A Climate Change Paradox (Part 2)

ocean heat hammer blogAUSTRALIA’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.
In my previous post, working from first principles, 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. 

I had calculated the heating sensitivity of Earth (kappa) by differentiating Stefan’s law for a temperature of 255K and this came out as 0.266C/watt/m2.  That figure is very much in keeping with the findings of others for example Soden and Held (2006) 0.25C/w/m2 , Hansen et al (1984)  0.26C/w/m2 , Bony et al (2006) 0.263C/w/m2 , Colman (2003) 0.30C/w/m2 , Kiehl (1992) 0.305C/w/m2 .  For a 3C rise, kappa predicts the additional retained heat is 3/0.266 = 11.3 watts/m2 for doubling of carbon dioxide.  A significant fraction of this 11.3 watts/m2 comes from the claimed positive feedback effect of rising water vapour.  My error occurred in calculating a current retained heat of 11.3 * 0.45  = 5.1 watts/m2  in 2006 (0.45 doublings of carbon dioxide)  because we have not seen the full equilibrium rise in temperature (otherwise there would be no net energy flow into the oceans) therefore we will not be experiencing all the claimed positive feedback from water vapour.  That means my figure of 5.1 watts/m2 is too high.

I repeat the calculations more accurately below.

If the feedback is proportional to the temperature, (water vapour increases exponentially with temperature but its effect is logarithmic therefore the effect will be the logarithm of an exponential which is linear) then it is indeed valid to allow for the positive feedback by adjusting the heating sensitivity of Earth rather than calculating the positive feedback explicitly in watts/m2.  In short, instead of using kappa (the sensitivity without feedbacks) use lambda the sensitivity with feedbacks factored in.  This is the approach adopted by many other scientists.

Popular reporting suggests a temperature rise between now and 2070 of 3C.  In fact checking back  to the IPCC 4th assessment report what is actually claimed is that a doubling of carbon dioxide leads to an increase of 3C which is somewhat different to popular reports.  Doubling carbon dioxide leads to a direct increase in retained energy of about 3.7 watts/m2 which would mean a value for lambda of  0.81 (3/3.7).

So how much heating has occurred?  The temperature of the planet has been going up and down all the time.  By selecting an appropriate reference year one can claim almost any warming one desires.  However several sources all claim that AGW only started around the end of the second world war and temperature changes prior to that time were of natural origin.  For example from Wikipedia;

  “The Intergovernmental Panel on Climate Change concludes that increasing greenhouse gas concentrations resulting from human activity such as fossil fuel burning and deforestation are responsible for most of the observed temperature increase since the middle of the 20th century.   The IPCC also concludes that natural phenomena such as solar variation and volcanoes produced most of the warming from pre-industrial times to 1950 and had a small cooling effect afterwards.   These basic conclusions have been endorsed by more than 45 scientific societies and academies of science”.

http://www.grida.no/publications/other/ipcc%5Ftar/?src=/CLIMATE/IPCC_TAR/wg1/005.htm shows 0.4C warming since about 1950 although I shows the temperature at that time changing by 0.2C in 5 years so the exact point chosen makes a large difference.

http://www.pnas.org/content/103/39/14288/F1.large.jpg   shows between 0.4C  and 0.5C

http://data.giss.nasa.gov/gistemp/2005/  shows about 0.4C since 1945

I also note that the government paper specifically talks about ocean heating since 1960 further reinforcing this point.  In fact their data shows no ocean heating prior to 1975. 

Using a temperature rise of 0.4C, and a value of lambda of 0.81 the extra energy radiated away from earth accounts for between 0.4/0.81 = 0.49 watts/m2 .  But IPCC claim that the direct effect of the rise in carbon dioxide in 2006 (the report was released in Feb 2007) was an increase in carbon dioxide forcing of  1.66 watts/m2 and a total impact from all direct factors (ie: excluding feedbacks)  of 1.6 watts/m2 .  This means that 1.6 – 0.49 watts/m2 or 1.11 watts/m2 of the total forcing must have gone into heating the Earth.  But the retained energy calculated from the government paper was 0.32 watts/m2  into the oceans (representing 85% of the total)  for a planetary total of 0.32/0.85 = 0.38 watts/m2.   1.11 versus 0.38 is still a discrepancy of  3 times although smaller than my previous claim of  9 times.

