Guest Post by Willis Eschenbach
People have upbraided me for not doing an in-depth analysis of the paper “Earth’s Energy Imbalance and Implications“, by James Hansen et al. (hereinafter H2011). In that paper they claim that the earth has a serious energy imbalance, based on the change in oceanic heat content (OHC). Here’s my quick analysis of the paper. A more probing discussion will follow.
Figure 1. What could happen if the ocean gets warm. Dangers include increased risk of lassitude, along with augmented consumption of intoxicants and possible loss of clothing, accompanied by mosquito bites in recondite locations.
Here’s how I proceeded for a quick look at the H2011 results. The paper says that during the period 2005 – 2010, the warming of the entire global ocean, from the surface down to the abyssal depths, is the equivalent of 0.54 W/m2 of energy.
When I read that, the first thing I did was make the conversion to degrees per year of oceanic warming. I wanted to see what they were saying, but measured in meaningful units. A half watt per square metre of energy going into the global ocean means nothing to me. I wanted to know how fast the ocean was warming from this rumored imbalance. The conversion from watts per square metre to degrees Celsius ocean warming per year goes as follows.
We want to convert from watts per square metre (a continuous flow of energy) to degrees of warming per year (the annual warming due to that flow of energy). Here’s the method of the calculations. No need to follow the numbers unless you want to, if you do they are given in the appendix. The general calculation goes like this:
An energy flow of one watt per square metre (W/m2) maintained for 1 year is one watt-year per square metre (W-yr/m2). That times seconds /year (secs/yr) gives us watt-seconds per square metre (W-secs/m2). But a watt-second is a joule, so the result is joules per square metre (J/m2).
To convert that to total joules for the globe, we have to multiply by square metres of planetary surface, which gives us total joules per year (J/yr). That is the total joules per year for the entire globe resulting from the energy flow in watts per square metre.
That completes the first part of the calculation. We know how many joules of energy per year are resulting from a given number of watts per square metre of incoming energy.
All that’s left is to divide the total joules of incoming energy per year (J/yr) that we just calculated, by the number of joules required per degree of ocean warming (J/°C), to give us a resultant ocean warming in degrees per year (°C/yr).
The result of doing that math for the 0.54 W/m2 of global oceanic forcing reported in H2011 is the current rate of oceanic warming, in degrees per year. So step up and place your bets, how great is the earth’s energy imbalance according to Hansen et al., how many degrees are the global oceans warming per year? … les jeux sont fait, my friends, drumroll please … may I have the envelope … oh, this is a surprise, there will be some losers in the betting …
The answer (if Hansen et al. are correct) is that if the ocean continues to warm at the 2005-2010 rate, by the year 2100 it will have warmed by a bit more than a tenth of a degree … and it will have warmed by one degree by the year 2641.
Now, I don’t think that the Hansen et al. analysis is correct, for two reasons. First, I don’t think their method for averaging the Argo data is as accurate as the proponents claim. They say we can currently determine the temperature of the top mile of depth of the ocean to a precision of ± eight thousandths of a degree C. I doubt that.
Second, they don’t use the right mathematical tools to do the analysis of the float data. But both of those are subjects for another post, which I’ve mostly written, and which involves the Argo floats.
In any case, whether or not H2011 is correct, if the ocean wants to change temperature by a tenth of a degree by the year 2100, I’m certainly not the man to try to stop it. I learned about that from King Canute.
w.
APPENDIX: Some conversion factors and numbers.
One joule is one watt applied for one second. One watt applied for one year = 1 watt-year * 365.25 days/year * 24 hrs/day * 60 minutes / hour * 60 seconds / minute = 31,557,946 watt – seconds = 31.56e+6 joules.
Mass of the ocean = 1.37e+18 tonnes
It requires 3.99 megajoules (3.99e+6 joules) to raise one tonne of sea water by 1°C
Joules to raise the entire ocean one degree Celsius = tonnes/ocean * joules per tonne per degree = 5.48e+24 joules per degree of oceanic warming
Surface area of the the planet = 5.11e14 square metres
1 W/m2 = 1.60e+22 joules annually
So the whole calculation runs like this:
.54 W/m2 *1.6e+22 joules/yr/(W/m2)
------------------------------------------------ = 0.0016 °C/yr
5.48e+24 Joules/°C
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yeah, willis!
sure has been a resurgence of really basic science around here lately.
it’s very nice.
if only it were about science, eh?
you’ll find you can’t knock em down with facts. you have a quibble but they have a cause. it’s a moral issue – sacrifice required. eventually we get to the real meat of the matter – the cannibal lunch. eventually there must be a rediscovery of morality. then we can decide not how but if we shall be prey.
To find out what the “oceans” are doing, measuring the top is silly. It is my opinion that the abyssal deep tells us what is going on overall with the oceans and we don’t measure temperatures there in any serious way. If the bottom of the ocean warms by 0.1 degrees, that is a huge amount of heat, whatever is going on at the surface notwithstanding.
