1.  The AGW movement claims there has been a global temperature rise of 0.5C over the last 60 years and that this is due to increasing CO2.  Both AGW proponents and sceptics accept that the relationship between energy retained and CO2 concentration is logarithmic (a constant increase in retained energy for each doubling of CO2).  The AGW movement data also shows that since 1900 CO2 has risen by very close to half a doubling  over this 60 year period.

IPCC have claimed in their 4th assessment report (summary for policy makers), that the most likely temperature rise by 2070, when CO2 will have risen by a further half doubling to twice the level in 1900, is a further 3C rise  (page 12).  Why would the first half doubling give 0.5C rise while the second half doubling gives 3C or 6 times as much rise?

2.  One claim I have heard is that it takes the climate a long time to respond to the change in CO2 concentration and we have not yet seen the entire rise from the first half doubling.  The same IPCC 4th assessment report (page 12, 13 and 14) indicates that if CO2 were stabilised at the current level, the temperature would rise by a further 0.2C over 2 decades stabilising at 0.7C above the 1900 level. 

If the current temperature rise is not yet at the equilibrium level then for the business as usual scenario the temperature rise by 2070 will also not be at the equilibrium level.  Yet the IPCC data suggests the equilibrium rise from the first half doubling is not even one quarter of the less than equilibrium rise from the second half doubling.  To me this is illogical.

3.   IPCC claim an increase in retained energy of around 3.7 watts/sqM for each doubling of CO2 (1.66 watts/sqM for the current rise page 4).  They admit this is much too small to result in a 3+ degree temperature rise.  The large temperature rise is based on claims of very large net positive feedback in the climate system.  

Yet, every natural stable system I can think of exhibits net negative feedback.   Indeed the terms stability and negative feedback are synonymous since negative feedback is what causes stability.  By contrast, positive feedback causes instability (such as tipping points where a large change in output occurs for a small change in input).   Stability does not mean zero change, it means the response to changes in input are small enough and sufficiently controlled so as to not cause system destruction or runaway.  If you want to argue that the climate system is not stable then I would why it has remained conducive to continued life on this planet for billions of years.  This is despite all the change in CO2 levels, volcanic eruptions, changes in solar output and orbital changes over the millennia.  To me, that is a very good definition of climate stability.

4.  The AGW modellers claim cloud feedback is positive.   AGW advocates seem to divide clouds into two categories, low clouds and high clouds.  Every report I have read acknowledges that low clouds cause cooling.  With regard to high clouds there is some dispute but the AGW modellers claim they cause warming.  Further they claim a warming planet results in a bias away from low clouds and towards high clouds thus exacerbating  warming, hence contributing to positive feedback.

At the same time they claim constant relative humidity in their models.  This means that as the temperature rises, more water must be evaporating.  Now unless we want to predict that the amount of water in the atmosphere is going to continuously rise until the oceans are suspended over our heads, more evaporation must imply more precipitation ie: more rain.  However, rain only comes from low clouds not high clouds, so more rain means more low cloud mass not less low cloud mass.  This contradicts the previous position.  If the claim is that both increase, then that means significantly more cloud mass in total.  Clouds are the biggest contributor to Earth’s albedo (the fraction of incoming solar energy reflected back out to space).  Rising total cloudiness means increasing albedo and the albedo is very strongly cooling.  The albedo already causes 100 watts/sqM to be reflected away from Earth.  To cancel out the entire impact claimed by IPCC for doubling CO2 only requires an increase in cloudiness from 60% to 62.4%.

An increase in temperature, leading to more evaporation, in turn leading to more cloudiness which reduces the solar input to Earth thus reducing temperatures is a description of negative feedback not positive feedback.

5.  The claimed “proof” of positive feedback is a model prediction of a hot spot in the tropics at mid troposphere levels.  However all the experimental evidence from many, many measurements has failed to find any evidence of such a hot spot.  In science, a clear prediction that is falsified experimentally means the underlying hypothesis on which the prediction is based is wrong.

6.  The reports documenting man’s CO2 emission use some scarily large numbers but these have to be viewed in the light of the overall system size.  For example, a million dollars is an extremely large amount of money for a private individual but it is almost petty cash for a government.  If we want to put the numbers into perspective we need to relate them to the size of the system.  Why not express CO2 quantities in terms of how many PPM 1 year’s emissions will raise or lower the atmospheric CO2 level (if all of it stayed in the atmosphere).  We could call that PPM equivalents.

In those terms, human emissions amount to about 2.7 PPM equivalents.  Now NASA have published a diagram showing annual CO2 transfers for the planet.  This shows terrestrial plants absorbing about 61 PPM equivalents.  We know that both rising CO2 and rising temperature favour faster plant growth.  That’s why horticulturalists artificially raise CO2 levels in glass houses to about 1000 PPM.  It is also why plants grow faster in the tropics than in cooler locations on earth.  More to the point, a recent study showed average plant growth has accelerated by about 6% over the last 30 years.  A 6% increase in plant growth means a 6% increase in absorbed CO2, from 61PPM equivalents to 64.7 PPM equivalents.  This means that human emissions have increased by 2.7 PPM equivalents but plants have increased their absorption by an extra 3.7 PPM equivalents over the same period.  The increased plant growth is consuming more than 100% of human emissions.  Is there another (natural) factor contributing to CO2 increases?

This response, more CO2 leading to faster plant growth which in turn consumes more CO2 is another example of the widespread bias towards negative feedback I alluded to earlier.   Apart from which, is increased plant growth and thus agricultural productivity bad?  I would have thought it was highly desirable.
 
7.  The AGW hypothesis is based on temperature rises between about 1975 and 1998 or about 25 years worth of data.  This is claimed to be definitive yet the last 10 years worth of data shows falling global temperatures.  This is claimed to be a short term aberration and of no consequence.  I do not see how 25 years can be considered definitive beyond dispute while 10 years of data is a short term aberration, too short to be significant.  I would have thought at least a 10:1 ratio would be necessary to make such a claim.

8.  If I adopt this 10:1 ratio by looking at the last 100 years worth of data I find 1910-1940 temperatures rising while CO2 was not.  1940 to 1975 temperatures falling while CO2 rising, 1975 to 1998 temperatures rising while CO2 rising and 1998 to 2009 temperatures falling while CO2 rising.   Three quarters of the period shows no correlation or negative correlation with CO2 and only one quarter shows positive correlation.  I do not understand how one can claim a hypothesis proven when ¾ of the data set disagrees with it.  To me it is the clearest proof that the hypothesis is wrong.

9.  For the last 10 years the global temperature data shows either no atmospheric temperature rise or indeed a falling global temperature.  Recently this has been claimed to be due to a combination of a quiet sun and changes in ocean circulation superimposed on the underlying warming trend.  The further claim is that when these effects reverse, warming will start again with a vengeance. 

If these natural processes can cancel out the impact of AGW then they are as powerful as AGW.  If they can overwhelm the impact of AGW to cause cooling they are more powerful, yet IPCC and other AGW proponents have claimed in previous assessment reports that solar influences are only a minor contributor compared to CO2. 

The  sun was unusually active during the latter half of the 20th century in contrast to its current inactivity and the ocean circulation was the opposite of what is now happening.  Thus the natural effects claimed to be causing cooling now would have been causing warming in the late 20th century.  If these natural effects are as large as the AGW impact then they would have caused half the observed 20th century warming.  If the natural effects now outweigh the AGW impact to cause cooling then they would have been responsible for more than half the observed 20th century warming.

This is not only in contradiction of the earlier IPCC claims, it also means that the actual impact of CO2 increases since 1900 is much less than the claimed 0.5C.  At most 0.25C and possibly much less even than that.

If in fact the temperature returns to the long term average over the next few years (as seems to be increasingly likely), it suggests that these natural processes were responsible for essentially all the observed temperature changes over the 20th century with negligible impact from CO2 changes.

10.  I have looked at the raw temperature record for the USA (USHCN data) and the Bureau of Meteorology data for Victoria, Australia.  Both show fluctuations of temperature with time but zero underlying trend for the last century.  By contrast, the official IPCC endorsed data shows a strong underlying upwards trend.  When I investigate why the difference, I find that the raw data has been adjusted for several supposed factors and every one of these adjustments created a warming trend.  This implies that the claimed warming trend is due to the adjustments, not the raw data.  In any less controversial scientific issue, such a result would be viewed with the greatest possible scepticism and would be extremely unlikely to be accepted.

When I examine the raw temperature data record for cities compared with nearby suburban or rural areas, I  find an extremely high signature of urban heat island effect.  Yet the people doing the temperature adjustments claim that urban heat island effects are negligible and do not require correction.  This is despite the fact that a significant proportion of the measurement stations are in cities. 

Such a clear factor not corrected for while other more subtle claimed factors are corrected casts further doubt on the correction protocol.  If there is an upwards bias in the corrections, it means the claimed warming trend is exaggerated and may in fact not exist at all.

11.  The mainstream media keep reporting that the current situation is increasingly dire and is much worse than even the previous pessimistic projections.  When I examine this statement I find that previous projections predicted rapid atmospheric warming during the last 10 years whereas in fact we have had cooling.  They predicted rapid increase in rate of rise of sea level when in fact the rate of sea level rise has recently declined.  They predicted a very rapid increase in Arctic summer sea ice loss whereas in fact, for the last 2 years, it has been increasing.  They predicted a rapid rise in hurricane incidence and severity when in fact there has been a decline.  To me the media’s many claims are not supportable.  I also consider it to be beyond simple error.  At best it is unpardonable gross carelessness in checking the data they are reporting and at worst it is deliberate bias in reporting.

12.  More recently, in response to the data showing no warming for the last 10 years, I have seen new claims that global land temperatures are now deemed irrelevant.  The newly discovered measure of importance is the rise in ocean temperature, since it is now claimed that this is by far the largest planetary heat sink.  If that claim is true, it makes all the previous data claiming to show strong global warming over the period 1975 to 1998 also irrelevant.  To suggest that from 1975 to 1998, the energy went into warming the land and air and then abruptly in 1998 it stopped doing that and the heat instead went into heating the oceans is, to me, completely absurd.  Nature simply does not work that way.  It is like claiming you put the kettle on, for the first minute the energy goes into heating the water and then abruptly it stops heating the water and starts heating the room instead.

