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 says:
December 24, 2010 at 2:15 am
“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.”
Yeah, that’s a sticking point for me too. IR is absorbed by water in a vanishingly thin surface layer which results in increased evaporation but no heating of the water. Visible light on the other hand penetrates hundreds of meters and does in fact heat the water. So called back radiation then cannot heat the water but in fact heats the troposphere at the cloud layer. The AGW boffins know this. It’s why their model of non-condensing GHG heating predicted a signature effect of more heating higher up in the troposphere than at the surface – the infamous tropospheric hot spot.
That’s all well and good and it does work that way but that way results in rather little surface heating. Therefore the boffins introduced a positive feedback effect from water vapor. They reason the increased evaporation rate raises the relative humidity of the air and it’s well known that humid air keeps things warmer than dry air. Thus the small surface temperature rise from more NCGHGs (CO2, methane, et al) fosters a rise in the condensing GHG (water vapor). If things actually worked that way we’d have a runaway greenhouse. But here’s the kicker. One of the more well established paleo-atmospheric facts that must be considered is that for most of the time in the past 500 million years the atmosphere held 10 to 20 times more CO2 than the present atmosphere and there was no runaway greenhouse. Global average temperature was at most were 8 degrees C warmer than today and moreover the higher temperatures were not evenly distributed but rather concentrated in higher latitudes with the effect of turning the earth green from pole to pole. That is the “normal” state of the earth’s climate. What we have today is a temporary, still rather cold, and long in tooth intermission in the full blown ice age that began about 3 million years ago.
Where I believe the AGW boffins go wrong is that there is no increase in relative humidity caused by increasing GHGs but rather an increase in the speed of the water cycle. RH remains constant there’s just more and faster transport of water vapor from surface to cloud layer and more rain. The carbon cycle speeds up too as the higher CO2 level and milder temperatures in the wintry north accelerates and expands plant growth which means more animals get fed and when they die more bacteria decompose them releasing their stored carbon back into the air which is then food for plants and the cycle continues.
Increasing CO2 is a good thing. Increasing warmth is a good thing. The only downside is rising sea level as it pretty much goes without question that as the wintry north gets warmer glaciers will melt but that process takes thousands of years. Wild terrestiral plants and animals have plenty of time to migrate away from the encroaching sea and (like it or not) humans will have to do the same. The net benefit to the biosphere as a whole though is tremendous as the whole world turns a lush verdant green.
What I mean to say is that we don’t have extra energy entering the system. CO2 does not cause extra energy to enter the system, unless we are saying that anthropogenic CO2 is revving up the Sun. AGW says that we have some of the constant incoming heat energy staying around instead of cycling through a leaky system. But since we can’t find it here, it must be leaving in a way that AGW has not been able to model.
Willis, the comment I made in your last thread wrt missing energy seems more apropos after this piece. That was that the atmospheric height has decreased. It was published in the AGU, http://www.agu.org/news/press/pr_archives/2010/2010-28.shtml . Allegedly, the thermosphere, between 55 & 300 miles, had lost 30% of its density by 2009 due to reduction in the solar wind. I came across a reference I can no longer find this year that put the contraction at 125 miles. To me, this would allow for a more rapid transfer of energy to space during times of low solar activity, slightly less energy into the system, but more going out exacerbating the minimal change in TSI.
Willis,
Follow your reasoning to its logical conclusion: In order to send more heat back into space, the upper troposphere must warm, since the only way it exchanges heat with space is via radiation and radiation depends on the temperature. So, what you are suggesting is that the upper troposphere in the tropics warms more than the surface.
However, to the extent this is true, it is already included in the models as a negative feedback called the “lapse rate feedback”. Now, I suppose you could argue that they are underestimating the lapse rate feedback…but then that would mean that the tropical tropospheric amplification should be larger than the models predict. And yet, most empirical data currently suggest that it is the same or smaller than the models predict. The data suggesting smaller is pounced upon by skeptics as evidence that the models are wrong (and sometimes wrongly claimed to show that the warming that is occurring can’t be due to the mechanism of greenhouse gases). While there is reason to believe that the long-term trends in the upper tropospheric balloon and satellite data has some artifacts, you now seem to want to claim that the actual temperature trend in the upper troposphere would be larger than the models predict.
I meant to add this from the AGU abstract, “The results showed the thermosphere cooling in 2008 by 41 kelvins (about 74 degrees Fahrenheit) compared to 1996, with just 2 K attributable to the carbon dioxide increase.”
CO2 causes cooling?! WUWT?
