Where Did I Put That Energy?

Guest Post by Willis Eschenbach

[UPDATE 2 AM Christmas morning, and of course Murphy is still alive and his Law is still in operation. I find a decimal point error in my calculations … grrr, I hates that, ocean energy flows shows at 1/10th size. Public exposure of error, the bane of any scientific endeavor.

And Murphy being who he is, the correction doesn’t solve the puzzle at all. It only makes it more complex. I have updated Figure 2 and some of the text, and added a third figure. The only good news is, it doesn’t affect my conclusions, there’s still something very wrong in the canonical climate equations.

Merry Christmas to all, it can only get better from here.]

In the Climategate emails, Kevin Trenberth wrote:

How come you do not agree with a statement that says we are no where close to knowing where energy is going or whether clouds are changing to make the planet brighter.  We are not   close to balancing the energy budget.  The fact that we can not account for what is happening in the climate system makes any consideration of geoengineering quite hopeless as we will never be able to tell if it is successful or not!  It is a travesty!

Although I sympathized with him, I was unclear about exactly where the hole was in the energy budget. However, my research into the climate sensitivity of the GISS model has given me some new insights into the question. Intrigued by the findings I reported in “Model Charged With Excessive Use of Forcing“, I wanted to look closer at the results from the NASA GISS climate model. As you may recall, I was trying to understand the low sensitivity I had calculated for the GISSE model. I went to the CMIP archive to see if I could get the top-of-atmosphere (TOA) forcing for the GISS model month by month, but the GISS folks didn’t archive that data. Rats.

Figure 1 (may take a moment to load). Anomalies in the heat content of the top 700 metres of the ocean from 1955 to 2003. Units are zettaJoules (10^21 Joules).

Someone pointed out on that previous thread that I was neglecting the ocean in my calculations … guilty as charged. The basic energy equation for the planet is that energy added to the climate system equals energy leaving the system plus energy going into the ocean. Energy can’t just disappear, it has to go somewhere. It either leaves the system, or it goes into the ocean. So I went off to see what the change in the heat content of the ocean has looked like over the period of record. The National Oceanographic Data Center (NODC) has the data. Figure 1 shows a movie of what I found. Not much of a movie, but it’s the first one that I’ve made in R, so I was happy about that. The legend says “∆H” where it should say “H”, but it’s 3AM and I’m not going to fix it. So how can this ocean heat content information be related to the question of climate sensitivity?

As you can see in Fig. 1, nature is a puzzle. Things happen in blobs and patches, without immediately obvious reasons. However, we can see that the heat content of the top layer of the ocean has increased since 1955 by a total of 154 ZJ.

First, a bit of math. Not much math, and not complex math. We’re looking at one of the fundamental equations of the current climate paradigm. The statement above was that:

Energy added to the climate system equals energy leaving the system plus energy going into the ocean.

Mathematically this can be restated as ∆Q (change in energy added, Joules/year) = ∆U (change in energy lost, Joules/year) + ∆Ocean (change in energy in/out of ocean, Joules/year), or

∆Q = ∆U + ∆Ocean (Joules/year)                          (Equation 1)

Note that this is different from a statement about a general equilibrium, which may or may not be satisfied in any given year. This is an absolute requirement, because energy cannot be created or destroyed. If we add extra energy to the system, it has to either leave the system via increased radiation or get stored in the ocean. There is no “lag” or “in the pipeline” possible with Equation 1. The atmosphere has far too small a thermal mass to store a significant amount of energy. The earth warms too slowly to serve as a reservoir for annual changes. Global ice amounts are fairly stable (although they might make a very small change over the long-term, global annual variations are small). So any large annual change of incoming energy has to either change the ocean storage or leave the system.

Now, the current climate paradigm holds that “U”, the energy leaving the system, is equal to the surface temperature “T” divided by the climate sensitivity “S” (∆U=∆T/S). This is another way of stating the idea that the surface temperature is linearly related to changes in the top-of-atmosphere radiation. [See e.g. Kiehl (PDF). Be aware that Kiehl uses lambda (λ) as sensitivity, which in my terminology would be 1/Sensitivity].

The current paradigm also holds (wrongly, in my opinion) that the sensitivity “S” is a constant. The IPCC says that the central value for the climate sensitivity constant “S” is about 0.8 °C per W/m2 (or 3°C per doubling of CO2). So according to the current paradigm, we can replace ∆U (change in energy leaving the system) with ∆T/0.8. This gives us:

∆Q = ∆T / 0.8  + ∆Ocean  (Joules/year)                 (Equation 2)

It struck me when I was looking into this that we actually have the means to test this claim of mainstream climate science. We have the historical forcings, from the GISS tables. We have the historical GISS temperatures. And we have the historical heat content of the ocean. (The conversion from Watts/m2 to joules/year is covered in the Appendix.)

Figure 2 shows annual changes in incoming energy (∆Q, red), outgoing energy (∆T/S, light blue), and energy moving into and out of the ocean ∆Ocean (dark blue). We can express them either in joules per year or in W/m2. I have chosen joules per year, to emphasize that this is the movement of actual energy that cannot be created or destroyed. It has to go somewhere, and there’s not many choices.

 

Figure 2. The missing energy puzzle. Every year, the amount of energy entering the system (red) should equal the energy leaving the system (light blue) plus the energy going into/out of the ocean (dark blue). It doesn’t.

Figure 3. Annual Energy Budget Error, ∆T/S + ∆H – ∆Q. Positive errors indicate excess heat in the ocean. Some folks have commented that they don’t like having photos in the background. This Figure’s for you.

As you can see, something is really, really off the rails in this. The total forcing Q is known through observation to take large drops after volcanic eruptions (from the volcanic aerosols reflecting away the sunlight), with similarly large and fast recoveries. But this is not reflected in the sum of the outgoing energy (∆T/S) plus the ocean changes. In other words, the forcing drops because of the volcanoes, but there is no corresponding drop in temperature or ocean heat storage as you would expect. The forcing springs back when the stratosphere clears after the eruption, but there is no corresponding rise in either temperature or ocean storage.

The real surprise is the absolute size of the missing energy. It is often more than 20 ZJ. This means that something very fundamental is wrong here.

Some of the possibilities for unraveling this koan are:

• Foolish math or logic error on my part. I don’t think so, as I have checked and rechecked my figures, units, and logic. But I’ve made plenty of mistakes in my life. Please check my numbers and everything else. [UPDATE – well, I sure called that one …]

• Bad data in one or more of the datasets. Always possible. However, the huge size of the discrepancy argues against that. Even though there are errors in all datasets, these would have to be very large errors. Even the forcings dataset is mostly based on observations (CO2 and volcanic aerosol changes). So bad data seems doubtful, it would have to be really, really bad.

• One of the datasets is off by one year, so the timing is wrong. That doesn’t work, though, correlation doesn’t improve with a lag or a lead.

• IPCC climate sensitivity is too large. If it were smaller, ∆T/S would be larger to help balance out the ∆Q. The problem is, the temperature changes are not well correlated with the forcing changes. In addition, the regression of (∆Q – ∆Ocean) on ∆T has an R^2 of 0.01. This means that the climate sensitivity has no explanatory power in respect to the error, regardless of its value.

• The change in energy at the top of the atmosphere (∆U) is not represented by ∆T/S. I would say that this is the most likely explanation. I think that the current paradigm, in which the temperature is linearly related to the forcing, is highly unlikely. Simple consideration of the complexity of the system discourages assumptions of linearity.

• The change in energy at the top of the atmosphere ∆U is correctly represented by ∆T/S, but S in turn is not a constant but a function of T “f(T)”. Thus the substitution in Eqn. 1 should actually be

∆U = ∆T/f(T)

This is a refinement of the previous possibility. I put this forward because of the obvious daily change in climate sensitivity in the tropics, with the sensitivity dropping as the day progresses and the temperature increases. Since that variation in the climate sensitivity occurs daily over about a third of the planet, the part of the planet where the energy enters the system, it is not unreasonable to think that the global climate sensitivity should be a function of temperature. (Note that even here the sensitivity is unlikely to be a linear function of temperature, as the natural situation contains clear thresholds at which the climate sensitivity changes rapidly.)

• Something else that I haven’t thought of yet.

I make no hard claims about any of this, as I don’t know where the missing energy really is. I don’t even know if this is the missing energy that Trenberth was talking about. My theory is that the energy is not missing, but that Equation 2 is wrong. My hypothesis is that the earth responds to volcanoes and other forcing losses by cutting back on clouds and thunderstorms. This lets in lots of energy, and as a result neither the air temperature nor the ocean heat storage change very much. I have detailed that hypothesis here.

About the only solid thing I can say out of this analysis is that if my numbers and logic are correct, then one of the fundamental equations of the current climate paradigm is falsified …

We’ll see how it plays out. All comments and explanations gladly accepted.

w.

[UPDATE: This discussion continues at Some of the Missing Energy]

APPENDIX: Converting Joules/year to W/m2 involves the fundamental relationship:

1 Joule is the application of 1 Watt for 1 second

So … one Watt/m2 applied for one year gives us 1 *  31.6E6 Joules/m2 per year. (Watts/m2 times seconds in 1 year.)

To get total Joules for the planet, we need to multiply that answer by 5.1E14 square metres, to include the total surface area. So one Watt/m2 of forcing, acting on the planet for 1 year, delivers 16.3E21 Joules/year (16.3 zettaJoules). This allows us to convert easily between Joules/year and W/m2

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147 thoughts on “Where Did I Put That Energy?

  1. something amaze my:earth is a rotating object, and I never found an energy budget off the “dark” side off the earth?

  2. I think the fundamental problem lies with the matters that I have been trying to address.
    Cloudiness and albedo actually decline when the system warms up because as part of the process the jets behave in a more zonal fashion and move poleward. Such a shift reduces the amount of cloudiness because the length of the main air mass boundaries greatly decreases with far less mixing and less clouds generated globally. Additionally reflectance decreases as the clouds move poleward.
    The reverse happens when the jets become more meridional and/or move equatorward.
    I first noticed an increase in meridionality and a reversal of the earlier poleward shift as long ago as 2000.
    Ever since then the global cloudiness and albedo have been increasing according to the Earthshine project.
    The ‘missing’ energy has therefore been lost to space because it was prevented from getting into the oceans in the first place.
    The reverse sign solar effect that I have been going on about has lots of implications. One of them is that a warmer world has less clouds not more clouds because of the jetstream shifting that I have mentioned.
    We need to fully integrate the reverse sign where necessary throughout current climatology and I’m pretty sure that once we do then all the puzzlement will disappear.
    (Or I will look like an idiot but ‘c’est la vie’.)

  3. So, it’s like the scene in the movie The Matrix where, Neo, is told “There is no spoon.”. So, there is no heat (Stored).

  4. Willis:
    Now you’ve done the calculations, why not compare your results with Trenberth’s papers and other peer-reviewed publications?

  5. You would have to question the veracity of the values for incoming dQ in figure 2. How was that obtained and does it bear any relation to reality? The same goes for dU. Like you say, they don’t add up.

  6. Willis, here’s a few thoughts about where else energy might go.
    Kinetics.
    Electro magnetics
    Hidden heat
    On an annual basis, as detailed in Paul Vaughans post today, there is a big exchange of angular momentum betwen the Earth’s crust and the atmosphere causing changes in atmospheric angular momentum and length of day. These changes must affect atmospheric pressure changes and ocean currents and sub crustal flows too, generating heat in the mantle maybe? Maybe it all ties in with Vukcevic’s stuff on geomagnetics and currents in the ring circuit too. Back EMF can soak up a lot of power, and affect the ionisation of the atmosphere.
    Welcome to the bigger puzzle.

  7. Ah, I am just a civil engineer, but surely energy gets stored in the land mass as well as in the oceans. Surface geothermal energy use is quite common in Germany and this energy comes mainly from the sun. Through flowing groundwater it can also be spread horizontally as well as vertically. So, still a big hole in the calculations.