13.  Looking further at the claim of warming ocean temperatures.  Late last century it was realised that the method of measuring ocean temperatures was extremely inaccurate and unreliable.  To overcome that, a sophisticated, global system of buoys was designed and implemented at very considerable cost and effort.  These buoys repeatedly dive down to measure temperatures  and then resurface to report back findings  This network is called the Argo network and it became operational in 2003.  Since becoming operational, it has shown ocean cooling.  Yet the scientists who claim ongoing ocean warming exclude the Argo data and the satellite data instead relying entirely on the earlier poor reliability methods.

The same scientific community which claimed a method was inaccurate and unreliable, designed and implemented  a new high accuracy measurement system, are now rejecting the new high accuracy data in favour of the older data they themselves viewed as unreliable.  How can that be justified?  Why is the data from the older less reliable method correct, while results from the new, high accuracy methodology are wrong?  What does that say about the scientists who designed the Argo system but apparently don’t trust its output?  To me it suggests selecting data to prove a favoured hypothesis, commonly called cherry picking.

Some sites are talking about “correcting” the Argo data.  Why should a carefully thought out, brand new, high accuracy system already require adjustment to its outputs?  Was a mistake made in the design?  Why are the proposed adjustments again in the direction of exacerbating the claimed warming?  When the raw data contradicts the hypothesis yet the “adjustments and corrections” all reverse that result so as to support the championed hypothesis, it’s time to start worrying.

14.  What mankind is doing by consuming fossil fuels is recycling CO2 that used to be in the atmosphere but got trapped in the distant past.  Is there a “correct” level of CO2?  What I have read suggests that the Earth was a more verdant place before the CO2 got locked up in fossil fuels.  Would the Earth be more or less pleasant a place if the carbon currently locked up in fossil fuels were again available to the biosphere.  Not just for humans but for all living things, plants and animals.  Surely we should consider that before we pick some arbitrary recent point in time and declare that the CO2 level at that time is the ideal to be maintained at all costs.

FROM a slightly different but related perspective, I see the AGW story continuously changing.  When one measure no longer trends the wanted way, a change is made to a new measure (change from surface to ocean temperatures and ocean acidity).  In one report, an effect is claimed to be negligible when that suits the hypothesis yet the same measure is later used as a reason to explain away embarrassing trends (Solar influence and ocean currents).  All the observed effects are very moderate (less than 0.5C) if present at all yet hysteria is generated on the basis of hypothesised extreme future outcomes (up to 6C rise and 10 meter sea level rises).  Outcomes far enough in the future so as to be un-testable yet close enough to impact people being born today.  Claims based on abstract models that fail even short term validation tests.   As a practicing scientist, I have seen this scenario more than once before, changing benchmarks and indicative parameters, rewriting predictions and predicted causes after the event, excusing erroneous predictions.  These are clear signs of propping up a false hypothesis.

There does seem to be clear evidence that temperature changed several times over the 20th century both up and down.  There is far less evidence for any underlying upwards trend due to CO2 and many reasons to question the data analysis that tries to demonstrate such a trend.
 
One of the arguments I often hear is “well even if AGW is not absolutely proven we should take action just in case its correct” – the precautionary principle.  I see two reasons to disagree with that. 

Firstly, if rising CO2 should bring about some warming it is by no means certain that this would be catastrophically bad or for that matter whether it would be bad at all.  It seems quite likely to me that the cure would be worse than the disease. 

Secondly, and to me much more importantly, there is another issue we need to consider and that is the law of unintended consequences.  Briefly this states that whenever you take action there will always be consequences you did not consider in advance and did not intend.  Since there are many more ways to be wrong than to be right there is a better than 50:50 chance that these consequences will be bad.  If the original action is based on a false premise it greatly increases the risk of bad unintended consequences.  The precautionary principle is based on the belief that there is no down side to taking action.  The law of unintended consequences tells us that there is always a down side and the cost versus benefit always needs to be carefully evaluated before acting. 

We are already seeing some very bad unintended consequences of the action taken so far over global warming.  The government driven initiative to use less fossil fuel by diluting it with ethanol is causing massive forest clearing the Amazon basin (to grow the ethanol feedstock) and is very significantly raising food prices causing even worse starvation in 3rd world countries.  Terrible as it is, this has not greatly impacted on western society but the next phase most certainly will.

There is another very serious unintended consequence that I would like to raise here; one that concerns me very deeply.  When I listen to the public AGW debate  I hear very high profile politicians and prominent public figures calling for people who openly disagree with AGW to be put on trial for treason.  I hear many cases of people losing their jobs because of voicing sceptical opinions.  I hear prominent global warming advocates refusing to enter into debates or trying to avoid debates by claiming the science is settled, and by claiming we do not have time, we have only weeks to act.  I hear AGW advocates resorting to personal attacks against people who disagree rather than addressing the technical issues they raise. 

I hear AGW proponents claiming to be the under funded underdogs, fighting to protect the planet against greedy capitalists, yet the reality is their funding is at least 1000 times greater than the sceptics funding.  I see many reports of scientists refusing to release their workings, thus preventing review of their methodology, despite the fact that their work was funded by public money. 

I see how the established media abandons balance in reporting by strongly favouring proponents of AGW, ignoring or denigrating sceptics and forcing most onto blog sites like this one.  I hear some environmental groups and activists publicly claim that its OK and even necessary to exaggerate the threat so as to get the public to engage. I see the courts condoning acts of vandalism and even violence against essential public infrastructure.  I see high profile public figures supporting such acts and claiming them to be reasonable and justified. 

In short I see our society abandoning some of our most vital democratic freedoms over this hysteria:  Free speech, impartial enforcement of the law, balance in reporting, freedom of information.  These are freedoms our forebears gave their lives to bequeath to us, they are our most valuable inheritance and we seem to be throwing them away over an unproven hysterical hypothesis.

More recently I have read articles from England advocating individual ration cards for petrol, heating oil, gas, electricity.  Is water and food next?  War time austerity as an ongoing future way of life?  A return to the agrarian poverty of the middle ages?  I note the new film “Not evil just wrong” has had to be distributed via the internet rather than traditional media.  One step from distribution through an underground network?  Will that apply to all future sceptical writing?   What about other writing contrary to the popular opinion of the day?

These are the issues that differentiate between a free democracy and a totalitarian regime and the further one goes down this path the harder it is to pull back.  History has shown us that the disease is far easier to acquire than to get rid of.

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Notes and Links

Michael Hammer graduated with a Bachelor of Engineering Science and Master of Engineering Science from Melbourne University.  Since 1976 he has been working in the field of spectroscopy with the last 25 years devoted to full time research for a large multinational spectroscopy company.

To read more from Mr Hammer click here and scroll down:  http://jennifermarohasy.com/blog/author/michael-hammer/

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/

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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

A reader of this blog, Michael Hammer, recently studied the official data from the US official weather stations and in particular how it is adjusted after it has been collected.   Mr Hammer concludes that the temperature rise profile claimed by the US government is largely if not entirely an artefact of the adjustments applied after the raw data is collected from the weather stations.

Does the US Temperature Record Support Global Warming?
By Michael Hammer

IN the US, the National Oceanic and Atmospheric Administration (NOAA) collects, analyses and publishes temperature data for the United States.   As part of the analysis process, NOAA applies several adjustments to the raw data. 

If we consider, the above graph, which shows, their plot of the raw data  (dark pink) and the adjusted data (pale pink), it is obvious that the adjustments have little impact on data from early in the 20th century but adjust later temperature readings upwards by an increasing amount.  This means that the adjustments will create an apparent warming trend over the 20th century.  [Click on the above chart for a better larger view, this chart can also be viewed at http://cdiac.ornl.gov/epubs/ndp/ushcn/ndp019.html .]

NOAA state that they adjust the raw data for five factors.  The magnitude of the adjustments are shown in Figure 2. 

Figure 2.  Form of individual corrections applied by NOAA. The black line is the adjustment for time of observation.  The red line is for a change in maximum/minimum thermometers used.  The yellow line is for changes in station siting. The pale blue line is for filling in missing data from individual station records. The purple line is for UHI effects (this correction is now removed).  [Click on the chart for a better larger view or visit the same website as for Figure 1.]

It is obvious that the only adjustment which reduces the reported warming is UHI which is a linear correction of 0.1F or about 0.06C per century, Figure 2.  Note also that the latest indications are that even this minimal UHI adjustment has now been removed in the latest round of revisions to the historical record.  To put this in perspective, in my previous article on this site I presented bureau of meteorology data which shows that the UHI impact for Melbourne Australia was 1.5C over the last 40 years equivalent to 3.75C per century and highly non linear.

Compare the treatment of UHI with the adjustments made for measuring stations that have moved out of the city centre, typically to the airport.  These show lower temperatures at their new location and the later readings have been adjusted upwards so as to match the earlier readings.  The airport readings are lower because the station has moved away from the city UHI.  Raising the airport readings, while not adding downwards compensation for UHI, results in an overstatement of the amount of warming. This would seem to be clear evidence of bias.  It would be more accurate to lower the earlier city readings to match the airport readings rather than vice versa.

Note also the similarity between the shape of the time of observation adjustment and the claimed global warming record over the 20th century especially the steep rise since 1970.  This is even more pronounced if one looks at the total adjustment shown in Figure 3 (again from the same site as Figure 1).  As a comparison, a recent version of the claimed 20th century global temperature record downloaded from  www.giss.nasa.gov  is shown in Figure 4. 

Figure 3.  Magnitude of the total correction applied by NOAA

[Click on the charts for a larger/better view.]

