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
LazyTeenager says: January 1, 2012 at 1:17 am
And a link for platinum resistance thermometry calibration by the NIST, to verify my initial guess was correct.
http://www.nist.gov/calibrations/upload/sp250-81.pdf
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That just proves that NIST can calibrate a Platinum RTD to .01C in a molten metal bath. If Argo were using RTD’s, the entire system would have to be calibrated, not just the RTD. That includes the current source to the 4-wire device, and the voltage reader as well. Either of those analog devices can be out of calibration, and either could be effected by the environment in a reversible fashion, meaning recal after buoy retrieval must mimic the deep ocean conditions (it doesn’t). Then there is the difference between NIST using liquid metal as a reference, which has a far higher thermal conductivity than sea water. How much does that affect the calibration? The RTD is self-heating and the thermal conductivity of the measured medium affects the reading.
But even supposing all these additional factors were insignificant, even your NIST reference only claims .01C accuracy, not anywhere near sufficient to support the .008C study results claim. But all this discussion is moot if DJ in another ARGO thread is correct:
DJ says: December 31, 2011 at 9:41 pm
Ok, it looks like the buoys use a “Scientific Thermistor Model WM 103″.
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This indicates the sensor is not even an RTD, it’s a thermistor. Totally different animal.
The Seabird Electronics page shows the calibration “standard” for the ARGO sensors as being ITS-90, but this is a temperature scale and not really a calibration standard. Dan in California has raised the perfectly reasonable issue of drift and stability of the current source and voltage measuring system. It looks like we don’t know for sure what sensors are being used, RTDs or Thermistors. I wonder if anyone ever put together an uncertainty budget for the devices and environment of this array? If this idea is unknown to anyone, I would suggest looking at an actual system and measurement as an example, see for instance Schwarz et al., Science, 282, 2230-2234, 18 Dec 1998.
I know that they call this a “Lagrangian” array, but these buoys cannot participate completely in all ocean circulation (they are buoys after all) and so they cannot remain with a single parcel of water forever.
Peter says:
Yes, it is continuous, as I said, and is enough to increase the SST by 1C in about 1 and a half years, in fact every one and a half years.
But, as we all know, that isn’t happening. So what gives?
Come on. The heat isn’t confined to the top meter, so your calculation is based on false assumptions. The heat isn’t confined at all, but spreads through the water and air in a complex environment, subject to currents, stratification in salinity, evaporation, the hydro cycle, etc. The oceans *are* warming, with the top 700 m holding about 10e22 J more heat in the last 30 years:
http://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/
That’s a huge amount of heat — equivalent to what the entire Earth receives in about a week.
Also, how come, according to Trenberth, Hansen, etc, has this 0.5C imbalance only come about within the last few years? (hence Trenberth’s ‘missing heat’)
No one knows — that’s what they’re trying to figure out. It’s pretty remarkable if you think about the numbers: the Earth receives an average of 340 W/m2, and they’re down to accounting for a missing 0.5 W/m2 — 1 part in 600. It’s as if you had $1,000 in your checking account and can’t account for $1.50. This is the way all sciences go — you keep honing in on more and more precision, trying to figure out what you’re missing.
Erinome,
1) That’s just the forcing we’re talking about, not the whole bondoogle.
2) Yes, I know it’s not confined to the top metre, but what’s actually happening is still orders of magnitude off from what one might expect. Besides, I did start by saying, “…let’s just assume for a moment that all the short-term heating takes place within the topmost few metres, and gradually dissipates through the rest of the ocean.”
3) No, the fact that the error is only 1 part in 600 is not remarkable at all, when taken in context. After all, the total temperature increase over the last century is only 1 part in 400.
Erinome,
Sorry, left a few bits out:
4) When a body of water is heated from the top, which part warms the quickest and the most?
5) And which part constitutes the effective radiating surface?
6) The way I see it, you have two options. Either the oceans are warming significantly and the imbalance is tiny or reducing, or the imbalance is large and not reducing but the oceans are inexplicably not warming significantly. Which is it? You can’t have it both ways.
Peter says:
2) Yes, I know it’s not confined to the top metre, but what’s actually happening is still orders of magnitude off from what one might expect.
No, it is not — professional scientists don’t go to sleep when errors of many orders of magnitude appear in their calculation.
First, change in ocean heat content ~ 10e22 J in 30 yrs ~ 0.1 PW
(http://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/)
Average that over the ocean’s surface area and you get a forcing ~ 0.3 W/m2. (I’m ignoring sea ice and all that.)
Now look at Hansen’s Figure 1: the net forcing (anomaly) for 1980 to 2000 is about 1 W/m2.