  8. tallbloke,
    “These changes must affect atmospheric pressure changes and ocean currents and sub crustal flows too, generating heat in the mantle maybe?”
    Which would lead to temperatures of millions of degrees – just as Al Gore predicted 🙂

  9. Ahh! Finally, I see mention of kinetic energy. I’ve sheepishly asked about this once before and got no response from anyone.. didn’t pursue it because I didn’t know if I was being ignored simply because I’m an idiot (idiocy being my personal null hypothesis) or because nobody knew.
    I don’t know how much energy is in the movement of air but it struck me that, even though they royally suck as an energy solution and are about as energy-efficient as a BLT with mayo, a few windmills dotted around can pluck quite a bit of energy out of the air.

  10. It’s great that a decent bloke like Willis can do this sort of work, present it to us for comments and hangs around (after some sleep this time) to answer questions. It’s like being given a new toy to play with for Xmas, thnx W.
    What gives me some additional optimism about this is the proxy records over the millenia show Ts rising to not much more than todays levels, then dropping back. If sensitivity is a function of T, the higher the T, the lower the sensitivity. A self limiting mechanism so to speak. (as the paleo records show)
    Do I have that right W?
    And if I do have that right, then we are essentially living through a rare warm period, and the “default” climate of the planet is cooler.
    Now there’s something to worry about.

  11. Lots of food for thought, thanks Willis. I don’t have a lot of faith in the OHC data from 1950 and even ARGO isn’t flawless. The Hadley centre said they were considering adjusting the old ship-based measurements downwards which would be very convenient for some. If there really is so much energy missing I wonder if anyone has looked in Al Gore’s hotel room?

  12. Willis – this was a really interesting post. No disrespect to Anthony, but could I suggest you also pose the same questions over on Judith Curry’s blog. As you know the Radiative Forcing threads over there have generated quite a lot of discussion and it would be interesting to see what the reaction would be to your interesting conundrum.

  13. Stephen Wilde says:
    December 23, 2010 at 3:47 am
    I think the fundamental problem lies with the matters that I have been trying to address.
    I haven’t had the time to keep up with everything you are saying, but I always appreciate your postings. As to the role of the jets in determining broad climate trends, I think you are right. Keep up the good work.
    Basil

  14. Willis;
    Maybe I am mistaken but if the energy input is from the sun then you have to correct one of your variables on calculating total joules for the year. Either time in seconds or the surface area is too large by approximately a factor of 2. Half the earth does not receive direct energy from the sun for approximately 12 hours each day. What would that correction do for your delta Q graph. Eyeballing it it would still be out of balance and your changing sensitivity as a function of temperature would probably come close to solving the difference.

  15. Thanks Willis for focusing on energy and not just temperature!
    It has been a bug of mine for a long time that the differences in (atmospheric) temperature represent massive energy flows that are not being properly looked accounted for. Bob Tisdale comes closest with his analysis of sea-surface temperatures, but I think a lot is still being missed.
    One confounding issue I have in trying to understand energy flows is the way the temperature is always given as the anomaly – usually on a monthly basis. This can show wide fluctuations (month to month) which are not necessarily the same as the actual energy in the system (if one month’s average is lower than the previous month, but the measured temperature stays the same, the anomaly will increase although the temperature didn’t).
    Another thing I have not seen explained (to my satisfaction, anyway) is the fluctuation in global temperature over the year: Is this a bias because of our northern hemisphere summer or a real change in the energy in the atmosphere? If real this reveals a massive flow of energy (presumably) between the atmosphere and the oceans happening twice a year!
    Anyway, I’ll keep reading and see if I can work some of this out from the articles here and elsewhere on the real climate websites (as opposed to RealClimate website!). Thanks again and Merry Christmas to you and the other contributors/moderators here at WUWT.
    Rob

  16. Roger Pielke Sr has been reiterating the need for using ocean heat as the measure of earth’s climate energy budget for years. I think the climate community is finally getting the message:
    See this telling admission by Trenberth: “Tracking Earth’s Energy: Where has the energy from global warming gone?”
    http://www.cgd.ucar.edu/…/Trenberth/trenberth…/TrenberthSciencePerspectives-1.pdf
    And my post “The Global Warming Hypothesis and Ocean Heat”
    http://wattsupwiththat.com/2009/05/06/the-global-warming-hypothesis-and-ocean-heat/

  17. Willis wrote, “The ‘missing’ energy has therefore been lost to space because it was prevented from getting into the oceans in the first place.”
    Bingo.
    OHC is dominated by natural variables: ENSO, Sea Level Pressure, and the AMO.

  18. Two things come to mind that should be large enough factors to consider in this analysis; Evaporation and plant growth.
    The evaporation of water requires two orders of magnitude more energy than increasing its temperature. Thus, a relatively small amount of increased evaporation would skew the results away from the energy remaining as latent heat–i.e. an ocean temperature increase. Although the resulting water vapor would have to be “stored” somewhere and the cloud-to-rain cycle time frame is relatively short.
    Another global means of energy storage is plant growth. Plant growth on land and in the ocean is necessarily using some of the energy to do complex chemical processes that result in the energy being “stored” in plant cell construction. Not sure of the relative magnitude of this, but I’d expect it to be large enough to consider.
    Since plant growth uses water, these factors may also be inter-related in some way. Though I’m not sure of how that relationship would play out in an energy budget.

  19. The earth atmosphere is not a slab, it is a dynamic fluid with all of the problems of fluid mechanics layered with heat flow. Think soaring birds to witness the dynamics. Not only does it transport birds but heat as well. Non trivial calculations at best.

  20. Figure 2 is a stunning graphic.
    One explanation for the difference may be that S varies with time duration. Intra-annual (winter-to-summer) temperature swings versus solar insolation at various locations throughout the U.S. incontrovertibly demonstrates that S is about 0.05 – 0.15 C/W/m^2. Your observation that S=0.8 C/W/m^2 is much too large for the rapid changes in forcing shown in Figure 2, is consistent with the much smaller value of S for intra-annual changes in forcing.

  21. Willis, where is the incoming energy (∆Q, red) being measured? If it was top of atmosphere, I suppose the instrument could see the effects of stratosphere contamination by volcanoes, but I don’t see why the air would get clearer than usual following recovery. If it is from space, it’s an albedo measurement and the recovery has to do with a reduction of cloud cover to let more energy in to restore the balance, but if that’s true, then the mechanism is not clear because the signal to restore is not evident in the ocean temps, at least globally. If it’s a land-based measurement it is capturing both volcanoes and reduction in cloud cover afterward. Is it possible that the signal is in the data but is smeared by a global average? The largest effects of volcanic dimming should be evident in the tropics where ocean cooling should be taking place. Perhaps the water is sinking there and warmer water is flooding in to replace it. The cooler ocean there should reduce cloud cover to restore the balance later, but you’re showing a very fast response in the incoming energy. I doubt the ocean can react that quickly, even regionally, though it has such heat capacity, the delta T there would be very small to measure.
    You’re showing a system with an extremely large negative feedback on the incoming side, it’s clearly restoring itself at incredible speed. It’s obviously seeking a target, and “knows” when it gets there, I just don’t see where the signal is that’s driving it. I suspect a regional effect that controls clouds. If true, it clearly has an amazing ability to recover. You’re looking at a system with both reactions taking place in a matter of 6 years or so, each with, say, 5 time constants in 3 years, for a TC of about 0.6 years. That’s fast.
    I could see the volcano side being related to the mixing rate of dust in the atmosphere / stratosphere. Perhaps this could be directly related to cloud seeding, with the dust causing a higher rate of rainfall formation than is otherwise normal. The clouds “rain out” faster, thus lowering their residence time upon which solar can be reflected, and more effectively reduce humidity, with a net lowering of cloud cover (since they do their job faster). Once the atmosphere is scrubbed clean, rainfall rates are reduced, and cloud residence time is longer before they are seeded for condensation.
    Whatever it is, it’s a really fast process.

  22. @Willis
    In the more settled science (what little there is) non-condensing greenhouse gas increase in the industrial age accounts for about 2 additional watts/m2 of forcing. Each watt should cause a rise of about 1 Kelvin (or 1 degree centigrade) if everything else is equal. Yet at most there’s only half that much warming in evidence. So the missing heat is about 1w/m2. It could be evenly distributed in the global ocean causing an almost imperceptable rise in its temperature well beyond the margin of detection error or it could be rejected by more efficient means of transport from surface to space or by a change which prevents it from ever reaching the surface in the first place.

  23. Jörg Schulze says:
    December 23, 2010 at 4:40 am
    “Ah, I am just a civil engineer, but surely energy gets stored in the land mass as well as in the oceans. Surface geothermal energy use is quite common in Germany and this energy comes mainly from the sun. Through flowing groundwater it can also be spread horizontally as well as vertically. So, still a big hole in the calculations.”
    Virtually no geothermal energy comes from the sun. It comes from hot spots in the crust where heat from the mantle gets close to the surface. The interior heat of the earth is left over from heat of formation and decay of radioactive minerals.

  24. @jorge (con’t)
    Not much solar energy is stored in land masses relative to the ocean. Ocean albedo is much lower than land and there’s well over twice as much ocean surface as land surface. You can’t go very wrong by looking at the big as “the sun heats the ocean and the ocean heats the air”.

  25. Mike on December 23, 2010 at 3:45 am says:
    “Considered heat energy to kinetic? Not sure how you measure this on a global scale”
    Interesting question, but it may not be much of a factor. Anyway, here is why I don’t think it is, but this is just opinion.
    We have basically three major sinks of kinetic energy. Moving atmoshere, moving water, rotating planetary mass. There are a few others, but I think they are pretty minor, especially longterm. As for atmosphere, any wind that is created eventually dies out by having its momentum converted back to heat. No good way to hide energy there for long. Water in ocean currents stores MUCH larger amounts of kinetic energy, but unless the currents are getting faster and larger on a global scale, you can’t hide energy there either. Also, the low speed of water — even if they do have a lot of mass — means that not much kinetic to heat potential is there. For instance, imagine that you have a current moving at two feet per second and were to suddenly stop its motion and let the kinetic energy change to heat. The warming would be the same as if you raised the water not quite an inch off the floor and dropped it. Not much. As for heat energy somehow going into the Earth’s rotation — the only way I can see just off hand is by transporting mass from the equatorial regions to the poles, or vice versa. If the polar ice caps were actually melting, we would see an increase in the length of the day as the polar mass moved toward the oceans and lower latitudes. If cooling were building up mass in high glaciers or high latitude ice caps, we would see length of day getting shorter. Either way, that would be a very small change since the mass of the earth is so large. I am too lazy to do the math, but my gut feeling is that it might be some change in day length out in the sixth or seventh decimal places.

  26. Mike says:
    December 23, 2010 at 3:45 am
    “Considered heat energy to kinetic? Not sure how you measure this on a global scale”
    Kinetic energy, unless used to permanently do things like store energy in chemical bonds or move matter higher up in a gravitational well where it doesn’t come back down anytime soon it all becomes sensible heat again through friction. Energy must be conserved. The books have to balance.

  27. @willis
    I don’t trust SST as a measure of energy stored in the ocean. The well mixed surface layer is only 300 meters deep and represents only 10% the thermal mass of the ocean. Even if we did have pretty accurate record of SST we have scant record of temperature below 300 meters and we don’t know for sure how fast the surface layer mixes with deep water or how much the mix rate varies under changing conditions.
    I think a better measure of energy content is global average sea level. Water doesn’t compress and it expands and contracts with changing temperature by a simple formula. It then becomes a question of separating volume changes due to thermal factors from volume changes due to more or less water in the ocean. Of course this assumes global average sea level is accurate enough for the task and on a year-to-year basis it probably isn’t but on a decade-to-decade basis it probably is.

  28. There is a huge amount of energy dissipated by moving large volumes of water around.
    Total fresh water inflows into all world seas and oceans is about one million m^3 / sec, or looking at it another way, one million metric tons of water is lifted into clouds (at x km height). Similar amount of sea water goes from Pacific into Arctic , and nearly 10 times in and out of it across the Greenland – Scotland ridge. These are tiny numbers in comparison what is going on in rest of the oceans; e.g. Florida current is 30x as large, Circumpolar current at Drake passage to 250m depth alone is ~ 200x and various Pacific currents are many hundreds times as large. All this energy sooner or later is released into heat (friction etc).
    It is not an even process, currents are not of constant velocity, and they oscillate on multi decadal scale. My investigation into the ocean currents led me to discover number of critical events, which appear to affect the mentioned oscillations, I named gateways.
    http://www.vukcevic.talktalk.net/NPG.htm
    I am reasonably confident that the ‘gateways’, once I get down to do some writing, may be considered as an important contributor to the oceanic oscillations.

