Guest Post by Willis Eschenbach
A number of people have said Hey, in your previous post, the missing forcing is going into the ocean, so it’s still “in the pipeline”. I had considered that, but it didn’t make sense. I’ve taken a closer look, and it still doesn’t make sense.
According to the IPCC calculations in that post, about 0.7 W/m2 was missing. Let us assume that it is going into the ocean. Here’s my numbers, please check them. The spreadsheet doing the calculations is here.
CONSTANTS
Specific Heat Seawater 3.85 Joules/gram/C
Ocean Volume 1.3E+18 m3
Ocean Area 3.6E+14 m2
Global Surface 5.1E+14 m2
Average Ocean Depth 3700 m
Ocean Density 1.025 tonnes/m3
Year To Seconds 3.2E+07 seconds/yr
INPUTS
"Missing" Incoming Radiation 0.7 W m-2 over earth's surface
OUTPUTS
Equiv. Incoming Radiation To Ocean 1.0 W m-2
Annual Energy 3.1E+07 Joules/yr
Warming Ability 8.2E+06 grams C-1 / yr
1 m2 Column Weight 3793 tonnes
Column Weight 3.8E+09 grams
Warming since 1850 0.11 C (from spreadsheet)
Current Warming Rate 0.22 C/century
Time To Warm 1° at current rate 465 years/C
The reason that it didn’t make sense to me is that if that is the case, if the imbalance over the last 150 has warmed the ocean a tenth of a degree, and heat in the pipeline (assuming the 0.7 W/m2 imbalance continues) is going to give us a degree of warming in just under five hundred years … I just couldn’t believe that people were seriously thinking that was an issue.
So I suppose that’s possible, that the IPCC is right, and that half of the incoming energy is going into the ocean, warming it at the rate of one measly degree every half a millennium … But if that is so, does that mean that for practical purposes (neglecting the one degree by the year 2565, which is meaningless in human terms) we cut all of the IPCC warming forecasts (excuse me, scenarios) in half? Doesn’t that make the effective climate sensitivity in the real world, for our Grandchildren, by the year 2050, half of the number promulgated by the IPCC? Because the heat in the pipeline from the 0.7 W m-2 imbalance (0.22 C/century) will give us a whopping nine hundredths of a degree of ocean warming by 2050, unmeasurably small.
What am I missing here?
[UPDATE] Bob Tisdale graciously provided a link downthread to the oceanic heat content numbers. His graph shows the global heat content increasing by 7.8 MJoules per year per square meter.
If my numbers are correct (please check), this corresponds to a heat uptake (global average) of 0.17 W/m2. That would warm the ocean by a degree in 1900 years, so I think we can neglect that … and surely that’s enough time to do the mixing.
The missing heat is on the order of 0.7 W/m2. The evidence doesn’t show anywhere near that amount of heat going into the ocean. Including the ocean warming as explaining part of the missing heat, that still leaves on the order of a half a watt per square metre missing in the IPCC-based estimate … the ongoing mathematical mystery continues. All assistance solicited.
My own feeling is that the climate sensitivity is not fixed, but is a function of T, the temperature. It decreases with increasing T. This can be seen clearly in the tropics.
In the morning the ocean is cool, and the skies are clear. As a result, the surface warms rapidly. Climate sensitivity (degrees of temperature change for a given change in forcing) is high.
By about 10:30 or so, the ocean surface has warmed significantly. As a result of the rising temperature, cumulus clouds form. Despite increasing solar forcing, the surface does not warm as fast. Climate sensitivity is lower.
In the afternoon, thunderstorms form. These bring cool air and cool rain from aloft, and move warm air from the surface aloft. They cool the surface, bringing climate sensitivity near to zero.
Finally, thunderstorms have a unique ability. They can drive the surface temperature underneath them below the starting temperature. In this case, we have local areas of negative climate sensitivity – the forcing can be increasing while the surface is cooling.
As you can see, in the real-world context the idea that the temperature is some mythical constant “climate sensitivity” times the forcing change simply doesn’t hold water. Sensitivity goes down as temperature goes up in the tropics, the area where the majority of solar energy enters our climate system.
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“So, willis has established what we already knew. The climate doesnt respond instaneously to GHG forcing.”
So how much of the warming of the 1990s would you blame on older forcings so we can establish how much more missing heat we have to find in order to make the models correct?
