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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Willis, I just found this topic and am leaving on vacation early in the morning so must make this short and sweet. I will carefully read your treatise and all comments when I get back in a week.
My take is that the “missing energy” comes from the production of groundwater from slow to recharge aquifers. This water is not in equilibrium with the water present on the surface of the earth. The largest, by far, bulk of the produced water is used for irrigation of food and fodder vegetation. In 1995, this fossil production amounted to 830 cubic kilometers.
The produced liquid water undergoes evapotranspiration and discharges into the air as water vapor, thereby changing the potential energy of the liquid water into kinetic energy at constant temperature. The water vapor rises until it condenses changing the kinetic energy back into potential energy there by releasing the absorbed latent heat as specific heat, which warms the air. After that the condensed liquid water causes the oceans to rise a calculated 2.6 mm per year. At that point the groundwater is in equilibrium with the surface water and becomes part of the hydrological cycle. So the temperature increase and the ocean level increase are a function of only they yearly produced water volume.
The 830 cubic kilometers of groundwater per year releases a huge amount of energy into the atmosphere that was not there before. In recent years, due to dropping aquifer levels, the volume of groundwater pumped for irrigation has started to decline, especially in US and parts of China. This groundwater from slow or no recharge aquifers fits your “model” very well, I think.
Additionally, I believe that there is a functional temperature control valve in or very near the Tropopause that thermodynamically displaces a part of the 4 ppm water vapor as the carbon dioxide content increases due to partial pressure effects. I base this temperature control scenario on the fact that the NOAA measured humidities in the mid and upper Troposphere have decreased each year since 1958.
I can go into more detail but that is the essence of my studies on the causation of global warming and ocean level rise.
JFD
Not sure where this leads but: When they made me take meteorology to get my journalism degree, the instructor said that as water evoporates, it absorbs heat and, typically, rises; however, when water condenses at altitude, typically, droplets fall and, by virtue of friction, generate heat, which is imparted to the surrounding air. Thus, evaporation and condensation both absorb and generate heat. The heat appears to be moved, as you say, from the surface to … somewhere else. While water vaper may tranfer heat to space at altitude, when water condenses it and the surrounding atmosphere is heated by friction when it falls. If I recall the lessons, surface temperature declines by about the same increase in temperature cause by friction in the upper atmostphere.
Not that this makes a big difference, but there does seem to be a bunch of entropy floating around.
Dan Daly: You don’t need to take friction into account to explain why the atmosphere is heated when water condenses. It happens for the same reason why water must absorb heat to vaporize: a phase change from the liquid to the gas requires the absorption of energy and a phase change from gas to liquid requires the release of energy. It is called the “latent heat of vaporization”.
Willis Eschenbach says:
I think then that you have created and destroyed a strawman. I don’t think climate scientists would claim that climate sensitivity applies down to these time- and length-scales. Climate sensitivity is measured by what happens over the long run, not about a tiny fluctuation. After all, over the short term there is no doubt that energy can go into a lot of different places…It can be absorbed into or liberated from the ocean, and so forth.
And, if you think the effect that you describe is a significant effect over the long term, then you should work out the consequences of your ideas and what they imply, which is where I was going with your notion here.
Happy holidays and best wishes to you as well!
E.M. Smith says:
Well, frankly, this sounds like a lot of hand-waving to me. I don’t think you’ll find that the 4th power function is all that dramatic over the absolute temperature ranges that we are talking about. (Over a small enough temperature range, the T^4 will look linear anyway, just with a slope four times as great as a T^1. So, as an example, if the absolute temperature increases by 1%, then the radiation increases by 4.06%. If the absolute temperature increase by 10% instead, then the radiation increases by 46.4%.) If we were talking about absolute temperatures that increased by factors of 2 or 3 or something, then yeah, the nonlinearity of the T^4 power would be quite important; however, for changes of 1 or 5 or even 10%, it ain’t very.
NovaReason says:
December 24, 2010 at 12:34 am
Thanks, that it it in a nutshell. It is just a thought experiment as I have not seen this area discussed before. Yes it could generated heat lower down, the above mentioned NS article says 5% of the condensation energy could be radiative and if the nuclei were continuously generated then the heat would rise together with the extraordinary buoyancy of water vapour. No net heat gain, just a spread of heat generation points closer to sea level. I will keep searching.
Christmas dinner calls and after all this is Willis’ thread.
Jim D said:
” 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.”
Jim, are you sure ?
Isn’t it just the air above the water that is made warmer by the cloud ?