  29. What drives the weather? Isn’t that a result of solar energy converted to kinetic energy? If it gets hot, don’t we have a storm, a tornado, or a hurricane? How much energy does one of them consume, and where does it come from?

  30. Ice is cold: 273.15 K
    Water is warm: 273.16 K + 333.55 kJ per kg (Enthalpy of fusion)
    Water vapor is hot: 273.16 K + 333.55 kJ per kg + 2257 kJ per kg (Enthalpy of vaporization)
    Steam is hotter: 273.16 K + 333.55 kJ per kg + 2257 kJ per kg + (4.18 kJ per (kg·K) X 100) (Water heated to its boiling point)
    Dry (saturated steam heated above the boiling point of water), steam is freaky: (No enthalpy of condensation until it cools to its saturation point)

  31. ******
    Jörg Schulze says:
    December 23, 2010 at 4:40 am
    Ah, I am just a civil engineer, but surely energy gets stored in the land mass as well as in the oceans. Surface geothermal energy use is quite common in Germany and this energy comes mainly…
    ******
    Nope. “Land” is a very good insulator (see how it protects from the red-hot mantle), so it doesn’t store heat — the rate of heat-flow thru it (either direction) is insignificant compared to solar input.
    And yes, there are localized exceptions, but even all that geothermal activity in Iceland doesn’t seem to make the air any warmer there. Same for Yellowstone Park.

  32. That was fun. Just wondering…
    What would J/y for the planet tell you? It might be useful for heat loss, but not heat gain from the sun (day/night, latitude, axis tilt). Bizarre how models fail to take into account little things like the effects of clouds, day versus night. Global averaging seems like a basic problem.

  33. Perhaps I read through too quickly but how was the energy accounted for which was consumed by plants? I’m assuming it’s a constant but I missed where it was and how it is used.

  34. Bill DiPuccio says: “Roger Pielke Sr has been reiterating the need for using ocean heat as the measure of earth’s climate energy budget for years. I think the climate community is finally getting the message…”
    The problem the AGW community will have using OHC data is that the NODC OHC data (Levitus et al 2009) portrays the effects of natural variables (ENSO, SLP, AMO), not anthropogenic greenhouse gases.

  35. Thanks for another interesting piece Willis. Could one part of the ‘missing’ energy be a diminishing of atmospheric mass by reduced water vapor. This seems to show that, especially in the upper atmosphere.
    http://i38.tinypic.com/30bedtg.jpg
    Somewhere I read that the atmosphere has diminished in depth ~125 miles in this solar minimum. I would assume less drag and a shorter LOD as a result. Further, with a shorter distance through the atmosphere, would not the system be more efficient at dumping heat to space?

  36. About geothermal energy, the extraction of it and the resulting cooling:
    http://translate.google.de/translate?js=n&prev=_t&hl=de&ie=UTF-8&layout=2&eotf=1&sl=de&tl=en&u=http%3A%2F%2Fwww.geothermie.de%2Fwissenswelt%2Fgeothermie%2Feinstieg-in-die-geothermie%2Foekologische-aspekte.html&act=url
    Scroll down to the last paragraph. They explain that projects are planned in such a way that only after a lifetime of 30 years significant cooling of the underground occurs (i would request an according guarantee in the contract…). And that, if a geothermal installation is used for cooling in summer, the heat in the underground can be replenished during the summer months.
    Sorry, the google translation is crappy… But no solar energy finds its way down there.

  37. rAr says:
    December 23, 2010 at 6:54 am

    Ice is cold: 273.15 K
    Water is warm: 273.16 K + 333.55 kJ per kg (Enthalpy of fusion)
    Water vapor is hot: 273.16 K + 333.55 kJ per kg + 2257 kJ per kg (Enthalpy of vaporization)

    Yeah but heat of enthalpy is latent which means it doesn’t register on a thermometer. The part that registers on a thermometer is called sensible heat. The latent heat only appears (or disappears) during phase changes. Latent heat of vaporization is the biggie being almost ten times the latent heat of melting (fusion). Although I’ve seen it in energy budgets I don’t think climate models adequately account for latent heat of vaporization which can rapidly and effectively suck heat from the surface making it colder while not heating the air immediately above the surface one tiny bit because the sensible heat of the surface is converted to latent heat of vaporization. Convection then carries the heat upward until it condenses and then the heat becomes sensible again but now that heat is thousands of feet above the surface – sometimes tens of thousands of feet in tightly wrapped convective cells. What matters is the air temperature at the height of a Stevensen screen where we live and breathe and plants grow not the air temperature in the cloud layer.

  38. Michael D Smith
    December 23, 2010 at 6:01 am
    Hi Michael,
    Upon first looking at Fig.2 I was startled at the speed of recovery of U (red line) but quickly realised that this was NOT an anomaly but an annual change.
    Perhaps you made the same error?

  39. Should we not also add ‘all life on planet earth’ to the energy matrix. Life requires energy for it to be created. How much energy has been captured & stored in the average four year old in in Glasgow? Or how much energy has been captured & stored in field of maize?

  40. Re:Dave Springer comment of 6:32 am above, where Dave says:
    “I don’t trust SST as a measure of energy stored in the ocean. The well mixed surface layer is only 300 meters deep and represents only 10% the thermal mass of the ocean. Even if we did have pretty accurate record of SST we have scant record of temperature below 300 meters and we don’t know for sure how fast the surface layer mixes with deep water or how much the mix rate varies under changing conditions.”
    Yes, this is correct. We’ve gotten better measurements of heat storage in the oceans since sometime in the 1990s (see Roger Pielke Sr.’s blog, lots of entries on this subject, search for “Josh Willis” to start), I think from satellites supplemented by unmanned devices which dive to as deep as 2,000 meters then resurface and send their data to satellite (Argo floats). Prior to this record, we didn’t have much of an idea of ocean storage of heat.
    I like where Willis is going with this, but if Dave is right as I think he is, perhaps Willis could use the data on actual heat stored in the ocean and redo the analysis only from the mid-1990s.
    Here is a link for an article which discusses “missing heat” since 2004:
    http://physicsworld.com/cws/article/news/42356
    More important, read especially this post at Roger Pielke Sr.’s website:
    http://pielkeclimatesci.wordpress.com/2010/05/21/update-on-jim-hansens-forecast-of-the-global-radiative-imbalance-as-diagnosed-by-the-upper-ocean-heat-content-change/

  41. Steven Kopits says:
    December 23, 2010 at 6:49 am
    “What drives the weather? Isn’t that a result of solar energy converted to kinetic energy? If it gets hot, don’t we have a storm, a tornado, or a hurricane? How much energy does one of them consume, and where does it come from?”
    Heat doesn’t cause storms per se. Temperature gradients cause storms. Differential heating causes gradients. Work can be accomplished as energy flows from greater to lesser. When there is no more temperature differential no more work can be accomplished. Storms don’t consume energy. They redistribute it across warm/cold boundaries eliminating or lessening the difference across the boundary and may accomplish some work in the process like demolishing a house or making tree limbs sway or causing waves on the ocean. Generally none of the work results in any long term energy storage. For instance work is accomplished by convection lifting water from lower to higher elevation but eventually that water comes back down. In many cases we tap that stored gravitational energy in the form of water wheels, hydro-electric turbines, and etcetera. We also tap the kinetic energy in winds. But unless we use that energy to form chemical bonds it all gets released back into the environment as waste heat.

  42. @Willis: “It has to go somewhere, and there’s not many choices.”
    Pedantic grammar niggling: Should be “there are not many choices”, not “there [is] not many choices.”
    Sorry, just really bugs me.
    Great post otherwise!

  43. ******
    Michael D Smith says:
    December 23, 2010 at 6:01 am
    You’re showing a system with an extremely large negative feedback on the incoming side, it’s clearly restoring itself at incredible speed. It’s obviously seeking a target, and “knows” when it gets there, I just don’t see where the signal is that’s driving it. I suspect a regional effect that controls clouds. If true, it clearly has an amazing ability to recover. You’re looking at a system with both reactions taking place in a matter of 6 years or so, each with, say, 5 time constants in 3 years, for a TC of about 0.6 years. That’s fast.
    ******
    Even the ocean isn’t a very good “accumulator” of heat, at least not below the short-term mixing level (I’d roughly guess ~300m). In fact, the oceans below the mixing-level store “cold” instead, from its stratification characteristics. If there is relatively little heat-storage compared to solar input, the earth’s “heat engine” should react very quickly to input changes — like you say, time-constants of around .6 yr or so have been observed. How it reacts depends on the nature of the feedbacks (+ or -), and like you say, the characteristic is of a highly negatively-fed-back control system. Like Willis suggests, a thermostat control.
    It explains quite a bit.

  44. Several years ago I had a conversation with Kevin Trenberth, where – as I remember – he pointed out to me that, on average, 30 Watt/m2 short wave absorption in the atmosphere cannot be accounted for by calculations based on HITRAN molecular data. He called this the biggest problem of the his energy budget calculations.
    The 30 W/m2 deficit also shows up in the work of Albert Arking, who had a Science paper on this topic in 1996. He suggested that this additional absorption occurs at fair weather situations, not at cloudy sky situations, as proposed by others.
    The total short wave absorption in the atmosphere is close to 100 W/m2, when I add 30 W/m2 to the 67 W/m2 absorption given in the energy budget graphs of the Trenberth et al papers. From calculations like those of Trenberth’s group, now concerning the long wave part ot the atmospheric spectrum, the results of 1.5 to 2 W/m2 additional CO2 greenhouse gas forcing are obtained. These results are the basis of subsequent climate model calculations which translate 1 Watt/m2 additional forcing into 0.7 degree Celsius temperature increase.

  45. I too think the jets bring a major source of trends to our atmosphere. However, I don’t see a firm Solar theory as a driver to their movement. I see instead an oscillating, in and then out of, balanced pendulum swing, driving and then following trends. Whatever energy leaks out into space is replenished by the Sun, which is why this leaky system seems to run on a perpetual internal, not external, engine that throttles up and then back in a somewhat unpredictable but nonetheless oscillating fashion.

  46. Re: “Note that this is different from a statement about a general equilibrium, which may or may not be satisfied in any given year. This is an absolute requirement, because energy cannot be created or destroyed. If we add extra energy to the system, it has to either leave the system via increased radiation or get stored in the ocean. There is no “lag” or “in the pipeline” possible with Equation 1. The atmosphere has far too small a thermal mass to store a significant amount of energy. The earth warms too slowly to serve as a reservoir for annual changes. Global ice amounts are fairly stable (although they might make a very small change over the long-term, global annual variations are small). So any large annual change of incoming energy has to either change the ocean storage or leave the system.”
    Although I’m hardly an expert on thermodynamics, it’s imperative that we all agree that this statement appears to assume the conventional physical framework — the gravity-centric universe and all of the models inherent to that system.
    Within the competing plasma cosmology, all bodies in space can acquire and trade electrical charge with each other and their surroundings. This electrical transfer *must* have energy consequences. In that view, this electrical energy is transferred from space to the Van Allen radiation belts, where it awaits discharge to the planet’s surface, and eventually to the core, in the process creating the magnetic and electric fields which we observe to be affiliated with the Earth.
    If this seems ridiculous to anybody, then they should answer why we observe lightning going to space at many miles up from the cloud layer? And, why do we observe the Van Allen radiation belts blink each time that a terrestrial lightning bolt strikes? Don’t forget that scientists have wondered at lightning’s ability to emit x-rays for many years now. These two legs are in fact critical components of this energy transfer system which we should not ignore.
    Also, why does Gerrit Verschuur observe the interstellar hydrogen to be extended in long twisted filaments? Are these shockwaves, as is suggested by conventional theorists — or more likely, the characteristic electromagnetic behavior of laboratory plasmas?
    Our plasma models have been designed to suit the dominant cosmology — which requires that our universe be electrically neutered. The Big Bang cosmology demands that electricity not be a first-order, driving phenomena — but, instead, some sort of second-order byproduct of the gravity-centric universe. This issue of how to model the cosmic plasmas is one of the pertinent questions in cosmology, upon which our selection of the appropriate cosmology depends.
    If we accept that bodies in space can exchange electrical charge with one another and their surroundings in space, then we essentially question the conventional physical framework itself. And, any student of the history of science will tell you that theorists are these days not eager to ask such questions. After all, we never trained them on the competing plasma-based cosmologies. So, admitting even the possibility of such a thing represents an admission that they are not the experts, as it calls into question many assumptions which conventional thinkers have come to think of as undeniable facts.
    But, the public does not have to share in their antipathy for the electric theories. We are not bound to their preferences, prejudices or education. We did not place the wager that they did. We are free to follow the evidence wherever it leads with an open mind to alternative inferences.
    So, I encourage the people of WUWT to learn about the behavior of plasmas within the laboratory, as it has the potential to settle all of these various enigmas which are discussed on this blog. We will not resolve the greatest questions in physics with band-aids. We have to revisit our assumptions, and reconsider the models for the universe’s preferred state for matter — the plasma models. After all, the Earth is bathing in plasma, and within the laboratory, plasmas conduct electrical current.

