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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A Physicist: – RESULTS —
Time to warm the deep oceans = 1357 years
Mean sea level thermal rise rate = 2.4 mm/year
Sea-level rise from thermal expansion = 3.2 meter
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Hmmmm … the preceding quantitative considerations (which anyone can verify for themselves) provide solid grounds for rational skeptics to consider the proposition that James Hansen is broadly correct, both in his science and in his appreciation of the practical implications of that science.
I always respect the proposition that James Hansen is broadly correct in his science. Your calculation shows that his policy prescriptions are not supported by his science. By the time the oceans have risen 720mm, there won’t be any fossil fuels left, so there isn’t any point in not using them except as a reserve to back up to solar, wind, nuclear, and biofuels. However, these are calculations from a simplified thermodynamic model; a careful review of all the detailed mechanisms of heat transfer (e.g. thermals, thunderclouds and thunderstorms), including limits on the parameter estimates and mechanisms for which rate parameters have not yet been estimated, shows that current science can not even rule out the possibility that increased CO2 will have a net cooling effect on the lower troposphere and surface. Thus, a rational skeptic should conclude that Hansen is broadly correct on the equilibrium thermodynamic analysis, but insupportable in his detailed predictions for the next 20 – 300 years.
Bomber_the_Cat says:
December 31, 2011 at 2:55 am
No, I haven’t got it slightly wrong. You can figure it either either way to get the number of W/m2 needed to change the OHC. You can either divide total joules by the ocean area or by the land area. One way there’s more area, so less W/m2 are needed. The SLT2011 paper gives both calculations. Hansen et al. used the calculation with the larger area (the whole earth) and the smaller W/m2. I have done the same.
w.
Willis, very helpful, as usual.
I was eyeballing your calculation in the appendix and couldn’t figure out where the “1.60e+22 joules” in the numerator was coming from. Is that just a well accepted ‘known’ or is it a result of a calculation using previously mentioned figures in your post? If the latter, what is the correct calculation (formula) to produce the 1.60e+22 result?
A physics says:
December 31, 2011 at 3:29 am
A physics, I have said many times that if you disagree with something I’ve said, QUOTE IT. For example, you seem to think that I’ve said that the fundamental physics of Hansen’s argument is intermally inconsistent. I said no such thing. So you’re fighting manfully … against yourself.
What I said was, the warming is trivially small, so small that it will take hundreds and hundreds of years for the ocean to warm by 1°C. For example, we can expect (if Hansen is right) a warming of a tenth of a degree by the year 2100 … and we don’t even know if we’ll still be burning fossil fuels at the turn of the next century,
My point is not that Hansen’s math is wrong, as far as I can tell it isn’t. My point is that the predicted temperature rise is both trivially small and glacially slow. If you want to waste your precious worry cells on that, be my guest. I’m concerned about kids starving around the planet, not a possible forecase tenth of a degree change in the ocean temperature.
w.
Alex the skeptic says:
December 31, 2011 at 6:06 am
Alex, what is being measured is the ocean heat content. This is the amount of heat in the ocean. We’re not measuring the heat as it goes in and out of the ocean. We’re measuring the temperature of the ocean, and using that to calculate how much heat it contains.
HTH, if not ask again,
w.
A physicist says:
December 31, 2011 at 6:51 am
Who are you, Rip Van Winkle? Hansen and others predicted said acceleration of the observed sea-level about thirty years ago now. The last three decades tested his prediction. It failed miserably.
Where have you been for the last quarter century?
w.
Willis, please let me commend to your closer attention and considered reflection Figure 3(c) of Dr. Hansen’s article, which summarizes the strong evidence from paleoclimatology that deep-ocean temperature swings of ±1.5 °C (relative to a mean value) are associated to radical alterations in the world’s climate.
If it should turn out (as Hansen has argued) that carbon-based energy economies in the 21st century can irretrievably commit our planet to climate swings of comparable magnitude, is that a “trivial” commitment?
Jeff Mitchell says:
December 31, 2011 at 9:17 am
Jeff, what Hansen calculated (and what I have done as well) is to figure the amount of energy (in joules per year) it would take to heat the oceans as much as the observations suggest that they have heated.
Then he (and I) calculated a theoretical amount of forcing, in W/m2, that if applied over the area of the earths surface would provide that number of joules per year of energy.
So it has nothing to do with sunlight, or shadows of mountains, or any of that. It is a theoretical number obtained by dividing the observed energy change (in joules per year) by the earth’s surface area, and converting that to watts/m2. We’re looking to calculate the size of the heating necessary to change the oceanic heat content, not talking about a real heating.
w.
