally went up as Thermals or E-T.

    You said “All of those are EXACTLY the same situation. In all of them, NET transfer is the only part that resulted in temperature change.

    Why is this different?”

    Because you are not using them to look at Temperature change, but at the GH Effect. This diagram shows energy transfers that are essentially in balance. So total temperature CHANGE is negligible. But what the temperature ACTUALLY IS depends entirely on the sicze of the flows. If SR was larger at 496 and BR was larger at 433, with the atmospheric window the same at 40, then your NET value would still be 23. But the surface and atmospheric temperatures would both be higher to emit this much more energy. Your NET analysis tells you nothing about the magnitude of the GH Effect because NETing the flows cancels it out.

    So, as an accounting exercise, yes you can simplify the diagram. Actually the diagram could be simplifed down to 341 in from space, 341 out to space, 1 from Atmosphere to Surface. That simplifies the NETing process as far as it can go.

    So why have a diagram like this at all? Because they are looking at what all the DIFFERENT flows are, not the NET result of some or all of them. Because each flow occurs for a different physical reason or reasons.

    For example 23 Reflected by Surface is because of the Albedo of the Surface, 78 incoming Absorbed by the Atmosphere is because of the absorption characteristics of the atmosphere’s gases for Short Wave radiation. 333 Back Radiation is driven by the temperature profile and composition of the atmosphere at different levels, and so on.

    So when you try to merge 2 flows together to get their NET value, that is OK for accounting simplicity, but is TOTALLY INVALID when trying to draw a conclusion about the operation of a physical process that only applies to ONE of those flows.

    It is the absorption properties of the GH gases that results in the SR flow dividing 356/40. Different GH behaviour would
    result in a different split. And the BR flow size has no relevence to this. So introducing the NET of these two flows as the basis for looking at the magnitude of the GH Effect is absurd. It introduces a gross mathematical error.

    It is like saying that if I have a pump that shifts 356 litres an hour of water up a hill then 333 litres an hour of this
    flows back down another channel, that the pump is only pumping 23 litres an hour. The pump is most certainly only moving 23/hour NET, but you are paying the fuel bill to ACTUALLY MOVE 356/hour.

    So trying to put a figure on the size of the GH Effect based on the 23 is total nonsense, un-physical gobbledeegook again.

    So far the 5 key things you have put forward to build your theory are all absurdity John:

    1. Atmospheric Temperature
    variations of the Northern Hemisphere drive the climate system on a sub-yearly time frame. I am sitting in Southern Australia writing this after one of the wettest Springs on record because of a La Nina event – an Ocean phenomenon.

    2. That that idea can then be extended to millenial timescales without any consideration of mixing between the hemispheres or atmosphere to ocean mixing and that some supposed NH Atmospheric driver is sufficient

    3. That the only part of Milankovitch cycle forcing that matters is the changes in NH Summer insolation, ignoring the entire season or the SH and in the process inflating the effect of MS around 20 fold.

    4. This absurd bit of sophistry about ‘forcings’, fluxes etc.

    5. That taking the NET of multiple flows allows you to comment on a process that only impacts on ONE of those flows.

    We have been talking for some time now, and you said you had a basis for your claims. Zero out of Five so far.

  20. inconvenientskeptic Dec 3rd 2010

    Glenn,

    You are completely disregarding everything you agreed with in the RHT articles. The amount of energy radiated by any object is calculated by the Stefan-Boltzmann equation, but that does not determine the amount of energy that is transferred.

    The discussion about radiative heat transfer shows how temperature differences regulate the amount of energy transferred between objects. That the radiative flux can be measured isn’t relevant because only the net energy transfer is relevant.

    That is why small temperature gradients result in small amounts of energy transfer and large gradients result in large energy transfers.

  21. Glenn Tamblyn Dec 4th 2010

    John

    The key point here is that you are conflating two different things.

    Yes, when looking at energy transfer and its capacity to effect temperature change, NET heat transfer, the sum of all the separate transfers IS what is relevent. But none the less, the separate individual transfers still exist.

    However, in the example here, the K&T diagram. there is no NET heat transfer (apart from a minor 0.9 w/M^2). This is an Energy budget that is in balance. So there is no temperature change.

    So amalgamate the flows to your hearts content. Its just energy accounting.

    HOWEVER, near the end of the post you slip in this liitle thing about the GH effect and how it is supposedly so small. This has NOTHING whatever to your supposed purpose of providing a tutorial on heat transfer.

    And the conclusion you draw is totally invalid for reasons I have mentioned earlier.

    I know you wont agree with this since your entire thesis seems to rest on this but this conclusion is invalid and un-physical. I am surprised that you introduced a major component of your thesis is such a understated way.

  22. inconvenientskeptic Dec 4th 2010

    Glenn,

    What this whole article covered changed because of two things. First that some people do not accept the GHE. Second is more obscure, but important is that they don’t accept any alternate that doesn’t produce the observed tropospheric temperature gradient.

    The focus on the net energy transfer from the surface does fully explain both observations. The final part of the article contains what was going to the the whole of the article, but it expanded.

    The idea the small temperature gradients exert significant warming is absurd. Anyone who has dealt with practical applications of heat transfer understand that the temperature gradient dominates. Pure applications of Stefan-Boltzmann do not accurately describe the RHT between two objects in near thermal equilibrium. Yes that energy exists and is flowing and can be measured, but the ability of that energy to cause heating is limited by the difference in temperatures. That is why engineers only work with the difference in the Stefan-Boltzmann for the two objects.

    That is the only proper method to describe the heating that results from RHT.

Web Design & Dev by

Mazal Simantov Digital Creativity