  47. Stephen Wilde says:
    December 23, 2010 at 3:47 am
    “Cloudiness and albedo actually decline when the system warms up… a warmer world has less clouds not more clouds…”
    Do I understand this correctly?! If the earth warms, there is less cloudiness and the albedo declines, which let’s in more energy from the sun. But, wouldn’t this mean that the earth would get warmer? So, a global warming would beget further global warming.
    May I assume that the converse also is true, that a global cooling would increase clouds and albedo, causing further global cooling?
    This sounds like an inherently unstable situation. Though we, miraculously, are at a climatic state that supports life, it would seem that we shouldn’t make any long-term plans, as either we’ll boil or freeze to death in short order.
    Unless, I misunderstand what you meant.
    BTW, this is a large objection that I have with the concept of positive forcings. If CO2 goes up, temps go up, and positive forcing causes temps to go even higher. In the next period, the then extant higher temps cause temps (through positive forcings) to go higher still… as infinitum. Unless CO2 falls, in which case the positive forcing will cause the opposite loop, and with it a snowball earth. Magically, humanity exists on the razor’s edge, threatened by imminent destruction from even a minuscule change in CO2 in either direction. Unless I misunderstand the concept of positive forcing, as well.

  48. Here is a repeat of a comment I posted a while ago:
    In a previous post (http://wattsupwiththat.com/2010/11/11/27720/) there is a comment by Spector on November 11, 2010 at 11:02 pm that includes a link to a doctoral dissertation by Andreas Lotter (http://archiv.ub.uni-heidelberg.de/volltextserver/volltexte/2006/6686/pdf/dissertation_lotter.pdf) on “Field Measurements of Water Continuum and Water Dimer Absorption …..”
    It seems to me that the paper includes a good overview of the current orthodoxy on climate change. However, there are some very surprising statements that should be brought to the fore when presenting the current orthodoxy (i.e. the “Consensus”) to the general public. On page 26, Lotter has a section titled “2.2.3 Excess Absorption”, which contains the following statement:

    Disagreement in Earth’s radiation budget between observations and global climate models has been a major concern in the climate community for several decades. Many attempts have been made to explain the observed excess of solar shortwave absorption, which is commonly referred to as anomalous, or excess, absorption. The solar shortwave absorption is by far the largest uncertainty in modeling the global radiative budget. … Widespread scientific interest in this topic was revived in the 1990s by a comprehensive analysis of satellite, aircraft and ground-based measurements, supporting the existence of excess absorption and quantifying its magnitude to be about 25 – 30W/m2 [Ramanathan and Vogelmann 1997]. (emphasis added)

    Compare to Lotter’s statement on page 20:

    Although the anthropogenic radiative forcing of 2.4W/m2 [IPCC 2001] is small compared to the natural one, it is of major importance to the future trend of Earth’s climate.(emphasis added)

    Notice that the excess absorption as stated by Lotter is 10 times larger than the purported anthropogenic forcing. It would seem that there there is a very large discrepancy between the theory (i.e. the physics) and the reality that dwarfs the purported effect caused by mankind. Given this very large discrepancy, how can anyone be confident in predicting how absorption will change in the future if the mechanisms of absorption cannot be explained in detail and with greater precision than the variable (i.e. AGW) that is the focus of the current debate? I wonder if this is not (IIRC) what Trenberth was referring to in his comment that it was a “travesty” that they have not been able to find the missing heat?
    It is very important to understand that the uncertainty isn’t whether or not the excess absorption exists and therefore that there is, presumably, warming as a result of it. The issue is that the excess absorption, through the focus on CO2 and the modeling assumption of a positive feedback by water, is being modeled without a clear theoretical explanation of how exactly and by what the excess absorption is being absorbed. Furthermore, given that the unknown related to excess absorption is estimated to be about 10 times greater than the anthropogenic effect, the modelers don’t seem to have any problem with what would appear to be unreasonably precise projections of what the anthropogenic effect will be. Major changes in public policy should demand a better accountability of what is unexplained, especially when the unexplained appears to be much greater than the purported effect (i.e. AGW) that the changes in public policy are being imposed to prevent or mitigate.
    Have I misunderstood something?

  49. This may not be relevant to this discussion but may be relevant to the energy in-out situation overall:
    If cloud cover is (as we perceive) a time function during the day, actually a surface temperature RISE function, the cloud cover cannot be averaged out, and nor can its impact on the albedo be averaged out on the planet simply as a function of area. Will this not result in a disproportionate impact on insolation?

  50. Not a scientist, but if I follow your arguement correctly:
    The “missing” heat energy could be converted to kinetic energy, i.e. wind.
    The extra wind will push on the land and trees, etc.
    Voila: Disrupted Continental Drift
    See, I knew we could connect SUVs to earthquakes 😉

  51. Willis, I think we have discussed some of this before.
    1)When you go from temperature to energy, do you take the 2meter temperatures of the air? That is one error for energy content, because the ground can be much hotter than the air above or much colder than the air above.
    2) Land surfaces are fractal, this means there is a lot more area than the map area that can absorb and radiate. Ocean surface is fractal too, but not to 700meters 🙂
    3) Land has variable gray body constants.
    4)There is kinetic energy in the system, ocean and atmosphere.
    All these have to be taken into account to get an energy balance, imo.

  52. joletaxi says:
    December 23, 2010 at 3:42 am
    something amaze my:earth is a rotating object, and I never found an energy budget off the “dark” side off the earth?
    I have worried about this too but I am not bright enough to think how to resolve it. There are two big issues for me.
    The first is that clouds on the ‘dark side’ keep the earth warm (we all know that a cloudy night is warmer) whilst clouds on the ‘bright side’ keep the world cooler. So any change in the cloud distribution between day and night will have major a major impact on the energy balance. So for climate sensitivity to be a constant the distribution of clouds between day and night would have to be independent of temperature. Does not sound likely to me.
    The second issue revolves around the impact of greenhouse gases. The altitude at which energy is radiated from the earth is a function of wavelength. Around the ‘atmospheric window’ between 8 and 14 micron the air is pretty transparent so at these wavelengths the radiating source is quite close to the surface. The same is true for a range of wavelengths below 5 microns. However at 3, 4, 5-8 amd 14-18 micron the absorption by water and CO2 blocks the direct radiation into space. The energy at these wavelengths goes through numerous absorption and re-radiation steps until it reaches an altitude at which radiation into space is possible. For the CO2 absorption peaks this is close to, or possibly within, the tropopause and for water vapour peaks it is at various altitiudes but typically a few kilometres up. The temperature at these altitudes is much less than the surface and so less energy is radiated than it would in the absence of these gases. This is the so called (but poorly named) greenhouse effect. Lower emissions at these wavelengths means higher emissions at other wavelengths (to maintain the energy balance) and that implies a higher surface temperature.
    My problem is that whilst the surface temperature over land changes considerably between day and night the temperature I would have thought that at higher altitudes it would be more constant. So whilst most of the radiation losses (over land) within the atmospheric windows will occur during the period between mid morning and early evening, radiation at wavelengths around the absorption peaks will be pretty constant during any given 24 hours. At night the surface is cold so much more of the energy radiated into space from the dark side of the earth must be drawn from horizontal energy flows which are not affected by the CO2 concentrations. How do the climate models deal with this?

  53. Occasionally the NWS issues a strong radiative cooling warning, meaning that any heat we might have had on the ground is rapidly heading up through our atmosphere, unimpeded by excessive greenhouse gas or water vapor (IE humidity and clouds in its many forms and degrees). I wonder if the average statistic of radiative balance catches these sudden upward releases of warmth?

  54. According to Dr. Pielke Sr., “The recent data (2004-2008), according to Josh Willis [who babysits the ARGO data and guards it like a Rottweiler –cg], is quite robust in showing no global annual averaged upper ocean warming.”
    We also have extensive satellite radiation data for those years. What happens if you take your equations with dOcean set to zero with data 2004–present? Anything interesting?
    By the way, the elder Pielke’s site (link at right) has a wealth of discussion of ocean heat content; search for that phrase to have a good time…

  55. Work to do with the pieces of the spectrum:
    1.Pick up all pieces of the puzzle. (all pieces are valid)
    2.Put them together in the same place.
    3.Assemble the puzzle.
    Last but not least: Get to the basics and make some “numerology”. 🙂

  56. “Bob Tisdale says:
    December 23, 2010 at 5:50 am
    Willis wrote, “The ‘missing’ energy has therefore been lost to space because it was prevented from getting into the oceans in the first place.”
    Bingo.
    OHC is dominated by natural variables: ENSO, Sea Level Pressure, and the AMO.”
    Actually Bob that was me. It’s nice to be in agreement.

  57. Bob Tisdale says:
    December 23, 2010 at 7:11 am

    Willis: Sorry to be the bearer of bad news, but the OHC dataset you animated is obsolete. It was replaced in 2009 with the OHC data based on Levitus et al (2009). Here’s the main webpage:
    http://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/
    Quarterly data is here:
    http://www.nodc.noaa.gov/cgi-bin/OC5/3M_HEAT/heatdata.pl?time_type=3month700
    And Annual data is here:
    http://www.nodc.noaa.gov/cgi-bin/OC5/3M_HEAT/heatdata.pl?time_type=yearly700

    Many thanks, Bob. I had heard that the dataset had been revised, but I couldn’t locate the new data. However, for the purposes of this analysis it doesn’t matter, since the swings in ocean heat content are nowhere near large enough to balance the budget. The revisions are minor from that perspective. I’ll redo the analysis with the new data, but it won’t solve the mystery.
    w.

  58. A number of people have asked about kinetic energy. All of the work done on the planet eventually (and generally on a short timescale) turns into heat. While the amount of this is critical for the constructal analysis of the planet, it makes no difference to my analysis.

  59. It seems to be, like a Christmas miracle, we are about to break all paradigmatic assumptions and social agreements/mutual or self caressing/holy science beliefs, regarding energy. Then we are about to find the truth.

  60. RHS says:
    December 23, 2010 at 7:15 am

    Perhaps I read through too quickly but how was the energy accounted for which was consumed by plants? I’m assuming it’s a constant but I missed where it was and how it is used.

    We’re looking at the annual changes in energy, and the amount going into/out of plants is (as you point out) about constant. So it doesn’t enter the analysis.

  61. Although I sympathized with him, I was unclear about exactly where the hole was in the energy budget
    Some “numerology”to identify those “holes” (just in case if inquisition friars went on holidays’ vacations):
    1/2=0.5
    2/3=0.66666666666 (Planck’s “constant” rounded: 0.66252. The difference caused by local field)
    3/4=0.75
    4/5=0.8
    5/6=0.833333333 (Regnault’s constant for gases: 0.082. Difference, id….)
    6/7=0.857142857 (the Law of Seven of seven= 1/7=0.142857142857142………)
    7/8=0.875
    8/9=0.888888889
    At the intervals of the musical octave, energy goes in and out.
    Enough for Christmas.

