Arguably the biggest challenge  this century will be to better understand  the Earth’s climate and how man effects it – so called Anthropogenic Global Warming (AGW). The basic science of climate is actually pretty  straightforward, however the devil is in the details. All the fierce arguments about AGW are concentrated around just one thing – climate feedbacks. The urgent calls for immediate action to “tackle” climate change are  based on the assumption that feedbacks will amplify by a factor of  ~3 an otherwise moderate temperature rise resulting from  a doubling of CO2 levels.   We also  know  that large natural variations in climate have occurred in the past and will continue to occur in the future, in particular regular ice ages for the last 3 million years. A new glaciation cycle would be catastrophic for mankind. What causes them and could  AGW actually delay or even offset the next ice age ?

Solar Power (see footnote)

The sun lies lies 1.4958×108 km from Earth and radiates energy to Earth. The sun’s surface temperature is 5,770K [(ref. Kopp & Lean 2011)] and its radius R is 6.955×10^5 km. Therefore the total radiation emitted by the sun (applying Stefan Boltzman’s law) is is 4*PI*R^2*sigmaT^4, which works out at  3.8205*10^26 watts.  The amount of radiation reaching the Earth at is 4*PI*RE^2(sphere at average Earth’s orbit radius RE) * rad^2/4 (ratio of circular cross-section of Earth to it’s surface area).   Although the Earth has an eliptical orbit, it works out that  the average annual radiation is almost exactly that of a circular orbit. The solar constant S0 is the incident solar radiation per m2 just outside the earth’s atmosphere and is also measured by satellite. This can be calculated using (R^2*sigmaT^4)/(RE^2)  which works out at  1361 watts/m2. When  averaged over the Earth’s surface (4piRE^2)/(piRE^2)  works out at  340 joules/m2/s-1.

The average global temperature of the Earth’s surface  is then determined by the effective black body temperature of the Earth observed from space. There are two main effects which need to be understood to estimate the  energy balance.

  1. The Albedo is the fraction of radiation which is reflected back into space by the Earth (from ice, clouds, land surfaces etc.) This is roughly 0.3 so that approximately just 239 watts/m2 is absorbed by the Earth’s surface which warms up and then radiates infrared heat according to Stefan Boltzman’s law.
  2. The greenhouse effect – g . We define g to be that fraction of IR radiation emitted from the Earth’s surface(SU) that is absorbed by the atmosphere(OLR-SU) (see below).  Therefore the outgoing radiation to space is (1-g)SU.  g has been measured to be approximately 1/3 which then implies a surface temperature Tsurf  given by  overall energy balance 2/3*sigma*Tsurf^4 =  239.4.  So Tsurf = 282 deg.C   The measured average Tsurf actually turns out to be  288 deg.C, but this back of the envelope calculation shows that the greenhouse effect raises the surface temperature from about 255 deg.C 

Greenhouse effect

Greenhouse gases absorb infrared photons from the surface , gain some kinetic energy and  re-radiate photons in  random directions. Some photons return to the surface, others re-interact diffusing energy up through the troposphere until it escapes to space. The main greenhouse gasses are water vapor H2O and Carbon Dioxide CO2.  Globally somewhere between 70 and 90% of the greenhouse effect is due to water vapor, but it varies rapidly on an hourly basis. CO2 on the other hand has a long lifetime and varies only gradually. For example, In the desert there is little water vapor and temperatures can fall to freezing overnight as infrared heat escapes to space.

The atmosphere is opaque to CO2 in the sense that the mean free path for infrared photons in the absorption bands is of the order of meters at the Earth’s surface . The density of CO2 falls off rapidly with height as does the temperature (adiabatic lapse rate). At a certain critical height photons in  CO2 absorption bands escape to space, but their energy is much less than it would have been if there was no atmosphere. The net result is an effective warming of the surface by downward IR as the Earth balances its energy. To calculate this properly needs radiative transfer codes which model the transfer of energy through the atmosphere. An example is Modtran [1]. The net effect of these calculations can be summarised in a single formula.

