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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An update for A Physic: here are the Envisat sea level data: http://indianweatherman.blogspot.com/2011/11/envisat-data-shows-global-sea-level.html
Falling consistently since 2007
Thanks for the post Mr Eschenbach.
The paper shows one thing clearly. If there is one hockey-stick graph apparent in the last few decades, it’s Hansen quoting himself! 🙂
Mike Bromley the Canucklehead says (December 30, 2011 at 11:49 pm): ‘So tell me, why would Hansen publish something like this, anyway?’
(1) To give Hansen’s explanation of why there’s been little warming in the last decade top billing in AR5, by…
(2) ..dismissing Trenberth’s “missing heat” and…
(3) ..blaming aerosols, which no-one can dispute because of the paucity of data on aerosols.
Rem: http://wattsupwiththat.com/2011/10/27/climate-scientists-and-their-excuses/.
Willis, I doubt that the oceans warm even as fast as you’ve calculated.
Virtually all of the warming takes place in the upper few hundred metres and especially at the surface. Surface warming would increase the heat loss from the surface (by radiation, convection and evaporation) which would in turn tend to reduce the imbalance, effectively reducing the amount of energy available to warm the deeper layers.
What does Henson aiming at? ….. Well, he said, there is “missing heat in the pipeline”, somwhere HIDING and his pipeline is the deep oceans, where the heat disappears into it …. Therefore we have the present 21 Cty temp plateau, where temps stay flat…….because its hiding deep down in the water…..Which means AGW IS RIGHT, because GOLBAL WARMING has not stopped but is only hiding!
But hiding……nothing escapes the sharp eyes of smart Henson…he measures the MISSING HEAT down to a fraction of 0,0016 (which is 16 ten thousaunds part of 1 degree) in the water, but what
about the global AIR temp increasing by +2 C until the year 2100???
Maybe a + 0,0016 C x additional 90 years of ocean heat should be equal to + 2 C until 2100?
Question to the Henson smart A PHYSICS: Please
translate the OHC warming into the 2 C atmospheric warming until 2100 and you will be
celebrated by all of us…..! We are waiting….Happy new Year + something to do…..
JS
A physics says:
December 31, 2011 at 3:39 am
“The most recent Jason-2 data update shows a return to rising sea-levels — ”
A physics, it does that every NH winter. It’s not seasonally adjusted.
A physics says:
December 31, 2011 at 3:39 am
alcheson says: Was looking yesterday for updated sea level data from it yesterday and seems its all disappearing from the web. I’m thinking the drop in sea level data it is showing is causing to much heartburn for the warmists so am expecting an “update” soon myself.
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?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A physics, I opened your suggested url that’s supposed to convince us that the ocean level is again rising; it needs a lot of faith for one to belive so. The oceans seem to have stopped rising and there is more of a stasis then a rise right now. Look at the graph again.
Willis,
Why is it that the energy transferred to the atmosphere by evaporation, and therefore the lowering of the ocean surface temperature, is not considered in the equation? Is it too small compared with the total energy pick up due to solar radiation? Just asking.
An additional note to calculation smart “A Physics”:
The present temp plateau since 2001 means that all the “missing heat” (i.e. no more atmospheric temp increase) went into Hensons secret deep hiding place……but how does the heat comes out again from there and enters again into the atmosphere??
The IPCC AR4, wg1 answers this question: The heat comes out again at a rate of half the value of 0.2 C global temp INCREASE per DECADE, which means the missing heat comes out at at a rate of 0.1 C/decade (2001-2010). Here you have a good calculation value, since IPCC AR4 is produced by more than 40 smart climate institutes, AR4 is their combined wisdom and they will NOT admit errors on the subject…. this just to help you a bit with the numbers in case you would get lost…. why would 0.1 C/decade come out of the water when global temps stay on a flat plateau and 0.0016 C are hiding in the water?
JS
Assuming the calculation is correct, one tenth of one degree by 2100 sounds pretty tame. But before we get too comfortable with that picture, I suggest another “macro-calculation”. If the oceans did warm 0.10 degree C., use the solubility tables to calculate how much CO2 the oceans would puke into the atmosphere. Add that total to the continuing man-made component and then do a simple greenhouse calculation for year 2100 to see whether the temperature effect is multiplied to any alarming degree. Hansen is obsessed with “positive feedback”. Ocean puking would certainly fall into that category.
