Guest Post by Willis Eschenbach
The canonical equation describing the energy balance of the earth looks like this:
∆Q (energy added) = ∆U (energy lost) + ∆Ocean (energy moving in/out of the ocean) (Equation 1)
This has been modified in the current climate paradigm (e.g. see Kiehl) by substituting in the following:
∆U (energy lost) = [∆T (change in surface temperature) / S (climate sensitivity)] (Equation 2)
which gives us
∆Q (energy added) = [∆T (change in surface temperature) / S (climate sensitivity)] + ∆Ocean (energy moving in/out of the ocean) (Equation 3)
As I detailed in “Where Did I Put That Energy“, the problem is that the data doesn’t bear out the substitution. In the real world, ∆U is very different from ∆T/S. There’s a whole lot of energy missing. I think that some of it is here:
Figure 1. Tracing the path of a tiny bit of energy through a simplified climate system.
Why does this count as some of the missing energy?
Note that all of the energy goes into evaporating the molecule of water. As a result, there is no net change in the surface temperature. Since the definition of the climate sensitivity is ∆T/∆Q, and ∆T is zero, that means that for this entire transaction the climate sensitivity is zero.
It is important to remember that Equation 1 is still true, and this situation complies with Equation 1. The amount of energy entering the system equals the amount leaving plus ocean storage (zero in Fig. 1). However, it does not comply with equation 2 or 3.
This certainly qualifies as a possible mechanism for the missing energy. Response time is fast, and it can move huge amounts of energy from the surface to the condensation level and eventually to space. Also, it is outside the ambit of the the climate sensitivity calculation, since the climate sensitivity for this transaction is zero.
Is this all of the missing energy? Can’t be. The missing energy is moving in huge amounts in both directions, both into and out of the system. However, the mechanism above is one-way. It can remove energy from the system, but not add energy. I say the extra energy added in the other direction comes from clouds clearing out when the temperature drops. But that is another story for another post.
My conclusion? Climate sensitivity is not a constant, it is a function of temperature. Note for example that the warmer the water, the larger a percentage of the incoming energy takes the path illustrated in Fig. 1. The formation of the clouds and thunderstorms is also temperature dependent. All of which makes the climate sensitivity strongly temperature dependent.
As always, questions, corrections, and suggestions are more than welcome.
w.
PS – Please don’t say “but you left out the greenhouse gases”. Yes, I did, but in this case they have almost no effect. The transport of the heat to the upper troposphere takes place in the thunderstorm, so it is protected from thermal exchange with the troposphere. At the top of the troposphere, where it leaves the thunderstorm, there is little atmosphere of any kind. From there it is free to radiate to space with little interference.
And in any case, GHGs will only modify rather than rule the effect. Sure, we might end up with a bit of surface warming rather than zero as in the above analysis. But the essence of the transaction is that surface temperature is not directly coupled to radiation. This means that the substitution done to get Equation 3 is not correct.
PPS — In fact, the system above does more than have zero effect on the surface temperature. When the thunderstorm starts, albedo goes up, storm winds increase evaporation, cold wind and rain from aloft chill the surface, and other cooling mechanisms kick into gear. As a result, the surface ends up cooler than when the thunderstorm started, giving negative climate sensitivity. But that is another story for another post as well.
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Keith Minto says:
December 23, 2010 at 10:27 pm
Keith, this is the path of a bit of energy. Certainly, other paths are taken. My point is that there is an energy path that completely dodges the surface. It comes in and just evaporates water. It does not raise the surface temperature at all. This gives a climate sensitivity of zero.
MikeA says:
December 24, 2010 at 12:12 am
Thanks, Mike. Thermohaline is far too slow to allow for the rapid in/output of energy.
There’s lots of observations that fit my model (nothing is ever proved). See my post on thunderstorms here.
steveta_uk says:
December 24, 2010 at 1:09 am
Not quite. What this example shows is that Equation 2 is not correct, because in the situation shown in Fig. 1,
∆U ≠ ∆T/S
We know this because ∆U (outgoing energy) is equal to ∆Q (incoming energy), and ∆T = zero.
This means that their substitution of Equation 2 into Equation 1 is incorrect, because Equation 2 is incorrect.
Sorry for my lack of clarity.
w.
RE: MikeA says:
December 24, 2010 at 12:12 am
The best way to avoid all the beautiful complexity of the earth’s systems of energy-balancing is to stand outside the system, and to devise some method of pointing a satellite at the sun to measure the incoming energy, and pointing a second satellite at the earth to measure the outgoing energy. That way you don’t have to enter the engrossing and fascinating subject of what the energy does while it is here.
