The CO2 problem in 6 easy steps is one of the most read old posts. That was written fifteen years ago. There are 15 years of more data, updates in some of the details and concepts, and better graphics to accompany the text. There is a slightly updated version that should be a bit more useful.
There is an effect on the environment.
The mean temperature of the surface can be deduced from the fact that there is a natural greenhouse effect. The net solar radiation absorbed at the top of the atmosphere is roughly equivalent to the net surface IR. In the absence of greenhouse substances, the amount of IR absorbed by the atmosphere is zero. The short wave radiation coming from the sun is called short wave radiation and the long wave radiation is called long wave radiation.
The greenhouse effect is caused by trace gases.
The fact that different absorbers contribute to the atmospheric infrared absorption is clear from the spectrum that can be seen from space. The number of absorption lines and the effects of pressure broadening preclude that from being calculated by hand. For some parts of the spectrum, the IR can be either absorbed by CO 2 or by water, but taking those overlaps into account, we find that 50% of the greenhouse effect is from water, 25% from clouds, and 20% from CO 2 The atmosphere's main components don't contribute to the greenhouse effect because they don't absorb much in the IR wavelength range.
Human emissions have led to an increase in trace greenhouse gases.
Since the pre-industrial era, methane has more than doubled, N 2 O has increased, and tropospheric O 3 has increased. The pre-industrial atmosphere did not contain new greenhouse gas compounds. The increased greenhouse effect is a result of all of these increases.
Fossil fuels, landfills, mining, oil and gas operations, agriculture, and industry are the main sources of these increases.
A useful diagnostic is radiive forcing.
Lessons from simple toy models and experience with more sophisticated GCMs suggest that any change in the TOA radiation budget is a good indicator of surface temperature change. The TOA radiation balance would change if the sun became stronger by 2%. The RF is defined by this. The TOA balance is affected by greenhouse absorbers and albedo changes. The calculation of the radiative forcing is a job for the radiative transfer codes that take into account atmospheric profiles. The most up-to-date estimates from Etminan et al are similar but slightly more complicated than the formula used in the report.
The logarithmic form for the CO 2 RF comes from the fact that certain wavelengths are already saturated and that the increase in forcing depends on the 'wings'. Lower concentration gases have straight forcings. The uncertainty about the global mean forcing is 10% because of the different assumptions about clouds. The order of magnitude is the same as an increase of solar forcing by 2%.
There are some changes to the radiative forcing concept. There are a number of processes that respond quickly to a change in aerosol concentrations that aren't related to the surface temperatures. After these adjustments have taken place, the ERF is more accurate in predicting the temperature rise. One such process is the stratospheric adjustment that happens with CO 2 since it has an important role in the stratospheric radiation balance. Depending on the spatial distribution of forcing agents, different feedbacks and processes might come into play and an equivalent forcing from two different sources might not give the same response. The factor that quantifies this effect is called the efficacy of the forcing, and it doesn't change the zeroth-order picture. Climate forcings can be added to the effect.
The total forcing from the trace greenhouse gases mentioned in Step 3 is 3.3 W/m 2 and the net forcing is 0.7 W/m 2 since the pre-industrial era. Aerosol effects are still the main cause of uncertainty. Increasing CO 2, with an increasing role for decreases in reflective aerosols, particularly in the US and EU, and increases in absorbing aerosols, particularly from India and China, are some of the factors driving current growth in forcings.
For a doubling of CO 2, climate sensitivity is 3oC.
The climate sensitivity is the response of global mean temperature to a forcing before any of the slower feedbacks kick in. Sensitivity can be assessed from any time in the past where the changes in forcing are known and the equilibrium temperature change can be estimated. The last glacial period is a good example of a large forcing (8 W/m 2 from ice sheets, greenhouse gases, dust and vegetation) giving a large temperature response and suggesting a sensitivity of about 3oC. You can combine this estimate with others from the 20th century to get a good idea of what the number should be. They came up with 3oC and a tighter uncertainty bound of 2.3 to 4.5oC.
The 0.75 oC/(W/m 2 ) is the result of converting the double CO 2 estimate to a more useful factor.
There is a significant number of radiive forcing.
By the time the climate reaches equilibrium, current forcings suggest the planet will warm 2oC. Warming could be more than 3oC if additional forcings reach 5W/m 2. We would not expect temperatures to rise if CO 2 emissions were to cease completely. Our flexibility allows us to end up between the two extremes.
On the scale of a planet they are a big deal. Changing statistics of heat waves, extreme precipitation, and coastal flooding are already being impacted by the warming. The last ice age was only 5 to 6 degrees cooler than the pre-industrial era. The worst case scenario has a full ice age unit of warming in a couple of centuries, compared to the 10,000 years it took before.
It's going to get more significant until emissions stop.
What's the answer to Q.E.D.
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