Article on how the research funding process in the medical field corrupts the validity of published results. This can be easily extended to climate science. http://www.theatlantic.com/magazine/archive/2010/11/lies-damned-lies-and-medical-science/8269/1/
“thats one of the points of running GCMs to do paleo work! ”
Yes, and so how do they incorporate the irrigation caused by melting glaciers when we are still arguing if irrigation causes cooling, warming, or both depending on the circumstances?
OK so I may be showing my ignorance here but if we turned off the Sun right now (stay with me) how long would it take for the atmosphere (not the ocean – the atmosphere) to cool significantly. 24 hours – a few days – longer? 150 years?!
It seems to me that the planet’s (heat) energy is constantly being topped up on very short (daily) timescales. Take that away and it gets cold (I suppose) very quickly. I’m not suggesting the Sun will be switched off any time soon; I just use it as an illustration that the atmosphere probably doesn’t store heat very well for long periods.
So those who propose some time lag is hiding the heat still need to explain where it is hiding. It is no good saying its coming along later. Coming from where? You can’t store heat without it getting hot somewhere – or doing work like moving currents around a lot more as Mr Hayworth suggests (October 24, 2010 at 4:34 am) but evidence seems to indicate that isn’t happening either http://www.earthweek.com/2010/ew100402/ew100402a.html.
So it’s not in the sea, it’s not in the air. In short it is nowhere on earth (unless someone can show otherwise). If it’s coming, where from? Where is it now?
Please don’t get caught up in the boiling pot argument; that the 0.7C warming of the atmosphere will eventually warm the oceans by 0.7C which adds up to 1.4C. It doesn’t. It adds up to 0.7C more uniformly distributed. Yes it might eventually warm the oceans a bit and trap more energy overall – if the atmosphere doesn’t cool first – but the IPCC’s headline surface heat going forward would still be half what they said it would be.
In other words if half the energy was being absorbed by the oceans (it’s not apparently) then half the next lot of energy would be too. If you are using that as an excuse for the difference between your theory and empirical evidence than your expected surface temperature deltas should also be halved unless you expect the sea to suddenly change its behaviour.
So to return to my first point; the time lags in the atmosphere are measured in far shorter time scales than one and a half centuries. Mr Mosher, the sea might be a truck but the atmosphere’s a Bugatti Veyron 16.4 Super Sport and 6 seconds is plenty for 120mph!
Bill Illis answered my first question as I was typing. The atmosphere would lose all its energy in 86 hours. So no “time lag” in atmospheric temperatures can be longer than that. The planet’s core temperature yes. Oceans – a bit. But the atmosphere no. Atmospheric temperatures are a reflection of the composition of the atmosphere in this 86 hour window. That’s all the time lag you get.
This “hidden heat forcing in the ocean” is fascinating. In fact, it’s exactly the opposite of the lava lamps we amused ourselves with back in the precamb…er, the ’60’s. The hot water sinks, hits bottom, reverses course — and SHAZAMM, global broiling takes place when it again reaches surface. Darn it, why couldn’t I have been more observant! I’d be famous and flying off to Tahiti to reveal the “Upside Down Theory of Heat Transference” to a host of sycoph…er, true believ…er, climatologists. I coulda’ been a contendah!
Steven Mosher says:
October 24, 2010 at 2:47 pm
I have said nothing, absolutely nothing, about an instantaneous doubling of CO2 as you claim above. As a result, your claims address an imaginary situation. They respond to something I didn’t do.
I have posted my spreadsheet, which clearly shows my year-by-year calculations. Your response strongly suggests that you have not looked at it. I applied the IPCC factors starting at zero and increasing over the 150 year period, at a rate approximating the log(CO2) increase. So they started at zero, increased slowly, then increased faster in recent years to the final IPCC values. This approximated the reality.
Here’s the issue as I see it. The IPCC numbers don’t balance. Some of the incoming energy goes into raising the temperature. Some of it goes into the ocean. And some, we don’t know where it goes.
This is not a long-term problem, despite the fact that it is occurring in a lagged system like the climate. It is an instantaneous problem. The IPCC says the forcing increased by a certain amount. We know some of that went into warming the global surface air temperature. And some of it went into warming the ocean. But where did the rest of it go? It can’t be created or destroyed. It didn’t go into the ocean. It didn’t raise the temperature. Where did it go?