Figure 4.  Temperature anomaly profile from NASA GISS

Since the total corrections for the US look so similar to the claimed temperature anomaly, it begs the questions as to what the raw data looks like without any corrections.  Does it show the claimed rapidly accelerating warming trend claimed by the AGW advocates?  To determine this I took the raw data from the USHCN graph shown in Figure 1 and plotted this using  a 5 year mean (blue trace), matching the smoothing in the NASA GISS profile shown in Figure 4.  The result is shown in Figure 5.  Please note that while the plot is one that I generated, the data comes directly from the raw data from Figure 1 published by NOAA. 

Figure 5  Plot of raw temperature data versus time (from fig 1) 5 point smoothing. Vertical axis degrees Fahrenheit.  Red line is a linear trend line. Green line is a 2nd order (parabolic) trend line. 

Clearly the shape of this graph bears no similarity at all to the graph shown in Figure 4.  The graph does not even remotely correlate to the shape of the CO2 versus time graph.  The warming was greatest in the 1930’s before CO2 started to rise rapidly.  The rate of rise in 1920, the early 1930’s and the early 1950’s is significantly greater than anything in the last 30 years.  Despite the rapid rise in CO2 since 1960, the 1970’s to early 1980’s was the time of the global cooling scare and looking at the graph in Figure 5 one can see why (almost 2F cooling over 50 years). 

A linear least squares trend line, created using the Excel trend line function (Red trace)  shows a small temperature rise of 0.09C per century which is far less than the rise claimed by AGW supporters and clearly of no concern.  However, the data shown in figure 5 bears little if any resemblance to a linear function.  One can always fit a linear trend line to any data but that does not mean the fitted line has any significance.  For example, if instead I fit a second order trend line (a parabolic) the result is extremely different.  That suggests a temperature peak around 1950 with an underlying cooling trend since.  Which trend line is the more significant one?  If there was really a strong underlying linear rise over the time period it should have shown up in the 2nd order trend line as well.  This suggests that it is questionable whether any relevant underlying trend can be determined from the data.

It would appear that the temperature rise profile claimed by the adjusted data is largely if not entirely an artefact arising from the adjustments applied (as shown in Figure 3), not from the experimental data record.  In fact, the raw data does not in any way support the AGW theory. 

Based on this data, the US temperature data does not correlate with carbon dioxide levels.  The warming over the last 3 decades is completely unremarkable and if present at all is significantly less than occurred in the 1930’s.  It is questionable whether any long term temperature rise over the 20th century can be inferred from the data but if there is any it is far less than claimed by the AGW proponents.

The corrected data from NOAA has been used as evidence of anthropogenic global warming yet it would appear that the rising trend over the 20th century is largely if not entirely an artefact arising from the “corrections” applied to the experimental data, at least in the US, and is not visible in the uncorrected experimental data record. 

This is an extremely serious issue.  It is completely unacceptable, and scientifically meaningless, to claim experimental confirmation of a theory when the confirmation arises from the “corrections” to the raw data rather than from the raw data itself.  This is even more the case if the organisation carrying out the corrections has published material indicating that it supports the theory under discussion.  In any other branch of science that would be treated with profound scepticism if not indeed rejected outright.  I believe the same standards should be applied in this case.

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Notes and Links

Interestingly, there was an earlier version of the NASA GISS data shown in Figure 4 which was originally published at http://www.giss.nasa.gov/data/update/gistemp/graphs/FigD.txt  While this site has now been taken down the data was apparently archived by John Daly and available at his website http://www.john-daly.com/usatemps.006.  The data is presented in tabular form rather than graphical form but appears to be either identical or extremely similar to that shown in my Figure 5.

Other contributions from Michael Hammer can be read here: http://jennifermarohasy.com/blog/author/michael-hammer/
[scroll down, click on the title for the full article]

Ross McKitrick, Ph.D. – Quantifying the Influence of Anthropogenic Surface Processes on Gridded Global Climate Data
http://www.heartland.org/events/NewYork08/newyork2008-video.html

Anthony Watts – http://wattsupwiththat.com/

Urban Heat Island versus Global Warming – A Study of One Region
By Michael Hammer

CITIES represent concentrations of commerce and energy use.  This energy release raises the temperatures in the immediate vicinity.  Cities are also areas where there is intense development with extensive masonry constructions, skyscrapers, paved surfaces and little vegetation.

Large masses of masonry and paving store heat during the day and release it at night keeping the night time minimum temperatures significantly higher than they would otherwise be.   As a result, cities are usually significantly warmer than nearby rural areas, especially at night.  This is termed the urban heat island effect or UHI and it can be very large.  For large cities such as New York or Tokyo, the UHI has been reported as raising minimum temperatures by up to 6-8C.  Even more modest cities like Melbourne show very significant UHI temperature increases.

More significantly, UHI increases as the size of the city increases and as the level of development rises.  Both typically increase with time which means the UHI increases with time.  This is exactly similar to the claimed global warming signature.  

People comment that they have experienced global warming for themselves.  That it is now warmer than it used to be and cite examples such as ice covered puddles in the past which they no longer see today.  If you live in a city (as the majority of people do) that is quite probably true.  However, what you are experiencing is not necessarily global warming but rather the impact of UHI in your immediate environment.  As already stated, the impact can be extremely large – several degrees in large cities.  Nor is it necessarily limited to just the city area.  If there is a prevailing wind and you are living down wind of the city centre then you will be enveloped in the spreading plume of warmth.   So, if we see signs of warming in cities is it UHI or is it evidence of global warming?

UHI has minimal impact on global temperatures because the cities represent such a small fraction of the total area of the total planet.  However, it can have a large impact on the estimation of global temperatures because so many of the measuring stations are in cities.  These stations will show a temperature rise with time which is the sum of any global heating plus the local UHI heating.  If the impact of UHI is not allowed for, the result will be an inflated estimate of global warming.  Even worse, many measurement stations which were originally sited in very reasonable locations are, through later developments, now severely impacted by nearby heat source such as an air conditioner waste heat vent or on top of bitumen paving.  This is yet another factor in addition to UHI adding to the warming bias. 

It is not reasonable to assume that this is allowed for by amalgamating data from a very large number of stations worldwide because many of these sites will be tainted by the same problem.  Even worse, tainted city sites will probably have the most comprehensive records.  Rural sites are more likely to have incomplete records due to the poorer infrastructure.  It is natural to place the greatest reliance on those sites with the most nearly complete data.

The IPCC claimed in the past that one of their corrections to the raw temperature data allows for UHI by applying a linear correction with time amounting to 0.06C per century.  However, in the latest revision to the historical global temperature record even this minimal correction has apparently been eliminated. 

At the same time, measuring stations that have moved from the city to the airport show lower temperatures at their new location and it is claimed that this needs to be compensated for by elevating the airport readings.  This would seem to be clear evidence of bias.  The airport readings are lower because the station has moved away from the city UHI.  Raising the airport readings, while not adding downwards compensation for UHI, results in an overstatement of the amount of warming. It would be more accurate to lower the city readings to match the airport readings rather than vice versa.
 
It is interesting to explore this issue by looking at the temperature record for the state I live in – Victoria, Australia.  The data presented below comes from the Australian Bureau of Meteorology data base published on their website www.bom.gov.au .  The annual average maximum and minimum temperatures have been used and it is worth noting that all these numbers are averages over 30 years so they reasonably reflect climate rather than weather.
 
Starting with Melbourne city centre the data is as shown in Table 1.

This data shows clear signs of warming – 1.7C since 1861 in the minimum temperatures.  Furthermore, the warming is far from linear.  Over the first 40 years the minimums rose 0.5C while over the last 40 years they rose 1.5C.  The maximiums were steady over the first 40 years yet rose 0.4 C over the last 40.  This pattern is extremely similar to the pattern of global warming claimed by AGW proponents.   However are we seeing global warming or increasing UHI?

We could differentiate by looking at temperature records from locations which are nearby by not in the city centre.  Since these would still be in metropolitan Melbourne, some UHI could be expected but it should be less.  Unfortunately the Bureau does not list any complete temperature records for nearby locations (exactly the incomplete record problem I mentioned earlier).  However the Bureau does list some data for several Melbourne suburbs and these are useful comparisons. 

Table 2 shows the minimum and maximum temperatures for various locations along with distance and direction from the city centre.

The thing that immediately stands out is that the latest temperatures from all of these sites is very close to the temperatures for Melbourne city centre in the late 19th century: 9.5 minimum and 19.7 maximum.  These sites are all reasonably close to Melbourne central and cover essentially all directions.  It is hard to believe that they were all cooler than Melbourne central in the 19th century.  Nothing in Melbourne’s topography would suggest that.

Only 3 sites have enough data to form any opinion about temperature trends and these all show some increase but far less than the city centre which is what one might expect from UHI.

We could get a stronger confirmation by looking at some site in regional Victoria.  These are likely to show much less UHI since the population centres are far smaller.  Again one is hampered by the lack of comprehensive data for most locations but there are a few sites for which the Bureau gives reasonably comprehensive data.  These are shown in table 3.

The data for Ballarat, Alexandra and Mildura suggest no temperature rise at all over the measurement period and especially (Ballarat and Mildura) over the last 3 decades.  Horsham data suggests some temperature rise early in the century but if anything cooling over the last 3 decades.  Cape Otway is questionable, there is an 0.7C rise in minimums but a 2.1C fall in the maximums most of which occurred in the early part of the century before the rapid rise in carbon dioxide. The last 3 decades have seen a return to the temperatures of the 1920’s.

Overall one would have to say the Bureau data suggests no significant warming over the last century and in particular the last 3 decades in Victoria.  On the other hand it does show significant UHI.  Consider that an increase of 1.5C in the minimums for Melbourne over the last 3 decades corresponds to 5C per century.  Averaging the minimum and maximum readings yields a rise from 14.7C to 15.7C over 30 years equating to 3.3C per century and Melbourne is far from the worst city in the world for UHI.  Look also at how non linear the UHI rise really is.  Compare that with a linear allowance of 0.06C per century.  For that to be appropriate it would mean that only 1 in 50 sites is showing the same degree of UHI as does Melbourne and the other 49 show no UHI at all, even then the linear allowance is not correct.

The data analysed here is real, high quality, data from Australia’s premier weather/climate organisation. It is completely at odds with the claims of about 0.6C of warming over the 20th century predominantly in the last 3- 4 decades.  Is Victoria really so anomalous or are the AGW claims questionable?