I think thermohaline circulation is one of the most under-funded and under-studied elements of the climate system. When you consider the “input” to the thermohaline currents undergo huge fluctuations, due to the difference between the seasons when ice is forming and the seasons when ice is melting, it makes sense that the current itself might reflect those fluctuations in some manner. Perhaps it throbs like a slow heart beat, with waves traveling along the thermocline. Then, perhaps, these fluctuations reappear at the surface at points where upwelling acts as the “output” of the thermohaline circulation. (Most focus is upon winds, as a cause of upwelling, and very little attention is focused on rate-of-flow.)
Perhaps, perhaps, perhaps. The fact remains, there is still much we don’t know.
What irks me about the likes of Hansen is their know-it-all attitude. Their brains are stuck in some sort of preconceived notion, and seem to atrophy rather than to seek further. Worse, they actively resist research dollars going to study things such as thermohaline circulation, claiming their computer models deserve it all.
The idea that thunderstorms serve as a safety-valve, releasing extra heat from the energy system, has always seemed a very obvious solution to me. Therefore Hansen must have a stock answer, to deflect research dollars back to his computer models, when fellows like Willis Eschenbach ask the blatantly obvious questions.
However all these fascinating areas of research are based on following the energy about once it arrives here on earth, and shifts from state to state, both via changes in latent energy and also via changing from the energy of a sunbeam to the energy involved in transporting massive amounts of water about. This complexity can be avoided by stepping outside the system, and measuring energy coming in and energy going out, via satellite.
Willis said:
“My point is that there is an energy path that completely dodges the surface. It comes in and just evaporates water. It does not raise the surface temperature at all. This gives a climate sensitivity of zero.”
This is a point that I have been pushing for some time in connection with the so called back radiation (or extra downward IR) from more CO2 in the air.
I’ve started from the position that it is for AGW proponents to demonstrate that there is any surplus energy left over from the extra IR once the enhanced evaporation has occurred given that evaporation is a net cooling process.
After loads of bluster and disbelief I have never seen it demonstrated, merely assumed.
So on that basis more CO2 cannot affect ocean temperatures yet it is ocean temperatures that control air temperatures. I see that as quite an obstacle for AGW to overcome.
So what does happen to the extra energy once converted to water vapour via enhanced evaporation ?
Just a miniscule unmeasurable and inconsequential increase in the speed and/or intensity of the water cycle.
Given that solar and oceanic effects on the speed of the water cycle seem to have the ability to shift the jet streams many hundreds of miles latitudinally and cause them to wave about meridionally I suggest that human CO2 might just shift the jets a few yards or so.
Not what I would call catastrophic.
The energy is missing, because it was not trapped by “enhanced greenhouse effect”. Lindzen&Choi and Spencer&Braswell presented by real life satellite data, that OLR is not being reduced as the models predict, basically because the alleged increase in tropospheric water vapor as secondary effect is missing, so total IR optical thickness did not change much.
Caleb said:
“I think thermohaline circulation is one of the most under-funded and under-studied elements of the climate system. When you consider the “input” to the thermohaline currents undergo huge fluctuations, due to the difference between the seasons when ice is forming and the seasons when ice is melting, it makes sense that the current itself might reflect those fluctuations in some manner. Perhaps it throbs like a slow heart beat, with waves traveling along the thermocline. Then, perhaps, these fluctuations reappear at the surface at points where upwelling acts as the “output” of the thermohaline circulation.”
I agree and have proposed just such a scenario to account for part of the 1000 year climate cycling we see from Roman Warm Period (and earlier) to date given that the thermohaline coirculation takes around 1000 years. The other part being solar induced.
The solar cycling is similar at present and approximately in phase with the THC cycling but there is no reason why they should always be in phase as I have discussed elsewhere.
Proposing that underlying THC cycle also has the potential to deal nicely with CO2 observations on the basis that upwelling from warmer THC waters created during the MWP would now be reducing the CO2 absorption capabilities of the oceans so as to at least partly produce the current steady CO2 rise which seems to be unrelated to anything else going on in the climate at present.
So, a lot to play for with regard to the THC, as you say.
“The idea that thunderstorms serve as a safety-valve, releasing extra heat from the energy system, has always seemed a very obvious solution to me.”
Take one more step and propose that the entire water cycle globally serves as a safety valve. The phase changes of water being the primary energy shifting mechanism.
Or rather some sort of modulator which always reacts in a negative fashion to any forcing either internal or external to the system in order to retain or regain temperature equivalence between sea surface and surface air temperatures.
That basic temperature being dictated by density and pressure differentials at the point of contact between sea and atmosphere plus solar energy input to the system at any given moment.
CO2 could then only have an effect if it significantly altered density and pressure differentials but it does not.
Another great post, Willis, and thanks. Science in high school was never this interesting.
Willis,
I enjoy looking at the research and analysis you do. They are very good.
