Greenhouse Gas	Simplified Relative Forcing	More complex version
CO2	F = 5.35 ln(C/C0)	F= 4.841 ln(C/C0) + 0.0906 (C - C0)
CH4	F = 0.036 (M – M0) – (f(M,N0) – f(M0,N0))
N2O	F= 0.12 (N – N0) – (f(M0,N) – f(M0,N0))

E is change in forcing
using the derivative of Stefan-Boltzmann:
dT/dE = 1/(4[sigma] T^3)
dT/dF=1/(4σT3).
gets:
dT=[alpha]ln([CO2]/[CO2}orig)/(4[sigma] T^3)

This is the equation without all feedbacks.

Substituting a doubling CO2 level (unrealistic, according to Lomborg)
and substituting T= 15 degreesC = 288.16K
dT=5.35ln2/(4*5.6705E-08*(288.16^3))
or
dT=0.6833 centigrade for a doubling of CO2 !!

That's physics. All the rest is models and hype.[ref]

From the point of view of the sun, the earth appears to be a disk with a radius R, so the total amount of power absorbed by the whole earth is the product of the arriving solar radiation times the area of a disk the size of the earth: P_Gain = π R² S(1-alpha)

Any object at a temperature T_K (in Kelvin) will emit thermal radiation at a rate given by: P_Loss= epsilon σT_K⁴ times it surface area. The factor epsilon is the emissivity (approximately 1), sigma is Stefan's constant, and the total surface area of the spherical earth (4 π R²). Recall that a temperature in Kelvin is T_K=T₀+T where T is the temperature in centigrade and T₀=273.15

In the steady state, the incoming radiation must balance the outgoing radiation. This leads to an energy balance equation for P_Gain=P_Loss:

[ref]

The radiative forcing for CO₂ is roughly proportional to the logarithm  4.4log(C) / log(2)  of its concentration, while for CH₄, the forcing scales like the square root [IPCC, 2001]. This implies that the higher the base level, the smaller the forcing will be from a fixed increase in concentration. [ref: [26]]  Using CO₂ concentrations of 270 and 540 ppm of , we get 35.5 W/m² and 39.0 W/m², a difference of 4.4 W/m².

From this NOAA web page:  (also this overview)

...net planetary radiative forcing changes roughly linearly in response to logarithmic changes in CO₂. Thus, a quadrupling of CO₂ gives another roughly 1°C direct warming over the direct 1°C warming for a CO₂ doubling, valid for the extreme assumption that water vapor mixing ratios and clouds do not change.

The log-linear relationship has been found to hold down to CO₂ concentrations to as low as one sixty-fourth of preindustrial levels. As CO₂ is decreased, the atmosphere's ability to hold water vapor collapses and the global temperatures drop sharply.  [ref]

• These lecture notes treat the atmosphere as a constant temperature black body, and claim a greenhouse effect factor of  1.189 x 255 K = 303 K.
• RealClimate discussion - Learning from a Simple Model.
• Real Climate: CO₂ colliding with itself in a tube of pure CO₂ broadens the lines about 30% more than does CO₂ colliding with N₂ or O₂ in air.
• Ray Pierrehumbert in Real Climate - Busy Week for Water Vapor
• Spencer Weart - Simple Greenhouse Models and an overview of the historical development.
• CO2 is cycled through the atmosphere in a period of about 7.5 years. See: http://www.whrc.org/carbon/index.htm Where it all goes to is not known http://www.whrc.org/carbon/missingc.htm but much of it gets transported to the deep ocean by the thermohaline circulation. That is replaced by CO2 that has remained in the deep ocean for around 1000 years, which is depleted in C14.
• the lapse rate generally increases with altitude in the troposphere. It starts out at about 4.75 K/km near ground level and increases to almost 9.8 K/km near the tropopause. The average is around 6.5 K/km.
• Water vapor at 1% corresponds to about 60% relative humidity at 15 °C [ref]
• Roger Pielke: Relative Roles of CO2 and Water Vapor in Radiative Forcing + comment: "...it is clear that the value of 3.7 Watts per square meter for doubling is not correct."
• GHG Radiation calculator.
• water vapor is roughly eight times more effective than carbon dioxide as a greenhouse gas (Hartmann 1994). [nasa]
• Wikipedia - Most of the infrared absorption in the atmosphere can be thought of as occurring while two molecules are colliding. The absorption due to a photon interacting with a lone molecule is relatively small.
• wiki - carbon dioxide is a linear molecule, but it has an important vibrational mode in which the molecule bends with the carbon in the middle moving one way and the oxygens on the ends moving the other way, creating some charge separation, a dipole moment, thus carbon dioxide molecules can absorb IR radiation. Collisions will immediately transfer this energy to heating the surrounding gas. On the other hand, other CO2 molecules will be vibrationally excited by collisions. Roughly 5% of CO2 molecules are vibrationally excited at room temperature and it is this 5% that radiates.
• http://en.wikipedia.org/wiki/Emission_line
• Science: The global warming feedback is based on the fact that cold air radiates less than warm air; if water vapor increases and is distributed to higher, colder altitudes, less heat is radiated to space and thus climate warms.
• [ref] Water absorbs the Infrared Radiation incoming from Sun because the frequency of the internal vibration of the water molecules is the same frequency of the waves of the solar Infrared Radiation. This form of Radiative Heat transfer is known like Resonance Absorption

