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.
Willis
As I understand it, the ocean HC is determined based on an assumption that it is only the top few hundred meters or so that contain the absorbed heat. Now any errors in this depth assumption will cause an energy imbalance, especially if there is significant mixing occurring at depth.
This is a topic that Pielke Snr had quite a “heated” discussion on with one of the AGW scientists earlier this year from memory.
Is a “tiny bit” of energy smaller or bigger than a bread box?
Schrodinger’s Cat says:
December 24, 2010 at 5:05 am
Thanks, Cat. You are generally correct, and it’s a bit more nuanced than that. As you say, IR (infrared radiation, also called “longwave” or “greenhouse radiation”, bad name but we’re stuck with it), does not penetrate into the ocean. It is all absorbed in the first millimetre or so. But this does not keep it from warming the ocean, because of the turbulence of the top layer. So while evaporation is greatly enhanced as you say, some of the heat is mixed downwards, because of the mixing action of wind, waves, currents, and spray.
Despite the mixing, this still leads to differences in the effects of longwave and solar (shortwave) radiation. One difference is in the immediat actual temperature change caused by the solar and longwave (IR) radiation. Suppose we have a change of say 13 W/m2 in solar radiation. Light penetrates deeply into the mixed layer (the top ~100 metres of the ocean that is constantly being mixed). The temperature change of the mixed layer due to that increase is about one degree C in one year.
Now imagine the same change of 13 W/m2 in longwave radiation. This time instead of being absorbed deeply into the mixed layer, it is absorbed in the skin. The temperature of the skin would rise very rapidly were it not for two cooling effects, mixing and evaporation. Which one predominates depends on the meteorological conditions. This is a very different (and very much quicker) temperature change from IR than from solar.
This whole subject deserves a post of its own … “but at my back I always hear, time’s winged chariot hurrying near” …
w.
“But this does not keep it from warming the ocean, because of the turbulence of the top layer. So while evaporation is greatly enhanced as you say, some of the heat is mixed downwards, because of the mixing action of wind, waves, currents, and spray.”
Maybe so but where is the evidence ? The mixing actions themselves increase evaporation even without any more downward IR.
Evaporation is a net cooling process. It always takes more energy from the surrounding environment than is required to provoke it so in fact it accelerates energy flow out of the ocean faster than energy flows up from below. Hence the cooler layer at the top of the oceans that is 0.3C cooler than the ocean bulk below.
More evaporation from extra downward IR would either enhance the coolness of that topmost layer or be neutral. It certainly couldn’t weaken it by warming the water otherwise that cooler layer could not exist in the first place.
I’ve put that issue to a lot of AGW proponents over the years. No satisfactory evidence ever seen as regards a net warming effect within the oceans from more downward IR.
E.M.Smith says:
December 24, 2010 at 7:02 am
Very good question. The specific heat of dry soil is on the order of 0.8, while the specific heat of seawater is about 4.0. So it would store about the same amount of energy as the top 200 mm of the ocean …
The quick-exchanging energy in the ocean is contained in the “mixed layer”, which world-wide is on the order of a hundred metres thick. So the mixed layer contains about 500 times the amount of heat as is contained in the top metre of soil.
The other problem, of course, is that the ground is slow to take in and release heat. This can be seen in the difference between the annual temperature swings over land and water. Since the heat is slow to penetrate the earth, the surface warms much more than the ocean where the heat penetrates deeply. However, I do like your thought that
I hadn’t considered that heat exchange mechanism. I don’t think that it is enough or frequent enough to serve as the source of the missing energy, but I’ll have to ponder it and run some numbers.
w.
Willis Eschenbach says:
December 24, 2010 at 12:36 pm
Willis I wouldn’t have thought too much of the LW warming at the surface skin would mix down. Remembering that the area with the warmest air, the tropics, are dominated by the so called “dolldrums”. Very little mixing happens in these areas.