The abstract says “We conclude that most climate models mix heat too efficiently into the deep ocean and as a result underestimate the negative forcing by human-made aerosols.” In the body of the paper they explain that models are not based on primarily on physics but are based on fitting parameters like aerosols so the model output matches Hansen’s favorite Global Average Temperature index (the one that assumes that stations 1200km apart are well correlated, that island airports are representative of large swaths of ocean, that urbanization effects can be corrected by warming historical measurements, etc).
Figure 2 is the thesis of the paper, a model output or freehand drawing (doesn’t really matter which) of “relative probabilities” of aerosol forcing (gray dotted line) that “prove” that the lack of warming is due to aerosols and not deep ocean heat loss. That is important because if heat is lost to the deep ocean (which is 90% of the volume), it is not coming back since water warmed from 34F to 34.1F cannot return to warm the ocean above the thermocline. If that water does return it will cool the surface and the atmosphere. It is not correct to call that “inertia” since the heat is lost, not merely delayed.
The IPCC AR5 will have total forcing at about +2.17 W/m2 for 2010.
If von Shuckmann 2011 and Hansen 2011 are right, there is 0.54 W/m2 going into the 0 to 1500 metre ocean and 0.07 W/m2 going into Land energy accumulation and Ice-Sheet melt.
So, that leaves 1.54 W/m2 (of direct forcing) available to warm the surface (there should be no lag in this beyond a few months). If temperatures are up 0.7C (including feedbacks), that results in 0.45 C/W/m2.
Still well below the expected 0.75 C/W/m2 that the theory is based on. There is less imbalance than Trenberth initially flagged as a travesty, but there is still energy missing.
Faster way is not to change units I think.
BTU = energy required to raise one pound of water one degree F
average depth of ocean 12000 feet
pounds of water per cubic foot 62
energy input 0.05W/ft2
1 Watt = 3.4 BTU/hr
hours/year = 8670
0.05*3.4*8670 = BTU/YEAR/FT2 = 1474
1474/(62*12000) = TEMP in F increase/year total ocean = 0.002F
Call it enough to raise average ocean temperature by 1F in 500 years.
The real question is the mix rate. If this energy were just going into the mixed layer (top 300 feet) then it would raise the temperature 1F in just 12 years. We would have easily noticed that. So either the mixed layer is mixing downward an order of magnitude faster than credible by known means or Hansen is badly mistaken about how much extra energy is arriving. Hence Trenberth’s infamous “missing energy”.
There IS one other possibility. The extra energy is indeed falling upon the ocean’s surface. It is indeed coming from anthropogenic CO2. But it simply isn’t being entrained in the ocean. There’s a good physical explanation of why it isn’t being entrained. YOU CAN’T HEAT WATER WITH LONG WAVE INFRARED RADIATION! It doesn’t work. All it does is raise the evaporation rate. Once you realize this is true everything starts making perfect sense.
A person with right brain damage will believe anything as long as it is self-consistent. (Iain McGilchrist, The Master and his Emissary”, Yale University Press, 2009) Actually, to be fair to Hansen, McGilchrist says the problem is with society in general and not just with people who actually have brain damage.
The fact that something is self-consistent doesn’t prove that it is right. Many fine debaters have produced wonderful self-consistent arguments about how many angels can dance on the head of a pin. 😉 Anyway, no matter what else you think about Hansen, he is a competent scientist. Any work he does will be self-consistent even if it is wrong.
Some people are unclear as to why 1/4 is used in the math calculations. Here is my attempt of an explanation:
If your planet was a flat circular disk that always faced the sun, you would divide by 2 (or multipy by 1/2) to calculate the average amount of sun hitting the oddly shaped planet as one half would be in constant shadow. If instead you had a half sphere planet, with a round, or half spherical part always facing the sun, you would now have a much larger surface area receiving the same amount of sun as the flat surface version. Now if you have a sphere, and that is indeed what we have, the math simply works out to multiplying by 1/4 to acount for the surfaces of the sphere that are not directly facing the sun and hence not receiving the full force one might get if the sun was directly overhead as well as the half of the planet that is in complete shadow.
One other useful representation is to consider a parallel beam flashlight (torch). While shining the light perpindicular to a surface, note the strength of the light. Now turn the flashlight so it makes an ever increasing angle away from perpindicular and you can easily see that the same amount of light “forceing” is now spread over a larger area, which is akin to the higher latitudes of the earth. Which is also a reason that less ice in the Arctic isn’t going to cause a runaway heating effect, because the angles are to great, and the entire Arctic is cast in 24 hours of darkness around the date of December 21, and the North Pole itself has 6 months of total darkness (no sunlight reaching its surface).