Svein S says:
December 31, 2011 at 12:40 am
Since the rate of heating is so small, there will be centuries for the ocean to mix thoroughly. As a result, the unevenness of the heating will not be an issue.
There are many other issues, Svein, stay tuned.
w.
Julian Braggins says: “I would like to defend poor maligned King Canute, he demonstrated his inability to stop the incoming tide to demonstrate to his sycophantic court and populace that he was not omnipotent”
I used to jump into that one, too, Julian; until an English chappie on the blogs advised me it depended which side of some border was used as reference. On one side they hated him and the story was that of a fool — on the other side they honoured him and the story was of a man of wisdom.
Some wandering around seemed to confirm that split of definitions, so now I lay low…
Please you are raising the temperature of one tonne of sea water by 1C not raise the water, something my physics teacher instilled into me at school.
All these alarmist claims seem to forget nighttime when there is no solar heating and lots of heat loss. Hansen’s claims are based on relating big numbers in the hope that these will panic people into believing him. When reality sets in there is nothing to fear.
Thanks Willis.
Thanks Willis for the calculations! One remark: the main warming is in the upper layer of the oceans, as the bulk of the deep oceans doesn’t warm that fast. In general, the GCM’s only consider the upper 250 m of the oceans (the “mixed layer”) as involved in temperature changes. Thus the “warming” is going faster, but at the other side, the W/m2 imbalance isn’t staying the same: at one side the theoretical forcing by CO2 is going up, but as the temperature of the ocean surface goes up, the direct radiation to space goes up with the fourth power, besides evaporation and convection towards the poles… Anyway the effect is miniscule.
jaymam says:
“The sun heats a quarter of the globe.”
Are you claiming that when it is daytime in one part of the world it is nighttime in three quarters of the world?
N. Atlantic OHC: http://bobtisdale.files.wordpress.com/2011/12/figure-101.png
We have in phase for the first time since the 17th Century the cooling PDO, the cooling part of the Arctic oscillation and the 1 in 179 years’ cooling solar cycle.
By 2020 N. Atlantic OHC, which has driven global OHC by warmed melt water from the Arctic [driven by low cloud albedo], will be back to normal.
Yeah! but when you do the maths – it takes all the grant funding hyperbole out 🙂
Thank you!
Shouldn’t you account for the ocean not covering the entire planetary surface?
Canute bade the tide to cease next to his palace on the banks of a tidal river, the Thames. The centuries rolled by and in 2008 the Houses of Parliament passed the Climate Change Act at almost exactly the same spot — so close in fact that it may well be that the Speaker sits where Canute did all those years before.
The difference is that the King knew his order was nonsense. So much for the Enlightenment.
JF
Canute, his flattering courtiers cried
Can do what he wants with the rising tide.
But he only wetted his feet when he tried.
(Punch)
Haven’t you got this slightly wrong Willis? You seem to have calculated the number of Joules over the entire globe, and then applied all of this to heating the mass of the ocean (as Mike McMillan said then also Brian H before he changed his mind).
The ocean is only about 70% of the surface area of the planet and energy falling on the land is not going to contribute directly to heating it. Surely your calculation should be
(0.7 ^ 0.54 * 1.6e+22 ) / 5.48e+24 kelvin per year
… which gives an answer somewhat less frightening and alarming
I’m an old chemical process guy. I got lost at “imbalance”. Mass and energy always balance. If you cannot balance them, you failed to adequately describe the process. If in and out don’t balance you are sent back to your room until, like a good little boy, you do your homework to get them to balance. Global mass/energy balance is a bit more difficult to measure but the process still applies. “Imbalance” and “energy budget” (whatever that is supposed to mean) simply describe inadequate measurement or understanding.
With 3000 drifting buoys, a replacement rate of 750 buoys pa; a range of temperatures measured by a typical buoy of about 10 deg C, as they rise and fall; a huge difference in ocean depths at buoy locations; a variation of 0.1 deg C seems rather meaningless.
As I have written many times, the thermal expansion/contraction of the connected oceans depends on the sea temperatures as measured at all depths. The onion skin approach is invalid, as Willis rightly shows by electing to present his calculations this way. Crosspatch is correct a few posts up.
Willis, if you push your calculations a little further, you’ll find that Hansen’s calculations and reasoning are reasonable and self-consistent. For example, Hansen asserts three things:
(1) The deep-ocean temperature swing associated to the thawing of an ice age is about 3 degrees C (per ocean data of Hansen’s Figure 3).
(2) Earth’s present energy imbalance is about 0.75 Watts per meter^2 (per Hansen’s Section 13.4).
(3) The latter energy imbalance is sufficient to produce major changes in Earth’s climate.
To check whether Hansen’s assertions are mutually consistent, let’s calculate the time-scale on which the energy imbalance (2) can produce the deep-ocean temperature change (1), and ask: Is the time-scale for deep-ocean warming short enough to justify concern (3) regarding climate change?