Also, the water temperature in these areas is already quite high, 28-30DegC so that extra little bit of warming would increase evaporation quicker than any mixing might send it below. But as usual, I could be wrong 🙂
Merry Christmas mate, thankyou for taking the time to post all those wonderful thought provoking essays, I love ’em.
p.s. there is a way to get the likes of Lacis et al to respond to your posts. Post under a pseudonym or get a trusted friend to post for you 🙂 As soon as they see your name, they know they can’t con you with their confusing pseudo answers so they run.
Joel Shore says:
December 24, 2010 at 7:32 am
Joel, good to hear from you. For those joining the discussion, Joel is a physicist. While I disagree with him sometimes, his physics is good.
This is one of the times we seem to be mis-communicating. I’m not talking about models vs. reality. I’m talking about observations versus the current climate theoretical paradigm.
Current climate theory says that ∆U (energy leaving the system) = ∆T (surface temperature change) / S (climate sensitivity).
As the example above shows, that’s not true. And climate models and their antics, while interesting, don’t even enter the discussion.
My best holiday wishes to you,
w.
E.M.Smith says:
December 24, 2010 at 7:59 am
Excellent thought, Chiefio. I’ll have to run some numbers and consider it. How much energy does it take to freeze a metre of soil? Hmmmm …
One problem that I see with that immediately is that permafrost probably only exists on less than 5% of the planet’s surface, so the effect would have to be huge to make a difference.
Jim D says:
December 24, 2010 at 10:02 am
Jim, take another look at the diagram at the top of the page. The problem is not that the surface is slow in warming, as you claim. The problem is that the surface doesn’t warm at all, because every bit of the incoming heat is used to evaporate the water molecule.
So no, time lags and delays don’t matter in this example. My point is that there is a path through the climate system that does not obey the canonical formula
∆U = ∆T/S
and that lots and lots of energy is taking that path.
Willis
One other point re the assumptions that are made re the warmed ocean layer, ENSO and NAO surely ensure that a constant depth is not a valid assumption. Im still with Pielke on this in that there are major errors in the warmed layer calc.
Terry says:
December 24, 2010 at 11:08 am
Two comments about that. First, the deeper it is, the slower it changes, and we are looking for something that is capable of moving large amounts of energy into and out of the system annually.
Second, I have used the heat measurements down to 700 metres in my analysis.
So the odds that the missing heat is hiding below 700 metres, but can still pop out to supply the missing energy in one short year is very doubtful.
Re:
Steven Keohane says:
CO2 causes cooling?! WUWT?
Joel Shore responds saying:
“Yes…The increase in greenhouse gases is expected to cause cooling of the upper parts of the atmosphere (the stratosphere and apparently the mesosphere and thermosphere too). The different temperature change structure expected in the vertical from greenhouse gases distinguishes it from what is expected, for example, for a warming due to an increase in solar radiation.”
My response:
And this is connected to catastrophic AGW/change/disruption how? CO2 is a bit player in warming or cooling of the stratosphere and any temperature change at that level leaves us untouched by that change.
At issue is whether or not a fraction of a % increase in CO2 leads to substantially warmer/cooler/extremes here on terra firma, in the pressure systems that surround us, and in our oceans.
I give you this: if the heat you say should be here warming us up is instead escaping to space, then it should show up in the upper troposphere somewhere as it passes through. But we can’t find it there. That is not to say it isn’t there. It could be a problem with how we measure it. I think as heat is escaping, it is difficult to capture its signature in the upper troposphere as I think it is a very localized, sudden, transient phenomenon, with at least two different kinds of escape hatch that move around. I know through experience that localized strong radiative cooling is a sudden large drop in temperature, as if it were on an oiled slide. And that cooling that occurs in and around thunderstorms can take your breath away and leaves you searching for a jacket in the middle of summer. These localized great escapes of heat are quite different than the slow rise in temperatures in regional areas. Might this balance out?
Willis, there are only three ways to increase the evaporation rate, 1) the ocean gets warmer, 2) the wind gets stronger, 3) the air gets drier. Which of these are you proposing happens?
The point of my previous message was that if you had S correct, you would not need an extra term. S critically depends on the time over which you measure dT.
