Thank you Andrew for pointing to this Make Sunset news which I had not seen.
I find their calculations to be both optimistic and misleading. "The key number -.62 W/m2 radiative forcing created for a year by injecting 1 Tg of sulfur" based on several studies - Ferrero et al 2012 did not inject aerosols but prescribed them in their model, they achieve -3.5 Wm-2 for a burden of 14.5 TgSO4, that's -0.7 Wm-2 / Tg S burden - Pope et al 2012 did not provide Wm-2 in their study - Kuebbeler et al 2012 provide an ERF (with cirrus adjustments) of -0.93 Wm-2 for 5 Mt SO2/yr, that's -0.37 Wm-2 / (TgS/yr ) - Pitari et al 2014 : G4 experiment for 5 Mt SO2/yr shows -1.54, -0.73, -1.27 and -1.31, that's -0.61, -0.29, -0.51, -0.52 Wm-2 / (TgS/yr) - Kleinschmitt et al 2018, table 7a : -0.35 Wm-2 / (TgS/yr) with a lower value from Niemeier and Timmreck (2015) on the same graph at -0.26 Wm-2 / (TgS/yr) - Dai et al. 2018 : equatorial 5 Mt-S/yr SO2 injection at 21–24.5 km results in 0.72 Wm-2 / (TgS/yr), note that's a very high injection point So -0.6 Wm-2/(TgS/yr) is a clearly an upper (negative) bound of what the literature says. And it's unlikely to be achieved with an injection that is not controlled at all. "How long do these particles create cooling? 1-3 years. For our purposes, we'll go with 2.1 years" - Kleinschmitt et al 2017 point to a residence time of 0.8 year for their model and that of Niemeier and Timmreck, see Fig 7d. - Heckendorn et al 2012 has a residence time of at most 1 year for low injection rates, see their Fig 4a But more importantly there is no reason to mutiply by the residence time... all the above numbers are for continuous injections. Therefore they already account for the residence time of S ! "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" This value of the ECS is also for a constant-in-time RF and therefore a continuous injection rate. One cannot use a steady state calculation to infer what a pulse injection would do. There is a whole lot of literature on "climate metrics" on how to compare short-lived and long-lived species. This is a typical example here with SO2 (1 yr) and CO2 (multi-century). There is no such thing as a best metric (it's partly a scientific, partly a policy choice) but it is important to avoid inconsistencies. Here Make Sunset uses something alike the GTPs (GTP for sustained emissions), see [ https://link.springer.com/article/10.1007/s10584-005-1146-9 | https://link.springer.com/article/10.1007/s10584-005-1146-9 ] , to draw an equivalence between the SO2 and the CO2 but then applies it to a pulse emission, which is why I say their approach is misleading. And there is this double counting with the residence time. In my calculation which I posted a couple of days ago, I implicitly chose a GWP1 (GWP with 1 yr time horizon) for my calculation, with the caveat that you have only offset the RF of the CO2 for one year. If one wants to go for a T calculation, I would suggest to use GTP20, GTP50 and GTP100 for pulse emissions to get a range of equivalences between g SO2 and CO2. Also in their Table : "RF efficacy decline of 1% for each additional TgS/yr" Although that's not part of the calculation, this is not supported by the above studies. The saturation effect is much more. Finally I did not see on their web site what 10 $ buys you. It seems 10 $ only buys you 10 $ of cooling. Could the "10 $ buys 1 gSO2" just be an extrapolation from MIT Tech Review? Best regards, Olivier De: "Govindasamy Bala" <bala....@gmail.com> À: "Andrew Lockley" <andrew.lock...@gmail.com> Cc: "geoengineering" <geoengineering@googlegroups.com> Envoyé: Mercredi 28 Décembre 2022 07:42:32 Objet: Re: [geo] Make sunsets - Calculating Cooling this is all good and well-known, but the cost of this commercial venture (as per the news) is way too high. For a 2deg offset, the calculations show ~4 TgSO2 of injection per year which translates to ~ 40 Trillion dollars per year at a rate of $10 per gram of SO2. Cost estimates have gone through the roof into the stratosphere from a few billion dollars to trillions of dollars. Well, looks this is what commercialization would do. At this rate, the cost of stratospheric aerosol geoengineering could be similar to the cost of mitigation.... Bala On Wed, Dec 28, 2022 at 5:07 AM Andrew Lockley < [ mailto:andrew.lock...@gmail.com | andrew.lock...@gmail.com ] > wrote: [ https://makesunsets.com/blogs/news/calculating-cooling | https://makesunsets.com/blogs/news/calculating-cooling ] DECEMBER 27, 2022 Share 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? 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, c, 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! 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