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Michael Hammer graduated with a Bachelor of Engineering Science and Master of Engineering Science from Melbourne University. Since 1976 he has been working in the field of spectroscopy with the last 25 years devoted to full time research for a large multinational spectroscopy company.

Other articles by Michael Hammer can be found here: http://jennifermarohasy.com/blog/author/michael-hammer/ 

The picture was taken in Melbourne in 2008 by Jennifer Marohasy.

Mr Hammer gives detailed instructions and formulae to enter for his DIY climate change model.  The model then calculates the temperature rise from carbon dioxide plus water vapour forcing and allows for the time constant in the system.  

A temperature rise by 2070 of 3C for a business as usual scenario, however, gives model output that is not compatible with what we know of past climates.   So, what is wrong with Mr Hammer’s model?

A SIMPLE MODEL OF THE IMPACT OF CARBON DIOXIDE ON GLOBAL TEMPERATURE
By Michael Hammer

The basic claim of the anthropogenic global warming theory is that rising carbon dioxide levels increase the retained energy and thus causes the surface of the Earth to warm.  A further claim is that this warming in turn causes water vapour concentrations in the atmosphere to rise causing even more energy retention in a positive feedback loop.

The relationship between concentration and energy retention is very widely accepted to be logarithmic in nature.  Thus the additional forcing from carbon dioxide is proportional to the logarithm of the concentration change.  In the case of water vapour the relationship is also logarithmic but the relationship between temperature and concentration is exponential.  Thus the relationship between temperature and additional water vapour forcing is the logarithm of an exponential which is linear.

A third point of significance is the claim that the ocean has enormous thermal mass and that this imposes a long time constant on temperature changes.  Since the  water vapour level depends on current temperature this time constant also affects the water vapour feedback. 

It is easy to incorporate these claims into a simple model as shown here, click on the image for a better/clearer and larger view.

IPCC in their 4th assessment report claimed that the increase from 280 to 390 ppm had increased direct forcing by 1.77 watts /m².  This translates to 3.7 watts /m² per doubling.   Thus the forcing from carbon dioxide becomes;

Forcing = 3.7 * log (current CO2 level/280)/log(2) which simplifies to
Forcing  = 12.3 * log (current CO2 level/280)
This is the equation defining the first box.

IPCC also claim the direct effect of doubling CO2 is a 1 degree increase in temperature hence the climate sensitivity is 1/3.7 C per watt or 0.27 C per watt.

This is the climate sensitivity term.

Dressler has recently claimed the water vapour forcing is 2 watts /m² / C  however this does not include cloud feedback.  To include that we will have to make some estimate of this value so this becomes a parameter we adjust in our model.

  The general form of the equation for a simple time constant is

 New output = K* new input + (1-K)* old output  where K = 1/time constant.

Technically this is known as an infinite impulse response digital filter.  It is probably not obvious why this should give a time constant but rather than explain filter theory here, those interested are urged to try the equation for themselves and confirm that it does indeed give a response of the form  (1- e^{-time/time constant}). 

The time constant is also not known with any precision so again we will have to make some estimate.  A second adjustable parameter in our model.

Mauna Loa data gives the carbon dioxide levels for the period from 1959 to 2008 and this conforms extremely well to the equation

CO2 concentration for year X = 0.012029X ² – 46.287X + 44828

Where X is the year starting at 1959

Because X is very large the equation is very sensitive and does require the number of decimal places given for coefficients to give the correct answer.  A less sensitive equation giving the same answer is

 CO2 concentration = 0.012 * X² + 0.843 * X + 315.2
 Where X = (year – 1959)

These equations predict that carbon dioxide will reach 560 ppm in 2071 which is exactly in line with IPCC claims.

The model can be created and run on an Excell spreadsheet.  Each column gives a different parameter as outlined below.  Successive rows gives results for successive years and we will use 111 rows to cover the years 1959 to 2070.  Since we have two parameters we can adjust we will enter these parameters in cells A1 and A2 as outlined below

Set A1 to the estimate of water vapour feedback coefficient (value entered by modeller)

Set A2 to the estimated time constant (value entered by modeller)
Set B2 = 1/A2  giving the value K from above

Then starting in row 4
A4 = 1959  (the year) incrementing by 1 for each row downwards  ie: set
A5 = A4 +1

B4 = 0.012 * (A4-1959)^2 + 0.843 * (A4-1959) + 315.2  the carbon dioxide level for that year using the above (less sensitive) formula

C4=  12.3 * log ( B4/280)  the CO2 forcing function for that year

D4 = C4 + $A$1 * F3   the total forcing function including water.  Column F is the estimate of temperature rise for that year

E4 = 0.27 * D4  the total forcing divided by the climate sensitivity

F4 = $B$2*E4 + (1-$B$2)*F3  our time constant.  Each value in column F gives the predicted temperature (above baseline) for the year as specified by the column A value for the same row.

Set F3  = 0 as an initial condition.  This is only to ensure a starting point for the time constant filter.

Now fill down columns B to F from row 4 .  Fill down column A from row 5 (we set A5=A4+1).  Do this for total of 111 rows so that A115 = 2070.

This is our model.  It embodies the IPCC data and should account for both the direct forcing from CO2 and the water vapour feedback effect claimed by IPCC. 

IPCC claim 0.5 C of warming up to 2008 and a further 3C of warming by 2070 for a total of 3.5C above 1900 temperatures.

Each change to A1 or A2 will automatically run the model giving the new temperature predictions.  Try first a water vapour feedback value of 2 watts/m² / C as claimed by Dressler (A1=2).   Adjust A2 to match the 0.5C rise in 2008 (I found a time constant of around 20 years ie: A2=20).  Note the total rise in 2070 – about  1.42C or 0.92C above today’s temperatures.  I could not find any choice of time constant which gave 0.5C in 2008 and 3.5C in 2070 (3C rise above 2008 value).

In order to fit both the 2008 claim and 2070 prediction it is necessary to increase the water vapour positive feedback coefficient to around 7 watts/m2 / C with a time constant of around 45 years.  However, there is a problem with such a scenario.  It means a 1C rise in temperature causes water vapour feedback to increase retained heat by 7 watts/m².    For a temperature sensitivity of 3.7 watts/m² / C that implies a further rise of 1.9C.  This is almost double the positive feedback needed for thermal runaway even without any external forcing at all.  Clearly, if that were the case, the climate we have had over the last several million years would have been impossible.  It would have boiled the oceans billions of years ago, irrespective of carbon dioxide levels.

If as many predict, cloud feedback is negative and possibly strongly negative, say -2 watts/m² /C or more, then a1 = 0 or negative.  Even with a very short time constant a value of A1 = 0 gives a maximum temperature rise by 2008 of 0.45C and by 2070 a further 0.53C.  Still stronger cloud feedback reduces these numbers even further.  Programming this model only takes a few minutes, I urge people to do that and explore the range of outputs.

The model suggests that a temperature rise by 2070 of 3C for a business as usual scenario is not compatible with a past climate that has been stable enough for life to have continued to flourish.  Question, where is the error in this model?

For those tempted to dismiss this on the basis that the model is too simple, consider first what such a statement implies.  It suggests that the other factors not considered above in fact account for most of the predicted temperature rise.  If so then the factors that are considered above are minor players.
 
Michael Hammer
Melbourne, Australia

More posts by Michael Hammer here: http://jennifermarohasy.com/blog/author/michael-hammer/

Computers are a tool allowing many calculations to be done extremely rapidly.  If we can describe a system we wish to explore via a set of interrelated equations we can then get a computer to repeatedly solve these equations with a small assumed time increment between each set of solutions and do it quickly. The output describes the future as predicted from the input equations.  This is a computer model.  It is important to remember that the model output is completely and exclusively determined by the information encapsulated in the input equations.  The computer contributes no checking, no additional information and no greater certainly in the output.  It only contributes computational speed.

In cases where the problem domain is comprehensively and accurately understood it is possible to construct a set of equations which very closely mirrors reality and in these cases model outputs can become quite reliable.  Finite element analysis and electronic simulation packages are good examples.  Even here though, a seemingly trivial error in input such as a single small missing factor can often completely invalidate the output and while the models are used extensively for optimisation the final optimised output is usually checked against reality before being accepted.

In cases where understanding of the problem is incomplete and uncertain, a large amount of information needs to be “estimated” or is simply omitted and this very rapidly causes model outputs to become extremely questionable.  Where models are used to explore a theory, very often the input data whether deliberately or not becomes heavily contaminated by the theory.  For example, the researcher is convinced something has a very strong effect so he makes the co-efficient for that parameter large or he is convinced another effect is negligible so he omits it completely.  Such a computer model is little more than the theory itself expressed in a different form. 

Evidence is independent information which can be used to support or destroy a theory.  The sort of model described above is not independent of the theory.  Thus to use the output from this sort of computer model to check a theory is akin to using the theory to prove itself, an invalid circular argument.  On the other hand, comparing the output of such a computer model with reality is equivalent to comparing theory predictions with reality and this can indeed be valid evidence.

It is crucial in evaluating climate models to determine the accuracy and comprehensiveness of the input data.  We can only include factors we know about and since we don’t anywhere near everything there is to know about climate there must be many omissions.  How extensive or significant these omissions are we have no way of knowing.  We also know there are things we do know about that are not included in the models.  For example Henrik Svensmark and Eigil Friis-Christenen from the Danish National Space Centre have carried out research which claims to show a link between rising solar magnetic activity and rising temperature.  In fact, their data shows exceptionally close correlation between cosmic ray flux and global temperature. This is not included in the model inputs.  Even for the causative factors we do know about and include there is still the question of how large is the impact of each factor.  In many cases, for the climate models the coefficients specified for each factor are little better than informed guesses.  For example, at present modellers have assumed that clouds provide positive feedback and that is what is embodied in their input data.  Yet there is significant evidence that cloud feedback could be quite strongly negative.  Thus not only is the magnitude of the co-efficient in question but even the sign is in question.