DS = 5.3Ln(C/C0)  

where DS is the extra radiative forcing (watts/m2) due to an increase in CO2 concentration from a reference value C0 to C.  If we take C0=280 ppm(pre-industrial revolution)   and C=390 ppm (now) then we predict an extra forcing due to man of 1.76 watts/m2. Similarly if we double CO2 concentrations by the end of the century the direct radiative forcing will be 3.67 watts/m2. How does the temperature of the Earth change in response? The answer is easy because the earth warms a little until it’s extra black body radiation balances again. Stefan Boltzmans quickly balances energy – it is the ultimate negative feedback.

S = sigmaT^4  so differentiating we get  DS = 4sigmaT^3DT

putting the numbers in ( T=288K) we can see that the predicted temperature increase DT is simply

1) For 1750->today  DT = 0.33 degreesC    2) A Doubling CO2 = 0.68 degreesK    Note that these increases are rather moderate, especially compared to the 4-5K increase seen since the last Ice Age.

One can also derive a formula for temperature increase versus CO2 concentration which works out to be DT=1.6Ln(C/C0). If you accept that all the observed warming from 1850 to date is due just to CO2 increases alone then a better fit is found using a modified formula of DT = 2.5 Ln(C/C0). After  you do this fit another phenomenum becomes clearly apparent over and above any greenhouse effect of CO2. The Earth seems to have regular natural climate oscillations with a 60 year cycle. We are now in the downward temperature cycle of this natural effect which may explain why we have seen no warming for the last 11 years. In fact it seems likely in this picture that no further warming will occur before 2020 when renewed rapid warming should reoccur.

The following curves are based on the IPCC emission scenarios for the next century, and use the fitted temperature dependence on CO2 above to extrapolate forward.

The 60 year oscillation seems to be  linked to the “Pacific Decadel Oscillation”(PDO) and the “Atlantic Multi-decadel Oscillation (AMO). However the  causes of these shifts in Ocean temperatures are not understood. Note  that  the blue and red curves predict relatively  moderate increases in temperature even if emissions of CO2 continue to rise. Eventually man must move to non fossil fuel energy because they will become uneconomic and politically  insecure. However on this evidence we seem to have  at least 50 years to find alternatives. For example Nuclear Fusion could finally become available providing limitless energy  before the end of this century. However  many scientists believe or are pressurised to believe that we have no time left and drastic action must be taken now to curb emissions. Their argument is that the Earth’s climate is sensitive to small changes in temperature acting to amplify

Climate Sensitivity/Feedbacks

This issue is the crux of the argument between “sceptics” and “realists” which spills over into name calling. So for example sceptics call realists – climate “alarmists” and realists call sceptics climate “deniers”.  The basic argument of climate sensitivity is the following.

A small rise in global temperatures should lead to more evaporation of water vapor and to  slightly more ice melting. Does more water vapor enhance warming further through extra greenhouse effect, or do clouds increase ? A net melting of ice will lower albedo in far northern and southern latitudes although far larger melting occurs every summer. Other feedbacks include a reduction  in the lapse rate from the dry adiabatic which acts against the greenhouse effect.  Climate  feedbacks are defined as shown below. A change in forcing DS from increasing CO2 is enhanced above Stefan Boltzman loss by extra feedback terms F leading to a larger (or smaller) temperature change DT.

Whether or not AGW is “dangerous” or not will depend on the magnitude and sign of F. If it is as large as IPCC reports assume  then temperature rises of 2-5 degrees C are predicted for a doubling of CO2 levels and this drives the whole climate change and carbon politics. However,  if F is zero or even negative then  a modest temperature rise of about 1 degree is expected which may even be beneficial.

The feedback parameters used by IPCC models are sumarised below (taken from [2])

The average feedback assumed by IPCC models then works out at around 2 watts/m2 per degreeC rise in temperature.  This reinforces the direct radiative forcing from increasing  CO2 yielding rises of between 2 to 5 degreesC depending on the model.  In fact these predictions were made in the original IPCC report from 1990 and can actually be compared to the data since then.

