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.

2. Planck's Law predicts that the Sun, having a surface temperature of 5,800 degrees, will radiate mostly at visible light wavelengths.


3. The sun-facing side of Earth receives 1,362 W/m² in a combination of visible and infrared radiation.

Source: Kopp & Lean

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.


5. According to Planck's Law, the Earth, being much cooler than the sun, will radiate mostly longwave infrared.


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

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

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 ).

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 ).

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

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

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"¹An 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:

  1. High water vapor feedback parameter

  2. Strong climate sensitivity parameter

  3. Positive cloud forcing

  4. 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.