I can’t see how this tiny bit more heat (anthropogenic) at the surface will have much of an affect on land. It won’t cause much of a difference in soil evaporation. It could be absorbed in the greening of the planet. Plus pressure differences will sweep some of it away to other locations. If it landed over areas experiencing strong radiative cooling, up it goes. Some of it would be taken out over the oceans. This would cause a bit more evaporation at the water’s surface but the tiny extra amount of evaporation would likely just be added to the already in motion hydrological cycle. It may just come down to the jets taking care of this tiny amount of heat, calculated by the AGW models to stay here, by moving it around to places that already have atmospheric escape hatches doing their thing. And since adding more CO2 has diminishing affects, I think the Earth’s system are dealing with it just fine. The reason why we can’t find it is because it isn’t here in amounts outside the standard error.
Caleb says:
December 24, 2010 at 2:00 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. ”
We have that and we still end up with Trenberth’s ‘missing heat’. In the catastrophic scenario we have 1/2 W/m2 hiding somewhere building up over decades that will suddenly stop hiding and kill us all, similar to the Loch Ness monster.
Without heat hiding somewhere in the system the observed surface temperature increase over the last 100 years is pretty close to what the physics says. I.E. A doubling of CO2 will cause a 1.2 degree C rise in global temperature all other things remaining equal, of which .8 degrees C is already ‘water under the bridge’ so to speak.
Of course the missing 1/2 w/m2 out of 1366 could be measurement error in the satellites that measure incoming/outgoing radiation or the argo buoy’s that measure ocean temps or the satellites that measure sea level.
Dave, I am thinking the only change I would make to your statement (which is on the whole entirely well thought out) is that our land masses have changed positions, re-directing currents and their teleconnected atmospheric systems in such a way as to freeze up the poles (of particular note the AO and AAO atmospheric systems, along with the Antarctic circumpolar current). I don’t think CO2 increases would green up the poles unless land location changes redirected oceanic currents.
By the way Willis, I love, love, love this thread. Thanks for starting it.
The climate is an open thermodynamic system as it has energy flowing through it. The missing heat cannot be considered without considering the energy required to keep the climate in its negentropic (i.e.: non-equilibrium) state. In my view any analysis of heat fluxes through the climate that ingores entropy must be wrong.
Oh, and “permafrost” tells you how much ground freezes / thaws each year.
Small map here:
http://nsidc.org/fgdc/maps/ipa_browse.html
Data about it here:
http://nsidc.org/data/ggd318.html
The main map is here with full size readable legend.:
http://nsidc.org/data/docs/fgdc/ggd318_map_circumarctic/index.html
and in the legend it says percent 10 – 20 meters down that’s frozen. So that says up to 20 m of depth CAN freeze / thaw each year. That’s going to hold a lot of heat…
Oh, and all the places NEAR the permafrost that does not show on the map but gets snow each winter will also freeze “to some depth” that varies with the place.
So there is a very large chunk of heat flux into and out of the earth itself each freeze / thaw cycle. I’d not ignore the frozen parts of the world and the dirty parts of the world…
harrywr2 says:
Regarding December 24, 2010 at 7:39 am
Caleb says:
December 24, 2010 at 2:00 am
”
Without heat hiding somewhere in the system the observed surface temperature increase over the last 100 years is pretty close to what the physics says. I.E. A doubling of CO2 will cause a 1.2 degree C rise in global temperature all other things remaining equal, of which .8 degrees C is already ‘water under the bridge’ so to speak.”
The vast majority of that rise in CO2 is only for the last 30 years, or 1/2 of a 60 year cycle. The 1.2 C rise only reflects in those thirty years, which is matched by previous natural, (non CO@ur momisugly induced) rises. Give us another 10 to twenty years and we shall see.
harrywr2, I believe Trenberth’s conclusion that AGW heat is hiding somewhere is partially based on a very short span of data actually measuring incoming and outgoing radiation added to a model. We do not have a 100 year’s worth, and it really should be 120 year’s worth, of this actual satellite data. Why do we need one longer than what we have? Because some of our natural oscillating cycles that have measurable affects on incoming and outgoing radiation have cycles of 60 years or more. Double that and you get a 120 year minimum to see just one or two cycles. Not exactly a sampling rate I would want to hang my hat on.
E.M. Smith, this past summer NE Oregon demonstrated consistently cooler soil temperatures at worm depth. I know. I dug into that soil looking for fishing worms. Worst year I can remember for gathering worms and coldest soil I have touched in my 54 year memory. Usually, after a rain, huge nightcrawlers could be picked up by the handfulls. I did not find a single nightcrawler on the road this last summer. Veggie gardens around here also suffered due to this rather cool soil. It is my opinion that the Earth underneath didn’t cause this, it was the depth of the winter freeze combined with very cool summer temps and cold cold rain whut dun it.
