causal chain from +300ppm co₂ to dangerous warming
1. Any warm object radiates energy at wavelengths depending on its temperature. The distribution of wavelengths is described by Planck's Law.
4. Earth reflects and radiates a total of 340.5 W/m². This is exactly ¼ of the solar flux, because the sun illuminates a disk (πr²) but the Earth radiates from a spherical surface (4πr²). This is radiative equilibrium.(Image: https://www.windows2universe.org/earth/climate/sun_radiation_at_earth.html)
5. According to Planck's Law, the Earth, being much cooler than the sun, will radiate mostly longwave infrared.(Image: https://phet.colorado.edu/sims/html/blackbody-spectrum/latest/blackbody-spectrum_en.html)
6. The area under the curve described by Planck's Law is the radiant flux (W/m²) which may be computed using a simpler equation known at the Stefan-Boltzmann Law.
7. If Earth had no atmosphere, it would radiate infrared smoothly across a range of wavelengths. Instead, Earth's atmosphere absorbs & re-radiates outgoing infrared causing the characteristically jagged emission to space. The area under the animated emission curve is constant.(Source: U of Chicago MODTRAN http://climatemodels.uchicago.edu/modtran/)
8. IR-active gasses suppress emission in some portions of the spectrum, requiring surface warming by more than 20K to re-attain radiative equilibrium. The warmer surface emits ~380 W/m², though only 340 W/m² escapes to space. Difference (~40 W/m²) is the greenhouse effect (GHE).(Source: U of Chicago MODTRAN http://climatemodels.uchicago.edu/modtran/)
9. CO₂ emissions are forecasted by Representative Concentration Pathways (RCPs). The worst-case scenario (RCP8.5) is sometimes referred to as "business-as-usual" but there is disagreement here; RCP4.5 may be more realistic and RCP8.5 may be a 'worst-case-conceivable' scenario.
10. If CO₂ concentrations roughly doubled (369→670 ppm) it is predicted to increase the GHE by +3.2 W/m², which in turn leads to surface and atmospheric warming.(page 1433 of the 5th Assessment Report https://archive.ipcc.ch/report/ar5/wg1/ ).
11. Warmer air can hold more water vapor, another greenhouse gas. The IPCC asserts that for every 1 W/m² CO₂ forcing, water vapor amplifies this "by 2-3x." Combined, how much warmer will Earth become?(page 667 of the 5th Assessment Report https://archive.ipcc.ch/report/ar5/wg1/ ).
12. Climate models run on supercomputers attempt to predict effects of additional water vapor and clouds in response to CO₂. These models do not agree on whether (or how much) additional heating or cooling this produces.Chart: Zelinka 2020 supplementary mat'l https://doi.org/10.1029/2019GL085782
13. Consequently, estimates of the climate sensitivity parameter describing how many degrees the Earth warms up given additional CO₂ forcing vary over a fairly wide range: 1.0-6.0.(Image: Knutti et al 2017 https://www.nature.com/articles/ngeo3017).
14. +3.2 W/m² forcing at a lower climate sensitivity parameter of 1.6 produces ~1.5°C warming after ~2xCO₂. The same forcing at a higher sensitivity parameter² of 5.3 results in ~5.0°C global warming.Image: "Long View on Climate Sensitivity" https://science.sciencemag.org/content/337/6097/917.full¹An Objective Bayesian Approach for Applying Fingerprint Techniques to Estimate Climate Sensitivity²The DOE E3SM Coupled Model Version 1: Overview and Evaluation at Standard Resolution
15. Those anticipating dangerous warming in their lifetime are effectively expecting:
High water vapor feedback parameter
Strong climate sensitivity parameter
Positive cloud forcing
Worst-case (RCP8.5) emissions scenario
16. My research seeks to avoid the uncertainties in climate models by directly analyzing spectroscopic satellite data to empirically measure the forcing effects of rising CO₂.