But the complexity of energy if far more complex then simple equations that you illustrate. CO2 does have some effect of blocking what would normally have been energy hitting the oceans to be absorbed/deflected. Add to this the surface salinity changes and the normal balance is totally changed into the cooling effect of oceans when also adding in cloudcover.
H2O is compressed gases that are forgotten as we are used to water being it’s own element.
Rotational energy is the planet pulling the atmosphere generating the pressurized environment and energy of up to 1669.8km/hr at the equator.
Rotational energy is already infused into the atmosphere and is the physical energy available for wind.
In current science, our planet needs not to rotate to produce the current theories.
Willis,
Penetration of solar radiation in the oceans is not very far into the oceans due to the planetary movement of rotation bending the energy in a semi-solid state.
On shore lines, the penetration is absorbed by the material under the shallow water to retain partial heat. Again it is only so far before the peneration is reflected back.
Ocean density becomes a factor as the deeper you go.
Thanks for the excellent post Willis. I think this clarifies part of the energy path and explains why models ignoring evaporation are flawed.
Not being an expert I prefer to keep a low profile and follow-up closely the AGW discussion as it has too big implications to ignore. Sadly it is rather difficult to find unbiased sources of information, this is why I want to thank all contributors for the effort and the high scientific debate one can find here.
Merry Christmas!
IR radiation from the GHG will be absorbed by the water molecules at the surface of the sea and the energy will cause the excitation of these molecules. They will vibrate (stretch, bend, etc) more vigorously, thus converting IR energy to kinetic energy. The more energetic of these molecules will escape into the atmosphere as evaporated water. The IR cannot penetrate the sea to any depth because water is effectively opaque to IR. In my view the greenhouse effect increases evaporation from the sea surface rather than raise its temperature.
What about the “extra energy” from below the Ocean surface
http://au.myspace.com/my/photos/album/965488/custom/list?u=1
Troubling increase in global volcanic activity,REMBERING ONE LAND VOLC’S = 85 SUBMARINE VOLC’S X 20 % ? INCREASE IN VOLCANO’S SINCE 1970.
Underwater volcanoes
Therefore, underwater volcanism should also be the greatest in 500 years. … In the U.S., precipitation has increased 20 percent just since 1970. …
http://www.iceagenow.com/ocean_warming.htm
http://australianconservative.com/2010/11/troubling-increase-in-global-volcanic-activity/
In his book, “Not by Fire but by Ice” the foremost authority on ice ages and magnetic reversals, Robert W. Felix, quoted Peter Vogt of the U.S. Naval Oceanographic Office who warned that,
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
“Almost all tectonic movement can be linked to magnetic reversals. Seafloor spreading, sea level changes, mountain growth, earthquakes, and volcanism all seem to speed up whenever the frequency of reversals speeds up.”
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Magnetic reversals are part of the cycles scientists have determined existed over the 4.5 billion years of the Earth’s existence. They range from the most ancient, the Devonian, to the Holocene, from 10,000 years ago to the present. “At least twelve (magnetic) reversals can be linked to extinctions and climatic deterioration during the last three million years alone,” says Felix.
people often say that people today do not know what real work is. Some 990 millimetres (39 in) of fresh water falls on each unit area of the Earth each year; some 70% of it having been distilled from salt water. This water was carried against a gravity well as high as 30,000 feet. When it made the gas/solid transition it dumped a lot of IR radiation at high altitude and caused a huge pressure/temperature drop.
Do you have any idea the amount of work is involved in the water cycle?
@Willis Eschenbach
> PS – Please don’t say “but you left out the greenhouse gases”.
But you didn’t leave out the most important gas (aka ‘control knob’) => water vapor.
CO2, by itself, doesn’t have much effect, as we can see on Mars (where it is almost 30 times more abundant per unit of surface area than on Earth): the mean surface temperature and black body temperature are about the same, ~210K.
CO2 does have voracious appetite for IR radiation in the main terrestrial radiation band around the 15 micron wavelength. So, on Earth, surface heat generated by insolation is totally absorbed in that main band within the first few hundred meters of the troposphere.
But this extra heat energy doesn’t just sit there, it tends to create rising convection currents which just makes your heat engine work faster, making the climate sensitivity smaller than than it would in a static environment.
You are on the right track. The next step is to show how energy flows from the tropic to the poles in the form of water vapor and clouds and how ice at the poles insulates and causes the earth to act as a capacitor saving energy. At the North pole, the annual freeze/thaw cycle serves as a pump stroke keeping the deep ocean currents going. That’s a lot of kinetic energy. As an aside, CO2 goes along for the ride and has no measurable effect on this constantly changing energy exchange. http://www.kidswincom.net/climate.pdf and http://www.kidswincom.net/CO2OLR.pdf.
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.