Carrying out the calculation the other way round, if 0.38 watts/m2  is being retained, then 1.6-0.38 = 1.22 watts/m2 must be being radiated.  If that was happening with an 0.4C rise lambda would have to be 0.4/1.22 = 0.328 C/watt/m2 .  A figure of lambda = 0.328 and kappa = 0.266 still suggests a small amount of positive feedback (lambda is greater than kappa) but far less than that claimed by AGW supporters.  A sensitivity of 0.328 would suggest an equilibrium temperature rise for doubling of carbon dioxide of 3.7 * 0.328 = 1.2C.  However in 2070 carbon dioxide will still be rising and the planet will still be warming, we will not be at equilibrium.  We could reasonably expect the same level of energy to be flowing into heating the earth as at present (about 0.38 watts/m2).   In that case the actual rise for doubling carbon dioxide would be (3.7 – 0.38)* 0.328 = 1.09C.  Since we are currently seeing 0.4C, that would mean a further rise between now and 2070 of 0.69C which is a far cry from the popularly reported 3C.

All this of course assumes that the starting data is correct.  In fact there are reports that the oceans have been cooling now for some years and that the steep rise shown since 1998 is an artifact arising from the change to the Argo buoys.   These two factors would reduce the 0.32 watts/m2 figure significantly. Also, there is significant dispute over the justification for the corrections applied to the raw temperature data which result in the claimed 0.4C rise.  The satellite data from UAH shows far less warming.  If these concerns have substance, then the impact of rising carbon dioxide is even smaller suggesting that the net feedback is in fact negative not positive and the temperature rise between now and 2070 would be less and possibly substantially less than 0.69C.

I apologise to readers for my error in the previous article and hope this sets the record straight.

Michael Hammer
Melbourne, Australia

Read Part 1 here: http://jennifermarohasy.com/blog/2009/07/a-climate-change-paradox/

26 Responses to A Climate Change Paradox (Part 2)

  1. bazza July 14, 2009 at 8:59 am #

    There is a lot to be said for peer reviewed literature.

  2. a jones July 14, 2009 at 10:47 am #

    You forget an important non sequitur in this argument.

    Heating of the oceans is supposed to increase water vapour in the atmosphere and thus amplify the warming effect.

    But of course it does not matter what caused the warming of the oceans, it might be increased CO2 but equally it might the stokers in the Infernal Regions working overtime.

    Moreover despite protestations to the contrary there is no observational evidence, and we have been looking very carefully, that this water based feedback effect eventuates in the real world.

    Nor for that matter despite the increase in CO2 can we trace it’s fingerprint in the temperature record.

    Likewise the Argo programme shows unequivocal cooling, up to 2006 NASA, Willis, Levitus et al etc. argued this was an error due to trying to splice the ARGO data to earlier data sets but it is now apparent that the cooling is real.

    So now they say it’s just a blip and we must wait a few more years. Don’t hold your breath, by then they are going to say its just a temporary natural effect and warming will resume shortly.

    And of course you might care to compare your results with those of Pielke senior and others.

    Kindest Regards

  3. steve from brisbane July 14, 2009 at 10:53 am #

    “By selecting an appropriate reference year one can claim almost any warming one desires.”

    And by selecting 1998, skeptics can (and do) claim almost any cooling they desire.

  4. Bill Illis July 14, 2009 at 11:01 am #

    The 0.32C /watt/m^2 is a short-term temperature response. The theory expects this ratio to rise in the long-long-term equilibrium response to approximately 0.75C /watt/m^2.

    The change over time is related to the lags in the climate system.

    None of the models use a higher ratio than 0.32C in hindcasts (and volcanic forcing is only 0.15C/watt/m^2). The recent MIT study which had temps at +5.2 by 2100 had the ratio rising to 0.55C/watt/m^2 by 2100.

    It is really just another tunable parametre to get one to +3.0C by 2100.

    Here is the climate response function that Hansen wants every to use now (effectively the rate at which the C/watt/m^2 ratio changes over time (0.32C (40% of 0.75C) in a few years – 0.45C (60% of 0.75C) within 100 years and so on).


  5. Ian Mott July 14, 2009 at 11:26 am #

    All this discussion over the validity of a 0.38w/m2 increase in retained heat from atmospheric forcing is quite irrelevant when compared to the actual direct heat absorption by oceans with or without cloud cover.