Anybody have the full text to this:
http://adsabs.harvard.edu/abs/2010AGUFMSA31B1737L
It would seem that temperatures in the stratosphere and mesosphere, and tropopause are teleconnected to the solar wind. So change in the solar wind is hypothesized to have an affect on the measured temperatures at these layers. Mind you, I don’t see how these changes greatly affect whether or not we peel off clothes or add downy jackets to our daily wear.
Pamela,
Due to the little matter of the lapse rate the temperature of the stratosphere controls the height of the tropopause and thus the pressure distribution in the troposphere.
Anything that affects stratospheric temperatures affects climate.
It is conceded by established climatology that extra UV when the sun is more active warms the equatorial stratosphere to lower the tropopause there, widen the tropical air masses and push the jets poleward.
However none of the models can get that effect to account for the sheer scale of observed jetstream changes.
Consequently it is necessary to go a step further. The equatorial effect on stratospheric ozone is only a part of what goes on.
Additionally when the sun is active there is increased ozone destruction from around the stratopause upwards. That cools the upper layers (as actually observed) and additionally cools the stratosphere (also as observed) despite that equatorial UV effect.
That is the only theory I have ever seen proposed that actually fits what happened in the real world without resorting to the assumed effects of CO2 and CFCs.
The first step in proving that scenario has been the recent finding that between 2004 and 2007 ozone amounts increased above 45km for a warming effect despite the sun being quiet and presumably when the sun was active ozone above 45km declined for a cooling effect exactly as I propose.
So the idea that all we see is simply internal system variability is not tenable.
Furthermore anyone who does not accept my alternative explanation whilst failing to provide yet another alternative is impliedly accepting AGW theory on the basis that there is no other explanation (than AGW) for a cooling stratosphere at a time of active sun.
Anyone who disagrees with AGW theory must have an alternative natural explanation for the apparently anomalous temperature trend in the stratosphere when the sun was more active.
I have provided one which is consistent with more recent findings so if AGW is to be challenged successfully we have to run with it unless someone has a better idea.
“Jim D says:
December 24, 2010 at 1:52 pm
Willis, there are only three ways to increase the evaporation rate, 1) the ocean gets warmer, 2) the wind gets stronger, 3) the air gets drier”
1) is based on a false premise. There is no need for the ‘ocean’ to get warmer. All that is necessary is for additional energy from any source to be captured by individual water molecules that are already on the cusp of evaporating. The more energy that is supplied the more molecules are affected.
The additional energy brings forward the moment of evaporation and when evaporation occurs more energy is drawn from the environment than was required to provoke it. Evaporation is always a net cooling process.
Jim D says:
“there are only three ways to increase the evaporation rate, 1) the ocean gets warmer, 2) the wind gets stronger, 3) the air gets drier. Which of these are you proposing happens?”
All three, it’s how a Hadley Cell works. If you simply accelerate Hadley Cells a little bit the excess heat ends up being dumped into the stratosphere.
http://www.newmediastudio.org/DataDiscovery/Hurr_ED_Center/Easterly_Waves/Trade_Winds/Trade_Winds_fig02.jpg
What is the ratio of LWIR energy emitted from:
a) LWIR energy emitted from 1 sq Meter of the earth’s surface (assume ‘standard dirt’ LWIR emissivity values for the earth’s surface for this value)
to
b) LWIR energy emitted from a 1 sq Meter ‘column’ of air running from just above the surface of the earth to the TOA and this would be LWIR emited upwards only from that atmospheric column (one could take value of overall LWIR exiting TOA and subtract the amount computed coming from the surface a) above to derive _that_ which is due to LWIR emissions from the atmosphere alone).
I will venture to say the value from the surface >> than that of that atmospheric column of air (LWIR out to space due to LWIR from air molecules comprising a column of air from the surface of earth to TOA altitude) .
.
Please Steven, let’s call that a hypothesis. It is not anywhere near being a theory. And when an idea is a hypothesis, the null hypothesis rules. Your posts, illuminating a hypothesis, should start with a question, which is the proper way to talk about a hypothesis. A theory is a statement.