The cloud prevents the energy in the air from escaping upwards as quickly as it otherwise would have done but at the same time it stops solar shortwave energy from penetrating the water. So which effect prevails over a diurnal cycle, the slight reduction in evaporation rates or the cooling effect of increased albedo ?
Generally speaking a cloudier world is a cooler world is it not ?
And the cloud analogy is not really applicable because it operates by alteriung optical depth but according to Miskolczi the increased CO2 has failed to alter global optical depth for the past 60 years which is the period of time when human effects are supposed to have affected natural processes.
Jim D said:
“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.”
I said that water molecules are heated but that the timing of evaporation is then accelerated so that there is no net heating of the ocean bulk.
A single photon does not supply latent heat. it supplies sensible heat which then provokes earlier evaporation and when evaporation occurs more energy is drawn from the local environment as latent heat than was acquired from the additional photon(s) that directly caused the change of state.
“Pamela Gray says:
December 24, 2010 at 4:47 pm
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.”
It would be more helpful if you could point out what is wrong with my theory/hypothesis rather than just criticising my non scientist writing style.
After all it does fit the observations rather well whereas established theories (or are they just hypotheses due to all their underlying assumptions) are just generating confusion because they do not fit observations without invoking an assumed effect from anthropogenic CO2 and CFcs.
How can one oppose AGW theory without having an alternative explanation as to why the stratosphere cooled whilst the sun was more active in the late 20th century ?
Without a ‘natura” explanation their assumptions become the only game in town don’t they ?
Jim D said:
“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.”
In the 3D bulk phase each water molecule has four strong hydrogen bonds, with to -H donors and two (:) receivers. At the atmospheric interface, water has a 2D surface, the top layer will have on average only 2 hydrogen bonds. As well as being bombarded by IR from the atmosphere, these molecules will also be bombarded by IR from below; from the thermal energy of the bulk water.
A little experiment for the summer. Take two children’s paddling pools and fill with the same amount of water and place a thermometer in each. Hang a thermometer on a thread above each. Pour a liter of light machine oil on one to stop evaporation. Place in noon-day sun. The water temperature of the oiled pool will be higher than the other, but the surface, air temperature will be lower.
Stephen, your statement, “Anything that affects stratospheric temperatures affects climate.” is an hypothesis without merit.
But first, my opinion: It is hypothesized that trace amounts of greenhouse gases in the stratosphere do have an affect on temperatures there (depending on the altitude). This can be calculated and demonstrated to match observations. But ozone changes have the larger affect, also calculated and demonstrated to match observations. The caveat, the temperatures of the stratosphere have only been measured for at best 2 decades, maybe 3. Anything prior to that is just a calculation based on hypothesized mechanisms. Therefore, all papers postulating this or that driver of stratospheric temperature changes are, in my opinion hypotheses that have yet to see the light of theory. Some have more merit than others.
Now to your statement. What is more established is that stratospheric temperature teleconnections with driving potential to lower tropospheric temperature patterns have no mathematical constructs. Not enough energy to be a driver down here. Metaphorically, to stir a pudding, you have to have something stronger than a feather. You state that jet stream movement requires quite a bit of energy. Your hypothesis has not been calculated yet to my knowledge here on this blog.
If you present yourself as an amateur scientist, that does not mean that you can function well below what is expected of professional scientists without being called on the carpet.
You postulate an unproven hypothesis, nothing more, and not very well in my opinion.
Stephen, actually on clear nights the ground cools more than the air, being a black body. On cloudy nights it cools less, same for the ocean. CO2 has the warming effect of clouds, though much weaker and sustained, while it doesn’t have the cooling effect in the day due to being transparent to light. If you imagine the ocean subjected to such forcing it can’t help but get warmer.
Hopefully you don’t really believe in Miskolczi and his radiosondes. It goes against basic physical science in textbooks (not just climate science). It will go the way of cold fusion soon enough when no one else finds what he did with his selected data.
On the other message, yes photons heat water molecules. Why can’t they just distribute that heat rather than evaporating. This is where the whole idea of evaporating balancing the GHG falls apart. Evaporation does increase, but only after the surface has warmed to a new Clausius-Clapeyron equilibrium. This is the basis of the water vapor feedback. You are saying evaporation cools it back to the original temperature. No, because the photons are still there keeping it warmer. The new equilibrium with these photons is a warmer temperature with more vapor at the interface.
DocMartyn, the IR photons don’t have enough energy to supply the latent heat needed to evaporate water. They will therefore all just go into heating the water. The evaporation rate is governed by the sustained interface equilibrium between vapor and water, which depends on temperature.