The issue that I am pointing at is the missing heat. I asked you in my last post where you thought is was going. I ask again, because I don’t know the answer.
Phil’s Dad says:
October 24, 2010 at 4:35 pm
—————–
You could also look at it as How long does the energy represented by a photon from the Sun spend in the Earth System before it is lost to space?
About 30.2 hours.
30% of the photons are reflected back to space almost immediately – in an average time of 0.00003 seconds.
70% spend an average 43 hours in the Earth System – some are captured by Ozone and then sent back to space in a millisecond or so and some might end up captured by the Ocean or Land surface and spend up to 1500 years in the Earth System, but the average of this 70% is just 43 hours.
This 70% of photons will spend time in 31 billion individual molecules on average before being sent off to space – in other words, every type of atmospheric molecule is constantly recycling the energies represented by a photon from the Sun – capturing and then releasing that energy in an average 0.000005 seconds which approximates a constant outward flow from the surface – it is not “back-radiation” – it is a constant outward flow which is provable by the lapse rate itself – and not just CO2 and GHGs are part of this, all the molecules are.
This all happens at the quantum level, at the speed of light and at the average relaxation time for a molecule. No climate model is going to be able simulate that accurately.
davidmhoffer says:
October 24, 2010 at 2:56 pm
David, thanks for your thoughts. You are correct that those are TOA (top of atmosphere) forcings. My understanding is that the “climate sensitivity” linearly relates TOA forcing changes to surface temperature changes … if that’s not the case, please point me to a reference that explains what “climate sensitivity” means.
Willis Eschenbach;
My understanding is that the “climate sensitivity” linearly relates TOA forcing changes to surface temperature changes … if that’s not the case, please point me to a reference that explains what “climate sensitivity” means.>>
Sorry Willis, I can’t. You have to follow all the references to references to references starting with this quote from AR4 WG1 2.8.1 where RF is short for Radiative Forcing:
” It should be noted that a perturbation to the surface energy budget involves sensible and latent heat fluxes besides solar and longwave irradiance; therefore, it can quantitatively be very different from the RF, which is calculated at the tropopause, and thus is not representative of the energy balance perturbation to the surface-troposphere (climate) system. While the surface forcing adds to the overall description of the total perturbation brought about by an agent, the RF and surface forcing should not be directly compared…”
Their words. NOT representative of the energy balance. Should NOT be directly compared. As I said, it was a while back that I went through it. Looked for some of the papers they refer to, mostly behind pay walls. Some I found copies of but they make reference to other papers, mostly behind pay walls. Lots of dead ends but finaly figured out that they were calculating CO2 doubling = 3.7w/m2 = 1 degree at the effective black body temperature of earth, but were being very vague in terms of how that should translate into surface temps, leaving one with the IMPRESSION that it is linear, but no where actually saying so that I have found. In fact, I recall distinctly reading an article either in AR4 or referenced by AR4 saying that temperature changes could be treated as linear in terms of changes in surface radiance. Duh, say WHAT? Which part of T to the power of 4 is linear? The cite was I think, Ramaswamy so I started digging. Turns out to be a reasonable approximation FOR SMALL CHANGES IN TEMP LIKE 1 DEGREE. The implication in the article at the beginning of the chain was that this is true across the board but it isn’t, and it is only implied, it didn’t actually say that.
But do the math. As you said before, you believe that sensitivity varies with T. The surface temp CAN’T be linear with radiative forcing calculated against effective black body that is 35 degrees colder than surface based on a constant times… T raised to the power of 4. Any warming as a consequence must raise the temps of cold things faster than the temps of warm things and if you pump enough warming into the system the temp differential between them gets smaller and smaller even though they are both going up.
If I find the time I will try and reproduce the whole chain, but it was a long time ago, lots of dead ends, and many hours of frustration. But linear its not.
CO2 in the climate system is not like gravity in the planetary motion. Simple equations needs to be replaced with complex computer models that simulate not just earth’s radiation budget but also energy sources and sinks with their time lags.
Energy can be stored in phase transitions like melting ice or in (bio)chemical reactions. Measuring all of them is a huge challenge. We can’t even accurately measure the CO2 created by man.