Sorry about your name. Replace “Steven” with Stephen please. Again I apologize. However, your post is so filled with assumptions and either/or statements that it has my dander up and my red hair flaming!
I refer to the longwave (IR) causing evaporation from the sea. I agree with the comments of Willis and Stephen Wilde.
Thinking about this in more depth, the stretching, bending, wagging and rotational effects are IR frequency dependent and characterisitic of the water molecule infra red signature. So more IR photons will cause more energetic vibrations of water molecules. The energy of the molecules can be regarded as thermal or kinetic. Possessing a higher energy means that these molecules behave in the same way as if they were heated. If you like, they were just heated efficiently by giving them energy at wavelengths at which they absorbed.
In addition to the enhanced movement of the hydrogen-oxygen bonds, any further energy input will cause the water molecules to move about more vigorously and break away from the surface into the atmosphere. This involves the effect of vapour pressure which itself is a function of temperature.
Then we get the latent heat of evaporation, which is very large.
I’m enjoying this debate but more pressing things are happening. I’m typing this after returning from a Christmas Eve party. All the family have gone to bed and I’ve just realised that my wife has removed the bottle of wine that was to the left of my keyboard. I am now into Christmas day by more than one hour so it would be very Geekish (is that a word?) to continue.
Very best wishes to Anthony and family, the moderators, Willis, and all of you.
[The mods strongly recommend finding (1) your wife or (b) your bottle of wine.
Your choice of order will be important in determining what you find after either (2) or (a) ….. 8<) Robt]
Stephen Wilde, there is an equilibrium vapor amount at a water-air interface given by Clausius-Clapeyron. There is no way to just add to the evaporation rate if temperature there is not changing. It is incorrect to think IR photons just cause evaporation, and not heating of water molecules. How can they distinguish, and does a single photon even have enough energy to evaporate a molecule by supplying sufficient latent heat? Not quite.
Pamela Gray says:
“Please Steven, let’s call that a hypothesis. It is not anywhere near being a theory. And when an idea is a hypothesis, the null hypothesis rules. Your posts, illuminating a hypothesis, should start with a question, which is the proper way to talk about a hypothesis. A theory is a statement.”
Excellent post, Pamela. Concise. There are way too many assumptions floating around.
And a great post by Willis, as usual.
Willis: As many times before, BRAVO. I’m certain you’ve hit on the extraordinarily large-scale phenomenon that obviates the otherwise static CO2 begets H2O begets even more H2O, all the while broasting earth with LW radiation of the AGW clique.
Here, the H2O just bolts into the stratosphere, gives back its heat as it condenses out to the (now) dry air that goes on to rid the heat to space (and form deserts where it comes back to earth on cooling, plus form the trade winds, yawn!). The water now falls back to earth cooling it, and maybe, sucks up a bunch of CO2 in doing so, putting that varmint in the confines of the ocean.
And, following what Pamela Gray says:
December 24, 2010 at 7:36 am
“…I can’t see how this tiny bit more heat (anthropogenic) at the surface will have much of an affect on land….”
the same thing goes on at temperate latitudes during summer, as massive thunderstorm systems set up in places like Oklahoma and Wisconsin and the Ukraine and so on.
So we now have a system that simply cuts across the radiation in/radiation out/radiation back models, and that incidentally, results in major features of the earth’s surface (deserts) and atmosphere (winds). My guess is that this is one of the key elements of the earth’s climate. All because of one little, uniquely odd molecule called WATER. There ain’t nuthin’ like it anywhere else that we know of.
Keep up the good work.
Schrodingers Cat, you are starting to come around to the idea that IR can heat the surface, and that in turn gives more evaporation. You don’t shortcut the heating like the others here seem to be trying to do.
The net effect of IR is actually cooling, because there is a net loss of longwave energy from the water surface, but its cooling effect is slightly offset by adding CO2 the way adding cloud cover does relative to a clear night. It is easy to imagine that an ocean under cloud cover at night is on average going to be warmer than one under clear skies. Same thing with CO2. No one talks about cloud cover enhancing evaporation, but it is the same physics as far as photons are concerned.