    The area between Lat 30N and 30S is approximately 33% of the planetary surface but 50% of the globes flat face presented to the sun. See http://en.wikipedia.org/wiki/File:Insolation.png
    Upper atmosphere insolation in this band is in excess of 400w/m2 while surface insolation influenced by cloud cover ranges from 180w/m2 to 280w/m2 and an average in the general order of 220w/m2. And this region is over represented by oceans, with 75% ocean compared to the global portion of 70%.

    When these oceans are not covered by clouds they absorb 97% of insolation or about 388w/m2. Clouds, having albedos between 40% and 75% have a very big impact on what the oceans below will absorb. Clearly if 75% of insolation is reflected before it gets to the ocean surface then only 25%, or 100w/m2 can get through to that ocean which will, in turn, retain 97% of it or 97w/m2. If a mid range 50% is reflected by clouds then 200w/m2 will be allowed through to the surface below where 194w/m2 will be retained by the ocean.

    The lower graph, in the link above, showing parts of the Indian Ocean with insolation of 260w/m2 or more indicate those parts of the ocean surface with lower cloud cover.

    So the general difference in retained heat between constantly cloud covered ocean and constantly cloudless ocean is 194w/m2.

    It is little wonder, then, that the climate criminals are trying to shift the focus to ocean temperature data while maintaining their blind faith in atmospheric forcing theory that hinges on, at best, 3.0w/m2 for a doubling of CO2. They refuse to even calculate changes in tropical cloud cover so they can claim that all oceanic temperature changes are driven by atmospheric influences, not by changes in direct absorption rates.

    It only requires a very small change in the rate of direct absorption by oceans to completely negate all calculations of heat transfer to oceans from atmospheric forcing by CO2. And clearly, as long as cloud cover continues to be treated as a constant in climate models then any pretence at validating those models with actual temperature data is exposed as fraud.

  6. Graeme Bird July 14, 2009 at 11:38 am #

    One doesn’t wish to start doing the maths on statistics that are probably dubious. What we really want to do right now is see if anyone can verify (or falsify) the validity of the data itself. Its probably a base lie of the sort that no good can come from building upon it.

    We have to understand how such a transparent racket has stayed in the air so long. And part of it is skeptics allowing themselves to be dragged down cul de sac arguments.

  7. Allen Ford July 14, 2009 at 12:16 pm #

    “We have to understand how such a transparent racket has stayed in the air so long. And part of it is skeptics allowing themselves to be dragged down cul de sac arguments.”

    Amen, Graeme. The flat earth skeptic deniers need concentrate on one issue only, and that is that 600 million years of geological history dismally fails to support the notion that atmospheric CO2 levels have any direct bearing on atmospheric temperatures. End of story.

  8. Louis Hissink July 14, 2009 at 2:27 pm #


    Isn’t it the usual protocol when an error is found, to raise the draw bridge, and then refuse anyone due diligence access to the data? At least that is the impression one gets from mainstream climate science.

    As a professional exploration geologist who knows all about making errors etc, your correction is to be applauded – pity the rest haven’t the professionalism. In any case peer review always works as intended in the engineering and physical sciences but falls apart in the deductive sciences.

  9. janama July 14, 2009 at 2:44 pm #

    But the government is telling us that climate change is increasing and we face more risks


    what a shonky set of charts and graphs, sheesh – they accuse Plimer of misrepresentations – how about this load of bulldust?

  10. Garry July 14, 2009 at 4:21 pm #

    1. at least the ‘Government’ line noted by janama has a single author, Will Steffen, “to wear the heat” if the BOM wish to distance themselves from this at some point.

    2. Michael, you have stated that “the claimed positive feedback is proportional to the temperature rise”. While this is what was stated, it is strange in and of itself, since the amount of water in the atmosphere would be expected to bear some relation to the vapour pressure of liquid water at a given temperature, and this roughly doubles every 11 deg C

  11. Malcolm Hill July 14, 2009 at 4:52 pm #

    The publication for the Fed Govt Department of Climate Change is disturbing if only for the implications of what is written.

    More brain dead Canberra Pubes making sure they have a sinecure for life, and all based upon a hypothesis that has holes in it from start to finish.

    How delightfully pretentious it is for them to do an internal risk asessment, but they cant do a basic cost benefit on AGW as it affects this country.

    These are the morons who will insist that we put a barnacle on the back side of our economy so that they can achieve a tick in the box for having lowered the temperature 0.003C by 2100

    Can it possibly be any dumber.

