Arguably the biggest challenge this century will be to better understand the Earth’s climate and how man affects 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.
- 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.
- 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 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 . 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
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 )
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.
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.
 S. Bony et al. How well do we understand and evaluate Climate Change Feedback Processes, Journal of Climate, Vol 19, P. 3445, 2006
 Relevant posts in this blog
- Part 2: The real cause of Ice Ages ? – Resonant dust clouds ?
- What causes interglacials? Part 1.
- Phenomenology of Ice Ages
- IPCC feedback contradictions
- Water World
- A fit to Global Temperature Data
- 1990 IPCC predictions confront the data
- CO2 greenhouse effects
- Does the Moon effect the Earth’s climate ?
 Kopp, G. and J. L. Lean, A new, lower value of total solar irradiance: Evidence and climate significance, Geophys. Res. Lett., 38