  62. “Bob Shapiro says:
    December 23, 2010 at 8:25 am
    Stephen Wilde says:
    December 23, 2010 at 3:47 am
    “Cloudiness and albedo actually decline when the system warms up… a warmer world has less clouds not more clouds…”
    Do I understand this correctly?! If the earth warms, there is less cloudiness and the albedo declines, which let’s in more energy from the sun. But, wouldn’t this mean that the earth would get warmer? So, a global warming would beget further global warming.
    May I assume that the converse also is true, that a global cooling would increase clouds and albedo, causing further global cooling?
    This sounds like an inherently unstable situation. Though we, miraculously, are at a climatic state that supports life, it would seem that we shouldn’t make any long-term plans, as either we’ll boil or freeze to death in short order.
    Unless, I misunderstand what you meant.”
    There is a misunderstanding there,Bob.
    I’m considering just the solar portion of the equation and ignoring the oceanic modulation for the moment.
    A more active sun causes overall system warming despite cooling the stratosphere for a faster exit of energy to space. The polar vortex intensifies with a faster upward transfer of energy so on the face of it that should result in overall system cooling and not warming.
    However the effect is to draw the jets poleward thereby reducing cloudiness and albedo so that more energy enters the oceans.
    The net effect is a warming system overall because the extra energy going into the oceans exceeds the extra energy lost to space from the intensification of the polar vortex.
    So it’s not a case of a positive feedback. Whether cooling or warming the albedo consequences are a negative feedback to the initial solar forcing and in fact exceed that initial solar forcing because of the composition and dimensions of the essentially water based system.
    The obvious question then is as to why a much more more active sun would not cause the oceans to freeze or a less active sun cause them to boil. The answer is that the extra energy entering the oceans from a more active sun is always greater than the extra energy expelled to space by the intensified polar vortices. Similarly the reduction in energy entering the oceans from a less active sun is always greater than the reduction in energy expelled to space by the less intense polar vortices.
    Thus the more energy from the sun the faster the hydrological cycle will run with warmer ocean surfaces, more zonal and/or more poleward jets and a faster expulsion of energy to space. Another negative feedback situation.
    So, if you follow my proposition correctly we have here an extremely stable system with sufficient negative feedbacks for virtually any situation which is why the oceans have been liquid for billions of years.
    But in the end for the physics to work there has to be a reversal of the consensus based sign for the solar effect somewhere in the atmospheric column. A more active sun must result in stratospheric cooling and a less active sun must result in stratospheric warming or my construct fails as currently set out.
    But see here:
    We see from this link that there was a cooling trend in the stratosphere whilst the sun was more active:
    http://www.jstage.jst.go.jp/article/sola/5/0/53/_pdf
    but note that they also say this:
    “The evidence for the cooling trend in the stratosphere may need to be revisited. This study presents evidence that the stratosphere has been slightly warming since 1996.”
    Now it is possible to argue, as AGW proponents did, that the stratosphere cooled because more CO2 in the troposphere reduced the upward energy flow. That is no longer tenable because CO2 has continued to rise but the stratospheric temperature trend has changed.
    The change in trend coincided with the declining levels of solar activity after the peak of solar cycle 23.
    And look what Joanna Haigh recently said:
    http://www.nature.com/nature/journal/v467/n7316/full/nature09426.html
    “An Influence Of Solar Spectral Variations On Radiative Forcing Of Climate.”
    “Our findings raise the possibility that the effects of solar variability on temperature throughout the atmosphere may be contrary to current expectations.”
    So it may indeed be that the wrong sign for the solar effect on the stratosphere has been adopted by all other current Models and Theories.

  63. Craig Goodrich says:
    December 23, 2010 at 9:42 am
    “We also have extensive satellite radiation data for those years.”
    There is significant disagreement among the satellites. TIM is reporting around 1361 W/m2, ACRIM is reporting around 1366 W/m2.
    http://spot.colorado.edu/~koppg/TSI/TSI.jpg
    Of course Hansen et al will say it doesn’t matter because they work with anomalies rather then absolute values.

  64. Energy can not be created or destroyed only changed . . . .
    Photosynthesis is the process of taking photons, and creating cloryphyll . . . & if wiki is correct
    ” The rate of energy capture by photosynthesis is immense, approximately 100 terawatts,[3] which is about six times larger than the power consumption of human civilization.[4] As well as energy, photosynthesis is also the source of the carbon in all the organic ”
    http://en.wikipedia.org/wiki/Photosynthesis
    I mean, doesn’t E=mc(squared) to me that means energy can be turned to mass and mass can be turned into energy. How that happens is a source of much theory and disussion.
    If I recall correctly, there used to be a group of Scientist that would guestimate the weight of the earth over time. . . . .I don’t know what happen to those people, but I recall that they certainly existed.

  65. trbixler says:
    “December 23, 2010 at 5:54 am The earth atmosphere is not a slab, it is a dynamic fluid with all of the problems of fluid mechanics layered with heat flow. Think soaring birds to witness the dynamics. Not only does it transport birds but heat as well. Non trivial calculations at best.”
    This is why I asked, in a post on Judith Curry’s Climate Etc, why no one has brought in some specialists from the computational fluid dynamics community. I submit that they have the modeling and statistical skills that others have demonstrated are undervalued some parts of the climate science community.

  66. Laurie Bowen says:
    December 23, 2010 at 10:56 am
    I mean, doesn’t E=mc(squared) to me that means energy can be turned to mass and mass can be turned into energy. How that happens is a source of much theory and disussion.
    That E=mc(squared) it’s absolutely wrong; Wasn’t it that nothing can exceed the speed of light?, why, then, the squared speed of light?
    I prefer E=hv (Planck’s equation). If the squared thing would have been true the whole solar system would have exploded with the first nuke.

  67. How about chemical reaction? An endothermic reaction consumes a lot of energy. Now, you might be saying, if there were significant chemical reactions happening in the atmosphere, why isn’t the composition changing over time. Well, you can still have chemical reaction without composition change if the reaction reaches steady-state and the reactants are replenished from the ocean (such as water), land (voc’s), etc. Similarly, the reaction products would have to find sinks somewhere (again, ocean and land). Nonetheless, I assume the order of magnitude is small, but it should be looked at.
    For examples, are forests passive with regard to the energy balance, or do they convert CO2, water, AND energy to cellulose? Similarly, about ocean plankton. Maybe a lot of low wavelength energy is being consumed by biological activity that is not being accounted for.

  68. @ Willis, DirkH, Beng, Dave Springer, etc,
    while the total amount of annual solar energy stored in biomass and land mass may not represent a substantially significant annual percentage, that energy is not ZERO or we would not be having this discussion about CO2 and AGW.
    After all, this discussion is ALL about human conversion of fossil fuels, limestone, etc. at it’s base, isn’t it. The fact is that we have significant trouble measuring these kinds of long-term energy/carbon sequestration processes but they exist all the same, and we would not be whizzing electrons at each other if they did NOT, period.

  69. Chris says:
    December 23, 2010 at 11:25 am
    We are getting closer……but we should be simpler.“It is more difficult for a rich man to enter the kingdom of God than it is for a camel to pass through the eye of a needle.” – Jesus Christ, The New Testament, Luke 18:18
    “A rich man”: A man with too much “pseudo-knowledge”, with too many details…and “the devil is in the details”
    We have to be “minimalists” 🙂 Water comes from the faucet and goes to the sink…..

  70. Dave Springer says:
    December 23, 2010 at 7:40 am
    “Yeah but heat of enthalpy is latent which means it doesn’t register on a thermometer. The part that registers on a thermometer is called sensible heat. The latent heat only appears (or disappears) during phase changes. Latent heat of vaporization is the biggie being almost ten times the latent heat of melting (fusion). Although I’ve seen it in energy budgets I don’t think climate models adequately account for latent heat of vaporization which can rapidly and effectively suck heat from the surface making it colder while not heating the air immediately above the surface one tiny bit because the sensible heat of the surface is converted to latent heat of vaporization. Convection then carries the heat upward until it condenses and then the heat becomes sensible again but now that heat is thousands of feet above the surface – sometimes tens of thousands of feet in tightly wrapped convective cells. What matters is the air temperature at the height of a Stevensen screen where we live and breathe and plants grow not the air temperature in the cloud layer.”
    I think we are pretty much on the same page except that heat and temperature are not the same thing. Heat is something that is applied to or remove from a substance and the change in sensible temperature over time of the substance that heat is being applied to or removed from is a measurement of the heat flow. The sensible temperature of air at the height of a Stevensen screen is a measurement of a heat flow at a given point in time.
    Heat can be stored as latent heat/potential energy and the most commonly occurring substance on earth that can absorb, hold and release large quantities of latent heat/potential energy via phase transitions initiated by a range of naturally occurring thermodynamic processes is water.
    If the GCMs are treating heat and sensible temperature as the same thing the models will never get it right.

  71. “The change in energy at the top of the atmosphere (∆U) is not represented by ∆T/S. I would say that this is the most likely explanation.”
    What I would do is break the data down into two groups, day and night. If there is a solar spectrum change where, for example, you have flat TSI but what parts of the spectrum carry that energy changes over time, that could change how the top of the atmosphere reacts. For example, a lot of short wave UV will heat up the top of the atmosphere during the day (but not at night). A shifting of that energy to longer wavelengths will allow more energy to penetrate deeper to the surface.
    The problem is that the spectrum of sunlight apparently changes. A second problem is that I don’t believe ocean heat is being properly measured. The top several hundred feet of the ocean does not contain the majority of the heat. The majority of the heat will be contained in the water below 1000 feet. A 0.1C change in the temperature of the deep water means a tremendous change in total heat in the system because there is just so much of it.
    Accurate monitoring of deep ocean floor water temperatures is, in my opinion, the only way to really get a read on total heat content of the oceans. Measuring temperatures of the top portion, what accounting for a lot of the heat, doesn’t account for the majority of it. The “average” depth of the Pacific ocean is 15,000 feet, Atlantic is about 13,000 feet and Indian is about 13,000 feed and they are highly stratified in both salinity and temperature. Measuring down to 700 meters is still just skimming the surface. ARGO can not tell us how much heat is in the ocean and there is a lot of that ocean below where ARGO measures.

  72. Simon Hopkinson
    Ahh! Finally, I see mention of kinetic energy.
    -=CUT=-
    I don’t know how much energy is in the movement of air but it struck me that, even though they royally suck as an energy solution and are about as energy-efficient as a BLT with mayo, a few windmills dotted around can pluck quite a bit of energy out of the air.
    You shouldn’t really describe the pressure exerted by wind on and object as kinetic. Kinetic energy is what is directly produced in a collision. Wind energy is mechanical in that it pushes the blades of the turbine round and this converts the mechanical energy too electricity via a generator.
    Energy can neither be created nor destroyed it can only be transformed. So from the wind to the point where the electricity is used we could say that the energy has merely been transported.
    Since this occurs entirely within our climate system no energy is lost. To understand why our climate warms or cools we need to know how much radiation is coming in from the sun and how much the earth is radiating out into empty space.

  73. Not a scientist, but if I follow your arguement correctly:
    The “missing” heat energy could be converted to kinetic energy, i.e. wind.
    The extra wind will push on the land and trees, etc.

    Yes, I’d like to know this too. Include in that waves, those huge waves during storms. That’s a lot of energy needed to do that. Just ignoring that energy loss as minimal is premature until it is at the least modeled, of not measured.
    It would not surpise me one bit that a lot of the sun’s energy beating down on us is consumed in winds, winds with particles, friction with the ground and water. Mechanical motion imparted because of wind.

  74. Not sure, because I didn’t see the details of where you got your numbers from, and haven’t put much thought into it, but are you interpreting the TOA “forcing” as the change in energy input? I understood “forcing” to be the change in net radiation before the system adjusts to restore equilibrium. After equilibrium has been restored by changes in the temperature structure of the atmosphere and other feedbacks, the energy imbalance is much less than the forcing number would suggest.

