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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@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”.
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.
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.
@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.
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.
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?
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)
******
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.
Ocean heat content (OHC) is calculated from Argo observations to a depth of 700m. Heat storage (Q) is a function of mass. So you cannot use SST since it is a massless measurement. I am not clear from Willis’ presentation how he is calculating Q.
The math of OHC is covered my paper “The Global Warming Hypothesis and Ocean Heat”
http://wattsupwiththat.com/2009/05/06/the-global-warming-hypothesis-and-ocean-heat/
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.
I think the thunderstorm idea is important. They are huge transporters of heat vertically. They also convert heat to electrical energy on a huge scale, moving currents from the surface all the way to the ionosphere.
http://www.albany.edu/faculty/rgk/atm101/sprite.htm
How much energy is lost there?
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
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.
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.
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?
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.
rAr says:
December 23, 2010 at 6:54 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.
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?
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?
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/
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.
@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!
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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.
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.
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.