(http://www.columbia.edu/~jeh1/mailings/2011/20110415_EnergyImbalancePaper.pdf) So these are already in the same ballpark. That forcing heats not just the ocean but the air above too, and land where there is no ocean, and melts ice and all that. This is where, obviously, you have to get into the details, but from an energy balance viewpoint the disagreement certainly isn’t orders of magnitude.
Now, if oceans are receiving an extra 0.3 W/m2 what does that mean for the SST, and does it agree with observations (http://www.ncdc.noaa.gov/ersst/)? I don’t know, but I don’t think it’s a simple problem given the size, depth, and dynamics of the oceans. Do you?
Let’s assume the heat is confined to the top 700 meters, to compare it to the ocean heat content link above. Then I find a rate of temperature change of ~ 0.3 K/century, in order of magnitude agreement with observations.
This is, admittedly, all back-of-the-envelope. But I don’t see errors of orders of magnitude that have you concerned.
can I ask,
what was the rate of change in ocean temperature between 1940 and 1970 ? (ish)
or between 1910 and 1940 ?
(mods, add to previous if possible please)
Erinome,
I’m prepared to concede the orders of magnitude bit – I didn’t take into account that we’re not dealing with a 0.5W/m2 step change in forcing – in which case the error would have been orders of magnitude.
However, it doesn’t alter the fact that the top few cm absorbs most of the incoming sun’s energy, and from which it’s mixed into the deeper layers down to the thermocline, at a rate dependent on turbulence etc. (water being a quite a poor conductor of heat) This means that a) the added energy is virtually wholly contained within the upper hundred metres or so, on average, and b) the topmost few cm will be disproportionately warmer than the rest, particularly during daytimes.
That said, it’s all rather complicated and there are a lot of things which don’t quite add up.
Unfortunately, now my break is over and I’m back to work, so I will no longer be able to devote much time to trying to make sense of it all. (at least until my next break)
Erinome says- “First, change in ocean heat content ~ 10e22 J in 30 yrs”
There is no measure of ocean heat content before about 2003, when ARGO was deployed. Even ARGO is a tragically sparse spatio-temporal sampling of OHC.
A claimed 3 decade change in OHC is a guess.
There is no measure of the claimed 0.5 W/m^2 intensity imbalance.
Its a guess.
“Then I find a rate of temperature change of ~ 0.3 K/century”
Woo, that sounds scary.. !!
AndyG55 says:
“Then I find a rate of temperature change of ~ 0.3 K/century”
Woo, that sounds scary.. !!
I suggest you retake high school physics…. Why don’t you tell us how much heat the upper ocean (700 m) will gain if it warms by, say, 0.3 K? Compare that to what the Earth receives from the Sun in a day, and what is transported from the tropics. Estimate how much the atmosphere will warm if that heat escapes into it. Finally, compare the assumed rate of SST warming to the observed rate.
chris y says:
There is no measure of ocean heat content before about 2003, when ARGO was deployed
Yes, it’s reconstructed. Like the MWP SST results that were highlighted on this blog a few days ago.
chris y says:
There is no measure of the claimed 0.5 W/m^2 intensity imbalance.
Its a guess.
There are measures of the imbalance, such as Harries et al, Nature 2001, Griggs et at Proc SPIE 2004, Chen et al 2007, etc:
http://agwobserver.wordpress.com/2009/08/02/papers-on-changes-in-olr-due-to-ghgs/
The extra forcing isn’t a “guess” — it is deduced via science, and subject to the same meaning and uncertainty that we rely on for a vast number of other scientific results.
AndyG55 says:
what was the rate of change in ocean temperature between 1940 and 1970 ? (ish)
NOAA’s reconstructed SSTs are here:
http://www.ncdc.noaa.gov/ersst/
Peter says:
That said, it’s all rather complicated and there are a lot of things which don’t quite add up.
Unfortunately, now my break is over and I’m back to work, so I will no longer be able to devote much time to trying to make sense of it all. (at least until my next break)
Yes, obviously it’s complicated. Very complicated. People are spending their careers trying to figure out the details. But I don’t see what you think “doesn’t add up.” It seems to me that, based on the back-of-the-envelope numbers I gave above, it all *does* add up to within half an order of magnitude or so (and then you need the details).
Also, I don’t see why added heat is constrained to the upper hundred meters (or so).
http://wattsupwiththat.com/2011/12/30/losing-your-imbalance/#comment-848913
“Over the six-yer recent period covered by Hansen (2005-2010), he reports a warming of 0.009°C.”
