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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How do you take into the cooling effect of the wind? If the ocean heats up slightly, the extra heat could easily be taken away from the surface by the wind.
Even if the surface water is cool, a strong wind such as northreaster can
blow enormous amounts of water and its energy onto the land.
How do you take into account the clouds Some of the forcing energy never makes it to the surface.
davidmhoffer says:
October 23, 2010 at 7:45 pm
Thanks, David. I am exploring the consequences of the IPCC forcings. That is why I have used their numbers, including the 0.12 W/m2 change in solar forcing over the last 250 years. I am definitely not saying that any of the IPCC numbers are correct. I am exploring the use of their numbers. Their numbers say we should have seen twice the warming in the last 150 years. I’m trying to understand why that is.
It looks like my post got lost in the ether or filter. I was pointing out that measurements of evaporation point to the opposite of what is expected by IPCC and others with raising temperature ie the evaporation has been going down over the last 30 or more years. see here http://www.rsbs.anu.edu.au/Profiles/Graham_Farquhar/documents/271RodericketalPanreviewIGeogCompass2009_000.pdf
This points to
a) lower air temperature than measured or even temperature reduction
b) a reduction of insolence -maybe due to more cloud
c) more complexity about evaporation than allowed in heat balances and models
or
d) all of the above.
cementafriend says on October 23, 2010 at 9:18 pm
Heh, that would be useful 🙂
Willis Eschenbach;
I am definitely not saying that any of the IPCC numbers are correct. I am exploring the use of their numbers. Their numbers say we should have seen twice the warming in the last 150 years. I’m trying to understand why that is.>>
It has been a while since I read AR4…. uhm, ok, skimmed, but I recall being unable to reconcile some of their numbers. After a bit I realized that their reference frame wasn’t consistent. They calculated sensitivity against pre-industrial levels but extrapolated various scenarios against levels calculated against the 1980-2000 mean which made various graphs and charts difficult to compare.
I did however come across one set of calculations that just made no sense until I figured out they were referencing global temperatures as measured at a specific altitude (14,000 feet?) rather than at surface. I’ve forgotten the specifics but do recall that the colder temps at that altitude resulted in a higher sensitivity calculation just based on Stefan-Boltzman. When I got that figured out I could turn that into an “at surface” sensitivity and make some sense of how they arrived at their projections. The hour being late and my vision blurring, I shall seek the respite of sleep, but assuming I am lucky enough to wake again in the morning, I’ll see if I kept any of those spreadsheets with all the numbers to figure it out.
You say:
Global Surface 5.1E+14 m2
“Missing” Incoming Radiation 0.7 W m-2 over earth’s surface
I have not checked your spreadsheet figures but does everybody realise that the radiation from the Sun appears on one side of the Earth only and not over the entire Earth’s surface.Therefore the area of the Earth receiving inward radiation from the Sun is one quarter of the total surface area of the Earth. However outward radiation should be calculated using the entire Earth’s surface.
IPCC sensitivity figures are off the mark. Based on a 0.7 degree change in temp for 110ppm increase in CO2 since 1850 (40% of doubling) yields a climate sensitivity of 1.85 degree C. At the lower end of IPCC estimates. This not taking into account potential exaggerations in global temp. data due to UHI. Considering a 1850-present rise in T of 0.5 degrees yields a CS of just 1.25 degrees.
Hard to loose something that isn’t there, unless of course it’s imagined.
Perhaps slightly O/T to the thrust of Willis’ post in examining the IPCC’s calculation methods, but pertinent to the question of “where is the lost heat”, it is worth considering the Earthshine project:
http://www.bbso.njit.edu/Research/EarthShine/
As they observe:
“Probably because of the lack of reliable data, traditionally the Earth’s albedo has been considered to be roughly constant, or studied theoretically as a feedback mechanism in response to a change in climate. Recently, however, several studies have shown large decadal variability in the Earth’s reflectance. Variations in terrestrial reflectance derive primarily from changes in cloud amount, thickness and location, all of which seem to have changed over decadal and longer scales.”
