A Climate Change Paradox
Posted by Michael Hammer, July 5th, 2009 - under News, Opinion.
Tags: Climate & Climate Change
AUSTRALIA’S Minister for Climate Change, Penny Wong, recently suggested that most of the global warming since 1960, about 85 percent, has happened in the oceans and that change in ocean heat content is thus the most appropriate measure of global warming.
But, calculating from first principles, according to this data the oceans have absorbed far less energy than the IPCC estimates for the impact of rising carbon dioxide levels. While the government data suggests a warming rate of 0.38 watts/ m2 the IPCC data suggests a warming rate of 3.6 watts/ m2 . This is a significant discrepancy of nearly 10:1 and needs to be resolved. If the oceans really are the major heat sink for the planet where is the rest of the energy going? Alternatively, is the error in the IPCC estimates.
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UPDATE JULY 14, 2009
While in the following calculations I determined a discrepancy of 9:1 in the rate of warming from Australian government data relative to IPCC findings. In reviewing these calculations I now realise I made a significant error. I had wrongly assumed that the claimed positive feedback from water vapour was proportional to the carbon dioxide concentration. This is not correct, the claimed positive feedback is proportional to the temperature rise and that change does make a difference to the calculations and needs to be corrected. The revised calculations still show a paradox although only about 3:1.
READ MORE HERE: http://jennifermarohasy.com/blog/2009/07/a-climate-change-paradox-part-2/
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Here’s my logic:
On June 24, 2009, the Minister for Climate Change posted ‘Response to Senator Fielding’s questions about the climate change science’ ( http://www.environment.gov.au/minister/wong/2009/tr20090624c.html ).
This article included the above graph and comments reproduced below. The straight red line on the ocean heat content graph, however, is my addition and was not part of the original article. The line was placed by eye and is not claimed to be a least squares line of best fit.
The quoted items below are taken from the Minister’s website.
“In terms of the climate system as a whole, only about five percent of the warming since 1960 has taken place in the air.”
“Most of warming since 1960 (about 85 percent) has happened in the oceans. Thus, in terms of a single indicator of global warming, change in ocean heat content is the most appropriate.”
“The change in ocean heat content since 1960 is shown in the figure below. Note the significant warming trend since 1998.”
I note that the graph is labeled ocean heat content which cannot be correct given that the value is shown as zero prior to 1975. However the text suggests it is actually change in ocean heat content which would seem reasonable. I have assumed that to be the case.
The graph shows that over the last 30 years the oceans have absorbed 15*1022 joules of energy and as the red line shows this has been very close to linear over that time. Using a linear approximation implies the oceans have absorbed about 15*1022 / 30 or 5*1021 joules per year.
How does this compare with the claimed degree of global warming from rising carbon dioxide – expressed in watts / m2. Convert ocean warming first to watts = joules per second. There are 60 * 60 * 24 * 365 seconds per year = 3.15*107 seconds per year. So the oceans are absorbing 5*1021 / 3.15*107 joules per second = 1.6*1014 watts
Now to get watts / m2 we need to divide the watts by the surface area of Earth. The Earth is a sphere of radius 3960 miles = 6336 km. Its surface area = 4*pi*radius2 = 5*108 sq km (Wikipedia quotes 5.1*108 sq km). Since there are 106 m2 per km2 this equates to 5*1014 m2. Thus the oceans are absorbing energy at the rate of 1.6*1014 / 5*1014 watts/ m2 which equals 0.32 watts/ m2.
The article states that 85 percent of the warming has taken place in the oceans which would seem to be saying that 85 percent of the retained heat due to AGW is being stored in the oceans. From this it follows that the total retained heat is 0.32/0.85 or 0.38 watts/ m2.
The Intergovernmental Panel on Climate Change in their 4th assessment report (summary for policy makers) claim (page 12, 4th bullet point) that “…..global average surface warming following a doubling of carbon dioxide concentrations. It is likely to be in the range 2 to 4.5C with a best estimate of about 3C”.
Now to get a 3C rise at the average claimed emission temperature (255K) requires an additional energy input (additional energy retained by greenhouse gases) of 11.3 watts/ m2. This assumes the 3C is an equilibrium level. If it is not then the retained energy must be still higher so the 11.3 is a minimum figure.
The ocean heat graph from the Minister ends in 2006. According to Mauna Loa data in 2006 the carbon dioxide concentration was 383 ppm which represents 0.45 doublings and hence an increase in global warming retained energy of 11.3 * 0.45 = 5.1 watts/ m2. Not all of this represents energy absorbed by the planet because of the claim that the planet has warmed. This warming will increase the energy radiated back out to space.