• The Earth must radiate back into space as much total energy as it receives, to stay in equilibrium. Adding gas to the atmosphere moves the site of this emission to higher levels, which are colder. Cold things radiate less than warm ones, so the system must warm up until it can radiate enough.
• When the surface emits invisible heat radiation, some of it is absorbed by CO2 in the middle levels of the atmosphere. Thus some energy transfers into the air itself, rather than escaping directly into space. Not only is the air thus warmed, but also some of the energy trapped there is radiated back to the surface, warming it further.

• Does Kirchhoff's Law apply to a greenhouse gas?  The gas will absorb radiation at certain frequencies, and radiate at the same frequencies.  It does not act like a black body.
• Is there any validity to the idea that when a greenhouse gas molecule absorbs radiation, this induces vibration which transfers motion, thus heat, to the surrounding atmosphere?  Does this process happen in reverse, ie, a collision induces a vibrational state which causes the GHG to emit a photon?
• Does the Stefan Boltzmann law apply to intensity of radiation emitted by a greenhouse gas at a certain temperature?
• How much effect is there from atmospheric pressure causing the absorption spectrum of a greenhouse gas to broaden?
• Can the downwelling longwave radiation be measured at the surface? Can we tell from the wavelength which greenhouse gas it came from?  Reference?

This model recognizes that when a greenhouse gas absorbs radiation, it re-radiates it in all directions, including up and down. Greenhouse warming is caused by the portion of longwave radiation that is returned to the surface. Adding more greenhouse gas reduces the amount of radiation that is prevented from leaving the Earth and is instead returned to the surface. More of the greenhouse effect takes place higher in the atmosphere where the ratio of carbon dioxide to water vapor is higher, implying that carbon dioxide is a relatively more important greenhouse gas than in the first model.

The average mass of the atmosphere is about 5,000 trillion metric tons or 1/1,200,000 the mass of Earth. According to the National Center for Atmospheric Research, "The total mean mass of the atmosphere is 5.1480×10¹⁸ kg with an annual range due to water vapor of 1.2 or 1.5×10¹⁵ kg depending on whether surface pressure or water vapor data are used; somewhat smaller than the previous estimate. The mean mass of water vapor is estimated as 1.27×10¹⁶ kg and the dry air mass as 5.1352 ±0.0003×10¹⁸ kg." [wikipedia]

• The ocean does not warm as quickly as the land.  Moisture levels are largely determined by sea surface temperature, which lags behind land temperature.  A warmer landmass on its own tends to increase the evaporation rate, which could lead to drying.
• Rainfall is also influenced by existing vegetation.  Increased vegetation generates more rainfall, in a positive feedback loop.  But it takes time for vegetation to establish itself.

