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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One way to do a quick check on that is to calculate the thermal expansion, and see what sea level rise would be, and compare that to actual sea level rise.
2.7.9 Physical properties of sea water NPL, for those interested.
So what happens to Nimo and his friends when the temperature goes up as stated. Are their more Nimo’s, less Nimo’s, bigger Nimo’s., etc. If it’s warmer does that Energy end up leading to a few more biological effects- more plankton, etc. Just wondering.
Re:ChE says:
December 31, 2011 at 7:39 am
“One way to do a quick check on that is to calculate the thermal expansion, and see what sea level rise would be, and compare that to actual sea level rise.”
The “true believers” and keepers of the satellite-measured sea levels at U, Colorado Boulder already cut that one off at the pass. If the actual, measured sea level rate-of-rise doesn’t give them the answer they seek, they introduce a “sea bed sinking” factor to account for the difference. I’m still chaffing over that stunt.
Willis says,
“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.”
The AGW and ocean acidification hubris is birthed from the false premises based on measurement precision and accuracy. From noise they divine trend, from trend they ascribe attribution and with attribution they foretell the future.
The systemic sampling, calibration, human and equipment errors as well as the “unknown unknowns” of the real world make me reject any science based on the “willful suspension of disbelief.” There was an age not too long ago that scientists would have laughed at anyone claiming the ability to see a long term trends in global temperature or pH measured in hundredths of a unit.
After a bit of work I was able to get the Argo viewer working from their web-site. It is a very good viewer, but also cranky to figure out. Definitely not a user friendly install.
Anyhow, the viewer lets you slice and dice the oceans graphically to get an idea of what is going on. The color banding is quite good at shosing very small differences in temperature.
What is quite apparent looking at the data graphically is that there has been no appreciable ocean warming recorded by Argo. There is nothing that the eye can detect in the colored profiles that shows heat is moving through the top 1500 meters of ocean. I urge every reader to take the time to install the Argo viewer for themselves.
If there is heat accumulating such that it will warm the planet 1 C in 500 years according to Hansen, then that would seem consistent with what I’ve seen. However, I would also say that the 1 C project from Hansen is likely misleading. To take 5 years of data and project 500 years is to ignore the error bars.
The Argo data is not perfect. There will be some amount of error in the numbers. Projecting 500 years from 5 magnifies the error by 100 times. So, if the Argo data has an error of .01 C, which seems possible, given that they have more than once adjusted the numbers, then Hansen may simply be projecting the error rates.
If this is the case, then the most likely situation is the Argo is showing that there is no heat accumulating in the oceans. The conclusion from this is that the energy imbalance calculated from the radiation models is a model artifact. As put forward in an another paper, this could be a result of from decoupling radiation from convection when calculating the energy budget.
The argo viewer is available here:
ftp://kakapo.ucsd.edu/pub/argo/Global_Marine_Argo_Atlas/Global_Marine_Argo_Atlas_setup.exe
The install instructions are available here:
http://www.argo.ucsd.edu/Marine_Atlas.html
This instructions page has some sample graphs on the right side of the panel showing the color banding to give you some idea of what the viewer will provide. I highly recommend taking the time to get the viewer working.
I’m intrigued by the idea that the total kinetic energy of the earth system may change over time. I’ve only recently seen this mentioned in the post on “unified climate theory”. It seems to me we need to understand how the kinetic energy of the water and gases change over time to get a grasp on the related temperature changes. Good post as always Willis and continued thanks for defending the true spirit of science.
Oh yea, this is a poignant demonstration of, “The science is settled !”
Fascinating to scan down the comments to assess the ebb and flow
of the concepts and the mental energy generated in this discussion.
Could this increase global warming ?
Barclay’s heat gun experiment sounds like fun,
but to make it relevant to the ocean he needs to add a bubbler
or something to churn up the surface like the real ocean.
Spray drops will get heated by the air, then fall back to the water.
Though I bet the sun is still the major influence on ocean temp.
cknlitl says:
December 31, 2011 at 7:36 am
therefore no physical heat can be transferred from the atmosphere into the ocean.
I spent the better part of 20 years sailing around the world on a sailboat. I never had the slightest notion that the air warmed the oceans. The air cools the oceans. The faster the air is moving, the more it cools the oceans.
Perhaps if the air was already 100 percent saturated with water, and hotter than the water, then perhaps the air could warm the water, but these conditions are not typical. Rain might under some circumstances warm the oceans, but again not likely as rain is typically colder than the oceans.
Sunshine warms the oceans. The more sunshine, the warmer they get. Near the equator, where winds are light and there is lots of sunshine, they are the warmest. As you move away from the equator winds increase and the oceans cool.
I’m a little puzzled on how the watts per square meter is calculated.
The actual amount of light that hits the earth is determined by the area contained by the circumference of the earth (its cross section), not its surface area. That is the area the earth blocks. This way the light is only counted once since the other side of the earth is dark. It also handles the angle of incidence problem.
Then you get to subtract the average of the cross section or shadow of the land on the area used for total energy calculation., light reflected from the frozen areas and clouds over the oceans.