The more extreme predicted temperature rises made in 1990 are not supported by the data. The flat temperature profile for the last 10 years,  as mentioned above could also be due to a natural 60 year oscillation.

Past Climates

The Earth is currently in a long lasting Ice Age interspersed with shorter interglacial warm periods. We are currently 10,000 years into the most recent warm period which likely will end within another 5000 years time.  Why the Earth began cooling about 3 million years ago to enter a series of ice ages remins a mystery. The driver for the ice ages are orbital variations of the Earth called Milankowitz cycles but the details are uncertain. The change in tilt angle of the earth’s rotation changes the strength of summer and winter for each hemisphere extending the arctic regions, and a clear signal for this is apparent in the data. However for the last 900,0000 years the cycle seems to be driven by changes in ellipticity (eccentricity) of the Earth’s orbit. These changes are not sufficient to explain the large temperature swings. Climate scientists who follow CO2 as being the main driver point to this as evidence of large climate sensitivity as CO2 concentrations change during an ice age from a cold 190ppm for high glaciation to about 280 ppm in an interglacial. However, it is not clear what is cause and what is effect. All this is discussed here.

Longer term geological evidence and the faint sun paradox essentially can rule out high climate sensitivity over the long term. We know that liquid oceans have been present on Earth as early as 4 billion years ago, when the sun was 30% less bright. This means temperatures cannot have been vastly different than today. As the sun strengthened feedbacks as high as 2 watts/m2/degC would have caused run away temperatures, and boiled the oceans. It seems likely that there are stabilising effects on climate which lead a water covered planet like Earth to self-regulate temperatures - further information here.

The next 20 years should pin down climate science and determine whether the doom mongers are correct.  Curbing carbon emissions is going to be almost impossible while the world’s population continues to grow.  My personal view is that humans have massively changed the global natural order and CO2 emissions are a symptom of this rather than the overriding  central issue. Only if and when population can be stabilised will we have a hope of balancing human needs with those of nature. Concentrating on CO2 emissions is probably a diversion from this primary problem. I think that the evidence supports the “sceptical” view that  temperatures will not rise by more than about 1 degree between 2000 and 2100. Despite this, the push to find new energy sources has a beneficial side effect of climate change policy, and is probably necessary. However, renewable energies currently have far too low energy density – wind energy for example in the UK comes out at just 2 watts/m2. Is it really worth covering the most beautiful parts of britain with 100 meter  high unreliable turbines, while China continues to burn cheap coal ? Solar energy farms in deserts, short term expansion of nuclear power until nuclear fusion is tamed are a better investment for us and for  the natural world.


[1] Modtran  on-line access here

[2] S. Bony et al. How well do we understand and evaluate Climate Change Feedback Processes, Journal of Climate, Vol 19, P. 3445, 2006

[3] Relevant posts in this blog


[1] Kopp, G. and J. L. Lean, A new, lower value of total solar irradiance: Evidence and climate significance, Geophys. Res. Lett., 38

Footnote:  The latest  accurate measurements of the solar constant are from SORCE TIM and give a value of 1360.8 watts/m2. This is lower than the previous value of 1367 watts/m2 still quoted on Wikipedia and used by most climate models. This is important also for energy balance calculations since the incident average solar radiation on Earth is 340 watts/m2 and not 342 watts/m2.

11 Responses to Climate

  1. Brad Keyes says:

    “Arguably the biggest challenge this century will be to better understand the Earth’s climate and how man effects [sic] it”

    I doubt it. Climate change has about as much impact on our lives as continental drift. Nobody you know is going to be inconvenienced, let alone killed, by the imperceptible drifting of the 17-year running average of weather. The bizarreness of our obsession with climate will take a few years to be widely acknowledged, but when it is, expect to see climate research return to its former status as a niche science of no particular urgency.

