causal chain from +300ppm co₂ to global warming
Any warm object radiates energy at wavelengths depending on its temperature, the distribution of which is described by Planck's Law.
3. Earth receives 1,362 W/m² from the sun in a combination of UV, visible and infrared radiation, but 29.5% is immediately reflected by clouds or the surface. The remaining 70.5% (960 W/m²) is absorbed by land, air and oceans.Source: Kopp & Lean https://doi.org/10.1029/2010GL045777
4. The sun illuminates the disk of Earth (area = πr²) but our spherical plant has an area = 4πr². To maintain energy equilibrium and steady surface temperature, the average square meter of Earth's surface must emit 240 W/m² (960 W/m² ÷ 4 = 240 W/m²).(Image: https://www.windows2universe.org/earth/climate/sun_radiation_at_earth.html)
5. From the Stefan-Boltzmann Law, we can calculate the surface temperature that will radiate exactly 240 W/m² (255 K). If we plug this temp. back into Planck's Law, we calculate that Earth will glow in a distribution of wavelengths mostly in thermal infrared (4-50 μm).
6. This would be the case if Earth had no atmosphere. Instead, greenhouse gasses (GHGs) absorb & re-radiate Earth's outgoing infrared, producing a jagged emission to space.(Source: U of Chicago MODTRAN http://climatemodels.uchicago.edu/modtran/)
7. IR-active GHGs suppress emission in some portions of the spectrum, requiring surface warming of about +33 K to maintain 240 W/m² of outgoing thermal infrared (equilibrium with the sun). But the warmer surface now emits 390 W/m², 150 W/m² more than it would without GHGs.(Source: U of Chicago MODTRAN http://climatemodels.uchicago.edu/modtran/)
8. This +33 K warmer surface temperature and the additional 150 W/m² thermal infrared is the greenhouse effect (GHE). Human additions of CO₂, CH₄, and other minor gasses have further increased this by ~3 W/m² so far.
9. How much warming does +3 W/m² produce?
Easier part is calculating effects from infrared absorption alone.
Harder part is how clouds, ice, and vegetation respond. Clouds and ice reflect a lot of sunlight, while trees absorb it. Climate models don't agree on these feedbacks.
10. Consequently, warming estimates have historically varied over a wide range: 1.0-6.0°C per doubling of CO₂ (Knutti-2017). Recently the IPCC AR6 report has concluded there is enough evidence to tighten this range to 2.5-4.0°C.(Image: Knutti et al 2017 https://www.nature.com/articles/ngeo3017).
11. Future warming also depends on how quickly & how much more GHG's are added. While some have feared worst-case-scenarios RCP8.5 or SSP5-8.5, current emissions projections much more modest (dire media headlines are usually based on RCP8.5 studies)