Willis, was your calculation taking this into account?
Let us probe more deeply into James Hansen’s reasoning and calculations.
Let us suppose that the Earth’s energy imbalance is 0.75 W/m^2 (as Hansen supposes in Section 13.4), and let this imbalance be due entirely to heating of the oceans. Let us ask, what will be the resulting rate of sea-level rise from thermal expansion?
To a very good approximation, it matters not whether the heat is absorbed via a rapid rise in temperature of the surface layers of the ocean, or by a slower rise in the deeper layers; the rate of sea-level rise is in either case is very nearly the same (but not exactly the same, because the coefficient of thermal expansion of water varies slightly with pressure).
So (according to Hansen) how fast is the ocean rising from thermal expansion only?
————————————————–
— CALCULATION —
physicsRules = {
timeToWarmTheOceans ->
iceAgeOceanTemperatureChange/rateOfOceanWarming,
rateOfOceanWarming ->
globalHeatingRate/(heatCapacityOfWater*globalOceanVolume),
globalHeatingRate ->
areaOfEarth*energyImbalanceHeatFlux,
meanSeaLevelRise ->
(globalOceanVolume/oceanArea) *
meanThermalExpansivityOfWater * iceAgeOceanTemperatureChange,
meanSeaLevelRiseRate -> meanSeaLevelRise/timeToWarmTheOceans
};
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,
oceanArea -> 0.71 * areaOfEarth,
heatCapacityOfWater -> 4.2 J/(gm K) * 1 gm/cm^3,
meanThermalExpansivityOfWater -> 300 * 10^-6 / K
};
timeToWarmTheOceans//
ReplaceRepeated[#,physicsRules]&//
ReplaceRepeated[#,geophysicalData]&//
ConvertToSI[#/year]&//Round//
Print[” Time to warm the deep oceans = “,#,” years”]&;
meanSeaLevelRiseRate//
ReplaceRepeated[#,physicsRules]&//
ReplaceRepeated[#,geophysicalData]&//
ConvertToSI[10*#/(mm/year)]&//Round//N//
Print[” Mean sea level thermal rise rate = “,#/10,” mm/year”]&;
meanSeaLevelRise//
ReplaceRepeated[#,physicsRules]&//
ReplaceRepeated[#,geophysicalData]&//
ConvertToSI[10*#/m]&//Round//N//
Print[“Sea-level rise from thermal expansion = “,#/10,” meter”]&;
— 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
————————————————–
Conclusion: Hansen’s predicted thermal expansion rise of 2.4 mm/year is a good match to satellite data showing an overall rise (thermal plus ice melting) of 3.2 mm/year. Moreover, if the associated heat imbalance of 0.75 W/m is sustained over centuries, 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. And finally, if it should happen that CO2 levels continue to increase, or if the negative forcing associated to aerosols should ever decrease, then there are reasons to expect that this heat imbalance will increase, and the rate of sea-level rise correspondingly accelerate, by the dual mechanisms of thermal expansion and polar ice-melting.
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.
So how about it? Does rational skepticism led WUWT to the conclusion that Hansen is correct?
All I can say is, after 20 years of scuba diving in the Pacific off the coast of Costa Rica, I have yet to feel any fewer freezing cold thermoclines in water that averages 80 degrees year round in depths to 100 feet. I know it’s completely anecdotal but, it sure says there ain’t a whole lot of “mixing” going on to level out or raise that top layer temperature!
In other words, my testicles would appreciate it if Hanson were right. My rational brain says he’s full of fecal matter! 😉
A Happy, Healthy and Prosperous New Year to you and yours, Willis, as well as to all those here!
I have a feeling this will be the one that a fork is stuck into AGW. It’s done!
Guys (and gals)
There seems yo be a widespread misconception about the watts per square metre thing.
Willis’ calculations are based on the imbalance, which is the total average incoming energy minus the total average outgoing energy. Factors such as day and night, angle of incidence, albedo etc etc are therefore already implicitly factored in.
Regarding the factor of 4 for the sphere/disc area ratio:
the climate modellers simply divide the solar constant by 4
to get the global average insolation, but what direction does it come from?
That is, what is the average solar altitude angle over the sunlit hemisphere?
Its a simple integral of Theta * cos(Theta), from 0 to 90 deg,
which equals Cos(Theta) – Theta * sin(Theta),
which for the interval from 0 to 90 deg gives an average of:
90 deg – 1radian = 32.7 degrees average solar altitude above the horizon.
Of course, the global average is half that.
Is a constant sun at 32.7 deg for 12 hours over half the Earth
any kind of meaningful model of how insolation is received?
We all know it isn’t.
For example, cloud albedo will be higher at low sun angles.
By the way, at any latitude the most frequent sun angle throughout the year
is that of winter solstice noon.
Moderator: why do I no longer get e-mails notifying new posts?
[REPLY: Don’t know the answer to that one, other than be sure you’ve checked the notify box below your comment. If problem persists, drop an e-mail to Anthony using the “contact” option on the “about” drop-down menu. -REP]
@ur momisugly Aphysicist
From the article…”The answer (if Hansen et al. are correct) is that if the ocean continues to warm at the 2005-2010 rate, …”
So Aphysicist Hansen does a FIVE YEAR STUDY, which, by the way, has not risen at your 2.4 mm per year but considerably less, which you extrpolate to 1,357 YEARS!!