Willis, I appreciate your work, and as usual, well done, but if Hansen’s paper had crossed my desk I wouldn’t have even looked at. It would have gone straight into the garbage bin. Hansen isn’t a scientist, he’s a carnival barker and has NO credibility whatsoever.
Mydogsgotnonose, the link that you supplied was second-hand, out-of-date, and cherry-picked to the least-well-calibrated satellite (Envisat). An up-to-date summary of all available satellite data shows that sea-level rise resumed in the last eight months of 2011. Hansen and his coauthors predict acceleration of the observed sea-level rise; the next two decades (or so) will test this prediction.
A physics says:
December 31, 2011 at 3:39 am
“The next two decades will be very interesting in regard to Hansen’s prediction, eh?”
The last two were very interesting too?
So, essentially, the missing heat could just be that it just takes a bunch of energy to melt ice and to hinder new ice from forming. What with all the missing ice and interstellar reasoning and what not. :p
Willis
See Jayman “The sun heats a quarter of the globe.”
Surface of a sphere = 4 Pi R^2
Sunlight area = Pi R^2.
Thus divide you area by four – which multiplies your heat rate by four.
See: Ferdinand Engelbeen
So for your first order analysis, recommend using just the top 250 m rather than the whole ocean.
Roy Spencer notes:
See: Do deep ocean temperature records verify models?Richard S. Lindzen GEOPHYSICAL RESEARCH LETTERS, VOL. 29, NO. 8, 1254, 10.1029/2001GL014360, 2002
Spencer provides a simple model including diffusion. See: More Evidence that Global Warming is a False Alarm: A Model Simulation of the last 40 Years of Deep Ocean Warming
Good one Willis.Making the inconsequential a worry seems to be becoming a more desperate process.
A Happy, Healthy and Prosperous New Year to all!
@Mydogsgotnonose
Declining sea-levels, just like temperatures not increasing, are more proof that the earth is actually warming in the long-term… 😉
Funny-funny… what was I gonna say:
I kept repeating for a while that rising temps are not proof that the rise is actually attributable to mankind – but I must admit that I am not sure whether that view is still (?) justified. What’s the word on that? Actually I thought I had read something to the contratry here recentry but didn’t follow up on it. Is there a non-warmist, non-wacko take (read: sensible) on the situation as to the degree of the human contribution, anyone? I must admit that I still wouldn’t get my knickers in a twist, since there has been more warming/cooling before in history, yet we are all alive and kicking today… I just don’t wanna run around and say human contribution to warming isn’t made out if it actually is.
W,
is the M^2 term the surface area of the Earth or 1/4 that number representing the area intercepting solar flux?
BC
Roflol
http://wattsupwiththat.com/2011/12/24/mann-hockey-stick-co-author-bradley-it-may-be-that-mann-et-al-simply-dont-have-the-long-term-trend-right/#more-53634
Just assume that nothing these people (global warming alarmists) have ever written, or will ever write, is worth reading. The probability is you will be more right than wrong, and just think of all the time you’ll save.
Note to file:
Add Hansen et al to the “ignore list”.
Wattsnext?
In less than a decade, the global warming “crisis” will be utterly discredited. Earth will be naturally cooling and humankind will be very concerned about the adequacy of global food supply. There will be bitter recriminations about the trillion=plus dollars squandered on the scam of global warming. Broken wind farms will litter the landscape, with no money to decommission them. Corn ethanol for motor fuel will be considered heresy. The names of the leading global warmists will live in infamy.
R.M.Barclay says:
December 31, 2011 at 12:29 am
Surface tension is the major player in this argument about heat “budgets” and it is being ignored. Try heating the surface of water in a bucket with a heat gun. Even though you are applying 450deg to the surface no heat is transferred immediately. It takes just over 10 mins of heating the surface before the surface tension is sufficiently reduced to allow the water to absorb heat. I don’t have the resourses to take this any further but the result convinces me that surface tension definitely interferes with heat transfer. I strongly suspect that the atmosphere does not have enough heat to overcome the surface tension and therefore no physical heat can be transferred from the atmosphere into the ocean. The ocean only accepts energy from the sun’s rays which penetrate the surface tension no problem. The ocean and the sun are therefore in lock step. Graphs of temperature against sun activity tend to bear me out. It also cures Trenberth’s “missing heat” problem.
RMB,
Your point is quite valid for calm waters. I think it would be quite interesting to look at the differential in rate of heat transfer for calm vs turbulent waters. I would bet money that the equations are not linear. If the CRU folks were attempting to accurately model temps, they would have to account for clouds, wind, & wave motion. It might be a little difficult to do without any worldwide sensor/data collection network.
Good luck with that …