  12. cohenite July 14, 2009 at 7:10 pm #

    Every AGW pronosis is predicated on water being a +ve feedback; MH’s revised calculations show that even if water is a +ve feedback that the increase in temperature will be far less than AGW predicts. But clearly water is not a +ve feedback; it is a moderator of temperature trends; rising temperature is mitigated by increased evaporation producing lower cloud and increased albedo and a wider water window TOA; the reverse applies for cooling temperatures. In short the greenhouse is always working at maximum for internal radiative process and constant externalities. It’s about time Miskolczi was revitalised.

  13. michael hammer July 14, 2009 at 7:58 pm #

    Garry you are quite right that the vapour pressure of water doubles about every 10-11C but the impact of increasing water vapour on retained heat is logarithmic as is the case for any green house gas. The logarithm of an exponential function is a linear function. Thus each 10C rise doubles the water vapour (at constant relative humidity) and each doubling increass the energy retained by the same amount.

    Mike Hammer

  14. cohenite July 14, 2009 at 8:36 pm #

    Of course the real problem with AGW climate sensitivity projections is that they always contradict empirical measurement; this is evident in the OHC graph from Senator Wong which is used in MH’s article; this graph clearly shows the divergence;


  15. Graeme Bird July 14, 2009 at 8:48 pm #

    I think the real problem with it is to even start talking about Lambda means you are buying into a fudge factor several steps into a model that is so unrealistic as to be otherworldly. The model even goes so far as to eliminate induction and convection, relying on radiation alone. Even its first assumption would seem to be saying that the CO2 DOESN’T have this effect. But would do so only if we observed certain other effects on a flat planet wherein we could ethnically cleanse induction and convection from this story. And not only induction and convection; Day and night. And not only day and night, induction and convection, but everything else pertaining to this story BUT radiation and atmospheric composition. All other factors jumbled into lambda or otherwise tacked on at the end somehow.

  16. Louis Hissink July 14, 2009 at 9:04 pm #


    1. Splendid show in Melbourne.
    2. Climate sensitivity projections? The graph shows 4 projections with a lonely label “observed” in a disconnected state.

    Prediction of future states of anything, is firmly in the realm of astrology and tarot card readings. Economists cannot get it right, Weather Bureaus only get it right 50/50, and so we wonder what the hubbub is about.

    Economically the Austrian School economists have it right, weather wise, no one has it right, but what are we to do with the mob who think they have it right. It get’s personal when they want to relieve our wallets of our cash without our approval, and this is what it is all about.

    AGW was, is and will be a possible pseudoscientific basis for subjecting us to an ecologically determined social system. It’s driven by the Fabians, despite their specious denials, and all for the common good, so we are told.

    It took a world war, a totally unnecessary one according to Pat Buchanans recent book, to detail the origens of the motives of our political adversaries.

    But they now control government, and we will look at what happens.

  17. cohenite July 14, 2009 at 10:31 pm #

    Thanks Louis; the discrepancy between Wong’s graphs for OHC and sea level and Will Steffans reprehensible scare-mongering is or should be serious; clearly there is a misrepresentation between the Wong graphs and the official data for OHC;


    and for sea level;


  18. Capn Jack Walker July 14, 2009 at 11:08 pm #

    Any NENSO hunters got any tips,

    We have 18 foot spike, we got two inch or three inch flywire, the rumor is the NENSOs will be the biggest we caught, so the rumor goes.

    They say she wallows and does the runner and we surf her wake.

    Any tips, the crew is full but tips we take when we hunt the mighty ENSO.

  19. Carbon Infidel July 15, 2009 at 11:10 am #

    Double that Allen Ford! I thought I was the only one. Been lurking here & there for some time and never heard this point before-its a good one. Even Wiki, an AWG fave has a similar graph!! Lets see who the Deniers are now! A question I cannot get a warmer to answer – were does the CARBON in FF come from ???

  20. Webster Hubble Telescope July 15, 2009 at 12:44 pm #

    This stuff is so passe.
    The real state-of-the-art math and science is in the study of oil depletion.
    Check out

    have at it, as your field is getting a bit crowded and you might want to rant and rail on some fresh ideas.

  21. Graeme Bird July 15, 2009 at 4:27 pm #

    Hard to know what you are up to here fella. But the idea that the really cheap accessible oil is showering itself on us as a slowing rate is all the more reason to avoid the carbon tax and the cap-and-kill and to be going hell-for-leather into deep sea drilling, diesel-synthetics, methyl-clathrates and nuclear.