“”So (according to Hansen) how fast is the ocean rising from thermal expansion only? 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””———————————————
Wow you really have boxed sceptics into a corner. I did not even bother with your math, the xercise is futile. Are you lazy teenager under another tag!! actually SST have cooled since the medieval warm period when the earth was warmer then now according to hundreds of studies. http://wattsupwiththat.com/2011/12/31/ssts-cooler-now-than-in-the-medieval-warming-period/
Either way, Hansen’s tale of CAGW is DOA. Do you accept that?
A physicist says: December 31, 2011 at 9:21 am
Rational thought cannot conclude Hansen’s emotionally biased perceptions are correct. You left out the water that irrigation adds to the hydrosphere annually, the equivalent volume to 2.2mm/year sea level rise.
Svein S. : To argue on the basis of averaging everything over the entire ocean volume is ridiculous, and has no meaning.
You should direct this comment to Hansen and others who promote AGW policies on the basis of claimed equilibrium responses of a simplified global thermodynamic model. Also, a recently proposed (discussed at WUWT) correction to account for the reduced warming of the last decade was based on an analysis very like Willis’ here, namely a more rapid transfer of heat from the upper to lower layers of the ocean; thus, Willis’ approach is within the range of mainstream climate science.
Willis! Another good article.
A physics says:
December 31, 2011 at 3:29 am
“Time to warm the oceans = 1357 years”
“. . . a period that is (1) short compared to CO2 residence times in the atmosphere,. . .”
Does this mean the residence time (r.t.) of CO2 is greater than 1,000 years? Or have I missed the intent? It seems the meaning of these combined statements does not come close to other statements about CO2 r.t. that I have seen on WUWT and other sites over the past couple of years. I think the period I have seen here may be closer to 50 years.
Other charts frequently copied on WUWT show temperature of the atmosphere changing more quickly also, or just from an historical record, say the time for decline of the Greenland settlements. I can search for these numbers (if need be) but my point is 1,357 years seems to be a long time relative to these other things mentioned.
Well Willis, a problem that I see with this whole situation, is that TSI is NOT a measure of earth incident ENERGY to be averaged as you just did.
Watts per square metre is an areal POWER density; not an areal energy density; and it arrives at earth at the rate of 1362 Watts per square metre, and not the 340.5 number that Trenberth et al use.
Tetal claim that the surface emitted power is 390 W/m^2 corresponding to a 288 K black body radiant emittance , and if that were true, the earth would be cooling rapidly.
But when the real arriving power rate is 1362, and less atmospheric losses etc, compared to that average 390 Radiant emittance number, then it is obvious why the sun can and does heat things up very nicely.
A Physicist: the next two decades (or so) will test this prediction.
We should sell t-shirts and coffee mugs with that slogan! The next two decades will test all of the predictions.
“”””” jaymam says:
December 31, 2011 at 12:35 am
Dan says:
December 30, 2011 at 11:42 pm
“Willis, I think the warming is only half of your result as the sun only heats half the globe.”
The sun heats a quarter of the globe. “””””
Well actually, the sun heats somewhat MORE than half of the globe.
For starters, the sun is NOT a point source of radiant energy; it has an apparent angular diameter of about 1/2 degree, and the earth is egligibly small in apparent angle at the sun, so the sun would illuminate 180.5 degrees out of 360; well if the earth had no atmosphere. But since earth does have an atmosphere, which has a graded refractive index greater than 1.0, then the sunlight is refracted somewhat more than the 0.5 degree angular diameter of the sun.
When viewing the green flash at sunset at Waikiki Beach, in Oahu, the sun is already completely below the horizon, at the moment the sun disappears from view. So better add at least another half a degree giving 181 degrees of daylight to 179 degrees of night.
Well even that is not correct, because twilight can last about an hour or so; maybe only a half hour at Waikiki. At 15 degrees per hour, that must be about 7 1/2 extra degrees of illumination.
Well you better draw yourself a diagram, to put in all the factors yourself; but it is quite clear that the sun ALWAYS illuminates somewhat more than half of the earth surface; and NEVER just a quarter of it; well excepting those rare total eclipses of the sun.
What makes you think that, given the deep ocean hasn’t warmed any in billions of years?
I will answer your question in three parts, David A:
(1) I agree with the conclusion of Hansen’s article that there exists an urgent need to sustain/improve the quality of the ARGO program and also of the satellite temperature-measuring programs.
(2) I agree too with the earlier post by commieBob that asserted: “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.”
(3) Combining (1) with (2), it is my considered opinion that Hansen is urgently advocating more-and-better ARGO and satellite data because Hansen anticipates that this more-and-better data is likely to confirm (not disprove) Hansen’s overall picture of climate change.
In summary of points (1-3), and after having personally checked the correctness of some of Hansen’s key calculations, it seems entirely plausible (to me) that Hansen’s overall picture of climate change will be proved correct.