So what is the impact of leaving out a factor from a model or having a wrong co-efficient?  It could be minor or it could be profound.  Lets take a completely hypothetical example, imagine the Svensmark effect contributed say half the warming of the 20th century and carbon dioxide the other half.  Leaving solar effects out would lead the model to predict half the observed warming.  But scientists adjust their model against known data to get the best possible match.  In this case that would lead to the coefficient for carbon dioxide being increased to twice the correct value implying a very large impact from carbon dioxide.  So adjusted, the model appears to match reality quite well over the limited period from 1975 to 1998.  However what about if solar magnetic activity falls (as now appears to be happening)?  In that case real world data would show a rapid decrease in warming (or even cooling) while the model output continues to show strongly rising temperatures.  In short the two errors cease to cancel and instead add to each other.

Thus, errors or omissions in the input may be masked by compensating errors in coefficients of known factors especially over the data set used to calibrate the model.  However, when the model is used to predict the future and that prediction is later compared with observed reality significant differences start to show up.

So can we ever really know if a model is a reasonable reflection of reality and thus a sound basis for predicting the future?  The only real way is to use the model to predict the future and then with the passage of time compare that prediction with the real world.  The longer the two agree the more faith one can reasonably put in the model.  On the other hand if the two disagree substantially, model credibility is rapidly eroded.  This process is often called model validation.

Such model validation is of course being done all the time on the output from climate models.  The trouble is that the model outputs depart very rapidly and significantly from reality and basically have failed all validation tests.  This would lead one to have no faith in climate models just as the skeptics claim.  AGW advocates respond to that by claiming that the models are focussed on predicting climate not weather.  Weather is about short term events and is highly chaotic in nature.  Climate is about longer term trends and is presumably less chaotic.  Since the comparisons have been over relatively short time scales that explains the mismatch. 

This is an interesting claim.  Nature obeys rigid immutable laws and thus is predictable given sufficiently detailed knowledge.  So the AGW claim really amounts to an admission that the models are incomplete and the lack of detail prevents prediction at the scale of days but may not prevent prediction at the scale of decades or centuries.  Such claims are not entirely unreasonable, averaging eliminates the impact of many complex short term variables, which are hard to quantify ,and thereby much of the chaotic nature of weather.  Climate can be considered as just long term average weather and maybe the models are good enough for reliable long term average predictions.  So it may not be reasonable to expect climate models to predict day to day weather.  In that case, over what time scale does it become reasonable to test the model output?

The northern hemisphere has just gone through a particularly cold severe winter.  I have not seen any suggestions the models predicted that and I am very confident I would have heard loud and clear if they had.  Thus one has to suppose time scales as short as a year are still too short.  Going further, the climate has been cooling now for 7 years and was static for 4 years before that yet the models predicted continuing strong warming over the same period.  This is much more serious for a number of reasons.  Firstly one would very realistically expect a climate model to offer accurate predictions over a time scale of a decade.  The fact that they clearly haven’t begins to suggest they are simply wrong.  This is particularly the case when one considers that the entire AGW hypothesis is based on only 23 years of warming (1975-1998).  Before then the earth was cooling.  If 1 decade is not long enough to differentiate between weather and climate then why would one suppose a bit over 2 decades was so dramatically better that it could form the foundation of the entire AGW hypothesis.  Maybe the period from 1975 to 1998 was also just an example of random chaotic weather.

Another problem is that according to the claims of AGW advocates we are running out of time.  We supposedly don’t have several more decades to see if the model outputs are correct.  Yet today’s data gives no basis what so ever for believing the model outputs represent anything approaching reality or form a reasonable basis for deciding future policy.

An alternative is theoretical analysis from first principles.  This is something which in my own small limited way I am trying to do, as are others.  Another way is to recognise that nature works by rigid adherence to natural law and is thus repeatable.  This means that we can look back through the historical record for similar situations.  If we can find such situations then the response that occurred then is a good indicator of what might happen in our immediate future.   This was exactly  the basis for the original carbon dioxide driven global warming claims.  Vostock Ice core data showed carbon dioxide levels and temperature  rising and falling together.  Cause and effect was claimed, proof that rising carbon dioxide caused temperatures to increase.  Since then, more accurate dating has shown temperature rises or falls 800 years before carbon dioxide responds.  This negates the original claims since it shows that  rising temperature causes rising carbon dioxide not vice versa. 

The most reliable data is of course the most recent.  Over the last century, from 1900 to 1940 we had significant warming with very little increase in carbon dioxide levels.  From 1940 to 1975 we had strong cooling while carbon dioxide levels were increasing rapidly, from 1975 to 1998 both carbon dioxide and temperature were increasing significantly and now from 1998 to 2009 we have cooling while carbon dioxide levels continue to increase.  That represents 40 years of no correlation, 46 years of negative correlation and 23 years of positive correlation.  What possible rationale justifies claiming 23 years of positive correlation proves the AGW theory while ignoring 86 years of negative or zero correlation.

There are many others who are going back further into Earth’s historical record with more skill than I have.  The reports I have seen suggest firstly that current temperatures are in no way abnormal, secondly that current carbon dioxide levels are also in no way abnormal and most importantly that the historical record shows little cause and effect between carbon dioxide level and temperature.  This is significant evidence that needs to be evaluated carefully with a cool unbiased head.  I would also suggest that the theoretical analysis from first principles can give very high quality answers and also warrants more attention.

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Michael Hammer graduated with a Bachelor of Engineering Science and Master of Engineering Science from Melbourne University. Since 1976 he has been working in the field of spectroscopy with the last 25 years devoted to full time research for a large multinational spectroscopy company in Melbourne.

Past contributions at this blog can be found here: http://jennifermarohasy.com/blog/author/michael-hammer/

An interesting theory, but now consider the following scenario;

We know the earth rotates about an axis tilted about 23 degrees relative to the sun.  This is what causes the seasons and what sets the Tropics of Cancer and Capricorn.  Imagine a location on the Tropic of Capricorn (23 degrees south) – say Mackay in Queensland.  In summer the sun is directly overhead – average solar input of around 310 watts/sq meter.  In winter the sun is at maximum elevation 44 degrees – average solar input of around 220 watts/sq meter.  That is a difference summer to winter of about 90 watts/sq meter which, according to Stefan’s law, without any feedbacks would give a temperature difference summer to winter of about 16 degrees.  The amount of positive or amplifying feedback claimed by the IPCC would inflate that about 6 times to more than 90 degrees C, extinguishing all life in Mackay.

Yet according to the long term records from the Bureau of Meteorology, the average summer maximum is 30.3C and the winter maximum  22C, a difference of less than 8 C.  That is not only far less than 90 degrees but is far less than even the 16 degrees predicted in the absence of any feedback at all.  How is that possible?

Maybe the thermal mass of the environment averages out much of the summer winter difference?  Unlikely, consider the significant temperature change between day and night.  If the temperature can change significantly in a few hours it could certainly change profoundly over 6 months.  Also, if the above were the reason one would also expect to see it similarly averaged out in other places.  Yet if we compare Mackay with say Alice Springs, both are at very similar latitudes yet again according to the Bureau of Meteorology long term records the summer maximum in Alice Springs is 36.4 and the winter maximum 19.7C a difference very close to the predicted 16C and double that of Mackay.  Interestingly, not only is the summer winter difference greater at Alice Springs but the annual average is also greater 28C versus 26C and this is despite the fact that Alice Springs is at an elevation of  550metres which should make it 3.5 degrees cooler.

What does stand out at Mackay relative to Alice Springs is that the humidity is much higher in summer than it is in winter.  Higher humidity means more water vapour content in the air and a higher summer temperature increases the water vapour content even further.  But isn’t this going the wrong way?  According to the IPCC, all this extra water vapour should massively increase the retained heat, making the temperature difference between summer and winter much larger not smaller.  It should also raise the average temperature compared to Alice Springs not reduce it.

Well maybe the green house effect acts very slowly taking a long time to become apparent.  Certainly IPCC has suggested exactly that with claimed time constants in decades.  Our senses can give us some insight into that claim.  Step outside any winters evening and you can immediately tell if the sky is cloudy or clear.  I am sure most of you will agree from personal experience that it will be much colder when the sky is clear and a thermometer will confirm it.  This comes about because clouds act exactly like greenhouse gasses, trapping energy radiated from the surface.  Indeed clouds form a significant part of the overall greenhouse effect.  Of course, clouds, unlike green house gases, also have a second effect and that is to reflect incoming solar energy away from Earth (the albedo effect).  Again anyone who has been outside when a cloud comes between them and the sun can testify that the drop in radiant energy is immediately detectable.  What our simple experiments are showing is that green house effects are clearly detectable at a very local level over time scales much less than a day, rather than only over 10’s of years.

So how is it possible that the summer/winter temperature variation at Mackay is so much less than the change in solar input would suggest?  The reason is that water vapour generates lots of feedback effects and many of them are very strongly negative  (feedback that reduces the impact of changes in energy input).  Evaporating water takes a very large amount of energy.  As more water evaporates in the summer it absorbs the necessary energy from the environment reducing the temperature rise.  Greater humidity also leads to more condensation and thus clouds which reflect a larger fraction of the incoming solar energy back out to space and away from Earth’s surface.  It also takes energy to lift the water vapour several kilometres into the atmosphere against earth’s gravity to the altitude where it condenses to form clouds and falls back as rain (after all that is where the energy for hydroelectricity comes from).  The temperature data clearly shows that these negative feedback mechanisms strongly dominate over the slight increase in retained energy with increasing water vapour concentration.

The IPCC temperature rise claims are based on an assumption of strong net positive feedback in our climate system yet natural systems virtually all exhibit strong negative feedback around an equilibrium point.  Negative feedback is the opposite of positive feedback.  It acts to oppose any disturbance acting on a system and seeks to maintain the current equilibrium.  In short it is a stabilising factor whereas positive feedback is a destabilising factor.  Long term stability of any natural system almost guarantees that there is strong negative or stabilising feedback in operation.  The climate, while showing periodic variations, has been stable enough for life to form and flourish for millions of years despite significant changes in forcing over the millennia and this makes it virtually certain that strong negative feedback is in operation.  The fact that IPCC claim a large degree of positive feedback in our climate system suggests there may be a flaw in their theory.