  22. Bruce July 16, 2009 at 9:40 am #

    Given the following:

    Total mass of ocean water on the planet = 1.384 × 10^21 kg
    Total surface area of oceans = 361 × 10^6 km^2
    Mean depth of world oceans = 3794 m

    A couple of questions from a non-scientist:

    At what depths are temperatures being monitored?

    At what rate do the oceans lose heat when not facing the sun?

    If the oceans are being heated from the top down, what effect do convection mechanisms have?

    What is the effect of ocean currents, at any depth, on heat transfer within the total mass of ocean water?

    Just wondering?

  23. Graeme Bird July 16, 2009 at 9:06 pm #

    The disgraceful truth of this story is that the lone paradigm of watts-per-square metre, based on land and air, has meant that the questions you ask have seldom been discussed. The model they use aggregates and everything to such an extent that it averages away most of what is interesting about climate.

    “If the oceans are being heated from the top down, what effect do convection mechanisms have?”

    I wouldn’t think it was only from the top down. The gulf stream, for example, subject to evaporation, begins to get saltier and heavier and then it down-wells in the sea of labrador . It forms part of the great ocean conveyor. Going from a fast-moving current of maybe 20 Amazons it must become a truly huge subterranean mass that must move like toothpaste. Because it takes 1600 years to go through one cycle.

    The upper oceans must be able to gain and lose a great deal of energy very quickly. Since they do so on a yearly basis in line with the earth getting closer to and then further from the sun. The rate at which this typically happens would seem to be a magnificent clue to follow up, and see how it all works. But 50 billion dollars of funding hasn’t seemed to elicit much in the way of the sort of analysis your questions are pointing to. In fact its only in the last few weeks that the leftists have started getting interested in imbedded oceanic energy. I’m not joking. The interest is as recent as that. Two and three years ago I was unable to get people to take this sort of thing seriously.

  24. Alex July 22, 2009 at 12:16 pm #

    This article reaches similar to another I have seen here…

    A 1998 paper by Idso (link found in the above webpage) is well worth a look. Idso describes “Eight natural experiments” which debunk the likelihood of doubling CO2 having sufficient radiative forcing to warm the planet by more than 0.5 deg C. The planet provides the evidence and the modellers havent calibrated their efforts against the actuality.

    Leaving for now the endlessly disputable graphs of historical temperature, consider the fundamental physics. How can anyone believe the fairy tale that 1.6W/m2 (a tiny torch bulb) will warm 10,000 kg of air (ie 1 atm pressure) by several degrees even over a century or more, when that air is circulating and re-radiating at night? And since 1 atm air pressure is equiv to only 10m ocean depth, and oceans cover 70% of the planets surface, a tiny tiny amount of ocean absorbtion to greater depths would see any increased atmospheric heat load (assuming exchange) disappear from measurement capability. We dont even need the cloud uncertainties to see that the temp increase estimates based on CO2 radiative forcing are hugely overestimated. Idso demonstrated the evidence is already right in our face.

  25. Allan Taylor July 24, 2009 at 10:37 am #

    The global warmers belief system is dependent on the apparent steady rising levels of CO2 in the atmosphere, currently quoted at ca 385 ppm. They use the figures from the measuring station on top of Mauna Loa volcano in Hawaii, which does emit appreciable CO2, which is said to be corrected for….. (maybe this is like having ground thermometers in car parking lots?)

    I am very suspicious of such results particularly when there seems to be no effort, or research into the variability of atmospheric CO2. Why rock the boat when we have the results we want? We are told there is almost perfect mixing of atmospheric gases. I wonder?

    Why not have a few dozen atmospheric CO2 measuring stations around the world to check on things? (Also being done by Russians, Chinese, Indians and Brazilians etc , to avoid any possible skullduggery, like the hockey stick graph)

    How does atmospheric CO2 vary radially from a coal-fired power station? What is the CO2 content of the atmosphere in the offices of the IPCC in New York?

    Such research projects abound and deserve a little of the umpteen billions of dollars spent on Climate Research.


  1. Jennifer Marohasy » A Climate Change Paradox - July 14, 2009

    […] READ MORE HERE: http://jennifermarohasy.com/blog/2009/07/a-climate-change-paradox-part-2/  […]

Website by 46digital