Here are the associated calculations (as automated in a program called Mathematica):
—————————————————————
— Calculations —
physicsRules = {
timeToWarmTheOceans ->
iceAgeOceanTemperatureChange/rateOfOceanWarming,
rateOfOceanWarming ->
globalHeatingRate/(heatCapacityOfWater*globalOceanVolume),
globalHeatingRate ->
areaOfEarth*energyImbalanceHeatFlux
};
geophysicalData = {
iceAgeOceanTemperatureChange -> 3 K, (* Hansen Figure 3 *)
energyImbalanceHeatFlux -> 0.75 W/m^2, (* Hansen Section 13.4 *)
areaOfEarth -> 0.51 * 10^9 km^2,
globalOceanVolume -> 1.3 * 10^9 km^3,
heatCapacityOfWater -> 4.2 J/(gm K) * 1 gm/cm^3
};
timeToWarmTheOceans//
ReplaceRepeated[#,physicsRules]&//
ReplaceRepeated[#,geophysicalData]&//
ConvertToSI[#/year]&//Round//
Print[“Time to warm the oceans = “,#,” years”]&;
— Results —
Time to warm the oceans = 1357 years
—————————————————————
Thus we verify that Hansen’s conclusions are physically reasonable: a global energy imbalance in the range 0.5-1.0 W/m^2 does suffice to warm the Earth’s deep-ocean water on a time-scale of order one thousand years; a period that is (1) short compared to CO2 residence times in the atmosphere, and (2) rapid compared to normal climatological processes.
Of course there is much more to be said — that’s why why Hansen’s article is more than fifty pages long — but at least the fundamental physics of Hansen’s argument is internally consistent and reasonable.
“They say we can currently determine the temperature of the top mile of depth of the ocean to a precision of ± eight thousandths of a degree C.”
We live in truly astounding times if they really can! Then again, they have been living on the edge of reality for some time now! I simply cannot get my head around that Willis! Help me out! Do they treat the oceans/seas as a still body with no currents, waves, no varying winds, no cloud cover? The list is endless!
What about the loss of heat from the oceans at night, and as the ocean temperature increases, surely the rate of heat loss at night would also increase. Also as ocean temperatures increase, more evaporation would take place also serving to hold temperatures in check.
2641 ? more like 3641
by which time there may perhaps only be one topic of conversation.
The most recent Jason-2 data update shows a return to rising sea-levels — consistent with the concluding prediction of the abstract of Hansen’s article, that prediction being “a near-term acceleration in the rate of sea level rise.” The next two decades will be very interesting in regard to Hansen’s prediction, eh?
Svein S says: December 31, 2011 at 12:40 am “To argue against Hansen´s analysis one needs to do better than this futile attempt.”
You have pointed out that the warming would be less than Willis has shown, so you have shown that Hansen is even more wrong than Willis.
Off topic, Willis, but since it’s the end of the year I can now say that “The Reef Abides” has officially won best blog posting title of the year for 2011. Cheers and Happy New Year!
We’re finally talking about the right subject.
1. Temperature is a symptom of the more fundamental variable – heat energy.
2. The heat energy of the Earth’s biosphere is completely dominated by the heat energy in the liquid water of the oceans.
3. The heat content of the atmosphere is small by comparison, and is in turn dominated by the energy stored in water vapor. The state change from liquid to gas requires (releases when reversed) so much energy that it forms a huge stabilizing flywheel.
The oceans are performing one of many of their very useful functions……acting as the world’s best heat sink, storing the excess heat until such time as the energy imbalance goes the other way and the oceans give up that stored energy. My preference is that they continue to store energy for a while to delay the onset of the next glaciation. Not that I will be around to see it.
Geoff Sherington: the problem Hansen is that his basic physics is wrong. As well as false ‘back radiation’, an elementary mistake to anyone properly trained in heat transfer, and the 33K present GHG warming claim [it’s probably ~9K], the aerosol cooling Hansen claims, -1.6 W/m^2, is bunkum. Assuming the same median direct cooling as in AR4, it means an increase of ~50% of the indirect cooling when that has substantially fallen recently as shown by falling N. Atlantic OHC.
The explanation is that the aerosol optical physics he pioneered is wrong.
A Physic: take out the sinusoid and these data show continued fall in sea level. It’s probably caused by the fall in OHC and increased Antarctic precipitation. When the Arctic is really frozen, about 2020, sea levels will have fallen substantially.
The exact level of GHG-AGW is a moot point. I wouldn’t be surprised if it was very low indeed because you can explain all present and palaeoclimate observations by change of cloud albedo.
ok at the risk of making myself look goofy,
hansens calcs are all assuming everything stays constant?
and
in Nature Nothing ever is,
solar lows highs etc for starters.
Iceland just got massive snow dumps i read, off their records, switzerland also, so even as a minor event, it affects albedo for some time till it melts or not.
none of which can be factored into anything, for long term use really.