[ref] The record obtained at these sites allowed us to evaluate the causes and effects of several major global events in Earth history, including:

1. Demonstrating that the latest Cenomanian-Turonian (C/T) ocean anoxic event was unrelated to sea-level change on million-year or 100-k.y. scales.
2. Suggesting that a major cooling spanning the Campanian/Maastrichtian boundary was associated with a sea-level lowering and inferred ice volume increase.
3. Correlating a latest Maastrichtian global warming with Deccan trap volcanism.
4. Linking the marine mass extinctions at the end of the Cretaceous with ballistic ejecta. In addition, we showed that collapse of the vertical isotopic gradient ("Strangelove Oceans") extended to neritic environments and that there was minimal change in sea level associated with the Cretaceous/Tertiary (K/T) boundary.
5. Establishing that low ¹³C and ¹⁸O and high kaolinite values were associated with the Paleocene/Eocene thermal maximum (PETM) in NJ neritic sections and that isotopic values remained low and kaolinite remained high throughout a thick section above the carbon isotope excursion (CIE). This reflects either that warmer and wetter climate persisted for >300-400 k.y. in NJ (unlike deep-sea records that show an exponential return to pre-PETM conditions after ~200 k.y.) or that the extremely rapid deposition of this section occurred in response to a cometary impact.
6. Showing that a large (~60 m), earliest Oligocene drop in sea level was associated with development of an ice sheet equivalent in size to the modern East Antarctic ice sheet, though sea level again rose by nearly 50 m ~1 m.y. later, suggesting near collapse of the ice sheet. The ice sheet subsequently grew and decayed numerous times in the Oligocene-middle Miocene.

• The concept of "melt extent" does not refer to a net loss of ice, as one might think. Instead it is defined here as "experiencing at least 1 melt day between April 1 - September 25". This metric is used because liquid water absorbs energy differently than ice and snow, making it easy to detect from satellites. So the red area is not actually melting, it just means it got warm enough for liquid water to appear at least one day that year.

• The dates 1992 and 2002 have been chosen (ie. cherrypicked) to select the lowest and highest values on record. 1992 was the year after the Mount Pinatubo volcanic eruption, which caused global cooling. The green line on the graph (drawn by me) shows the rate of increase presented on the maps, which is many times greater than the actual average rate of increase, shown by the red line.

• Why does the temperature rise in the early part of the century have no affect on sea ice extent?
• Why does the decline in summer sea ice extent begin in 1950, while the cooling trend does not reverse itself until 1970?
• Why does the caption attached to the graph suggest the change in sea ice extent is accelerating?  A regression taken from 1900 will give an exponential curve.  But visually at least, the decline seems to start abruptly, and looks linear after that.

These maps show the difference between “normal” sea ice extent (long-term mean), and the year indicated. The long-term average minimum extent contour (1979-2000) is in magenta. The ice extent for each year is shown by the edge of the colored region; within that extent, color bands show differing levels of sea ice concentration. Blue indicates areas where concentration is more than the long-term mean; red shows areas where concentration is less than the long-term mean. The 2005 map shows a marked reduction in extent over the past four years, all of which were also below average.

In 2002 and 2003, the ice pack also experienced much lower concentrations during the minimum, especially true north of Alaska. However, the ice cover has been much more compact during the minimums of 2004 and 2005, yielding small negative or even positive ice concentration anomalies within the ice pack.

• These satellite instruments suggest a variation in annual mean TSI of the order 0.08% (or about 1.1 W/m²) between minimum and maximum of the 11-year solar cycle. [IPCC 6.11]
• Solar irradiance change has a strong spectral dependence [Lean, 2000], and resulting climate changes may include indirect effects of induced ozone change [RFCR; Haigh, 1999; Shindell et al., 1999a] and conceivably even cosmic ray effects on clouds [Dickinson, 1975]. Furthermore, it has been suggested that an important mechanism for solar influence on climate is via dynamical effects on the Arctic Oscillation [Shindell et al., 2001, 2003b]. [ref]
• Time-dependent experiments produce a global mean warming of 0.2 to 0.5°C in response to the estimated 0.7 W/m² change of solar radiative forcing from the Maunder Minimum to the present. (from IPCC 2001). But, from IPCC 2007:  Changes in solar irradiance since 1750 are estimated to cause a radiative forcing of +0.12 [+0.06 to +0.30] W/m², which is less than half the estimate given in  IPCC 2001.
• A U.S. National Academy of Sciences panel estimated that if solar radiation were now to weaken as much as it had during the 17th-century Maunder Minimum, the effect would be offset by only two decades of accumulation of greenhouse gases. As one expert explained, the Little Ice Age "was a mere 'blip' compared with expected future climatic change." [ref]
• A half of a percent change in solar output could raise temperatures, eventually [over a century], about three-quarters of a degree Celsius, which, coincidentally, roughly equals the observed warming in the past century,” says Hansen. [ref]