    The biggest challenge is to understand and arrest processes such as cancer and dementia, which will destroy the lives of most of the people you know.

  2. oldfossil says:

    Clive, feel free to moderate this out of existence as I’m not sure I want it recorded for posterity.

    The essence of the AGW argument is that Earth has an ideal average temperature of say 15C. Lukewarmers like me claim that it makes no difference if this temperature climbs to 16, 17, or even 18C.

    Obviously I’m wrong, but so are the warmists. Earth may very well have an optimum average temperature, a Goldilocks temperature. But some regions are going to be too hot and others are going to be too cold. The regions that are just right: are they in the majority, or are they a small minority in between two extremes?

    To try and put a number on it I went to and downloaded the data into Excel.

    Then I fired up Google Earth and established the northernmost and southernmost latitudes of each country, capturing this on my Excel worksheet.

    Next I created 18 zones each 10 degrees of latitude wide, and allocated the world population between those 18 zones. Where a country spanned multiple bands, I split the population of that country equally between the zones.

    Although my method leaves PLENTY of room for improvement, errors will probably balance out. As the Aussies say, near enough is fair enough and fair enough is good enough.

    The results: figures in millions

    Latitude 00 – 10 1233
    Latitude 11 – 20 1056
    Latitude 21 – 30 1389
    Latitude 31 – 40 1485
    Latitude 41 – 50 979
    Latitude 51 – 60 666
    Latitude 61 – 70 53
    Latitude 71 – 80 48
    Latitude 81 – 90 34
    Total 6943 (agrees with wiki as at 22 January 2013)

    From the sharp drop-off in population, I might guess that once you cross latitude 40 going towards the poles, the environment is less suitable for habitation. I might then guess that the reason for this is low temperatures. But those are only guesses and on a site like this, visited mainly by the extremely bright, knowledgeable and experienced, I’m not going to make myself look any more stupid than absolutely unavoidable.

    But a more refined version of this information could be used to answer a simple question: who are the winners and who will lose from global warming?

    I might not be as bright as you guys but I’m smart enough to see that this is the central problem in the climate debate.

    • Clive Best says:

      I think your analysis is about right. There are less people living in cold dry polar regions because there is less food available and more effort is needed to keep warm. The tropics are warm and damp and food is plentiful. The climate in the tropics is dominated by the oceans which maintain comfortable temperatures around 30C. It is only in the centre of continents like Australia and Africa that very hot dry deserts form. Very few people live there.

      One interesting fact that is not well known is that Southern Hemisphere summers receives about 10% more solar radiation than the northern hemisphere because it coincides with the shortest distance between the sun and the earth. This is a much larger effect than any conceivable AGW effect.

      I am also a luke warmer. Doubling CO2 alone is calculated to raise temperatures by about 1C globally – no big deal. It is only by the far less clear argument that the net effect of water results in a positive feedback, that the IPCC scientists derive much higher predictions. It is beginning to look like these high feedback values from H2O are not true. The whole CAGW science/politics/industry is like an inverted pyramid fed with vast governmental/inter-governmental funding. Right at the bottom of the pyramid is CO2 radiative transfer theory and immediately above that is positive H2O feedback. If positive H2O feedback fails then the whole lot collapses.

      • oldfossil says:

        Thanks Clive for your very informative reply. I’ve enhanced my population spreadsheet with an arithmetically better split between latitudes, as well as land areas derived from Iain Inglis’s excellent spreadsheet at Now I have population densities by latitude which I intend to post here shortly.

        You have identified a 60-year climate cycle and I wonder if water vapor is not the underlying mechanism? This is of course pure speculation. Unfortunately I won’t be alive in 2020, when you expect warming to resume, and as I don’t believe in an afterlife I can’t even console myself with the prospect of watching to see who’s right from heaven or hell or wherever!

  3. Brad Keyes says:

    “If positive H2O feedback fails then the whole lot collapses.”

