Some of the Missing Energy

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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Stephen Wilde
December 26, 2010 10:29 am

Interesting stuff about optical depth here:
http://icecap.us/images/uploads/WHY_CLIMATE_MODELS_FAIL.pdf
Note that water vapour varies much more that CO2. But instead of causing a huge positive feedback, water caused a strong negative feedback, and reduced the optical depth trend (green line) to 2.58 10-5 X 60 years = + 0.0015, or about 0.083% in 60 years. This means that water vapour has offset 78% of the greenhouse effect of CO2 change over the last 60 years. This is very significant! Note also that there has been a dramatic drop in water vapour at all altitudes in 2008, which is not included in the above calculations. I do recognize that the early NOAA data might be less accurate than more recent data, but this is what the data shows. This data supports Miskowski’s theory of the greenhouse effect. Miskolcki shows the standard theory uses inappropriate boundary conditions. When real boundary conditions are used, he shows that the atmosphere maintains a saturated greenhouse effect, controlled by water vapor content.

Stephen Wilde
December 26, 2010 11:28 am

Joel,
I don’t see anything there about optical depth over the last 60 years as measured by satellites. Have missed something ?

Jim D
December 26, 2010 11:28 am

I thank Joel for digging up those references on direct observations of CO2 affecting outgoing longwave. The Griggs reference is, I think, the particular one I had in my memory, or something very like it.
Regarding water vapor we have
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/figure-3-20.html
from the IPCC report that uses satellite data and total column water vapor, which is more important than mid-tropospheric values, since most of it is near the surface.
On the other point, atmospheric constituents are vital to the effect you were talking about since mass is not varying. This alone explains the greenhouse effect, and how much CO2 can change it.

Stephen Wilde
December 26, 2010 11:33 am

Jim, Joel,
You need to explain to me why you are referring me to data about Outgoing Longwave Radiation when I am asking about optical depth.

Jim D
December 26, 2010 11:47 am

If you are reducing OLR, you are increasing optical depth as long as the surface temperature isn’t cooling to compensate.

Jim D
December 26, 2010 1:15 pm

Willis, we all know that when you make a step change in forcing dU, T doesn’t respond immediately. S is effectively very small or zero in the first seconds. How long does S take to reach the full climate sensitivity? I say several years at least. What does this mean? It means the “missing energy” is just a temporary situation representing thermal inertia, because changing the surface temperature in a climate system actually has deeper impacts in the ocean and soil that have to get into the new equilibrium. The missing surface energy is just going into warming these deeper layers. Averaging over long enough beyond the dU change, the missing energy goes to zero, as T reaches its full response.

Stephen Wilde
December 26, 2010 2:05 pm

“Jim D says:
December 26, 2010 at 11:47 am
If you are reducing OLR, you are increasing optical depth as long as the surface temperature isn’t cooling to compensate.”
I’d prefer to work from a direct measure of optical depth so as to exclude the effect of temperature variability at the surface or in the atmospheric column.
OLR changes could be a consequence of factors other than a change in optical depth. For example, a change in the vertical temperature profile could change OLR without changing optical depth.

Jim D
December 26, 2010 3:39 pm

I am still trying to understand Miskolczi’s definition of optical depth. It seems to be St/Su where St is the part in the window region of the OLR. If so, this is not including the greenhouse gas OLR in his definition, which therefore is not surprisingly insensitive to GHGs. Is this a correct interpretation? Why not use total OLR over surface emission which gives optical depths nearer 0.5 instead of 1.8. His high optical depth is because he is taking only the window fraction, which is just a function of the window width he chooses.

Pamela Gray
December 26, 2010 6:25 pm

Stephen, this paper is a good short article that reflects my current understanding of the teleconnections between the stratosphere and troposphere with regards to the AO. The bottom line is that most studies see the primary relationship as non-influential in terms of the stratosphere as a driver of the AO.
http://www-eaps.mit.edu/~rap/papers/AO_revised.pdf

Joel Shore
December 26, 2010 7:12 pm

Stephen Wilde says:

I do recognize that the early NOAA data might be less accurate than more recent data, but this is what the data shows.

Actually, that radiosonde humidity data is complete garbage for determining long-term trends, as has long been recognized in the literature (you can find a reference in the Soden paper that I linked to) and does not agree with satellite data. Note that the Soden paper shows that both the long-term trend and the shorter-term fluctuations (e.g., due to El Nino and La Nina) show the positive water vapor feedback.