Willis—Your type of thinking and research is what meteorologists, like myself, love.
We observe what you postulate.
Dave Springer says: The net benefit to the biosphere as a whole though is tremendous as the whole world turns a lush verdant green.
Well, in an extreme case, but using the IPCC
predictionsprojections it’s not very much greener….http://chiefio.wordpress.com/2010/12/12/what-me-worry/
has the Koppen-Geiger maps of the world now and as the IPCC “reimagines” it.
You can see differences… if you squint enough and get really really close to the screen 😉
Frankly, I don’t see a darned thing to worry about even IF AGW is happening. IFF we had AGW, it certainly isn’t Catastrophic AGW. So CAGW is just incredibly bogus, even if AGW were real, and AGW looks to be an overblown fantasy.
I really do recommend a look at those graphs. Biggest changes I could spot were more hospitable crop land in southern Canada and Russia, a bit nicer Ukraine and Belarus, and more of the Pacific Northwest gets a bit of the Mediterranian Climate that folks all over the world seem to love.
It looks like Chile might get a bit nicer, too. And Southern Alaska warms up a great deal to being almost as warm as Fargo North Dakota 😉
(For folks not familiar with it, Fargo is often the coldest darned part of the “lower 48” in any given winter and has become a bit of a metaphor for “frozen bippy”…) “Bippy” being a ’70s metaphor for “sit upon”… “sit upon” being a euphamism for… but I digress 😉
I’ll bet my Meacham, Oregon pass against your Fargo.
Here are some of Oregon’s Arctic Queens
http://www.oregonphotos.com/Meacham.html
Steven Keohane says:
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.
Love the graphics Willis, nice job trying to simplify a complex subject for a guy like me. I was wondering about the significance of gravity as I looked at your diagram. If the gravitational field strength on the earth varies over time, even just a little, would that introduce a significant delta in the energy balance? My first guess would be that a weaker G force would allow the water molecules to rise faster and farther up to TOA and release more energy to space. Conversely, a stronger G force would contain the water molecules closer to the earths surface and less energy would be released to TOA. Happy holidays to you and all the WUWT community.
Willis Eschenbach says:
December 24, 2010 at 1:37 am
(In a response to Keith Minto)
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.
A simple question:
Are we measuring the energy in to the earth’s system at the same place that we measure the energy out (hopefully well above the atmosphere) and are we then measuring the energy reaching the earth’s surface?
Are we also measuring the reverse: energy leaving the earth’s surface and then the energy leaving the earth’s system?
If so, I would think we can easily observe what is happening although not necessarily exactly where or how.
Just wondering.
@Pamela Grey:
Folks need to dig in the dirt more often. It focuses you on the truth. I had cool garden soil later in the year than usual, but not too bad. You reminded me: decent worms, too; though they were closer to the surface than usual. We have it “the other way around” down here. They retreat deeper in summer as the soil dries and becomes too hot, rise when it’s cooler and damper. Hmmm… A “worm index” of temperature …. they only like a particular warmth / wetness band. So my worms also said cooler and wetter summer / fall.
At any rate, thanks for the insights from up your way. It’s folks that dig in the ground, see things, and have to grow food who know what’s happening. Guys sitting in office buildings in New York City playing Climate Nintendo don’t…
Joel Shore says: Follow your reasoning to its logical conclusion: In order to send more heat back into space, the upper troposphere must warm,
Your argument is based on the falacy of over averaging the data. In time and in space.
The AREA of warmth could increase a bit. The TIME during a given day that is warm could lengthen. The PEAK could rise briefy mid-day but otherwise have no long term effect.
The air THICKNESS could become less (as it has) allowing for different lapse rate effects.
And finally, “warmer” does not allow for the fact that the temperature is a POOR PROXY for HEAT. Expansion of the air as it rises (into our thinner air blanket) changes the temperature without a change of heat. So using words like “warmer” is misleading.
In this posting:
http://chiefio.wordpress.com/2010/12/02/does-convection-dominate/
I reference this paper:
http://hal.archives-ouvertes.fr/docs/00/31/68/93/PDF/angeo-19-1001-2001.pdf
that looks at the change of temperatures in the troposphere on a daily basis and finds that it tracks the daily cycle of the sun rising and setting and is different from place to place. So, with a 4th power function on radiation, and with the peak dumping the heat “right quick” inside HOURS… Just how does any “increased warming” of a small percent hang around more than a few minutes?