If, as I believe, the net feedback from water vapour is  negative rather than positive then the actual temperature rise by 2070 even with a doubling of carbon dioxide is likely to be less than the half a degree predicted in the absence of feedback, probably no more than 0.2 to 0.3 degrees.

by Michael Hammer
Melbourne, Australia 

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Michael Hammer graduated with a Bachelor of Engineering Science and Master of Engineering Science from Melbourne University. Since 1976 he has been working in the field of spectroscopy with the last 25 years devoted to full time research for a large multinational spectroscopy company.

Some sceptics complain that the GCMs do not realistically simulate climate because there are many processes that can’t be adequately modelled including cloud formation.  Michael Hammer, an engineer who specializes in spectroscopy, is also sceptical of the GCM but his criticism is more fundamental.  In the following paper, using the basic laws of spectroscopy, he shows that a significant portion of energy loss from the Earth’s surface is by direction radiation to space at wavelengths not absorbed by carbon dioxide and other greenhouse gases.    This is in direct contrast to the IPCC explanation that there is low radiation from the Earth’s surface to space and potentially high radiation from the atmosphere to space.

Science is a process of getting it wrong and hopefully learning – on this single issue Michael Hammer and the IPCC can’t both be right.  

AN ANALYSIS OF THE EFFECT OF GREENHOUSE GASES IN THE ATMOSPHERE
By Michael Hammer

1. SUMMARY

Kiehl and Trenberth in 1997 published a global mean energy budget for Earth.  This budget has significant implications for the proposed greenhouse mechanism and indirectly leads to the concept of an equivalent radiation altitude for Earth which changes with greenhouse gas concentrations.  The K&T and similar models form a basis for the global circulation models used in climate science.

This analysis derives a partial global energy budget based on an analysis of the observed atmospheric lapse rate, and basic laws of spectroscopy, which is at considerable variance with the K&T findings.  The differences have significant implications for the greenhouse mechanism and suggest that the concept of an equivalent radiation altitude has no meaning. 

It also suggests that the amount of positive feedback attributed to water vapour by these global circulation models is impossible and thus that the temperature rise postulated from the predicted increase in carbon dioxide concentration is greatly exaggerated.

2. INTRODUCTION

Greenhouse gases in the atmosphere act entirely through radiative processes.  Earth’s net energy balance is also entirely due to radiative processes since a planet in space can only gain or lose energy by this means.  For these reasons, this paper is primarily concerned with an analysis based on radiative effects. 

While this paper specifically mentions the Kiehl & Trenberth model in some detail (since it is the model used by the IPCC), it is recognised that there are other models also used in modelling, for example, the one quoted in “An introduction to Three-Dimensional Climate Modelling” by Warren Washington and Claire Parkinson ISBN 0-935702-52-0 University Science Books.  While they show some differences compared to the K&T model they seem to share the same basic structure of low radiation from the surface to space and high radiation from the atmosphere to space.  This is the dominant issue being questioned and the K&T model is used here as a convenient example.

3. THE ROLE OF CONVECTION AND LATENT HEAT

This paper is primarily concerned with radiative processes.  This should not be taken as denying the role played by convection and latent heat.  Clearly these processes have enormous effect within the troposphere and indeed are a dominant cause of our weather.  They are also extremely significant in distributing heat around the planet and especially in energy transport from the equator to the poles.

Convection and latent heat effects impact on energy loss to space by changing the temperature versus altitude and latitude profiles within the atmosphere.  The variation in height and temperature of the tropopause with latitude is an example of this.  These represent perturbations superimposed on radiative processes.   While their effects are reduced by averaging over the planet, it is acknowledged that the impact does not entirely cancel out because of the non linear relationship between temperature and energy radiated.  Ignoring these effects thus introduces approximations which reduce the precision of the results obtained.

None the less, it is claimed that the mechanisms discussed in this paper are the dominant mechanisms controlling heat loss from this planet and the conclusions following from the analysis are extremely relevant in assessing the impact of green house gases in the atmosphere.

4. SOME BASIC SPECTROSCOPY

If a material absorbs light, one might intuitively expect the amount of light absorbed to be proportional to the concentration of the material, so that doubling the concentration doubles the amount of light absorbed.  This is not the case as can be seen by a simple thought experiment.  Imagine we have a piece of material which absorbs 50% of the light incident on it transmitting the other 50%.  Doubling the concentration of material is exactly equivalent to adding a second identical piece of the material behind the first piece.  The first piece absorbs 50% of the light incident on it transmitting the remaining 50%.  The second piece being identical does exactly the same, absorbing 50% of the light that passed through the first piece and transmitting 50%.  Thus the net light passing through the two pieces is not 0 but 25%.  If we have n identical pieces the transmission will be 0.5ⁿ.

The relationship between concentration and light absorbed is not linear.  Spectroscopists use the term absorbance to define the degree to which a sample absorbs a particular wavelength of light.  Absorbance is defined by  the equations;

Fraction of energy transmitted  =  10 ^{–absorbance}
Fraction of energy absorbed     =  1 – 10 ^{–absorbance}

If a sample has an absorbance of 1, it means that it absorbs 90% of the light incident on it, transmitting the remaining 10%.  The absorbance of a sample is directly and linearly proportional to the amount of absorbing material in the light path (Beers law).  Thus if a particular sample has an absorbance of 1 then doubling the concentration of the absorbing species for the same path length or doubling the path length with the same concentration will change the absorbance to 2.

5. THE SIGNIFICANCE OF EMISSIVITY

All material substances both absorb radiant energy incident on them, and emit radiant energy at a rate dependent on their temperature.   The degree to which they absorb incident energy is often called the absorptivity and the degree to which they emit energy is often called the emissivity.  However from Kirchoff’s law of thermal radiation the emissivity and absorptivity must be equal to each other.

The absorptivity/emissivity is a property of the substance and its form.  A highly polished surface absorbs and emits less energy than a dull surface and a white surface absorbs and emits less energy than a black surface.  What Kirchoff’s law is stating is that absorption of radiant energy and emission of radiant energy are reciprocal processes, a material that does not absorb will also not emit and vice versa.  The same factor governs both to an equal extent.

Most of the atmosphere is made up of nitrogen and oxygen which do not significantly absorb infrared energy because their emissivity in this portion of the electromagnetic spectrum is exceptionally low.  This means they also do not emit significant infrared – they are not greenhouse gases.  Other gases however have a very strong ability to absorb energy at some wavelengths between 4 and 50 microns (the approximate range of emission wavelengths from earth’s surface).  They are the greenhouse gases and the most significant is water vapour followed by carbon dioxide and then methane and ozone.  Because their emissivity is high at the absorption wavelengths and low at other wavelengths they also selectively radiate energy at these same absorption wavelengths.
 
5. AN ANALYSIS OF THE KIEHL AND TRENBERTH MODEL

This model is documented at;

www.cgd.ucar.edu/cas/abstracts/files/kevin1997_1.html
(from Bull Amer. Meteor Soc, 78, 197-208 1997). 

There is an update dated 2008 at;

 chrisclose.wordpress.com/2008/12/10/an-update-to-Kiehl-and-trenberth-1997/ 

both documents specify very similar numbers.  The K&T model (2008 update) specifies the following energy flows all with the units watts/m2.

Incoming solar radiation   341
Reflected solar radiation   102
Energy radiated from earth’s surface  396
Surface radiation absorbed by the atmosphere 356
Energy radiated from surface directly to space  40
Energy emitted by atmosphere to space  169
Energy emitted from clouds to space   30
Energy transported to atmosphere via
Convection and latent heat  of water vapour  97
Solar radiation directly absorbed by atmosphere 78

This data shows that energy input to the atmosphere via radiative processes = 356 + 78 = 434 watts/m².  Energy input via convective processes = 97 watts/m².  Thus energy input to the atmosphere is dominated by radiative processes (82% radiative and 18% convective).

It should also be noted that the global circulation models GCM’s use a concept called the equivalent radiation altitude.  This is a hypothetical altitude from which it is assumed long wave radiation back out to space emanates.  Changes in greenhouse gas concentrations are assumed to change the equivalent radiation altitude.  Changes to this equivalent radiation altitude together with the known lapse rate through the atmosphere are used to calculate changes in surface temperatures.

There is a well known and documented temperature versus altitude data (lapse rate) for Earth’s atmosphere.  This temperature profile is established and maintained by the need for energy balance at every altitude.
 
The lapse rate consists of an almost linear decrease in temperature with altitude from the surface (+14C) to the top of the troposphere – the tropopause (at between 10 – 14 km altitude) where the temperature is between about -60 and   -80 C depending on latitude.  Above the tropopause (in the stratosphere) the temperature rises, again almost linearly, to a maximum of about -20C at an altitude of about 50 km.

The tropopause is thus a cold region sandwiched between warmer regions above and below.  For this situation to be stable (and it is stable), the tropopause must have a way of losing energy to a colder sink – otherwise it would warm up due to energy input from the adjacent regions.  The only colder region available is space itself and the only energy transfer mechanism available is radiative loss.

Thermal emissions from the tropopause will all be in the 5 micron to 50 micron wavelength range (governed by the temperature of the emitter) and can only occur at the characteristic absorption/emission lines of the green house gases.  There is however a problem with this scenario.  Ten percent of Earth’s atmosphere is above the tropopause in the stratosphere and the greenhouse gases in this region would normally absorb the emissions from the tropopause. 

Further, since the air in the stratosphere is warmer, the downwards radiation onto the tropopause would exceed the upwards radiation from it leading to net energy gain not loss.  Yet the tropopause is colder than the stratosphere so it must have a mechanism for losing energy.