I don’t see anything there about optical depth over the last 60 years as measured by satellites. Have missed something ?

We haven’t had satellites monitoring this stuff for 60 years. The Soden paper essentially measure relative humidity (by measuring the infrared radiation passing through the atmosphere in certain frequency bands), which is the same thing that the reference that you gives reports…except that your reference uses radiosonde data of this that is known to be unreliable, especially for assessing long-term trends.

Note also that there has been a dramatic drop in water vapour at all altitudes in 2008, which is not included in the above calculations.

…Which is exactly what one expects if water vapor is a positive feedback, given that the temperatures in 2008 dropped quite dramatically due to a strong La Nina.

Stephen Wilde
December 27, 2010 4:00 am

Pamela,
That link is limited to short term wind induced anomalies.
For climate purposes we need to consider long term stratospheric temperature trends such as the cooling observed throughout the late 20th century tropospheric warming trend. Conventional climatology says that all the layers should warm together when the sun is active but they didn’t. That is what encouraged the AGW proponents to propose human intervention.
Anyway, back to the point. A warmer stratosphere lowers the tropopause and a cooler stratosphere raises the tropopause whatever the cause of the temperature change.
The reason is the lapse rate so look that up if you need to.
The height of the tropopause dictates the size, intensity and position of the air circulation systems in the troposphere.
So if one changes stratospheric temperatures the perceived climate will change because the air circulation systems shift, especially the jets.
That is established climatology.

Stephen Wilde
December 27, 2010 4:05 am

Joel,
Actually you have commented on the points made in the extract that I quoted. I should have put it in quote marks.
So I am left having to sort out the mess caused by two ostensible experts (which I am not) who present entirely different assessments.
However the Miskolczi finding fits well with my proposition about a variable speed for the water cycle such that any increased optical depth would be negated by an increase in the speed of the water cycle.
So I’ll go with Miskolczi until I find something better.

Pamela Gray
December 27, 2010 5:49 am

I’m wondering if:
Since the heat they are looking for is in the form of LW radiation, it seems logical to ask where can such heat be stored? If not the oceans (an unlikely source because it can’t store any of it except a tiny fraction that may, as some have suggested, get mixed in at the top most layer along with short wave solar radiation and eventually make it to the deeper layer via the http://oceanmotion.org/html/impact/conveyor.htm), then where? Could it be that this is where the notion starts about weather pattern disruption? That this LW heat, that at one time could simply escape but now gets bounced back to the surface and can’t escape, is causing almost immediate changes to weather? Could this be where the idea of “extreme” comes from?
If this is part of AGWer thinking, it forms a conundrum. If it’s getting stored in deep layers of the oceans, it can’t be causing “climatic disruption” (their term for what I think is more properly called weather pattern disruption) at the surface. If its being used at the surface to cause weather pattern disruption, it can’t be getting stored somewhere. If my “wonderings” are full of it, enlighten me.

harrywr2
December 27, 2010 7:53 am

The models do a poor job with Hadley cells. The observed vs modeled changes are significantly different. Climate models that can’t reasonably simulate the observed changes in Hadley cells are pretty useless. Of course since we don’t know why the Hadley cells are acting the way they are it’s hard to simulate them.
http://journals.ametsoc.org/doi/abs/10.1175/2008JCLI2620.1
The authors find that observed widening cannot be explained by natural variability. This observed widening is also significantly larger than in simulations of the twentieth and twenty-first centuries. These results illustrate the need for further investigation into the discrepancy between the observed and simulated widening of the Hadley cell.

Joel Shore
December 27, 2010 8:43 am

Stephen Wilde says:

However the Miskolczi finding fits well with my proposition about a variable speed for the water cycle such that any increased optical depth would be negated by an increase in the speed of the water cycle.
So I’ll go with Miskolczi until I find something better.

Well, don’t be surprised to find yourself pretty lonely then in the scientific community, given that Miskolczi uses a data set that nobody seems to believe is accurate for the purposes that he uses it for.

Joel Shore
December 27, 2010 9:07 am

I am using annual data. I have never heard anyone claim that climate sensitivity varies from year to year. If it does, what is the nature of the variations? Does it change in regards to temperature or other variables? How much does it vary?
Because on an annual basis, what comes in has to equal what goes out plus what is stored.