  75. Willis,
    I have been looking into earth/soil temperatures in the South Island of NZ where there are good records at numerous sites going back to the around 1930’s at depths of 0.1 m, 0.2 m, 0.3 m, and 1.0 m, and reasonable records from the late 1970’s onward at 0.5 m.
    At all depths down to 1.0 metres the annual average soil temperature for the South Island has essentially the same interannual variation as the annual mean surface (2 m) air temperature for the South Island. The multidecadal trends in soil temperature are similar to those of the air temperature. The interannual annual upwards/downward spikes in soil temperature have the same timing as those of the mean air temperarture.
    The inter-seasonal signal is only slightly muted at 1 metre depth. The seasonal lag at one metre depth is only of the order of 1 month or so. It is clear that these changes in soil temperature penetrate more than 1 metre into the soil.
    In addition data on the temperature of river follows essentially the same seasonal pattern as air temperature. Given the intimate connection between river water and widespread alluvial aquifers it is clear that there must be stong seasonal change in “shallow groundwater” temperature many metres below the surface. Furthermore one would expect the magnitude of this seasonal affect to also reflect the magnitude of interannual air temperature variation.
    Clearly air temperature variation does leave an imprint on earth-temperature and fresh-water temperature. While one could argue that temperature is a non-intensive variable, it is hard to see how one can change the soil/earth temperature without simultaneously changing the soil/earth heat content and the shallow groundwater heat content.
    I suspect these temperature/heat (energy) factors impact on earth and river and groundwater on a worldwide basis. The storage significant quantities of heat is not limited to the oceans. Earth temperatures evolve on seasonal, interannual and decadal timescales in concert with the local mean air temperature. The volume/mass involved probably extends 5 to 10 metres below the surface though the depth of penetration will be highly variable.
    If you chose to ignore heat storage in soils and groundwater across continental land masses you need to do more than a bit of simple hand-waving. You need to show that this potential storage is trivial before making such an assumption.

  76. If sst is increasing.
    If there is a thermohaline circulation (cool salty water sinking in the arctic).
    If the THC is surface warm traveling to arctic and cold traveling at 2000 to 4000 metres down towards antarctic (arrival time 700 years?).
    If Argo dives to 2000 metres they will not see the antarctic traveling THC.
    “Estimates of Meridional Atmosphere and Ocean Heat Transports Kevin E. Trenberth and Julie M. Caron” suggest 1.27± 0.26 PW of heat is carried by THC north
    If you heat the north going surface layer which then sinks warmer and travels south at below 2000 metres warmer this must surely be a good hiding place for a fair bit of missing TSI energy! (for a few hundred years)

  77. Hi Willis,
    There is another (smallish) ocean heat factor: the 0-700 number shows most of the warming, but not all. One recent estimate of the heat accumulating below 2000 meters is about 0.1 watt per square meter (3.15 megajoules/square meter per year). There is also likely some (and maybe a little more) between 700 meters and 2000 meters… maybe another 0.15 – 0.2 watts per square meter.
    But that doesn’t help with the apparent large short term fluxes that don’t balance. The most likely explanation is that the resistance of the atmosphere to heat loss to space (AKA greenhouse effect) varies with weather patterns. Big short term changes in loss of heat to space…. with no obvious explanation.

  78. Jeff Alberts says:
    December 23, 2010 at 7:56 am (Edit)
    @Willis: “It has to go somewhere, and there’s not many choices.”

    Pedantic grammar niggling: Should be “there are not many choices”, not “there [is] not many choices.”
    Sorry, just really bugs me.
    Great post otherwise!

    Thanks for the props. Regarding the grammar, yes, I know. However, I tend to write the way I speak, and that construction is quite common in speech. For example, we say “There are a lot of problems”, but we don’t say “there are not a lot we can do about that” …
    All the best,
    w.

  79. joletaxi says:
    December 23, 2010 at 3:42 am
    s

    omething amaze my:earth is a rotating object, and I never found an energy budget off the “dark” side off the earth?

    joletaxi, that’s because we are dealing with annual averages. Not to say that it doesn’t make a difference, but it likely won’t in such an average.
    w.

  80. BillD says:
    December 23, 2010 at 4:28 am

    Willis:
    Now you’ve done the calculations, why not compare your results with Trenberth’s papers and other peer-reviewed publications?

    I read Trenberth’s paper, and he didn’t address this issue. What other papers and publications that deal with this issue would you recommend?

  81. tallbloke says:
    December 23, 2010 at 4:32 am

    Willis, here’s a few thoughts about where else energy might go.
    Kinetics.
    Electro magnetics
    Hidden heat
    On an annual basis, as detailed in Paul Vaughans post today, there is a big exchange of angular momentum betwen the Earth’s crust and the atmosphere causing changes in atmospheric angular momentum and length of day. These changes must affect atmospheric pressure changes and ocean currents and sub crustal flows too, generating heat in the mantle maybe? Maybe it all ties in with Vukcevic’s stuff on geomagnetics and currents in the ring circuit too. Back EMF can soak up a lot of power, and affect the ionisation of the atmosphere.
    Welcome to the bigger puzzle.

    Thanks, Tallbloke. The thing about kinetics (work) and electromagnetics is that at the end of the day, it all turns to heat. The major work is moving the ocean and the atmosphere. To get an idea of how fast that work is turning to heat, consider what would happen if the forces that circulate the ocean and earth stopped operating. How long would it take for the atmosphere and the ocean to stop moving? I’d say they’d be mostly dead still in a week or two, with every bit of their mechanical energy turned to heat.
    Regarding “hidden energy”, that’s just giving the problem a name. Where is it hidden, and how?
    The beat goes on,
    w.

  82. Jörg Schulze says:
    December 23, 2010 at 4:40 am

    Ah, I am just a civil engineer, but surely energy gets stored in the land mass as well as in the oceans. Surface geothermal energy use is quite common in Germany and this energy comes mainly from the sun. Through flowing groundwater it can also be spread horizontally as well as vertically. So, still a big hole in the calculations.

    Jörg, a couple points. First, there is nothing “just” about a civil engineer. I wish more engineers would get involved in climate science.
    Second, geothermal energy comes, as the name implies, from the “geo” and not the sun.
    Finally, if you go outside on the hottest day and dig down a foot or so, the ground will be quite cool. The earth is a good insulator, which is why lots of creatures live underground. So although you are right that the earth can store energy, it can’t accept and release it fast enough to serve as a reservoir for the annual changes.
    w.

  83. RobB says:
    December 23, 2010 at 5:31 am

    Willis – this was a really interesting post. No disrespect to Anthony, but could I suggest you also pose the same questions over on Judith Curry’s blog. As you know the Radiative Forcing threads over there have generated quite a lot of discussion and it would be interesting to see what the reaction would be to your interesting conundrum.

    I posed some questions to Andrew Lacis over on Judiths fine blog, but all that got proven was that do I have a mystery power. Not as good as Superman, I can’t see through walls, but my scientific questions have been scientifically proven to make climate scientists disappear. Neat, huh?
    I do like the idea, though. I should cross-post the 411 of the idea there, with a link back to here …
    w.

  84. chemman says:
    December 23, 2010 at 5:41 am

    Willis;
    Maybe I am mistaken but if the energy input is from the sun then you have to correct one of your variables on calculating total joules for the year. Either time in seconds or the surface area is too large by approximately a factor of 2. Half the earth does not receive direct energy from the sun for approximately 12 hours each day. What would that correction do for your delta Q graph. Eyeballing it it would still be out of balance and your changing sensitivity as a function of temperature would probably come close to solving the difference.

    Chenman, the forcings database is from NASA GISS. It is already measured in watts/m2 (total downwelling energy divided by total earth’s surface). So there is no need for the adjustments you discuss above. They have all been included already.

  85. Willis,
    I guess I don’t understand the CHANGE in energy. I was trying to line up the periods of solar minimum to solar max thinking that would be the largest increases in energy and it doesn’t work. Could someone please explain to me what is causing the large deltas?

  86. Well of course there’s an anomoly, you haven’t homogenized the data or applied “the trick”. Sheesh!! Isn’t it obvious?

  87. Willis, just how many times do I have to repeat this. There is no ‘equilibrium’, the term you are looking for is ‘steady state’. This is a VERY important distinction as steady state thermodynamics, which has a huge literature, is very different from equilibrium thermodynamics. The efflux of heat from the Earth is a case of irreversible thermodynamics, a sub-field of ssTD.
    The whole energy diagram is bollocks, similar to what biochemists were up to in the late 60’s before metabolic control theory (Kacser and Burns); MCT eventually coupled to classical control theory and this opened up a whole range of known, explored, maths to be applied to biological systems (we can now look to Lyapunov stability in steady states).

  88. OK, it finally sunk into my thick head, the large drops are aerosols from the eruptions and the rises are from the atmosphere clearing. The solar cycle would be practically invisible at this scale.

  89. Willis, I don’t think you can use the same sensitivity, S, for all forcing frequencies. The system is like a forced harmonic oscillator. If you drive it too quickly the amplitude (sensitivity) decreases. It is a system with inertia, and the phase lags the forcing, causing this lack of response.
    This also explains why using annual data for GISS in your previous post gives low sensitivity, when if you had smoothed it out over decades you would have seen it increase to the more normal values of 0.7 or 0.8.

  90. Hi Willis – please could you add a start/stop function to the graphic? This would help with scrolling through and observing specific locations over time. Thanks.

  91. Rob R says:
    December 23, 2010 at 2:37 pm


    If you chose to ignore heat storage in soils and groundwater across continental land masses you need to do more than a bit of simple hand-waving. You need to show that this potential storage is trivial before making such an assumption.

    Rob, you’re talking to the wrong guy. I didn’t “choose” to ignore heat storage in soils. Equation 1 above is settled climatology, and has nothing at all to do with my description of it. I agree with it, but I am certainly not the originator of that equation. Run the numbers yourself about the amount of missing energy, and see how much the top metre or two of the earth would heat up if that enormous amount of energy were actually being stored there. You’ll be very surprised.
    Because to disprove equation 1, you’ll have to do more than a simple bit of handwaving …

  92. walt man says:
    December 23, 2010 at 3:06 pm

    If sst is increasing.
    If there is a thermohaline circulation (cool salty water sinking in the arctic).
    If the THC is surface warm traveling to arctic and cold traveling at 2000 to 4000 metres down towards antarctic (arrival time 700 years?).
    If Argo dives to 2000 metres they will not see the antarctic traveling THC.
    “Estimates of Meridional Atmosphere and Ocean Heat Transports Kevin E. Trenberth and Julie M. Caron” suggest 1.27± 0.26 PW of heat is carried by THC north
    If you heat the north going surface layer which then sinks warmer and travels south at below 2000 metres warmer this must surely be a good hiding place for a fair bit of missing TSI energy! (for a few hundred years)

    A lot of people are ignoring the need for speed. You need a possible system that can accept or release a great deal of energy in a short time. Deep ocean currents are a lot of things … but they are not a quick-reacting system.

  93. kuhnkat says:
    December 23, 2010 at 4:53 pm

    Willis,
    I guess I don’t understand the CHANGE in energy. I was trying to line up the periods of solar minimum to solar max thinking that would be the largest increases in energy and it doesn’t work. Could someone please explain to me what is causing the large deltas?

    kuhnkat, good question. Those are the changes resulting from volcanic eruptions. See my previous post for the total forcings and the individual forcings.

  94. slow to follow says:
    December 23, 2010 at 6:54 pm

    Hi Willis – please could you add a start/stop function to the graphic? This would help with scrolling through and observing specific locations over time. Thanks.

    I would if I knew how … you could download it, it’s just an animated gif. Hope that helps.
    w.

  95. Willis,
    Here in the temperate part of Australia, when it’s hot, it’s dry.
    When it’s cold, it’s wet.
    I take it from this, that cloudiness plays a great part in determing temperaure, reflecting heat back into space before it lands.
    Plus the latent heat of evaporation after rain, taking moisture and energy from the drying land back into the upper atmosphere and out to space.
    Plus thunder storms doing the same.
    Unless your incoming heat measure accurately captures these effects, then your formula will be all wrong.
    To me, the climatologists have built a very sofisticated superstructure on shifting sands – the lack of understanding of the basic forces and structures of the climate.

  96. “Dave Springer says:
    December 23, 2010 at 6:32 am
    I think a better measure of energy content is global average sea level.”
    This calculation would be extremely complex. Normal water with no salt has a maximum density at 3.98 C. So water could warm up from 2 C to 4 C and actually contract. Sea water acts similarly. See http://nsidc.org/seaice/intro.html

  97. Willis, what about the heat going into the massive volume on Antarctic ice? Not just the sheer volume but the great abilty of that ice mass to absorb heat and send it down where there are ice at -60ºC.
    There is a big difference between the relation air temperature have with ocean temperatures at 4-30ºC in the surface, and that with ice Antarctic tempertures way down below zero degree.