Where exactly in the paper does Hansen report “a warming of 0.009°C”, becauee I can’t find that number here;
http://www.columbia.edu/~jeh1/mailings/2011/20110415_EnergyImbalancePaper.pdf
or here;
http://pubs.giss.nasa.gov/docs/2011/2011_Hansen_etal.pdf
or here;
http://www.atmos-chem-phys-discuss.net/11/27031/2011/acpd-11-27031-2011.pdf
or here;
http://www.atmos-chem-phys.net/11/13421/2011/acp-11-13421-2011.pdf
Zero for four, someone around here isn’t telling the truth, and it sure isn’t Hansen.
Of course, if one were to assume that the ENTIRE ocean volume were to heat up, on AVERAGE, by 1°C, and that the heating can only come from one place, the surface, one would also want to know what the temperature/salinity/density distribution with depth would look like.
I mean do I really need to quote from Hansen’s own paper? As in the deep abyssal ocean is not warming at anywhere near the same rate as the upper 700 meters.
One thing we can say with certainty, is that the ENTIRE ocean would not heat up uniformly, therefore we can catagorically state, that any hypothetical calculation that ASSUMED a uniform temperature increase over the ENTIRE ocean in the same amount of time, would be TOTALLY bogus.
Then to top it all off, do an extrapolation from six years of data, in a linear fashion no less, all the way out to the year 2461. Four significant digits? You Betcha!
hmm, so the rate between 1910-1940 was faster than between 1970 -2000. then it was slower (maybe zero) for a while between 1940-1970 .. must be because of the massive increase of CO2 in 1910, but stopped in 1940,
take a short term linear appoximate trend , and extrapolate out to 100 years !! DOH !!!!
EFS_Junior says:
January 2, 2012 at 3:42 pm
Junior, you’re not following the story, it’s just different units. Over that 6 year period Hansen reports a warming for the entire ocean of 0.54 W/m2. This corresponds to a warming for the entire ocean of 0.009°C. It is what Hansen says for the warming of the global ocean, but as I reported in the head post, he gives in in W/m2 for the entire ocean, and I converted that to degrees C of warming for the entire ocean.
Hey, not only did I do that, I gave the exact calculation at the bottom of the head post, so folks like yourself could follow it. If you were paying attention.
w.
PS—I do not take accusations of “not telling the truth” lightly. In essence, you are calling me a liar, which is a slimy thing to do. I’ll overlook it because of your immaturity, but be sure I won’t do it twice. It turns out that you simply weren’t following what I’d done. Accusing me of lying because you don’t happen to understand something, that’s no way to go through life, my friend …
REPLY: Junior has has been the center of a lot of attention here at WUWT for bad behavior, mainly because he’s usually out of line, he’s on permanent troll bin status, which means his comments get extra moderation attention. – Anthony
Erinome-
You say there is a measure of ocean heat content before 2003. You state that it is reconstructed.
I rest my case.
Remarkably, you claim that the 0.5 W/m^2 measurement has been made. You list some papers on measurements of outgoing spectra to infer changes in CO2 concentrations, forcings, etc. That is not a measurement of the 0.5 W/m^2 intensity forcing. You need to integrate total incoming intensity over the entire Earth’s surface, subtract the total outgoing intensity over the entire Earth’s surface, and then integrate over some length of time to smooth out the wild variations in both of these values, perhaps over several years. That is then a single data point. The measurement requires a repeatability of <0.1 W/m^2, to provide some confidence in the 0.5 W/m^2 imbalance being tossed about. And, of course, this measurement must be available at a variety of different CO2 concentrations to see if it has anything to do with CO2. 100 years of data would be a good start, to cover at least one complete cycle of some of the known natural climate cycles that exist.
As I said, the 0.5 W/m^2 number is a guess. Or, if you wish a more technical term, a hypothesis.
Erinome says:
Look up ‘thermocline’.
Peter says:
January 2, 2012 at 6:44 am
“However, it doesn’t alter the fact that the top few cm absorbs most of the incoming sun’s energy,”
You’re entitled to your own opinions Peter but not your own facts. Most solar radiation is NOT absorbed in the first few centimeters of the ocean. You’re off by a factor of 100. 40-60% of the energy is absorbed in the first few meters. It’s up to 100 meters before it’s 99.9% extinguished.
Below is a simple graph breaking down penetration depth by wavelength.
http://www.nature.com/nrmicro/journal/v5/n10/images/nrmicro1746-i1.jpg
Chris Y: All science is hypothesis.
Joules Verne: It’s not my opinion.
I’m not saying they’re right but, amongst others, http://en.wikipedia.org/wiki/Thermocline :
Perhaps that’s supposed to be metres.
Having said that, IR back-radiation definitely does not penetrate far.