Calculating Cooling

How do we know how much cooling we're creating with our "clouds," and how does this compare to warming from carbon dioxide emissions?
Estimates vary, but a leading researcher cites a gram offsetting a ton:

"a gram of aerosol in the stratosphere, delivered perhaps by high-flying jets, could offset the warming effect of a ton of carbon dioxide, a factor of 1 million to 1."

and, again:

"Geoengineering’s leverage is very high—one gram of particles in the stratosphere prevents the warming caused by a ton of carbon dioxide."

Let's dig into the numbers that we're using to support this claim. Fortunately, much smarter people have studied this for decades. Let's review some of their work and calculate our climate cooling impact.

Radiative Forcing?

Radiative forcing is the key concept here. This is how much energy enters the atmosphere vs. leaves it. An increase in radiative forcing leads to warming, and a decrease causes cooling. Here's a more detailed explanation. Measured in watts per square meter (W/m^2), we're over 3.1 W/m^2 of increased radiative forcing since 1750. 

Reflective Clouds

How much reflectivity can we get from our clouds? Here's the summary we're working from:

This number isn't pulled from thin air. As the author explains: "This sulfate efficacy value differs from that used in Smith and Wagner (2018) (which considered only incoming radiation) and falls towards the center of the values present across recent literature (Ferraro et al 2012, Pope et al 2012, Kuebbeler et al 2012, Pitari et al 2014, Kleinschmitt et al 2017, Dai et al 2018)."

The key number here: 
-.62 W/m2 radiative forcing created for a year by injecting 1 Tg of sulfur

But, we're using SO2. So, SO2/S mass ratio means we get half as much cooling per Tg:
-.62/2 = -.31 W/m2 radiative forcing per Tg SO2/year

CO2's Warming

How much does carbon dioxide warm the planet? I was surprised about the uncertainty band here. IPCC says between .27 and .63 C per 1000 gigatons co2:

So: 1000 gigatons CO2 = +.45C

Converting Units

Now we've got all the information we need to do our math. First, a conversion: temperature to radiative forcing. From the first table above, .7C per W/m2

So, we'll convert our radiative forcing per Tg SO2 to temperature change: 
-.31 W/m2 * .7C per w/m2 = -.217 C per Tg SO2/year

Residence Time

How long do these particles create cooling? 1-3 years. For our purposes, we'll go with 2.1 years (although further particle optimization, higher injection altitudes, and other changes may eventually result in much greater residence time).

So, 2.1 years particle life * -.217C per TG SO2/year = -.4557 C per Tg SO2 launched for 1 year

Putting It All Together

So, how many grams of "cloud" to offset 1 ton of co2's warming impact for a year? 
1000 gigatons co2 = +.45C
1 Tg SO2 = -.4557C
1000 gigatons co2 ~ 1 Tg SO2
1 gigaton = 1,000 Tg, so:
1,000*1,000 = 1,000,000 Tg co2 = 1 Tg SO2
dividing both sides by 1T:
1,000,000 g co2 = 1 g SO2
1 metric ton = 1,000,000 g:
1 metric ton co2 = 1 g SO2

So, with uncertainty bands on all of this, a gram offsets a ton: one gram "cloud" offsets 1 ton of co2's warming impact for a year.

Here's the spreadsheet I used to calculate this, with links to sources. 

There are arguments to compare this in different ways (joules, etc.); many of these have strong merits. Because buyers of voluntary carbon credits are focused on co2 equivalence, we've gone this route.

As with all our work here, please let us know if you think we've made a mistake and we'll correct! 

(image via Lexica)

Edited 12/28 to include links to David Keith's work.