A solution to this apparent paradox is that there is an abrupt change in the greenhouse gas composition at the tropopause such that the tropopause can radiate at wavelengths which the stratosphere is not capable of absorbing.  The tropopause represents a temperature inversion which greatly inhibits convection and when that is coupled with the fact that water vapour is carried up from Earth’s surface principally by convection, one would immediately suspect water vapour as the variable component – high concentration in the troposphere and low concentration in the stratosphere.  This suspicion is confirmed by the two quotes taken from the following link;

http://www.metoffice.gov.uk/education/secondary/teachers/atmosphere.html

“The atmosphere is well mixed below 100 km, and apart from its highly variable water vapour and ozone contents, its composition is as shown below”

“As well as a noticeable change in temperature, the move from the troposphere into the stratosphere is also marked by an abrupt change in the concentrations of the variable trace constituents. Water vapour decreases sharply, whilst ozone concentrations increase. These strong contrasts in concentrations are a reflection of little mixing between the moist, ozone-poor troposphere and the dry, ozone-rich stratosphere.”

This information explains how the tropopause can remain colder than the air above and below.  It also explains why temperature rises in the stratosphere.  Ozone is a strong absorber of ultraviolet energy from the sun and such absorption will warm the stratosphere.  The energy gained will be re-emitted as thermal infrared energy at the absorption/emission lines of the greenhouse gases present, mainly CO2 and methane.  The energy absorption by ozone is greatest at around 50 km altitude which is why the temperature peaks at this point and the temperature profile down to the tropopause is essentially an upside down version of what happens in the troposphere.  

It should be noted that the tropopause radiates at all wavelengths corresponding to greenhouse gas absorption/emission lines but those greenhouse gases present in the stratosphere also radiate back down onto the tropopause and since they are warmer, the downward radiation exceeds the upwards radiation.  Thus the only net energy loss from the tropopause occurs at the wavelengths corresponding the water vapour absorption/emission lines.

Since the tropopause can radiate relatively strongly at the water vapour absorption/emission lines (strongly enough to keep itself cold) it follows that the emissivity at these lines must be relatively high which also means that the absorptivity is also high for the reasons discussed in the earlier section titled “the significance of emissivity”.  Couple that with the fact that water vapour concentration is higher at lower altitudes and it follows that the tropopause (possibly together with a small region immediately below it) will be opaque to radiation at the water vapour absorption/emission lines.  That means that emission from lower in the atmosphere directly to space becomes impossible at the water vapour absorption/emission lines because the energy is re-absorbed by the region at or immediately below the tropopause.

The implication is that thermal energy from the surface can escape to space in only two ways.  First, by surface emission escaping directly to space at wavelengths which the greenhouse gases do not absorb.  Second, by emission from the tropopause at wavelengths corresponding to the water vapour absorption/emission lines. 

It is possible to gain at least some idea of the relative magnitude of these two emission mechanisms.

Ozone absorbs essentially all radiation below 290 nanometers (UVC radiation) .  It further absorbs approximately 90% of radiation between 290 and 320 nanometers (UVB radiation) plus a decreasing amount of UVA radiation up to about 350 nm.  The amount incoming solar radiation in these wavelength ranges can be determined by solving Planck’s equation for a 5800K emitter (scaled to 341 watts/m² total) at wavelength increments of, say, 5 nanometers and then numerically integrating over each wavelength range.  The result is 8.3 watts/m² for UVC, 6.3 watts/m² for UVB and 8.3 watts/m² for UVA up to 350 nm.  The total absorbed by ozone is 8.3 + 0.9*6.3 + 0.5*8.3 = 18.1 watts/m² .  It should be noted that ozone absorption peaks at around 50 km altitude which should be above most of the albedo effects.

The ultraviolet energy absorbed by ozone is not capable of being re-emitted at the same wavelengths because the gas is too cold.  Instead it will be re-emitted as long wave radiation at the CO2 and methane absorption/emission lines.  For a maximum stratosphere temperature of about -20C the black body radiation between 14 and 15.5 microns is 17.5 watts/m2 which is in reasonable agreement with the calculated energy absorption by ozone.  

The remaining incoming solar energy is either reflected back out to space (due to Earth’s albedo) or is absorbed lower in the atmosphere or at the surface.

The overall albedo of Earth is 0.3 so 341 * 0.3 = 102 watts/m² is reflected back to space leaving  341 – 102 – 18.1 = 221 watts/m² to be absorbed at or below the tropopause.  All of this must be radiated back out to space as long wavelength radiation if thermal balance is to be maintained.

There are many water vapour absorption lines below 8 microns.  Between 14 microns and 15.5 microns carbon dioxide absorbs strongly and above 15.5 microns water vapour again has many absorption lines.  Between 8 and 14 microns there is a window where the atmosphere offers little if any impediment to direct radiation to space from the surface. 

Retrieved from http://en.wikipedia.org/wiki/Atmospheric_windows

“The atmospheric window refers to those parts of the electromagnetic spectrum that are, with the earth’s atmosphere in its natural state, not absorbed at all. One atmospheric window lies approximately at wavelengths of infrared radiation between 8 and 13 or 14 micrometres[1].”
[1]   ISBN 0521339561 Houghton, J.T. The Physics of Atmospheres

And;
Retrieved from “http://en.wikipedia.org/wiki/Water_absorption”
Cotton, William (2006). Human Impacts on Weather and Climate. Cambridge: Cambridge University Press. ISBN 0521840864. “Little absorption is evident in the region called the atmospheric window between 8 and 14 μm”
Solving Planck’s equation on a spreadsheet for a 288 K source at wavelength increments of 0.2 microns and then numerically integrating yields energies as follows;

Below 8 microns     45 watts/m²
8 microns to 14 microns 143 watts/m²
14 microns to 15.5 microns   28 watts/m²
Above 15.5 microns  174 watts/m²

Interestingly, the energy radiated by Earth’s surface over the strong carbon dioxide absorption band between 14 and 15.5 microns is 28 watts/m² which is in good agreement with the value typically claimed for the energy retained by carbon dioxide.

It is also important to note that the regions below 8 microns and above 15.5 microns are not totally opaque.  There are multiple absorption lines but there are gaps between these lines where substantial energy can escape to space, especially in the wavelength region above 15.5 microns.  If this were not the case, line broadening through increasing concentrations of green house gases would have little if any impact on incremental energy retention (discussed in more detail later).  This substantially adds to the 143 watts/m² calculated above.

6. THE IMPACT OF CLOUDS

The above numbers do not allow for the impact of clouds.  Clouds are droplets of liquid water and in the thermal infrared, water has an emissivity very close to 1 (hence the high emissivity of earth’s surface at these wavelengths). It is therefore reasonable to expect clouds to act as grey or black body absorbers with an emissivity approaching 1 as the clouds get thicker.  This would mean that thick clouds would absorb all the thermal infrared energy incident on them and in turn emit energy as a black body from the cloud top.  Since the cloud top is colder than the surface, the energy emitted over the atmospheric window will be lower.  How much lower is easy to calculate by integration of Planck’s law given the known atmospheric lapse rate of 6.5C per kilometer and the height of the cloud.
 
Thin clouds with an emissivity less than 1 would have a smaller impact.

Only a portion of the Earth’s surface at any given time is cloud covered and much of the dense cloud is low altitude cloud, thus a reasonable estimate for the Earth as a whole would be that clouds reduce the energy escaping to space in the atmospheric window by no more than about 15% to 20%.

The radiation from the cloud tops is admittedly no longer radiation directly from earth’s surface but it is still black body radiation and the fraction in the atmospheric window (and in the gaps between the lines at other wavelengths) can still escape directly to space without impediment from green house gas effects.  Thus, while clouds do cause some attenuation, their action does not negate the basis of the hypothesis being presented in this paper.

7. ENERGY RADIATION FROM THE TROPOPAUSE

Earlier discussion suggested that the tropopause can only generate net radiation to space at the water vapour wavelengths which means below 8 microns and above 15.5 microns.

Again solving and numerically integrating Planck’s equation over these wavelengths for a temperature of 213K (-60C) yields a total energy of 82 watts/m ².  Surface/cloud plus tropopause radiation must equal 221 watts/m² implying the net energy radiated from the surface and cloud tops would have to be about 139 watts/m².  However the presence of gaps between emission lines suggests the tropopause radiation will be somewhat lower and the surface/cloud top radiation higher.  When this is taken into account the numbers are entirely consistent with earlier calculations.  Purely as a hypothetical example, if we assume cloud cover causes 15% attenuation and 17% of the energy in the below 8 micron and above 15.5 micron ranges is not absorbed we get;

Surface/cloud emission = 0.85 * ( 143+0.17*(45+174)) = 153 watts/m²
Tropopause emission = 0.83 * 82                                  =   68 watts/m²
Total emission                                                              = 221 watts/m²
 
Water vapour also has very strong absorption bands in the NIR centred at 1.45 microns, 1.95 microns 2.5 microns plus other weaker lines.  There is a significant amount of incident solar energy at these wavelengths and that energy will be rapidly absorbed once water vapour concentration becomes appreciable, which means at or close to the tropopause.  As a consequence, much of the energy emitted from the tropopause is not energy that has percolated up from the surface but rather energy absorbed directly from incoming solar radiation at or near the tropopause.

8. IMPLICATIONS OF THIS ANALYSIS FOR THE KIEHL TRENBERTH MODEL

The global mean energy budget claimed by K&T suggests the vast majority of the energy radiation to space comes from the atmosphere.  It paints a picture of an atmosphere which absorbs almost all surface emissions and then re-radiates a variable amount of this to space.  This implies that slight changes in concentration can vary the fraction emitted thus changing temperatures.  Hence the concept of an equivalent emission altitude and the prediction of a high sensitivity to changes in greenhouse gas concentrations.

The picture emerging from this analysis suggests the opposite, with most of the energy reaching the ground being radiated directly back to space from the surface or cloud tops in the windows between the atmospheric absorption lines.  It implies an atmosphere which blocks almost all the energy radiation from the surface to space at the GHG wavelengths while barely impeding energy radiation to space at other wavelengths.  In this scenario, changing GHG concentrations can only affect warming via line broadening. 

The concept of an equivalent emission altitude is not needed and indeed has no meaning in this scenario.  Energy loss to space from Earth’s surface can only occur directly from the surface/cloud tops or from the tropopause although the relative magnitude of each could change with changing greenhouse gas concentrations.