The graphs show a variation in albedo of up to 2% over a 6 year period.
2% of 1365 w/m2 = 27 w/m2.
And they’re looking for a piddling 0.7 watts?
Every one of their models that assumes a constant albedo for earth is clearly, simply, wrong.
Travesty or not, Trenberth and his mates will never find the heat, because it just ain’t there; it has evidently buggered off.
What about heat coming from below? Thermal vents etc. Admittedly tiny compared to all the oceans but are they a factor?
“COMMENT: I think you mean to say “heat sink” rather than storage heater, its certainly not warming much. – mike.”
No I meant storage heater. Imagine what happens to 1sqm of of ocean water during a 24hr period. It heats up during the day and radiates some of the back into the atmosphere during the night, with a small amount, dT, being retained in deeper levels. Without this effect, air temperature at night would be lower than that measured. Now imagine what happens to that same 1sqm of water over a year, or any period where energy in is changing. The ocean behaves like a storage heater.
I have read all the above comments and Willis’ original article.
If there is a more theoretical science basing complex and obscure calculations on aspects of a natural occurence that are at best little known, and at worst not even dreamt of, I have yet to come across it.
No wonder Climate science is termed ‘post normal’.
tonyb
Willis, checking your math i keep coming up with ~463 years if the excess was 1 Wm-2 and 661 years if 0.7 Wm-2 but I guess it’s always good to land on the conservative side! I went by it a slightly different direction, computing in SI first to get mass of the 1 m2 3700m column, then at specific heat to get joules to raise it 1 K irregardless of when. Then seperately, 0.7 W/m2 for a year of seconds gives the joules of excess energy in a year. Took first divided by second to get years, 661 years. Change the 0.7 to 1 and I get 463 years. You might have been a bit low. ☺
The hubris of climate scientist is quite amazing. Just as computers were suppose to cut down on the need to print, but instead made thousands of charts as well as all writing much easier to produce and lead to much greater printer use, so computers and computer models take thousands of POORLY known actual numbers, and numerous equally POORLY understood physical processes, and arrive at certain answers of global disaster; coincedentaly demanding trillions of dollars NOW, even though with out China and India on board these trillions will have virtualy no effect.
Climate science is “arm waving through computers at hummingbird speed.”
What goes around …
The next thing to conviently forget is that climate sensitivity is an equilibrium concept. It tells you the temperature that you get to eventually. In a transient situation (such as we have at present), there is a lag related to the slow warm up of the oceans, which implies that the temperature takes a number of decades to catch up with the forcings. This lag is associated with the planetary energy imbalance and the rise in ocean heat content. If you don’t take that into account it will always make the observed ’sensitivity’ smaller than it should be. Therefore if you take the observed warming (0.6°C) and divide by the estimated total forcings (~1.6 +/- 1W/m2) you get a number that is roughly half the one expected. You can even go one better – if you ignore the fact that there are negative forcings in the system as well (cheifly aerosols and land use changes), the forcing from all the warming effects is larger still (~2.6 W/m2), and so the implied sensitivity even smaller! Of course, you could take the imbalance (~0.33 +/- 0.23 W/m2 in a recent paper) into account and use the total net forcing, but that would give you something that includes 3°C for 2xCO2 in the error bars, and that wouldn’t be useful, would it?
From a response to Milloy and Monckton doing the same thing in 2006…
I’m beginning to wonder if we can rely on any of the numbers in the IPCC reports other than the page numbers. Or do they remain constant until the final chapter and then suddenly increase?
Willis, you don’t have to look for that lost heat. It doesn’t have to be somewhere, nor does it have to be “lost”. It only needs to exist in the future. At this moment, the only thing that you would need is some kind of radiative imbalance.
Put a boiling pot in the fire with some water. Low fire, no boiling, constant temperature. Now you raise the fire. The fire is strong enough to make the water boil, someone tells you. But three minutes pass and the water is hotter but is not boiling. You say, where is the missing heat? If the water is not boiling, where is it? Well, it is nowhere. It is ON ITS WAY to the water. It will exist in the future, by slow accumulation due to the existing radiative imbalance (more heat is comming than is leaving the water.