A physicist says:
December 31, 2011 at 9:21 am
Is Hansen broadly correct? He is broadly correct in the sense that the Argo and other data, when analyzed in a particular way, say there has been a minuscule warming. Over the six-yer recent period covered by Hansen (2005-2010), he reports a warming of 0.009°C. Less than a hundredth of a degree.
The issue I raised above is not whether that 0.009°C is “broadly correct”. It is whether it makes a scrap of difference in the real world if it is correct. I say no.
w.
The majority of the warming is seen over land as shown fairly obviously by the BEST land record. The implication that the ocean is not capable of warming so fast makes this situation worse and has consequences for droughts and heat waves too.
Please, Willis, are you able to specifically quote some of these predictions? In their exact words? From peer-reviewed sources?
A search on Google Books finds zero predictions of “sea-level rise” accompanied by the words “accelerated” or “acceleration” in any scientific book published in or before 1981.
A similar search of the Inspec publication database, of peer-reviewed articles published before 1981, mentioning the phrase “sea-level rise” accompanied by “accel*”, found no articles.
A similar search of Hansen’s publications, but without year restriction, found the first mention of sea-level rise acceleration in Hansen’s 2005 article Earth’s energy imbalance: confirmation and implications
I admit to a certain curiosity, Willis, as to the source of your confidently-stated yet possibly mistaken information. I applaud, however, your maxim “QUOTE IT”.
George E. Smith; says:
December 31, 2011 at 10:14 am
C’mon, guys, read the dang underlying documents. NOBODY IS TALKING ABOUT TSI. Not me. Not Hansen. The “watts per square metre” we are discussing is a purely mathematical calculation of the joules required, divided by the area of the earth. It has nothing to to with “areal energy density”. It is simply CONVERTING BETWEEN UNITS.
Look, you can measure an oceanic energy content change in several kinds of units. You can measure it in joules per square metre per year. You can measure it in joules worldwide for a year. Or you can measure it in watts per square metre needed to provide that amount of energy. Or measure it in total watts worldwide, if you want to. Or you can measure it in degrees centigrade of oceanic warming per year. All of these units measure the same thing, change in oceanic heat content, and you can convert mathematically from one unit to another.
All that I am doing is converting units, from their units (watts per square metre) to my chosen unit (degrees C of warming per year). It has nothing to do with TSI or with dividing by 4 or anything like that. It’s just converting units.
w.
A physicist says (December 31, 2011 at 9:21 am):
“then within approximately 1000 years the ocean temperature rise will reach levels that paleoclimatologists tell us are associated with massive melting of the polar ice caps”.
I thought the Arctic was supposed to be ice-free 10 years from *now* (*now* being defined as whatever year the claim was made)?
Peter says: December 31, 2011 at 10:35 am
Time to warm the deep oceans = 1357 years
———————————————————————–
It is not possible to change the temperature of the deep oceans. Radioactive decay heats the oceans from below, and surface conditions heat and cool the oceans from above, but the deep ocean temperature does not change. The reason for this is that water density is a function of temperature. Maximum density is about 4C. Warmer water is less dense, and colder water is turning to ice, which is also less dense than liquid water. You can heat surface water down to the thermocline, and you can change the depth of the thermocline, but you can not change the temperature in the deep ocean.
In other words, if you heat the deep ocean, that heat is conducted/convected upward, and if you cool the deep ocean, that chunk of postulated cold water is also conducted/convected upward. This is something submarine officers understand very well, because their lives depend on it. Climate scientists seem to have not quite figured this out yet.
And while I am being snarky, any engineer can tell you that measuring temperature to an absolute accuracy of .008 C is just plain silly. Precision, yes, accuracy, no.
here is a plot of Argo showing E and W hemispheres 60N to 60S, 2004 thru 2011
http://www.flickr.com/photos/57706237@N05/6608424023/in/photostream
http://www.flickr.com/photos/57706237@N05/6608424249/in/photostream
Have a look for yourself. Do you see any trend anywhere in the Argo data?
Where is the catastrophic warming? Where is there any evidence of warming?
The oceans of the earth for the past 7 years. NO TREND
Is that a bunch of Warministas I see having a conference on that sandy point?
Willis Eschenbach says: December 31, 2011 at 11:43 am
The issue I raised above is not whether that 0.009°C is “broadly correct”. It is whether it makes a scrap of difference in the real world if it is correct. I say no.
w.