The Climate Research Unit at the University of East Anglia ( http://www.cru.uea.ac.uk/cru/info/warming/ ) shows the claimed warming in 2006 was 0.4C. SkepticalScience.com ( http://www.skepticalscience.com/global-warming-stopped-in-1998.htm ) shows temperature rise graphs from three sources and all show about 0.4C temperature rise in 2006. Using the same claimed effective emission temperature as above (255k), a rise of 0.4C will increase emitted energy by 1.5 watts/ m2. Thus the net additional energy retained by Earth will be 5.1 – 1.5 = 3.6 watts/ m2.
This presents a considerable conflict. Ocean heat assessment suggests earth is gaining energy at the rate of 0.38 watts/ m2 while carbon dioxide analysis suggests the rate is 3.6 watts/ m2. This is a difference of nearly 10:1 in two different analyses of the same quantity. Both cannot be right.
I note that the Minister specifically draws attention to the “significant warming trend since 1998”. This could be taken to mean a claim that the linear slope does not apply.
This is a somewhat risky assumption since there are other periods where the slope is well above the slope of the red line. None the less, using the local slope over the years since 1998 corresponds to about 8.8*1021 instead of the average of 5*1021. That would make the retained heat in the oceans about 0.56 watts/ m2 for a total retained heat of 0.66 watts/ m2. This is still 5.5 times lower than IPCC claim for the impact of carbon dioxide. Also, if we accept the higher slope since 1998 it means the average ocean energy absorption over the earlier years is reduced to 8*1022 joules over 23 years corresponding to 0.22 watts / m2. Since the carbon dioxide concentration from the Mauna Loa data in 1998 was 366.6 ppm this represents 0.39 doublings equivalent to an additional 4.4 watts / m2 or about 3 watts/ m2 after allowing for temperature rise making the discrepancy over those years worse (3 vs 0.22 is a ratio of 13.6:1)..
What the Minister’s own data shows is that the oceans have only absorbed between about 9 and 14 percent of the excess anthropogenic global warming energy implied by IPCC data. Yet they claim the ocean absorption represents 85 percent of this energy. The oceans are by far the biggest heat sink on the planet. If they are only absorbing at most 14 percent of the excess energy it is extremely difficult to see where the rest of the energy could be going.
Could the error be in the ocean heat content – maybe the exponent should be 23 not 22? Oceans cover 70 percent of the Earth’s surface or 3.5 *1014 m2. If the energy is spread over the top 700 m as the graph caption states, the volume of water is 3.5 * 700 * 1014 = 2.45 * 1017 m3 . Water has a thermal capacity of 4.18 million joules per degree per m3. Hence the 15 * 1022 joules will raise the surface ocean temperature by 15 * 1022 / ( 2.45 * 1017 * 4.18 * 106 ) degrees = 0.15C (This by the way is exactly the same result as Bill Kinninmonth cited in his email to Professor English reproduced on Joanne Nova’s website.). This result assumes the energy is distributed uniformly throughout the 700 meter depth. If it is concentrated near the surface the rise would be higher. To match the IPCC predictions the energy absorption would have to be 5.5 to 10 times higher suggesting an ocean temperature rise of at least 0.8C to 1.5C over the last 30 years. No such rise has been reported.
It would seem that the only plausible alternative left is that the error is in the IPCC estimates and that the current value should be about 1.5 +0.38 = 1.88watts/ m2 (additional energy radiated plus rate of energy storage in the oceans). If so by 2070 the additional energy input over today would be 1.88 * 0.55/0.45 = 2.3 watts / m2 (We have had 0.45 doublings with a further 0.55 to go by 2070.).
Such an energy rise at equilibrium would give an additional temperature increase of 0.6C. This is of course if we assume that the currently claimed temperature rise is correct and is all due to carbon dioxide.
So many assumptions and such a paradox!
Michael Hammer,
Melbourne, Australia
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Notes and Links
This article has been cross-posted at Joanne Nova: http://joannenova.com.au/2009/07/06/the-antidote-to-150-million-quadrillion-joules/
More from Michael Hammer here: http://jennifermarohasy.com/blog/author/michael-hammer/
Related information:
http://wattsupwiththat.com/2009/06/02/anomalous-spike-in-ocean-heat-content/#more-8132
http://www.woodfortrees.org/plot/hadcrut3vgl/from:1994/to:2010/scale:0.1/mean:10/plot/hadsst2gl/from:1994/to:2010/scale:0.1/mean:10/plot/uah/from:1994/to:2010/scale:0.1/mean:10
http://www.sciencemag.org/cgi/content/abstract/309/5732/284 versus
http://www.john-daly.com/mobydick/oceans.htm
“In AGW-land, heat can magically hide and then jump out and say ‘boo!’ at the proper time.”
How do you explain the 1998 spike?
I explained a possible way of looking at it earlier. If Forbush events punch heaps of joules in the ocean AGAINST the “rythym” of the sun-ocean dance, then instead of moving up to a new energy plateau we would expect the energy to be released step-fashion into the air over a number of months causing unseasonably hot weather.