Vincey, you are correct, but it doesn’t contradict anything that I said. Yes, if there is an energy imbalance it must be felt by increasing temperatures. And that is exactly what we are seeing. As long as we see increasing temperatures, we cannot discard that the current CO2 levels can take us to a +1,5K annomaly. Of course the big problem is that the GHE is not the only process affecting the temperatures, and because of that we cannot know if the effect of the CO2 has stopped or continues, because a stop in the temperature increase can be caused by other random factors playing in the opposite direction. Their guess is that, if only CO2 was at play, we would continue to see warming, and if we don’t see it for a few years it is because of noise in the signal. Well, I don’t believe it, but it doesn’t mean that it cannot be true. To discard that possibility we need a much longer period of cooling or at least no warming.
A climate sensitivity of +3K for a doubling of CO2 means that, when you double the CO2 concentration, the climate will stabilise at a +3K annomaly. It doesn’t say anything about how long it takes it to reach that temperature and stabilise (big effort made at the thought of a stable temperature… but hey, that’s what they say). It can be a much more gradual process that only “stabilises” a century after you have doubled the CO2 concentration. In the mean time, the energy is not anywhere. It is comming.
“To discard that possibility we need a much longer period of cooling or at least no warming.”
STATE OF THE CLIMATE IN 2008 Special Supplement to the Bulletin of the American Meteorological Society
Vol. 90, No. 8, August 2009
“The trend in the ENSO-related component for 1999–2008 is +0.08±0.07°C decade–1, fully accounting for the overall observed trend. The trend after removing
ENSO (the “ENSO-adjusted” trend) is 0.00°±0.05°C decade–1, implying much greater disagreement with anticipated global temperature rise.”
“Near-zero and even negative trends are common
for intervals of a decade or less in the simulations, due to the model’s internal climate variability. The simulations rule out (at the 95% level) zero trends for intervals of 15 yr or more, suggesting that an observed absence of warming of this duration is needed to create a discrepancy with the expected present-day warming rate.”
Not all that long a period of time is required to invalidate the models.
From: Tom Wigley
To: Kevin Trenberth
Subject: Re: BBC U-turn on climate
Date: Wed, 14 Oct 2009 16:09:35 -0600
Cc: Michael Mann , Stephen H Schneider , Myles Allen , peter stott , “Philip D. Jones”, Benjamin Santer , Thomas R Karl , Gavin Schmidt , James Hansen , Michael Oppenheimer
Kevin,
I didn’t mean to offend you. But what you said was “we can’t account
for the lack of warming at the moment”. Now you say “we are no where
close to knowing where energy is going”. In my eyes these are two
different things — the second relates to our level of understanding,
and I agree that this is still lacking.
Tom.
++++++++++++++++++
Kevin Trenberth wrote:
> Hi Tom
> How come you do not agree with a statement that says we are no where
> close to knowing where energy is going or whether clouds are changing to
> make the planet brighter. We are not close to balancing the energy
> budget. The fact that we can not account for what is happening in the
> climate system makes any consideration of geoengineering quite hopeless
> as we will never be able to tell if it is successful or not! It is a
> travesty!
> Kevin
>
Bill Illis says:
October 24, 2010 at 7:33 pm
You could also look at it as How long does the energy represented by a photon from the Sun spend in the Earth System before it is lost to space? About 30.2 hours.
Thanks for the new numbers Mr Illis. I think we are broadly on the same page with this one. As I see it this represents the outer bounds of the energy equilibrium time lag for changes in the atmospheric composition. As an extreme illustration if we double the time that energy (represented by photons) is delayed, by giving it twice as many molecules to play with, we would double the time that energy sticks around to perhaps 2.5 days to a week. At the same time temperatures would rise by what; 30C?
Whether it is 30hrs or 43hrs or 86hrs; energy doesn’t stick around in the atmosphere for long. Oceans, rocks and stuff yes. Atmosphere no. (I’ll just reiterate briefly that very little of the “missing energy” seems to be in the oceans after all this time.)
