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
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
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.
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.
@ur momisugly 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.
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…..
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.
“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.
It was the Grinch wot dun it!
After all, he stole Christmas!
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.
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.
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.
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.
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)
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.
Jeff Alberts says:
December 23, 2010 at 7:56 am (Edit)
@Willis: “It has to go somewhere, and there’s not many choices.”
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.
joletaxi says:
December 23, 2010 at 3:42 am
s
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.
BillD says:
December 23, 2010 at 4:28 am
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?
tallbloke says:
December 23, 2010 at 4:32 am
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.
Jörg Schulze says:
December 23, 2010 at 4:40 am
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.
RobB says:
December 23, 2010 at 5:31 am
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.
chemman says:
December 23, 2010 at 5:41 am
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.
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?
Well of course there’s an anomoly, you haven’t homogenized the data or applied “the trick”. Sheesh!! Isn’t it obvious?
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).
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.
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.