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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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
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.
Werner Brozek says:
December 23, 2010 at 8:31 pm
“Dave Springer says:
December 23, 2010 at 6:32 am
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
walt man says:
December 23, 2010 at 3:06 pm
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.
@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.
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.
@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?”
Brian H says:
December 24, 2010 at 12:31 am
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.
Myrrh says:
December 24, 2010 at 2:38 am
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.
Dave Springer says:
December 25, 2010 at 7:34 am
Interesting, Dave, thanks for fighting my ignorance, didn’t know that. Good water density calculator here says the same thing.
w.
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.
“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.
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.
Hi Willis,
Your fig 3 seems to bear some kind of relationship (not perfect but clearly related) to the southern oscillation index SOI
http://tallbloke.files.wordpress.com/2010/12/willis-energy-soi.jpg
Cold some of the energy be involved in shifting the atmosphere around creating the pressure differences which drive ENSO?
Could the energy error be generated by the mishandling of clouds (and hence insolation at the surface) by the equations?
Werner Brozek says:
December 25, 2010 at 6:27 pm
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.
Willis – an example of the diversity of life fed and supported in the Carbon Life Cycle from the energy of one tree – http://www.treesforlife.org.uk/forest/species/oak.html
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.
– should be “leveling off”, my typo.
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.
Mod: typo — miss the “off” after “rant” [not “not”]
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.
That’s a remarkable salinity graph. The postulated level is 35%!! Which is 10X the actual seawater level, which is around 3.5%.
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/