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Willis, I think you have summarized the entire AGW/skeptic argument. If I throw an ice cube into an Olympic swimming pool, 100% of scientists will say “It cools the water” and 97.4% of skeptics will say “It doesn’t matter!” (The other 0.6% will argue over the quantity of water in the filter system.)
To explain the two plots of Argo data above:
What I did was to slice the Argo data vertically by longitude and average all the data from 60N to 60S. This then gave a single number for the average temperature of the ocean at the longitude on that date. I then plotted this with time on one axis and longitude on the other, to provide a time series analysis of average ocean temperature by longitude, to see if there was any trend in any of the oceans. As can be see from the plots, to the resolution of the human eye there is no obvious trend.
These two plots represent almost the entire dataset for Argo. The plots have different color scales so don’t be thrown by that. Also, because of the distribution of land, the oceans are not evenly distributed north and south, so they vary in temperature according to longitude.
All of this took a few mouse clicks with the Argo Global Marine Atlas.
Well written, Willis.
An anecdote:
I did a calculation (many more 10^x notations, much more ‘back of the envelope’, but still giving a result in Δ°C) when Jo Abbess crowed about an increase in ocean enthalpy (heat content to her!). I submitted it as a comment. IIRC, I ended with a sarky ‘and your point is?’. Response – reams of hand-waving. My rational (dare I say scientific?) response was met with silence and the bit-bucket.
She, if you don’t recognise the name, is the one who caused Black (of the [ho, ho] unbiased BBC) to alter a headline which admitted the possibility that cAGW might not be proceeding according to plan, by threatening ostracism.
I decided to add no further to her traffic statistics.
With respect, Dan in California, your post is factually incorrect.
The ARGO floats are spec’d to an absolute accuracy of 0.002 deg C and a drift of 0.0002 deg C/year.
And you can easily verify those specs for yourself, Dan. The Sea-bird Electronics Corporation will cheerfully sell you, from their on-line store, your very own Argo float sensor module: the SBE 41/41CP CTD Module for Autonomous Profiling Floats.
That’s some mighty impressive engineering, and fun to boot ! 🙂
Dan in California says:
December 31, 2011 at 12:12 pm
The reason for this is that water density is a function of temperature. Maximum density is about 4C.
Good explanation. The 4C temperature has been mentioned a few times on this site as a puzzle. This explains quite nicely the mechanism.
cui bono says:
December 31, 2011 at 12:02 pm
I thought the Arctic was supposed to be ice-free 10 years from *now* (*now* being defined as whatever year the claim was made)?
Gore and Hansen must have slipped a decimal point. Even if you raise temperatures 10C, the melting time is on the order of 10,000 years. So, apparently “now” is 9990 years from now.
I am no scientist. But all this stuff about the land vs water got me thinking.
If the w/m2 near the poles is zero, that means there must be a very hot zone near the equator, to balance it all out.
Now we know that the globe is tilted a few degrees on its axis, so that hot spot is not bang on the equator, but it oscillates around it during the year. Now When I looked at the globe, it was clear that the hot spot shines on the ocean for most of the year.
er.. thats it.(go easy on me, i didnt even know the sun rotates till anthony told me in September)
@Dan in California December 31, 2011 at 12:12 pm,
Dan, you’ve aimed your snark at the wrong person. If you re-read my comment you’ll notice I’m actually on your side.
Why answer Willis’ objection with more calculations? It seems this misses the point Willis was making, and Willis can correct me if I am wrong, but one does not counter the assertion that 0.008C is not a resolvable temperature change, by engaging in more calculations about what things will be like in 1357 years, but rather in why you believe 0.008C is resolvable right now with the sensors at hand.
When you are dealing with uncertain quantities, a person ought to be able to provide a best answer, and I assume Hansen’s 0.009C is just that, but also the uncertainty involved. Did Hansen provide an uncertainty and how did he calculate it? Does the uncertainty to several sigma include 0.000C as a possibility? Often the advocates of warming to catastrophic warming do not bother to inform us about uncertainties. Does anyone know this; how are the ARGO buoys capable of maintaining calibration?
Finally, There are quite a lot of influences on sea level besides thermal expansion, some of them dynamic influences such as currents. Is someone telling me that satellites are capable of measuring the average sea level rise (the entire ocean surface I presume at one time) to a resolution of at least 2.5mm? Do we no longer have to rely on any other measures of sea level? I’d appreciate hearing from anyone on this topic.