But, I think Trenberth’s whole point is that we can’t measure all these quantities accurately enough now to see what is happening, at least on a yearly basis. Note that the typical size of your excursions in your graph are about 1 W/m^2. If we were really able to measure all of the radiative quantities to this degree of accuracy, then Trenberth wouldn’t be complaining (and people wouldn’t be using, at minimum, several years of ocean heat content data to diagnose how far the earth is out of radiative equilibrium).

I have gotten as far as “I think that I can show by observational datasets that the current paradigm is incorrect”. While I appreciate your invitation to look beyond that, the first step is establishing that the paradigm is in fact incorrect. I’m not doing anything past simple falsification right now.

I think that you conclusions are based on a combination of misinterpreting what the paradigm is saying and taking data beyond its accuracy. What you have done is confirmed what Trenberth said, which is that we are not currently able to measure all of the quantities to the sufficient fraction-of-a-Watt-per-meter-squared precision that would be needed to understand what is happening to energy in the climate system that is accumulating due to the small imbalances due to radiative forcing.

Pamela Gray
December 27, 2010 9:32 am

Let’s just say Stephen, that there is more than one change in stratospheric temperature to consider. Your thoughts on ozone depletion and signs of recovery in light of your thesis?
http://www.jstage.jst.go.jp/article/sola/5/0/53/_pdf

December 27, 2010 11:25 am

Very interesting post, thanks Willis.
If the Earth’s climate did not have means of self-correction, it would have gotten stuck in one of the extremes many, many centuries ago.
Happy New Year!

Stephen Wilde
December 27, 2010 11:53 am

Pamela,
That link is one which I have referred to regularly and it is fully accommodated in my proposals already.
May I suggest that you actually read what I say ?
Joel Shore said:
“Well, don’t be surprised to find yourself pretty lonely then in the scientific community, given that Miskolczi uses a data set that nobody seems to believe is accurate for the purposes that he uses it for.”
Since the scientific community has a serious problem explaining why AGW now seems so weak in the face of natural variability there isn’t much point joining them just to avoid loneliness. Anyway loneliness will disappear with a bit more evidence of what the natural processes are and can do.
harrywr2 said:
“Of course since we don’t know why the Hadley cells are acting the way they are it’s hard to simulate them.”
Now you are getting to the heart of it. They don’t know why ANY of the major circulation systems behave as they do.
My proposals provide just such an explanation and as time passes the real world is behaving as it should by my account.
If one adds a top down solar effect on the vertical temperature profile in the atmosphere and modulates that with bottom up oceanic variability then the pressure distribution changes and in particular mid latitude jetstream variations become fully explicable.
To achieve that top down solar effect I increasingly think that the secret is to regard radiative physics as largely irrelevant. What seems to matter most is chemical reactions caused by variations in the the energy and particles reaching us from the sun. Those reactions alter ozone quantities differentially at different levels to alter the vertical temperature profile so as to ultimately alter the height of the tropopause so as to alter the pressure distribution beneath.
The role of radiative physics is then merely to try and restore equilibrium after the chemical reactions have done their work.

Pamela Gray
December 27, 2010 4:01 pm

Interesting paper here on stratospheric temperature change. Three models were run, one with ozone depleting substances, one with greenhouse gases, and one with natural forcings. Natural forcings were quite capable of producing changes in ozone that then produced changes in the stratospheric temperature.
http://www.atmos-chem-phys-discuss.net/10/17341/2010/acpd-10-17341-2010.pdf

Pamela Gray
December 27, 2010 4:12 pm

Here’s another one that uses models and observations to describe the ozone-stratospheric temperature connection. It seems that several new and improved models are including a natural forcings only version.
hmmmmm.
http://www.springerlink.com/content/n56tw2k9xj546247/

Jim D
December 27, 2010 6:28 pm

I am still waiting for a reply to my previous comment.
http://wattsupwiththat.com/2010/12/23/some-of-the-missing-energy/#comment-559429
Why is Miskolczi ignoring the emitted longwave from the atmosphere when defining his optical depth? This is probably why he didn’t see any sensitivity to CO2 changes, and really explains a lot. To be relevant to climate you have to use the optical depth of the complete IR spectrum, which he didn’t. He just looked where you don’t expect to see a change, and indeed reported no change there. Is this the way to interpret his results?