<p>Table 6.2 on p. 10 <a href="https://www.ipcc.ch/site/assets/uploads/2018/03/TAR-06.pdf" rel="nofollow noreferrer">here</a> contrasts the logarithmic radiative forcing of <span class="math-container">$\ce{CO_2}$</span> with the square-root forcing of <span class="math-container">$\ce{CH_4}$</span> and <span class="math-container">$\ce{N_2O}$</span>, and the linear forcing of CFCs. Are there similar results for the cooling effects of species such as <span class="math-container">$\ce{SO_2}$</span> and <span class="math-container">$\ce{H_2S}$</span>? (<a href="https://www.ipcc.ch/site/assets/uploads/2018/03/TAR-05.pdf" rel="nofollow noreferrer">The previous chapter</a> discusses aerosols, but doesn't appear to contain a similar table.) Is there any theoretical basis for these specific relationships in either case?</p>
<p>It has been estimated stratospheric aerosol injection of <span class="math-container">$\ce{SO_2}$</span> would require only <span class="math-container">$\sim1\ce{Mt}$</span> to mitigate the warming effects on Earth of <span class="math-container">$\sim1\ce{Tt}$</span> of <span class="math-container">$\ce{CO_2}$</span> (atmospheric half-lives aside), suggesting the relationship is closer to linear than logarithmic. But that's just my guess, plus it doesn't preclude e.g. a square-root relationship.</p>

CC BY-SA 4.0
2021-08-10T23:16:32.743Z
"Is there any theoretical basis for these specific relationships in either case?" - The greenhouse effect requires for the infrared Rosseland optical depth of the atmosphere to rise, in order to raise the temperature of the surface. The optical depth directly provides a 'blanketing' of hotter layers, reducing outward flux, and hence provides forcing (defined as total flux in minus total flux out). The scalings of forcing vs species concentration comes from computations of line blanketing and saturation effects. The latter however involves many thousands of lines, and is hence not trivial.
AtmosphericPrisonEscape
CC BY-SA 4.0
2021-08-11T00:15:53.507Z
The various scalings (lin,log,square root) can be understood by considering the detailed physics of line saturation - a lecture is e.g. http://www.bartol.udel.edu/~owocki/phys633/Phys633-notes1.pdf   and the plot you are interested is on page 68.
AtmosphericPrisonEscape
CC BY-SA 4.0
2021-08-11T07:23:07.117Z
@AtmosphericPrisonEscape Does the Milne-Eddington model also explain cooling effects?
J.G.
CC BY-SA 4.0
2021-08-11T12:55:18.217Z
I don't think so, which is why I didn't post this as a full answer, but merely as comment. One would have to extend the model by adding albedo and flux reduction effects by the anti-GHG.
AtmosphericPrisonEscape
CC BY-SA 4.0
2021-08-11T12:56:48.490Z
@AtmosphericPrisonEscape Is "anti-forcing" the best term for what $\ce{SO_2}$ does, or is there some jargon I should learn?
J.G.
CC BY-SA 4.0
2021-08-11T12:59:36.940Z
"Negative forcing" seems to be the commonly accepted terminology - but then I am not working in terrestrial climate. There were mentions around table 6.6 on page 376 in Chapter 6.
AtmosphericPrisonEscape
<climate-change>
How do radiative forcing and anti-forcing scale with concentration?
J.G.
# How do radiative forcing and anti-forcing scale with concentration?

(Asked by: username_0 on 2021-08-10)

Table 6.2 on p. 10 [here](https://www.ipcc.ch/site/assets/uploads/2018/03/TAR-06.pdf) contrasts the logarithmic radiative forcing of $\ce{CO\_2}$ with the square-root forcing of $\ce{CH\_4}$ and $\ce{N\_2O}$, and the linear forcing of CFCs. Are there similar results for the cooling effects of species such as $\ce{SO\_2}$ and $\ce{H\_2S}$? ([The previous chapter](https://www.ipcc.ch/site/assets/uploads/2018/03/TAR-05.pdf) discusses aerosols, but doesn't appear to contain a similar table.) Is there any theoretical basis for these specific relationships in either case?

It has been estimated stratospheric aerosol injection of $\ce{SO\_2}$ would require only $\sim1\ce{Mt}$ to mitigate the warming effects on Earth of $\sim1\ce{Tt}$ of $\ce{CO\_2}$ (atmospheric half-lives aside), suggesting the relationship is closer to linear than logarithmic. But that's just my guess, plus it doesn't preclude e.g. a square-root relationship.

**Tags:** climate-change

> **Comments:**
> **username_1**: "Is there any theoretical basis for these specific relationships in either case?" - The greenhouse effect requires for the infrared Rosseland optical depth of the atmosphere to rise, in order to raise the temperature of the surface. The optical depth directly provides a 'blanketing' of hotter layers, reducing outward flux, and hence provides forcing (defined as total flux in minus total flux out). The scalings of forcing vs species concentration comes from computations of line blanketing and saturation effects. The latter however involves many thousands of lines, and is hence not trivial.  
> **username_1**: The various scalings (lin,log,square root) can be understood by considering the detailed physics of line saturation - a lecture is e.g. http://www.bartol.udel.edu/~owocki/phys633/Phys633-notes1.pdf   and the plot you are interested is on page 68.  
> **username_0**: @username_1 Does the Milne-Eddington model also explain cooling effects?  
> **username_1**: I don't think so, which is why I didn't post this as a full answer, but merely as comment. One would have to extend the model by adding albedo and flux reduction effects by the anti-GHG.  
> **username_0**: @username_1 Is "anti-forcing" the best term for what $\ce{SO_2}$ does, or is there some jargon I should learn?  
> **username_1**: "Negative forcing" seems to be the commonly accepted terminology - but then I am not working in terrestrial climate. There were mentions around table 6.6 on page 376 in Chapter 6.  

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## 0 answers