• Cold weather kills the mountain pine beetle. Mountain pine beetle eggs, pupae and young larve are the most susceptible to freezing temperatures.
• In the winter, temperatures must consistently be below -35 Celsius or -40 Celsius for several straight days to kill off large portions of mountain pine beetle populations.
• In the early fall or late spring, sustained temperatures of -25 Celsius can freeze mountain pine beetle populations to death.
• A sudden cold snap is more lethal in the fall, before the mountain pine beetles are able to build up their natural anti-freeze (glycerol) levels.
• Cold weather is also more effective before it snows. A deep layer of snow on the ground can help insulate mountain pine beetles in the lower part of the tree against outside temperatures.
• Wind chill affects mountain pine beetles, but is usually not sustained long enough to significantly increase winter mortality.

Untruth 1

Gore says: A sea-level rise of up to seven metres will be caused by melting of either West Antarctic or Greenland ice cap in the near future. Cities such as Beijing, Calcutta and Manhattan would be devastated.

Judge says: "This is distinctly alarmist, and part of Mr. Gore's 'wake-up call.' It is common ground that if indeed Greenland melted, it would release this amount of water, but only after, and over, millennia, so that the Armageddon scenario he predicts, insofar as it suggests that sea-level rises of seven metres might occur in the immediate future, is not in line with the scientific consensus."

Untruth 2

Gore says: Low lying inhabited Pacific atolls are being inundated because of anthropogenic global warming. "That's why the citizens of these Pacific nations have all had to evacuate to New Zealand."

Judge says: "There is no evidence of any such evacuation having yet happened."

Untruth 3

Gore says: The shutting down of the "Ocean Conveyor" would lead to another ice age.

Judge says: "According to the Intergovernmental Panel on Climate Change, it is very unlikely that the Ocean Conveyor (an ocean current known technically as the Meridional Overturning Circulation or thermohaline circulation) will shut down in the future, though it is considered likely that thermohaline circulation may slow down."

Untruth 4

Gore says: Two graphs relating to a period of 650,000 years, one showing rise in CO2 and one showing rise in temperature, show an exact fit.

Judge says: "Although there is general scientific agreement that there is a connection, the two graphs do not establish what Mr. Gore asserts."

Untruth 5

Gore says: The disappearance of snow on Mt. Kilimanjaro is expressly attributable to global warming.

Judge says: "The scientific consensus is that it cannot be established that the recession of snows on Mt. Kilimanjaro is mainly attributable to human-induced climate change."

Untruth 6

Gore says: The drying up of Lake Chad is a prime example of a catastrophic result of global warming.

Judge says: "It is generally accepted that the evidence remains insufficient to establish such an attribution."

Untruth 7

Gore says: Hurricane Katrina and the consequent devastation in New Orleans is due to global warming.

Judge says: "It is common ground that there is insufficient evidence to show that."

Untruth 8

Gore says: Polar bears have drowned swimming long distances to find ice.

Judge says: "The only scientific study that either side before me can find is one which indicates that four polar bears have recently been found drowned because of a storm."

Untruth 9

Gore says: Coral reefs are bleaching because of global warming.

Judge says: "The actual scientific view, as recorded in the IPCC report, is that, if the temperature were to rise by 1-3 degrees centigrade, there would be increased coral bleaching and widespread coral mortality, unless corals could adapt or acclimatize."

Two more, from Real Climate