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. Some of the energy increases the mean evaporation rate of the earth and is transmitted to latent heat before being released, but most of the extra energy is lost to the atmosphere for a time as it is contained within the ocean, but eventually it is radiated from the ocean as LWR and increased latent heat in water vapor.
In actuality, due to the more intense southern sun’s SW radiation being trapped in the oceans, the earth is gaining energy in the southern hemisphere summers, and losing energy in the northern hemisphere summer. The extra energy is just hidden in the oceans for a time while the northern hemisphere summer reacts on a more sensitive atmosphere, creating a rise in atmospheric heat, but a net loss to the planet relative to the southern hemisphere summer.
AJStrata says:
December 23, 2010 at 8:41 pm
“There are two very large and very dynamic energy sources (external energy from the Sun and internal energy from our molten core).”
Energy from the core neglible. It amounts to a few milliwatts per square meter. Compare that to energy from the sun which is a few hundred watts per square meter. The energy coming in from the sun is 100,000 times greater than the energy upwelling from the core of the earth. The reason is simple enough – rocks are excellent insulators.
Excuse the double paste in the last paragraph please.
I might have the answer. After reading the above post, I inclined to think all that missing energy is pent up in all the climate hippies and that’s why they’re so up tight and so tense they’re struggling not to go ballistic.
Remember that smoke trail over California a while back, even though no rocket fuel what so ever where ever found to have been gone missing, or miss-appropriated, and everything sold was accounted for? Aaah-Ha!
* The ‘tiny bit of energy’ in steps 1 and 2 of your figure fits with long wave IR ( back radiation), which would be absorbed immediately at the surface. (Inbound shorter wave radiant energy (from the sun) is more likely to penetrate deeper below the surface.)
* If we take a step earlier in the process (before your Step 1), the initial LW IR sent from the warm surface toward the atmosphere is absorbed by H2O and CO2, and most of that is converted to kinetic energy (temperature) through collisions with air molecules.
So …. the initial IR transmitted up from the liquid surface is absorbed and warms the air above the surface, kick starting the upward convection as described by anna v and others. And any long wave IR back radiation is absorbed at the surface, vaporizes a bit of water which caries that energy as latent heat up with the already rising warm air as described by Willis. The result, as described by Stephen Wilde is –
“Just a miniscule unmeasurable and inconsequential increase in the speed and/or intensity of the water cycle.”
BTW,
I should have added that the above model is one small system the systems of ‘captured’ of energy I was attempting to address. It is accurate and does show how energy is consumed without effecting temperature or climate. There are systems within even this one. The energy to evaporate a water molecule (or any of elements and compounds in the oceans) is simply the start of the energy consumption. Then there is the build up of potential energy as wind and thermal energy raise that molecule up into the upper atmosphere. When the molecule condenses it loses some of its energy, but the wind can keep it aloft until sufficient mass develops to create a rain drop. In between the water vapor can freeze, liquefy or return to gas – sometimes many times over.
When we have high humidity we have lots of the energy stored in the atmosphere. But there is still lots of water stored in the oceans and in the land. High humidity means a different climate response for that region of the globe.
And the journey of a water molecule is just one mechanism. What about the wave actions and the pounding of shores – which consume energy. The complexities of volcanic eruptions and dust particles which change the absorptive nature of the atmosphere.
The number and intensity of all these individual physical processes divert and consume and release energy into the overall energy balance I mentioned at the top of this post. And our confidence (error bars) on these processes means we do not have the knowledge and experience to know the world temperature today within a degree – let alone 50-100 years ago. And forget 100-1000 years in the past or future.
Flip a coin, it would be just as accurate.
Willis, while I find these posts well written and interesting, I also feel I ought to point out that we’re sitting on top of a 6 × 10^21 ton mass of very “hot stuff” that is a large nuclear reactor filled with molten iron.
Measuring the temperature flitting back and forth in the wisp of air clinging to the surface seems to be ignoring a very large elephant mass in the center of the “room”…
While temperatures in the soil tend to stabilize several feet down, the top layer is not a constant temperature. Take a spherical shell the size of the earth and about a meter thick. What’s the heat content of a 5 C temperature change?… All that rain water does not just sit on the surface. A lot of it enters the soil and takes it’s heat with it…
I prefer to come at it from the perspective of anthropogenic CO2 increased LW radiation coming back to heat us (IE water, air, land). This extra heat can be calculated. However, since scientists can’t find it here on Earth, how is it being released back to space? First off, the extra heat from anthropogenic CO2 is quite small compared to what naturally occurs with greenhouse gases teleconnecting with natural oceanic and atmospheric conditions. The only thing we need to model then is how the various systems are handling (and apparently getting rid of) this tiny bit of extra heat, not how it handles any and all heat.