The fact that we are now 0,7º hotter instead of 1,5ºC doesn’t mean that we cannot be 1,5ºC hotter later on, IF there still exists a radiative imbalance that keeps bringing on warming.
I personally don’t think that this is the case and don’t believe in such a future warming, but the AGWers’ reasoning regarding this point doesn’t have the flaw that you pretend it has.
Whether numerics are right or wrong it is not of much consequence. As an engineer I am used either to do approximations or accurate calculations. Two should not be mixed up. In this case it is clearly an approximation which can be used as a pointer and no more than that.
In my view, considering the factors involved, precise calculations are next to impossible, also the surface temperatures are no good guide of the heat content in lower layers.
But more importantly, it is the principle on which these calculations are based. It is assumed that the Earth’s hydrosphere is alternatively heating or cooling, which may be case, but it is not only factor or even major one.
Major factor is ‘the absorbed heat redistribution between equator and poles’, and this process waxes and wanes on decadal scale, so any calculation of temporary heat loss or gain in my view is something not to be given much credence.
I quite agree. I have always said that cloud has a great control on temperature and in both directions, depending on conditions. So cloud can be positive or negative and act as a thermostat.
“the forcing change simply doesn’t hold water.”
How true! The reason? :
The water simply does’nt hold the forcing change!
I see statements here of people defending the IPCC numbers and logic like:
“Ocean waters take a long time to mix below 700 meters”. No links to data.
What about tides? Every day in 12 hour intervals a giant column of water from the bottom up is being dragged through the oceans lifting the surface at least 40cms and up to 20 meters in shallows. Doesn’t this turbulence have a wake that will pull waters down and bring waters up, all the way from the bottom, in addition to that of hitting under ocean mountains? How could this be explained away in the millenia needed to mix the waters?
There is no reason why the “missing” heat should not have been transformed into another form of energy. For example, a very slight speeding up of ocean currents could account for a huge amount of energy, given the very large volumes of water involved. We do not measure the currents sufficiently accurately to be sure this is not happening.
Alex Heyworth says: October 24, 2010 at 4:34 am
For example, a very slight speeding up of ocean currents could account for a huge amount of energy, given the very large volumes of water involved.
Entirely agree. See my post:
http://wattsupwiththat.com/2010/10/23/more-oddities-with-the-ipcc-numbers/#comment-514417
Hi,
The ocean has an effective thermal depth, due to the manner in which it warms, of around 950m, roughly 1km clculated from the mean vertical thermal diffusivity and the mean vertical velocity. The top warms most and first and the lower part barely if at all. In periods of rapid warming the effective depth would be somewhat less. Try multipling you temperature increase by about 3700m/1000m for a start.
The 0.7W/m^2 you calculated would I think refer to the imbalance at the end of the 20th C or perhaps upto 2005 for AR4. So you should concentrate on the OHC gradient in say the previous decade or perhaps from 1990 to now. I thnk you should find slopes in the 0.6 – 0.7 W/m^2 range.
Alex
richard telford says:
October 23, 2010 at 1:17 pm
The oceans are not well mixed!
That depends on your point of view. Ninety percent of the ocean has a pretty constant and consistent temperature very near three degrees centigrade. The ten percent of it that is warmer than that is the first few hundred meters below the surface.
The sixty four thousand dollar question is what factors determine the rate at which the (usually) warm shallow surface layer mixes with the vast frigid depths. If the mix rate slows the atmosphere will warm and if the mix rate increases the atmosphere will cool. If the surface and deep waters were to approach equilibrium, which would be about four degrees centrigrade, the earth will be in a full blown ice age. Now -that- is just cause for concern.
Regarding Nylo says:
October 24, 2010 at 3:21 am
What?, your missing heat is in the fire you turned up. It is a “travesty” we can not find it, but as we do not know the energy budget of the planet, it is not surprising.