  98. Baa Humbug says:
    December 23, 2010 at 5:02 am

    And if I do have that right, then we are essentially living through a rare warm period, and the “default” climate of the planet is cooler.
    Now there’s something to worry about.

    As has been observed in the paleo record, there seem to be two basic default modes, Hot House and Ice Box. The former sits around 25°C for millions or 100s of millions of years, and then flips to Ice House, which does likewise. There may be one or two way stations that last a mere few 10s of millions of years.
    Maybe the kind of timing that wobbles in and out of the plane of the galaxy provide?

  99. I made a few comments over at Dr. Curry”s blog on this subject, and got some responses that both agreed with and disputed my assertion. It concerns an area of thermodynamics that I have not heard discussed much, if indeed at all, on any climate blogs both skeptic and alarmist.
    If I remember my thermodynamics professor correctly (it has been many years!) the energy equation always involves creating entropy. This results in a certain amount of the energy being lost from the climate system forever. There is also the fact that much of the energy has been used to do work (enthalpy) that may or may not show up as heat in the system. Much of it is also lost to the climate system forever.
    Anybody out there that remembers more of their thermodynamics classes than I do?

  100. Bruce;
    If entropy is indistinguishable from averaged heat or other lowest-contrast (no-gradient) states, then you need to specify your baseline. Since the Earth is not a closed system, what is high-entropy locally may not be so vis-a-vis its wider environment. So energy that “smooths out” in a patch of the planet surface or liquid-gas envelope is not energy which has vanished, it is energy which is unavailable for local work; as soon as that patch is hooked up to the cosmic background, though, it is again on a (fairly steep) gradient.
    So I don’t think you can say that high-entropy energy is lost to the climate system forever if it has somewhere else it can still leak to. And it does.

  101. But here’s a quibble I retain with those who assert that all work done by wind and wave etc. on the Earth’s surface rapidly turns into mere heat:
    If I place a weight on a shelf, it has/stores potential energy. If I then return it to the floor, whether gently or by dropping it, that energy becomes heat.
    However, if I move it 20′ away, but at the same height, it has no added potential energy. No simple way of unwinding that displacement into heat is evident. Similarly, work done by moving masses of air and water hither and yon does not spontaneously (or in any other evident way) degrade to heat. The “dismissive” way of thinking of such work done seems to say that the displacement “doesn’t count” as real work (unless it was done against the gravitational field). No heat energy was lost/used/tied up?

  102. Steven Kopits says:
    December 23, 2010 at 6:49 am
    What drives the weather? Isn’t that a result of solar energy converted to kinetic energy? If it gets hot, don’t we have a storm, a tornado, or a hurricane? How much energy does one of them consume, and where does it come from?

    NOAA gives a good calculation here:: http://www.aoml.noaa.gov/hrd/tcfaq/D7.html
    The cloud and rain formation: “This is equivalent to 200 times the world-wide electrical generating capacity – an incredible amount of energy produced!”
    and the kinetic energy: :“This is equivalent to about half the world-wide electrical generating capacity – also an amazing amount of energy being produced!”
    That is a lot of energy from one hurricane in one day and it puts the hubris of the human race in perspective. The hydrologic cycle is massively more powerful than most people seem to comprehend.

  103. Energy added to the climate system equals energy leaving the system plus energy going into the ocean.
    Appears to me, uneducated as I am in this, lacking dimension.
    How much energy is used and produced and kept, by life on earth? Plants take in energy from the sun using it for their own growth in life and from that apex more and more complex life systems utilise some of that energy with man at the bottom of the triangle, using it for growth and work which doesn’t ‘escape from the system’. How much energy does one ant use from the sun in its lifetime via plants?
    It appears to me, caveat as above, that AGW has created a lifeless system in thinking in this ‘energy balance’ much as it has done with CO2 with its destruction of the dynamical system which is all life by thinking of plants merely as ‘carbon sinks’, somewhere merely to store CO2; from which the used to be known fact that CO2 was food for all living carbon life forms is practically unknown and now at the absurd reasoning from not knowing it, that it can defy gravity and stay removed and out of reach from the carbon life forms which evolved from its property of being available at ground level. This equation is flat and lifeless. Life is your missing energy.

  104. Willis Eschenbach says:
    December 23, 2010 at 7:42 pm
    walt man says:
    December 23, 2010 at 3:06 pm
    If sst is increasing.
    If there is a thermohaline circulation (cool salty water sinking in the arctic).
    If the THC is surface warm traveling to arctic and cold traveling at 2000 to 4000 metres down towards antarctic (arrival time 700 years?).
    If Argo dives to 2000 metres they will not see the antarctic traveling THC.
    “Estimates of Meridional Atmosphere and Ocean Heat Transports Kevin E. Trenberth and Julie M. Caron” suggest 1.27± 0.26 PW of heat is carried by THC north
    If you heat the north going surface layer which then sinks warmer and travels south at below 2000 metres warmer this must surely be a good hiding place for a fair bit of missing TSI energy! (for a few hundred years)
    “A lot of people are ignoring is the need for speed. You need a possible system that can accept or release a great deal of energy in a short time. Deep ocean currents are a lot of things … but they are not a quick-reacting system.
    Willis”
    Willis, is it not possible that some systems receive energy quickly, but manifest it slowly? While riding a bicycle up a steep hill I can quickly increase the energy in my legs, which, if I am in a low gear will efficiently manifest as a change in speed, but if I am in a high gear this speed change will manifest far slower. Do we really have the understanding and sensitivity in all of our measuring to capture the energy budget as it changes form, phase, and location, or are there possibly slow changes in thermocline depths, hydrologic cycle speeds, atmospheric elevations, large ocean currents etc, that can receive energy quickly but manifest it as temperature slowly or even imperceptibly in regard to our ability to capture these changes?
    Also have you looked at the annual cycles in all that you are measuring to see if the earth’s seasonal energy pulse can reveal some of this mystery? Sunlight, falling on the Earth when it’s about 3,000,000 miles closer to the sun in January, is about 7% more intense than in July. Because the Northern Hemisphere has more land which heats easier then water most people state that the Earth’s average temperature is about 4 degrees F higher in July than January, when in fact they should be stating that the ATMOSPHERE is 4 degrees higher in July. In January this extra SW energy is being pumped into the oceans where the “residence time” within the Earth’s ocean land and atmosphere is the longest
    As these immense changes in SWR TSI happen annually, then how much and how rapidly changes in those things you measured in Figure 1 and Figure 2 match these annual changes, as well as changes in albedo and cloud cover should give deeper insight relative to heat and energy flux within our earth system.

  105. Brian H.
    I agree completely with you about the fact that the work done by wind and waves etc., does not turn into mere heat. It went into doing work that will probably never be returned to the atmosphere or oceans as heat. This amount of energy is massive as Ian W has pointed out. The point I am trying to make about the entropy losses is much the same. If you cannot account for it directly by measuring it, you cannot assume it goes into mere heat either.

  106. Woot! My Quibble Question was #500,000! I win, I win! I’m currently try to extract a list from Anthony of the swag I can expect from him.

  107. As for the displacements, they are not without consequence. Thinking on it, they affect the LOD in some measure, as the center of gravity of the planet has been shifted. Etc.

  108. Pamela Gray says:
    December 24, 2010 at 8:18 am
    “Maybe we should be measuring the greening of the oceans. Kelp anyone”
    Pamela, yes Kelp, plankton blooms, etc. This bio energy has massive fluctations and the organic matter falls to the bottom as ocean snow. On land under the heat of the day it would make a large compost pile indeed. Take just salmon for instance, this past year their population increased dramaticaly:
    http://www.google.com/url?sa=t&source=web&cd=7&ved=0CD4QFjAG&url=http%3A%2F%2Fonline.wsj.com%2Farticle%2FSB10001424052748703657604575005562712284770.html&ei=478VTYTVFImqsAPghYGxAg&usg=AFQjCNH-KNwWceCMOxZ8VYvJ10ben3gugQ
    How much energy such process gobble up for how long I have no idea, which is a travesty I think. (-;

  109. Brian H says:
    December 24, 2010 at 12:31 am

    But here’s a quibble I retain with those who assert that all work done by wind and wave etc. on the Earth’s surface rapidly turns into mere heat:

    I resemble that remark! (Archie Bunkerism)

    If I place a weight on a shelf, it has/stores potential energy. If I then return it to the floor, whether gently or by dropping it, that energy becomes heat.
    However, if I move it 20′ away, but at the same height, it has no added potential energy. No simple way of unwinding that displacement into heat is evident.

    Friction as the block was moved through the air is where the energy went. Both the block and the air heated up a tiny bit. That’s not counting the energy you expended to keep it aloft and walk with it of course. That also heated the air, your body, your shoes, and the floor.
    The frictional heating might seem imperceptable but it’s there. A dearth of friction is why satellites can orbit the orbit the earth so long and a plethora of friction is why it burns up when the orbit decays.

  110. rAr says:
    December 23, 2010 at 11:54 am
    re; heat
    I hear ya. “Heat” isn’t really a technical term and is loosely used for energy quite often. Latent heat and sensible heat are technical terms. So let’s call it energy that is being transported from surface to cloud layer by vaporization and that energy won’t register on a thermometer during transit. All a thermometer will indicate is a cooler surface after evaporation and warmer air in the cloud layer after condensation.

  111. John says:
    December 23, 2010 at 7:51 am
    “We’ve gotten better measurements of heat storage in the oceans since sometime in the 1990s (see Roger Pielke Sr.’s blog, lots of entries on this subject, search for “Josh Willis” to start), I think from satellites supplemented by unmanned devices which dive to as deep as 2,000 meters then resurface and send their data to satellite (Argo floats). Prior to this record, we didn’t have much of an idea of ocean storage of heat.”
    Argo is an improvment to be sure but the average depth of the global ocean is 4000 meters so Argo still misses half of it. It has been deployed for less than 10 years. Average spacing is 300 kilometers so you get one data point for every 90,000 square kilometers. It misses entirely any portion of the ocean covered with ice which seems like a relatively important bit of the ocean to measure.
    Adding insult to injury:
    http://en.wikipedia.org/wiki/Argo_%28oceanography%29#Data_results

    Data results
    It is not yet possible to use Argo data to detect global change signals.[9]
    [edit] Data results from year 2006 with undetected errors
    The Argo Network has [3][10] shown a continuous declining trend in ocean temperatures. The trend was overstated in media reports because of published data with undetected errors in year 2006. In March 2008, Josh Willis of NASA’s Jet Propulsion Laboratory did report that the Argo system show no ocean warming since it started in 2003. “There has been a very slight cooling, but not anything really significant,” Willis has stated.[11] A lot of media has reported the uncorrected data results[12] and even though the revised corrected data appeared in 2008, many articles and arguments still use and promote the uncorrected data results from 2006.[13] [14]
    [edit] Data results from year 2008 and after
    In an article from November 5, 2008, Josh Willis states that the world ocean actually has been warming since 2003 after removing Argo measurement errors from the data and adjusting the measured temperatures with a computer model his team developed. [3][10]
    Here is a graph with the 2008/2009 Argo network data included. [15]

    The raw data showed that the global ocean was cooling but since that result didn’t jibe with AGW dogma some asshat adjusted the data so it showed a warming ocean. Isn’t that just precious?
    So what should Willis use in his calculation – the raw data which shows a cooling ocean or the adjusted data which shows a warming ocean? Inquiring minds need to know.