So if there is any “hidden energy” it must be Mr Nylo’s (October 24, 2010 at 11:24 pm) theological energy. “In the mean time, the energy is not anywhere. It is comming.” Mr Nylo I didn’t see a /sarc anywhere in your piece so I guess you mean it. Unless you thinks that energy that “is not anywhere” but is somehow destined for us later is so daft no one could miss the joke. (Quantum physicists weigh-in by all means)
“Yes, if there is an energy imbalance it must be felt by increasing temperatures. And that is exactly what we are seeing.” But that imbalance can not last longer than the time it takes for all the energy in the (open) system to be exchanged.
“missing heat”
The IPCC says the forcing increased by a certain amount. We know some of that went into warming the global surface air temperature. And some of it went into warming the ocean. But where did the rest of it go? It can’t be created or destroyed. It didn’t go into the ocean. It didn’t raise the temperature. Where did it go?
I will suggest that you look into the two box model that Lucia, nick stokes and Arthur smith put together. That will help you understand the time constant problem better and why you cannot calculate the response as you did. You’ll need more than the back of an envelope for this one.
The series of posts is quite long and involved and the basic issues everyone needs to understand are there. happy reading.
http://rankexploits.com/musings/2009/two-box-model-algebra-for-ver-1-test/
http://rankexploits.com/musings/2009/two-box-model-now-assuming-surface-temperature-are-mixed-values/
but to answer the question. once you do the calculations correctly then you will be left with some choices:
1. a lower sensitivity (within lukewarmer bounds)
2. more going into the ocean that you think.
Mr Mosher (October 25, 2010 at 9:06 am) I agree with your conclusions 100%.
assuming the IPCC have everything else right…
“Once you do the calculations correctly then you will be left with some choices:
1. a lower sensitivity (within lukewarmer bounds)
2. more going into the ocean that you think.”
In either case it is true to say that the surface temperatures will be lower than IPCC scenarios. In 1. this is self evident and in 2. unless the sea suddenly changes its behaviour it will continue to absorb (nearly half) the heat.
That leaves us with a most likely business as usual case of 1.5C of surface warming by 2100 for which (to close the circle) I think our Grandchildren would forgive us.
International JournRecent energy balance of Earthdal of Geosciences, 2010, vol. 1, no. 3 (November)R. S. Knox and D. H. Douglas
“In summary, we find that estimates of the recent
(2003–2008) OHC rates of change are preponderantly
negative. This does not support the existence of either a
large positive radiative imbalance or a “missing energy.””
This paper makes perfect sense to me. Perhaps you can explain where it is in error.
@Rabe, ShaneCMuir:
The “comparative mythologist” and “physicist” behind Thunderbolts.info also claim Earth was — until a few thousand years ago, but within human cultural memory — in orbit around a brown dwarf star, which through an electrical process (scarring Mars, our moon, and elsewhere), violently ejected the gas giant planets, itself becoming Saturn.
Somehow Earth came to rest — a few thousand years ago — into a habitable orbit around the Sun, and not only did life survive, but humanity did too.
Come on!
Get real.
I spent several hours reading their ideas about plasma being important for the formation and structure of galaxies and even electricity, not nuclear fusion, powering the Sun.
I’m not even saying these ideas are completely implausible. Certainly there is that little pesky problem of “what the heck is dark matter, which we can’t find, and we assume exists, because otherwise the galaxies would fling its star systems away in a single rotation?”
That’s a big problem with the standard cosmological model. There are others.
So maybe these Thunderbolts guys would do well to drop the “Earth revolved around proto-Saturn, itself a brown dwarf star, a few thousand years ago, and humanity survived the break-up of that star” bit if they want to be taken remotely seriously. As it is now, they come across as fancifical loonies and mystical e-book hucksters.
ShaneCMuir, don’t be deluded.
*******
steveta_uk says:
October 23, 2010 at 5:16 pm
Slightly off-topic, but can anyone explain why the deep oceans are so cold? They appear to be sandwiched between a surface at approx 15C, and a mantle that’s even hotter.
I’ve found numerous documents that state that the deeps are cold as there is no sunlight. But where do they lose heat to to get so cold?
********
The cold bottom-water at around 4-6C, which makes up the vast majority of the ocean volume, is a relic of previous cold periods and/or present glacier/sea-ice melting sinking below the top surface. Being sandwiched between the ocean bottom (crust that has a very high insulation value & hence little heat transfer from the hot interior) and warm surface water (which is stratified & isolated due to density differences) preserves its “coldness” for long times — perhaps thousands of yrs.