The very large difference in surface versus atmospheric emission levels predicted from this analysis compared to the Kiehl Trenberth model calls into question the basis of global circulation models based on K&T or other similar data.  It also calls into question the reliability of the output from such models and in the predictions flowing from those models.

It is possible to reinforce this finding by a completely different analysis which is shown below.

9. A SPECTRSCOPIC ANALYSIS OF GREEN HOUSE GAS ABSORPTION

Imagine a single greenhouse gas which absorbs energy at only one specific wavelength.  As the greenhouse gas absorbs energy it heats up until the energy it emits equals the energy it absorbs.  Because it only has significant emissivity at the absorption wavelength the energy will be re-emitted at this wavelength. However, the emitted energy will be emitted in all directions.  Since the atmosphere is a thin continuous shell covering the entire earth it has only two surfaces, an inner surface adjacent the planet itself and an outer surface adjacent to space.  Radiation leaves the atmosphere through one of these two surfaces.  Thus, radiating in all directions in effect means 50% will be emitted towards space and 50% returned to the planetary surface.

A very simplistic first approximation would be to say if the absorbance of the gas column is N then the gas absorbs 1- 10-N per unit of the incident energy and 50% of this is returned to the earth’s surface giving an effective energy retention of

Energy retained = 0.5*(1-10-N).  (1)

That may be correct when N is very small (<<1) but is grossly in error for higher absorbances because it ignores repeated re-absorption and re-emission of energy within the gas column.

As the absorbance of the gas column rises, repeated absorption and re-emission becomes very significant.  In this context we must again remember that the same emissivity covers both absorption and emission so that emitted energy will be predominantly at the absorption wavelengths thus facilitating repeated absorption and re-emission.  By the time the atmospheric absorbance has reached 1,   90% of the energy at the absorption wavelengths is being absorbed which also means that much of the energy emitted by the atmosphere will be re-absorbed within the atmosphere, possibly going through several absorption re-emission cycles within the atmosphere.
 
To analyse this situation, imagine we treat the entire gas column as stack of 1 absorbance layers.  As a first order approximation, assume that each layer absorbs all the energy it receives from above or below and maintains itself in thermal equilibrium by emitting an equal amount of energy, half towards the surface and half away from the surface.  The result is shown diagrammatically for an N absorbance atmosphere.

Where

E₁ is the total energy absorbed by layer 1
E₂ is the total energy absorbed by layer
E_n is the total energy absorbed by layer n
E_N is the total energy absorbed by layer N

Equations (2) to (5) are obtained by summing energy into each layer.

Substituting (2) into (3) gives E₂ = 2 * E₃ / 3 (6)
Rewriting (4) with n=3 and then
Substituting (6) into it gives E3 = 3 * E₄ / 4 (7)

In general for the nth layer E_n = n/(n+1) * E_n+1 (8)
Replacing n by n-1 in (8) gives E_n-1 = (n-1)/n * E_n (9)

 Since equn (9) holds for any n we can replace n by N to get
From (9) EN-1 = N-1/N * EN
Substituting into (5) gives EN = (N-1)/2N * EN +1
And rearranging EN = 2N/(N+1) (10)

If we expand (8) as a series we get;
E_n = n/n+1 * E_n+1
     = n/n+1 * n+1/n+2 * E_n+2
     = (n/n+1) * (n+1/n+2) * (n+2/n+3) *…* (N-1/N) * E_N

Cancelling common terms gives En = n/N * E_N (11)

Substituting for EN from equn (10) gives
En = 2n/(N+1)

The energy radiated away to space is 0.5 * E₁ = 1/(N+1)    (12)
The energy returned to the earths surface is 0.5* E_N = N/(N+1)   (13)

 Equations 1 and 13 are plotted below. Interestingly, even below 1 absorbance equation 13 gives essentially the same result as equation 1 and can thus be treated as a reasonable approximation over the entire absorbance range.

 10. INTERPRETATION OF THESE RESULTS

Heinz Hug (http://www.john-daly.com/artifact.htm) has measured the absorbance of the atmospheric column of CO2 at 280 ppm and reports a total absorbance in excess of 2000. The above calculation suggests that the fraction of energy at the absorbing wavelength which is radiated to space is only 1/2001 or 0.05%. This is in agreement with the analysis derived from the temperature versus altitude profile.

In the case of water vapour, it is only necessary to note that Fourier transform infrared spectrometers with an optical path length of well under 1 meter need to be either purged with dry gas or packed with desiccant and sealed in order to avoid unacceptably high energy loss from water vapour absorption and that the troposphere is 10,000 meters thick (more than 10,000 times the path length) to realise that a similar situation exists for water vapour.

11. THE IMPACT OF LINE BROADENING

Both of the above analyses suggest that greenhouse gases almost totally block energy loss to space at their absorption/emission wavelengths. This implies that significant energy loss from the surface or cloud tops is by direct radiation to space at wavelengths where the greenhouse gases do not absorb. Given that, one might be tempted to conclude that since the greenhouse gases already absorb everything they can, further increases in concentration should have no impact. This is not the case because of an effect known as line broadening.

The absorption versus wavelength profile for a green house gas line does not have infinitely steep sides. As concentration rises the line centre will saturate but absorption out in the wings of the line are not yet saturated. Further increases in concentration have no impact on the behaviour at the line centre but do slightly increase absorption out in the wings. In effect the line slowly broadens as the concentration increases. It is this effect that gives rise to the well known logarithmic relationship between concentration and energy absorbed.

In fact, the unsaturated lines of greenhouse gases are so narrow and therefore absorb so little energy, that the overall impact of a greenhouse gas does not become significant until the line centres saturate and the line start to broaden. This means that all greenhouse gases of significance are likely to display the logarithmic relationship between concentration and energy absorbed.

As the lines broaden they further constrict the wavelengths at which radiation can escape from Earth’s surface to space. For the same energy to be emitted from a narrower window implies higher energy density at the remaining wavelengths which implies a higher surface temperature.

In the case of carbon dioxide, the IPCC in their fourth assessment report stated that the increase from 280ppm to 390 ppm increased energy retained by 1.77 watts/m². Applying the logarithmic relationship;

1.77 = n * log (390/280)
from which it follows that n = 12.3.

The increase from 390 ppm to 560 ppm (2070 projection from IPCC 4^th assessment report) would increase retained energy by 12.3 * log (560/390) = 1.93 watts/m² . Applying Stefan’s law at 288 kelvin (+14C) we find that each degree rise in temperature takes 5.4 watts/m² . Thus the direct effect of the rise in carbon dioxide is 1.93/5.4 = 0.36C.

IPCC inflates this to about 3C by assuming massive positive feedback from water vapour. A 3C rise implies an additional 16.2 watts/m² of which 16.2 – 1.93 or 14.3 watts/m² must be coming from water vapour. The CRC handbook of chemistry and physics shows that water vapour content at constant humidity rises exponentially with temperature roughly doubling for each 10 K rise in temperature. This can be expressed as

water vapour concentration is proportional to 10 ^{(temperature/33.2)}

A 3C rise in temperature increases water vapour concentration by 10 ^(3/33.2) = 1.23 (23%). Applying the same calculations as for carbon dioxide

14.3 = m * log (1.23) from which m = 159 and each doubling of water vapour changes energy retained by 159 * log(2) = 48 watts/m² .

The earlier Planck’s law calculations suggested water vapour at +14C retains at most 219 watts/m2 (in fact less when one allows for gaps between absorption lines). Coupling that with the CRC handbook data that water vapour doubles or halves for each 10C change in temperature, a sensitivity of 48 watts/m2 per doubling implies the following;

14C energy absorbed/emitted <219 watts/m²
+4C energy absorbed/emitted < 171 watts/m²
-6C energy absorbed/emitted < 123 watts/m²
-16C energy absorbed/emitted < 75 watts/m²
-26C energy absorbed/emitted < 27 watts/m²
-36C energy absorbed/emitted      0 watts/m²

This is completely incompatible with water vapour radiating substantial amounts of energy at -60C which is necessary to explain a cold tropopause.

12. CONCLUSIONS

Both the analysis from basic spectroscopy and the analysis based on atmospheric lapse rates give similar results and imply that greenhouse gases almost totally block energy loss to space at their absorption/emission wavelengths. That in turn suggests that a very significant portion of the energy loss from Earth’s surface is by direct radiation to space at wavelengths where the greenhouse gases do not absorb.

This is in conflict with the Kiehl & Trenberth model and other similar models which suggest that most of the energy loss to space is from the atmosphere. If the atmosphere emits little energy, and then largely from the tropopause and stratopause, the concept of an equivalent radiation altitude has no meaning. Further, the analysis suggests that most of the radiative energy loss from the atmosphere to space is re-radiation of solar energy absorbed high up in the atmosphere.

Surface temperature will increase with increasing greenhouse gas concentrations due to line broadening. The direct effect of carbon dioxide (in the absence of any feedbacks) using the IPCC quoted sensitivity and their postulated rise in carbon dioxide from 390 ppm to 560 ppm will contribute 0.4 degrees by 2070. The IPCC claim that positive feedback from water vapour will increase that to about 3C would imply a sensitivity of 48 watts/m2 per doubling in water vapour concentration. Such a high sensitivity is not compatible with the observed atmospheric temperature versus altitude profile.

It should be noted that this analysis does not predict no radiation to space at the greenhouse gas absorption lines. There is still energy at these absorption lines emitted to space. For the well mixed greenhouse gases such as CO2 and CH4 this energy largely emanates from the stratosphere and is powered significantly by UV absorption of incoming solar radiation by ozone plus some absorption of surface radiation at 9.6 micron . In the case of water vapour, the energy emanates from near the tropopause and is powered significantly by near infrared absorption of incoming solar radiation by water vapour.

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Michael Hammer graduated with a Bachelor of Engineering Science and Master of Engineering Science from Melbourne University. Since 1976 he has been working in the field of spectroscopy with the last 25 years devoted to full time research for a large multinational spectroscopy company.