El Nino events seem to follow Forbush events a lot of the time. Although I don’t think this is a perfectly cut and dried matter.
Michael, a good reason for comparing with what others have done is to debug your logic. Compared with Hansen et al, you’re in agreement on the ocean heating side, but have a vastly greater radiative input. So that’s where to look.
Start with this sentence:Now to get a 3C rise at the average claimed emission temperature (255K) requires an additional energy input (additional energy retained by greenhouse gases) of 11.3 watts/ m2. I don’t know where you get that from, but it is far too high. You’ve asked people to spot the flaw, but the fact is that you’ve gone around a big logical loop, with this as an unexplained step, when there is a simple, far more primary figure that you could work from.
It looks to me like the curves are bogus, according to Pielke, Sr. According to him, there has been no increase in ocean heat content for several years.
http://climatesci.org/2009/05/18/comments-on-a-new-paper-global-ocean-heat-content-1955%e2%80%932008-in-light-of-recently-revealed-instrumentation-problems-by-levitus-et-al-2009/
Sombody already provided the link; sorry for the repitition, I should have read all the comments. But maybe it’s good for emphasis. Wonder where Wong got her graphs?
I have seen the link to Pielke above which shows no accumulated joules as observed in the oceans. As I understand it, because the oceans are hundreds of times denser than the atmosphere, then the amount of heat equivalent to a 1 degree temperature anomaly in the atmosphere would be equivalent to a tiny fraction of a degree if sequestered in the oceans. How are they supposed to measure such tiny increments of temperature? Wouldn’t the error bars be greater than the measured temperatures?
Hello Nick; Sorry to take so long to get back to you, I was distracted by other matters.
I gave the background to my figure of 11.3 in earlier replies but lets play by your numbes for a while. You commented in an earlier post that the true sensitvity should be 0.6C/watt/sqm. Lets examine this. According to IPCC (4th report) we have had 1.7 watts/sqM increase in retained energy from CO2 and doubling CO2 retains 3.7 watts/sqM. That means there is a further 2 watts/sqM increase between now and 2070. At 0.6C/watt/sqM that equates to 1.2C rise. But IPCC 4th report claims 3C rise by 2070 – a big difference. So maybe you argue that CO2 is not the only effect, other effects make up the difference? If so why harp on CO2 reduction it would only be 40% of the problem, why not harp on the 60%.
However IPCC and ther AGW movement strongly imply the 3C rise is due to CO2. If the 3C rise is due to CO2 then the sensitivity would have to be 1.5C/wat.sqM. Now you claim a total of 1.8 watts/sqM retained heat at present and 0.6C rise. I have a problem with the 0.6C since the story is that only temp rise since about 1960 is due to CO2 before that it was natural and since 1960 the sites I quote (AGW sites) all suggest 0.4C rise but again lets play by your numbers. For 0.6C rise at 1.5C/watt/sqM the extra radiated heat would be 0.6/1.5 = 0.4 watts/sqM. If I accept your claim of 1.8 watts/sqM retained heat that leaves 1.4 watts/sqM going to hetaing the earth. Compare that with the 0.38 watt/sqM you say you agree with and we have an almost 4:1 discrepancy.
If I accept your figure of 0.6C/watt/sqM there is the paradox that the rise by 2070 should be only 1.2C not 3C – a very significant difference. Using that 0.6C/watt/sqM with an 0.6C rise suggests 1 watt/sqM extra radiated energy leaving 0.8 watt/sqM absorbed which even so is double the 0.38 figure you say you substantially agree with – in short using your numbers there are 2 paradoxes, firstly the reatined heat is still double what can be accounted for and the projected temperature rise due to CO2 is overstated by 2.5 times.
I respectfully suggest there is a problem.
Michael,
I tracked down your reference here. I see the problem. As I say, you have a logical loop, and there is a loop gain. You’ve used the IPCC fig of 3C, which was calculated from the increase in IR retained, multiplied by a sensitivity which included positive feedback. Then you’ve divided by a sensitivity kappa which did not include feedback to get a radiative load again. The second figure is smaller, so the end result (11.3) is much higher.
[...] and that change in ocean heat content is thus the most appropriate measure of global warming. In my previous post, working from first principles, I determined a discrepancy of 9:1 in the rate of warming from [...]
There is heat loss as the Earth radiate back into space as well as the fact that the ice in the Arctic and Antarctica melt into the ocean and increase the heat absorption capability of it; hence keeping the planet cool and the rate of global temperature rise at a slow pace at the moment. I guess when there is great migration of refugees affected by rising sea level come knocking then the climate-change deniers will take notice and panic.
It is uncleared to me that whether skeptics have taken into account that a vast amount of carbon dioxide will be absorbed by plants, the sea, and the increased number of algae which should be calculated in the model. Also why don’t skeptics look at coastal and island communities being affected by rising sea level as well as the erratic weather pattern changes that affect many farming communities around the world.