And with it dumped where it arrives, how does it warm “globally”?
So, yeah, I guess you are right. The top of a thunderstorm might be a nearly trivial degree warmer for a few seconds in the middle of the day, then return to the same stability point it was at before (thank you 4th power function…)
And this matters to me not one whit and has NO impact on the world.
I wonder how many joules of energy were used to evaporate the water that was just dumped on Cali. And how much of that left to space.
As I mentioned on the previous thread, and some have alluded to here, a missing piece in your equating dU to dT/S is time. If you add dU instantly, dT does not change instantly. In the earth system, if dU is added on one time scale and dT responds on a slower time scale, the value of S will change with time from a very small value to an asymptotic value maybe near 0.7 or 0.8 K per W/m2 over many years depending on what time window you are looking at. The climate sensitivity is the limit of what dT achieves given long enough to respond to dU. Clearly one year is not long enough and S is effectively smaller if you want to write the equation this way without time-dependence. You would improve the understanding a lot by using time dependence and a heat capacity (or thermal inertia) to relate energy to temperature. The equation for a forced harmonic oscillator, as I mentioned on the previous thread, is more appropriate, because it shows why higher frequencies have lower responses.
We only have to think of one vector, up against the gravity well. We have a body of salt water and on its surface we have free, hydrogen bonded water molecules and water molecules that form the hydration sphere around ions. The very surface layer is dynamic and has less water molecules with binding affinity than those below as they are at an 3 to 2 dimensional interface. These molecules are being bombarded by gas molecules, mostly N2 and O2 which are about 60% heavier that a water molecule. The water molecules thus gain energy by being bombarded by the air and those on the right hand side of the Boltzmann distribution are converted into the gaseous state. The air ‘cherry-picks’ the water molecules with the highest energy content and the bulk aqueous phase cools.
You can direct a hair dryer, 1500W with a temperature of 65 degrees centigrade, across the surface of bowl of water and you will not get equilibrium. The water will never reach the temperature of the air stream; it will instead remain cool and evaporate. Pools of water are never at the same temperature as the noon air temperature, they are cooler. Air currents cool water by asset-stripping the hottest molecules, a similar system is used in super-cooling liquid He; laser light is fired over the surface and the gaseous He molecules, which have a higher than average temperature than the bulk, are energized and removed from the system in the bulk vacuum.
A gaseous water molecule is then carried aloft, always, on average, getting a better exchange of collision energy from N2 and O2 water molecules. They gain energy and move up the gravity well, again overall, the light water molecules cool the N2/O2 and move ever higher. As they go higher there are less and less collisions, as there are fewer molecules with the energy required to fight the gravity well. As they bounce up, they also slow, due to gravity. High up, a larger fraction of the molecules they encounter are water molecules, rather than N2/O2, due to gravity fractionation. The concentration of gas, at fixed temperature (or heat) with altitude is an exponential function that is dependent on its mass. Very light gasses like H2 and He are fractionated all the way into space and escape the gravity well completely whereas Cl2, which is fatally toxic at concentrations as low as 10 ppm, is harmless if one is above 12 feet . During WWI the rats in the trench’s were not equipped with gas masks and were able to survive German Cl2 attacks by climbing the few trees on no-mans-land.
Our water molecules are now high up and upon collision with each other can form hydrogen bonds. This can only happen to the molecules that are at the left hand side of the Boltzmann distribution; the remaining population is now hotter than the previous average. As the ice particle grows it gain mass, gaining mass makes further mass gain more likely. The collision energy between a gaseous water molecule and a, say (H2O)60, ice particle results in energy transfer to the particle and the binding of the incoming gaseous water molecule.
As the ice particle grows, it will begin to fall. The bottom face will be ablated from impacts with the atmosphere, absorbing heat, and the ice will melt. Upon melting it will maintain a temperature of freezing point, with the molecules on the right hand side of the Boltzmann distribution being stripped by collisions. In this super cooled form it is at the temperature where it can dissolve the largest amount of CO2. During its decent, the rain drop will collect CO2. 3.34 mgs of CO2 will be dissolved in every ml of water; 76 mM CO2 in pure, ice cold rain drops.
The bulk of this CO2 will enter the Seas and Oceans, which would explain the very rapid equilibrium between atmospheric and Oceanial CO2 sinks, with a t1/2 of about a decade.
The hotter it gets, the higher up water goes and the longer it falls.