    You mean we’ll finally be able to turn off the cli-sci funding spigot (or clamp off the haemorrhage, if you prefer) and redirect our money, effort and attention to, you know, non-imaginary problems?

    Then the collapse is a moral imperative. As soon as possible. Wouldn’t you agree, Clive?

    (For technical considerations I’d amend it to: if positive feedback fails then the whole lot collapses.)

    FWIW, it collapsed for me as soon as the following thought occurred to me, which Lindzen puts more eloquently than I could (though it doesn’t by any means depend on his formidable authority):

    If climate has not “tipped” in over 4 billion years, it’s not going to tip now due to mankind. The planet has a natural thermostat.

    It makes nil difference whether or not Lindzen himself has successfully isolated and characterised the mechanism of the thermostat. The point is, it exists and it’s as dependable as the sunrise. The climate is not going to tip.

    Or have I missed some subtlety?

  4. Brad Keyes says:

    My formatting was unclear, but this:

    If climate has not “tipped” in over 4 billion years, it’s not going to tip now due to mankind. The planet has a natural thermostat.

    was a quote from the Professor. Though, as I suggested, it might as well have come from a junior-school geology teacher. It’d be just as self-evident.

    Again, unless I’ve missed some subtlety, it seems to me that every able-bodied person in climate science is morally obliged to bring about the collapse of “the whole lot” now, if not sooner.

    • Clive Best says:

      You have it spot on.

      The argument of Lindzen is convincing. The Earth must have a natural thermostat because otherwise life could never have evolved over the last 4 billion years. Liquid Oceans have existed for well over 3 billion years and are essential for multi-cell life. The Oceans have not boiled away despite a 30% increases in solar output, Meteor strikes, super volcanoes, super novae and (far less important) CO2 levels 10 times greater than today. The oceans must be the Earth’s natural thermostat.

      You could call it the “anthropic principal”.

      The climate is stable to external CO2 forcing since otherwise we, the IPCC, and Greenpeace would not even be here to worry and fuss about it. Overall the Earth is immune to whatever minor disturbances humans can produce.

  5. garhighway says:

    Some thoughts:

    I’m not aware of anyone thinking that there is an ideal temperature that we must strive to keep the earth at. Instead, we have the simple fact that we have built a global civilization around the current climate, with cities, ports, transportation infrastructure and much, much more locacted based on the the climate and environment of the last 150 years or so. That doesn’t make the climate of the last 150 years the “right” one, it just means that if we choose to change it (as we are current doing), we will be creating significant costs for ourselves in having to relocate or modify all of that infrastructure.

    And I would love to hear more about the science behind the anthropic principle. From where I sit, it sounds like you are saying that you’ve embued the Earth will will and a soul, and while you are at it made sure it was a benign one.

    • Clive Best says:

      I don’t believe there is an ideal temperature for the earth either. Humans would probably thrive a bit better in a slightly warmer climate, and we would certainly need less fuel and less food to live in temperate regions. We already de-forested Europe and much of North America before discovering fossil fuels (coal) around 1750.

      The anthropic principle originated in basic physics and cosmology? The physical constants seem to be incredibly fine tuned in our universe so that atoms are stable, galaxies and stars can form and evolve, chemical elements fused in supernovae. Life needs a previous generation of stars, a planet with a circular orbit at exactly the right distance from a star, liquid water etc.

      Once life gets started it effects the chemistry of the atmosphere and the geology on the planet. The atmosphere is no longer in chemical equilibrium. CO2 gets pumped out of the atmosphere and oxygen is released. H2O stabilizes temperatures. Finally man comes along and asks how could all this have happened on Earth? Well the anthropic principal says that it happened because we are here to ask the question. There are millions of planets without life. Perhaps there are millions of parallel universes without stars and without life. We can’t be aware of those ones.

      There have been liquid oceans on earth for at least 3 billion years. The climate is remarkably stable since during that time the sun has brightened by 30%. Whatever we do to CO2 levels the climate overall will remain stable for another billion years, and life will continue.

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