“DocMartyn, the IR photons don’t have enough energy to supply the latent heat needed to evaporate water. They will therefore all just go into heating the water. The evaporation rate is governed by the sustained interface equilibrium between vapor and water, which depends on temperature.”
Have a look at the actual structures of water molecules in the liquid phase. The reason that water and ammonia have such high boiling points is due to hydrogen bonding. The water molecules at a water:air interface do not have the same hydrogen bonding network as those beneath. Moreover, as energy is the thing that puts a molecule there, the water molecules at the surface will have higher than average energy. There is a big difference between boiling water and evaporating it under a gas stream. Chemists use N2/vacuum lines to ‘dry’ salts without heating. You can get rid of water while dropping the temperature. If you play a nitrogen stream at ambient temperature over a salt solution you dry it and drop its temperature. The gas stream strips water molecules, preferentially stripping molecules with the highest energy.
Willis,
Something NOT considered is the pattern of WIND.
Wind has a rotational pattern.
How can I prove this?
A snowflake! When evaporating water vapour is freezing with a wind, the water vapour has to be spinning two dimensionally in order to achieve a flat plane of the snowflake.
Pamela, judgmental criticism by itself is too easy; more difficult is to take a partially/ poorly-formed idea with a grain of potential and improve it. Constructive criticism requires suggesting improvements. You obviously have much to offer. Do you think your expertise is worth offering to Stephen’s thinking? In other words, could he “have something there” or not? If “no,” it would be better if you would cut to the chase regarding why not, while cutting out the unhelpful sniping. If “yes,” then it would be great if you could help him develop it.
Interesting discussion. Living in the Keys I tend to think more about hurricanes than snow. The average hurricane losses about 600 trillion Watts per day in rain out. Wind energy is about 1 trillion Watts per day. Blocked incoming radiation is probably between 1 and 10 trillion Watts per day. Wave energy produced I have never seen estimated. I just think it is amazing how big that tiny bit of energy can be for just one storm day.
Willis, is it not possible that some systems receive energy quickly, but manifest it (meaning make it perceptible to us) slowly? 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, Jet stream latitudes, cloud formations and locations, sea life blooms and crashes, 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?
Each wavelength of incoming TSI has a different residence time within the atmosphere, land and ocean. This residence time is of course affected by it own inherent properties as well as all of the material it encounters. Only two things can effect the energy content of any system in a radiative balance. Either a change in the input, or a change in the “residence time” of some aspect of those energies within the system.” The longer the “residence time” the greater the energy sink capacity. The greater the energy capacity, the longer it takes for any change to manifest, and in the case of OHC this involves years, not annually. This makes your caption statement for Figure two inaccurate; “ Figure 2. The missing energy puzzle. Every year, the amount of energy entering the system (red) should equal the energy leaving the system (light blue) plus the energy going into/out of the ocean (dark blue). It doesn’t.”
According to John Daly’s references many ocean inputs take about 8 years to manifest in the atmosphere. http://tallbloke.wordpress.com/2010/12/06/john-l-daly-the-deep-blue-sea/
Evaporation conduction of latent heat may vary far more then realized and set a limit on further tropical temperature increases. (Newell & Dopplick’s (1979) calculations that tropical temperatures cannot rise any further.)
Also have you looked at the bi-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 bi-annually, then how much and how rapidly changes in those things you measured in figure 2 match these bi-annual changes should give deeper insight relative to heat and energy flux within our earth system. I think figure two needs to be refined to capture this seasonal flux.
Thank you for your excellent articles that both educate and stimulate further thought.
Pamela Gray sais:
“Stephen, your statement, “Anything that affects stratospheric temperatures affects climate.” is an hypothesis without merit. ”
On the contrary, it is established climatology. I’m puzzled by your lack of awareness of that.
Even a temprary warming of the stratosphere from say a so called sudden stratospheric warming event changes the pressure distribution below to mimic a negative AO.
Also differential UV warming of the equatorial stratosphere from imteractions with ozone in the stratosphere is supposed to lower the tropopause, widen the tropical air masses and push the jets poleward.
I am not putting forward speculative statements. Instead I take established propositions, compare them with observations and set out some of the logical implications.
What puzzles me greatly is that since CO2 became the universal bete noir such an approach appears to have been neglected by the climate establishment yet it should be at the heart of the science.
Your personal opinion of the quality or otherwise of my work is of little interest. It has received favourable responses elsewhere.
“Jim D said:
“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.”