So for most parts of the world (other than the below-freezing ones), the cold bottom-water is actually a heat-sink, not a heat source. This makes the vast majority of the ocean volume a poor reservoir of “heat” — in fact, it’s a source of cold for affected areas — look at the east Pacific.
Of course, those areas that normally are governed by these cold currents would see a temp rise if the bottom water warmed, but the amount of heat necessary to raise such a vast amount of bottom-water even just a degree would be huge. During warm periods of the earth (like 60 mya) the bottom-water is not nearly as cold — it was as much as 60F (15C) instead of today’s 4C. This is because during those periods there was negligible sea-ice/glacier melting.
Dear Anthony, Willis, and all,
today I am facing a puzzle and I am not sure where to turn to . . I hope this thread didn’t go cold.. My only resources for this are two wiki-pages, so perhaps the answer is as easy as someone was describing the Revelle-factor incorrectly, but if I take whats written there at face value, here is what I see:
If you assume, that the ocean were about 1°C colder during the little ice age 200 years ago than now and use Henry’s law to calculate the difference you get according to wiki:
http://en.wikipedia.org/wiki/Henry's_law
that the constant k_H(T) = k_0 e^-[ 2400 (1/(273.15+T) -1/298) ]
and T is something like 16°C and 17°C for the ocean surface
This leads to a difference in this number of about 2.8% and
in the wiki carbon-cycle you can read:
http://en.wikipedia.org/wiki/Carbon_cycle
“The factor for the ocean is about ten: that is, for a 10% increase in atmospheric CO2, oceanic storage (in equilibrium) increases by about 1%, with the exact factor dependent on local conditions. ”
In other words:
If the near surface ocean warmed by 1°C since then, the raise of the CO2-concentration in the atmosphere is a natural consequence (almost completly with very little room for an anthropogenic contribution).
In order to explain this a bit more, I see there two sources and a sink:
The sea, the burning of fossil fuel and the sea again. The sea can easily take up any anthropogenic contribution if the temperature is right!
Could you comment on this math?
Thank you,
LoN, puzzled
Laws of Nature says:
October 29, 2010 at 1:33 am
Laws, I look at it a different way. Rather than deal with theory I go more for observations. In the Vostok record, a temperature swing of about 10° leads to a CO2 swing of about 75 ppmv.
Setting aside the question of logarithmic response, we get a 1° temperature change leading to a CO2 swing of 7.5 ppmv. Lots of error in that, lots of plus and minus, but that’s the general idea.
This makes it improbable that the current rise in CO2 is due to a change in ocean temperatures.
Dear Willis,
thank you for you answer!!!
(this thread is not dead yet :))
You wrote:
“Laws, I look at it a different way. Rather than deal with theory I go more for observations. In the Vostok record, a temperature swing of about 10° leads to a CO2 swing of about 75 ppmv.
Setting aside the question of logarithmic response, we get a 1° temperature change leading to a CO2 swing of 7.5 ppmv. Lots of error in that, lots of plus and minus, but that’s the general idea.”
Well, I have to say that the first time I read it I all of a sudden got even more puzzled:
We are talking about temperature dependence and you cite some data from ice and ice-water . .
Well, I now know, that the Revelle-Faktor and the Law of Henry are both temperature dependent and somewhat counteracting.
If you assume that the surface sea water warms from 16 to 17 degrees C, then Henry tells you, that about 2.8% of the gas in the water goes into the atmosphere, however, the Revelle-factor gets smaller and the atmospheric CO2 content only rises by 23% instead of the expected 28% (all number need further checking .. it is quite hard to get reliable sources herre)
Now along comes you and tells me something about CO2 in ice cores . . why me is puzzled . .
– if the water and air would be in CO2-equilibrium when it freezes, it should have a constant ratio, since only the temperature determines the CO2 amounts
– if it is not in equilibrium the cold water near the poles should have more CO2, than the average sea water (due to the temperature)
– and when you cool it further down, it should tend to extract the CO2 from the air bubbles over time (I assume, that Henry’s temperature dependence doesn’t care much if the liquid freezes) . . could it be that the low CO2 content in ice simply is due to Henry?
That brings me to the answer:
Just because a “10° leads to a CO2 swing of about 75 ppmv” in ice does not have to say anything about what happens in the oceans at a temperature change from 16 to 17° . . !?