  112. Werner Brozek says:
    December 23, 2010 at 8:31 pm
    “Dave Springer says:
    December 23, 2010 at 6:32 am

    I think a better measure of energy content is global average sea level.”
    This calculation would be extremely complex. Normal water with no salt has a maximum density at 3.98 C. So water could warm up from 2 C to 4 C and actually contract. Sea water acts similarly. See http://nsidc.org/seaice/intro.html

    Seawater does NOT act similarly. Salinity changes everything. It expands continuously from the freezing point.
    The following graph shows density vs. pressure of seawater:
    http://www.nature.com/nature/journal/v428/n6978/fig_tab/428031a_F1.html

  113. walt man says:
    December 23, 2010 at 3:06 pm

    If sst is increasing.
    If there is a thermohaline circulation (cool salty water sinking in the arctic).
    If the THC is surface warm traveling to arctic and cold traveling at 2000 to 4000 metres down towards antarctic (arrival time 700 years?).
    If Argo dives to 2000 metres they will not see the antarctic traveling THC.
    “Estimates of Meridional Atmosphere and Ocean Heat Transports Kevin E. Trenberth and Julie M. Caron” suggest 1.27± 0.26 PW of heat is carried by THC north
    If you heat the north going surface layer which then sinks warmer and travels south at below 2000 metres warmer this must surely be a good hiding place for a fair bit of missing TSI energy! (for a few hundred years)

    THC flows anywhere from 2 meters per second on the surface (Gulf Stream) to 10cm/second at 1000 meters depth. Distance from equator to pole is 9,600,000 meters. At even the slowest speed it would take 96 million seconds or about 3 years.
    I did this calculation to see when we should expect to see arctic ice melt acceleration in response to El Nino. The lag time should be only about a year because El Nino is north of the equator, ice extends south of the pole, and the current is close to the surface for part of the journey.
    Where did you get a figure of hundreds of years? It’s more like hundreds of days.

  114. @walt man (con’t)
    If you look at the arctic ice extent history
    http://arctic.atmos.uiuc.edu/cryosphere/IMAGES/seaice.anomaly.arctic.png
    you see what an acceleration in ice melt beginning in 2001-2002 which lasted for about 5 years until 2006-2007 then flattened out at a lower extent since then. This seems to line up pretty well with the 1998 “Mother of all El Ninos” and a transport time northward of the abnormally warm water on the conveyor belt of about 3 years and the effect on the ice taking about 5 more years after the leading edge arrived to play out all the way in long term ice melt.
    All the hoopla about arctic ice melt during the period 2001 – 2007 is, as far as I’m concerned, directly attributable to the 1998 El Nino. What caused the El Nino is a different question but the usual suspect is slowing of trade winds which slows down mixing of warm surface layer and cold deep layer allowing the surface to get warmer than it would otherwise. The weaking of the trade winds is of course (like everything else) blamed on global warming even though there’s been no notable increase in frequency or intensity of El Nino nor of La Nina for that matter. In fact one of the worst La Ninas evah (since early 1950’s anyhow) happened right about the same time the arctic ice retreat finished stepping down in 2007. We get severe droughts where I live during La Nina and the 2007-2008 drought was the worst since the 1951-1952 drought. At times like those we pray for Atlantic hurricanes to hit the Texas coast and push rain bands hundreds of miles inland because we don’t get much from the Pacific side during a La Nina.

  115. More correlation between 1998 El Nino and arctic sea ice melt.
    http://science.nasa.gov/science-news/science-at-nasa/2010/12mar_conveyorbelt/
    About halfway down the page is a graph showing oceanic conveyor belt speed from 1991 to 2010. It was slowing down until 1998-1999 then reversed direction and began speeding up and continued speeding up until 2006-2007 where it flattened out. Notably, in the article itself, it said the warm shallow current sped up while the cold deep current slowed down. This aligns perfectly with accelerated ice melt beginning in 2001-2002 and ending in 2006-2006. I strongly suspect these correlations are not merely coincidence but rather are cause and effect.

  116. @willis
    Some “missing heat” might be in latent heat of melting but given that antarctic ice growth about balances out with arctic shrinkage we’d only turn the problem from missing heat into missing ice melt. Maybe we could make a board game out of it. You know, like “Where in the World is Carmen Sandiego?” only this would be “Where in the World is Trenberth’s Missing Heat?”

  117. Brian H says:
    December 24, 2010 at 12:31 am

    But here’s a quibble I retain with those who assert that all work done by wind and wave etc. on the Earth’s surface rapidly turns into mere heat:
    If I place a weight on a shelf, it has/stores potential energy. If I then return it to the floor, whether gently or by dropping it, that energy becomes heat.
    However, if I move it 20′ away, but at the same height, it has no added potential energy. No simple way of unwinding that displacement into heat is evident. Similarly, work done by moving masses of air and water hither and yon does not spontaneously (or in any other evident way) degrade to heat. The “dismissive” way of thinking of such work done seems to say that the displacement “doesn’t count” as real work (unless it was done against the gravitational field). No heat energy was lost/used/tied up?

    Good question, Brian. The work done to displace it horizontally cannot be 100% efficient. Some of it goes into heat. So yes, that is taken into account, because even moving things horizontally in a gravity field creates heat. When you are gambling at the Thermodynamics Casino, the House Rules are prominently displayed on a marquee as you enter:
    1. You can’t come out ahead.
    2. You can’t break even.
    3. You always lose at least a little bit.

  118. Myrrh says:
    December 24, 2010 at 2:38 am

    Energy added to the climate system equals energy leaving the system plus energy going into the ocean.
    Appears to me, uneducated as I am in this, lacking dimension.
    How much energy is used and produced and kept, by life on earth? Plants take in energy from the sun using it for their own growth in life and from that apex more and more complex life systems utilise some of that energy with man at the bottom of the triangle, using it for growth and work which doesn’t ‘escape from the system’. How much energy does one ant use from the sun in its lifetime via plants?

    Myrrh, you are right about life using a huge amount of energy. The thing about the energy used by life is that on a global annual scale, it’s right around a breakeven deal. Take a mature natural forest as an example. Overall, in a year, about the same amount of energy is taken up and stored in new trunks and roots and leaves as is released by the rotting away of dead trunks and roots and leaves. It has to be that way or else over thousands of years, energy would either build up or be lost in the forest. If it did that, the forest would continue to get hotter and hotter or cooler and cooler. Since we don’t see that, we can say that there is at least a rough balance between energy stored and energy released in the forest. And in addition, the forest can’t rapidly change the rate at which it either accepts or releases stored energy. The forest can’t double the volume of wood it contains in a year, for example. So it can’t be the quick takeup or release mechanism we’re looking for.
    Having said that, however, it does strike me as I write this that plankton numbers in the ocean can vary rapidly in quite short timespans (plankton “blooms”), so there’s a possibility. I’d have to run the numbers. My guess is that it would be too small, though. Thanks for the question, brings up new ideas.

  119. Dave Springer says:
    December 25, 2010 at 7:34 am


    Seawater does NOT act similarly. Salinity changes everything. It expands continuously from the freezing point.

    Interesting, Dave, thanks for fighting my ignorance, didn’t know that. Good water density calculator here says the same thing.
    w.

  120. Willis, forests are only part of the plant life on earth, (grasses are the majority plant life), which in its entirety is the base for all carbon life forms on earth, without plants we would die. This energy from the sun is being used by plants constantly recycling themselves in birth, growth and decay and in feeding all the non-plant carbon life forms which are also constantly recycling in birth, growth, decay – the energy from the sun is being utilised in work in every aspect of growth and movement within the Carbon Life Cycle – on land and in the sea. This is a continual cycle of heat production used and regenerated by life itself which stays on earth. Heat produced by the all plants as they turn sunlight into sugars, carbohydrates, proteins and so on through all the fauna carbon food chain. Think of it as an inverted triangle, the plant life at the bottom spreads up through all life forms from the smallest to the largest and most energetic at the top. This, Life, is a dynamic, energetic system; Life uses the sun’s energy here. Life is energy.

  121. “Dave Springer says:
    December 25, 2010 at 7:34 am
    Seawater does NOT act similarly.”
    Thank you for correcting me Dave. Looking back on the graph I alluded to, it appears there was some truth to what I said, but only below a salinity of 24, however since it is 35 at the present time, what I said does not apply. In the temperature versus density graph you allude to, there is a curve, so there would be a different expansion going from -1 to 0 than from 24 to 25. So while the calculations would still be complex, they would be so for a different reason than I initially thought.

  122. I would add that NASA claimed that the earth biosphere has been greening. That is, it has been substantially GROWING. If the oceans have been doing the same there should have been a net storage of energy until the increase peaks.

  123. Werner Brozek says:
    December 25, 2010 at 6:27 pm

    Thank you for correcting me Dave. Looking back on the graph I alluded to, it appears there was some truth to what I said, but only below a salinity of 24, however since it is 35 at the present time, what I said does not apply. In the temperature versus density graph you allude to, there is a curve, so there would be a different expansion going from -1 to 0 than from 24 to 25. So while the calculations would still be complex, they would be so for a different reason than I initially thought.

    The thermal expansion curve doesn’t matter for the same reason the curve of the earth doesn’t matter on a football field. You’re looking at such a small part of the curve that it is essentially a straight line. We’re looking for an average temperature change of perhaps 0.01C in an ocean where 90% its volume is at a nearly constant 3C. The curve won’t matter because there is essentially no difference in the thermal expansion rate of seawater at 3.00C vs. 3.01C.

  124. Also, a good piece on the first attempt to estimate the number of insect species dependent on (the energy of) one species of tree – http://faculty.plattsburgh.edu/thomas.wolosz/howmanysp.htm
    Erwin is basically saying that despite having collected a very large number of insects, the number of new species represented by those insects shows no evidence of leveling of (see below), so there is little evidence that he has reached the point of diminishing returns. In other words there are still large numbers of species yet to be discovered, which supports his massive estimate of species diversity.

  125. Arghh!
    Thanks (NOT) to those who patiently and condescendingly explained that movement involves friction and losses which end up as heat. Irrelevant. Please read what I actually wrote, not what you patronizingly imagine I wrote because it’s easier to respond to. /rant
    (To pit-nickers who miss the “not” after “rant”, I point out that the leading / means “end”, so the usual “off” is either redundant or a double negative, meaning “end of off”, which logically reduces to “on”. )
    OK, so again: ASIDE from all losses and mechanical frictions etc., etc., expended in displacing horizontally without gaining or losing potential gravitational energy, there is a NEW CONDITION with the moved mass. This, I believe, necessarily means energy was both expended and in some manner “stored” in that change. Similarly to the solid weight in my thought example, relocated mega-masses of air and water also consumed and store energy in some fashion — otherwise there’s free motion going on. Yet every model and explanation of “work done” in the GCMs seems to net all that out at zero.
    Perhaps this is valid. But it is NOT explained by hand-waving about friction, etc.

  126. I see a subthread here discussing other pathways in the analysis of the energy balance. Energy is stored in chemical bonds as well as heat, electrical, mechanical, potential wells, etc. Interestingly, most public discourse of this subject concentrates on radiative transfer: heat and light. I see at least one commenter wondering about the relative magnitude energy stored in carbon bonds due to photosynthesis. I believe an easy ballpark calculation could be performed by mentally reversing the process: I believe we know approximately the magnitude of the total biomass on earth, and its approximate constitution. It shouldn’t be too hard to determine the energy one could derive by burning it (converting those bonds to heat), thereby obtaining a pretty good estimate of the energy lost in such bonds. Trouble with considering biomass as an energy sink, however, is that if biomass remains constant then it does not act as a sink at all — only if it is increasing. I believe it is doing so, as has been reported here but I don’t have a reference and certainly don’t recall even orders of magnitude. I imagine the error bars are almost as large as the delta, so while the calculations would reveal interesting possibilities they probably wouldn’t tell us that much for sure.
    I suspect another interesting calculation might come from considering the accumulation of carbonates in the ocean. Limestone forms under the ocean (thereby using up a great deal of carbon dioxide). This is an exothermic reaction. We can probably estimate its magnitude with pretty narrow error bars, given that it is a straight chemical/physical process dependent in a simple way on substrate, temperature and so on. I’ve often wondered at the fact that the deep ocean has been warming while the shallow ocean is cooling. Could this not be attributed to carbonate formation? I’ll leave that to the chemists and physicists in the crowd.

  127. That’s a remarkable salinity graph. The postulated level is 35%!! Which is 10X the actual seawater level, which is around 3.5%.

  128. Chiefio has an interesting postulate/observation: when CO2 gets high (basalt floods, etc.) bio-activity ramps up and gradually drives it down to starvation levels (200+ ppm), until the next big injection. The vast bulk of this is ocean bacteria and phytoplankton, which dump carbonates onto the seafloor, making chalk and limestone. It is not a slow process. It’s the fastest biological cycle on the planet.
    http://chiefio.wordpress.com/2010/11/30/clathrate-to-production/

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