A single photon does not have enougfh energy to evaporate a molecule on its own. It simply adds to the energy already held by the molecule to bring forward the timing of evaoration. Evaporation is an ongoing processs always happening due to pressure, density and temperature differentials. IR just speeds it up rather than causing it ab initio.
The latent heat of evaporation is not provided by the incoming photon even if it tips the moleclue into evaporating. The latent heat is taken from the surrounding environment and is always far greater than the energy in the photon that tipped the molecule into a change of state.
So one photon with say one unit of energy can tip a molecule of water into changing state to a vapour but the surrounding environment loses many more units of energy to latent heat for a net cooling effect.
If you think there is any surpus energy left over from incoming photons of IR after such a net cooling process has taken place then you must prove it. As it stands your position and that of AGW theory in general is illogical.
Jim D said:
“Hopefully you don’t really believe in Miskolczi and his radiosondes”
What has ‘belief’ got to do with anything ?
So has the atmospheric optical depth changed over the past 60 years ? I have seen lots of personal comments about him and his work but without that point being addressed.
Jim D said:
“CO2 has the warming effect of clouds, though much weaker and sustained, while it doesn’t have the cooling effect in the day due to being transparent to light.”
CO2 does have the same ability as clouds to slow down the upward rate of energy loss. No dispute.
However CO2 is not perfectly transparent to light which is why I raised the optical depth issue. Co2 molecules block and reflect upwards again incoming energy just as much as they block and reflect downwards again any outgoing energy.
So just like clouds, but to a much lesser degree (as you point out) extra CO2 has an effect on both incoming and outgoing energy.
So to get a significant net warming effect from CO2 one needs also to see a change in optical depth.
If there is no change in optical depth then it must be assumed that extra downward IR from more CO2 is balanced by more upward IR from blocked incoming energy redirected back upward.
Just as for clouds the extra IR redirected back downward when the cloud is present is more than compensated for by downward energy being blocked but because clouds are much more opaque than CO2 then for clouds the amount of incoming energy sent back upward is much greater than the amount of outgoing energy bounced back downward. That is how clouds increase the optical depth. Perfect transparency can only achieve equality of effect. Even perfect transparency cannot make molecules send more back down than they send back up yet that is what is claimed for CO2 molecules.
In order to send more energy down than than is rejected and sent back up an individual molecule has to generate more energy internally like a sort of perpetual motion machine.
However increased total atmospheric density from more molecules overall or from an increase in denser molecules resulting in greater optical depth will send more energy back down than is rejected to space until a new and higher equilibrium temperature is reached because it is density that slows down the net rate of energy transmission. That is why planets covered by dense clouds of any material can get very hot at the surface.
Optical depth changes (equating to density) are the measure of the net balance whether it be clouds or GHGs or both. So has optical depth changed or hasn’t it ?
Regarding Miskolczi, I have not seen anyone confirm his data, but on the contrary satellite data which is much more precise in directly measuring the effect of CO2, does show its effect increasing. For me the weight of direct measurements is greater than the weight of Miskolczi’s indirect radiosonde approach, but people can choose for themselves.
Stephen Wilde said
“However increased total atmospheric density from more molecules overall or from an increase in denser molecules resulting in greater optical depth will send more energy back down than is rejected to space until a new and higher equilibrium temperature is reached because it is density that slows down the net rate of energy transmission. That is why planets covered by dense clouds of any material can get very hot at the surface.”
This is almost correct, except that optical depth depends not only on density but atmospheric constituents, especially the greenhouse gas percentages.
Also the idea that CO2 has any significant effect on visible light compared to its infra-red effect is not borne out by the facts.
Stephen Wilde,
You obviously are much more knowledgeable than I, but, I would ask you to change your terminology on CO2. It absorbs and emits LW. There is a fundamental difference in what happens in these two scenarios. If CO2 reflected and scattered only it could not heat the surrounding air mass.
Jim,
Can you link me to any satellite data relating to optical depth , please?
Atmospheric constituents affect optical depth too, agreed. It’s hard to cover everything in a blog post without losing one’s drift. However, absorbing solar LR and radiating it back upwards is similar to the reflection of visible wavelengths by clouds.
kuhnkat,
Noted, thank you. However there is some reflection and scattering too is there not ? And upward or even sideways radiation of LR has much the same effect as reflection and scattering in overall energy transfer terms.
Stephen Wilde says:
There are a bunch of references given in here: http://skepticalscience.com/empirical-evidence-for-co2-enhanced-greenhouse-effect.htm
There are also studies relevant specifically to the water vapor feedback such as this paper by Soden et al. http://www.sciencemag.org/content/310/5749/841.abstract and various papers by Dessler.