Supervolcanoes tail risk has been exaggerated?

Link post

This is a linkpost for the peer-reviewed article “Severe Global Cooling After Volcanic Super-Eruptions? The Answer Hinges on Unknown Aerosol Size” (McGraw 2024). Below are its abstract, my notes, my estimation of a nearterm annual extinction risk from supervolcanoes of 3.38*10^-14, and a brief discussion of it. At the end, I have a table comparing my extinction risk estimates with Toby Ord’s existential risk guesses given in The Precipice.

Abstract

Here is the abstract from McGraw 2024 (emphasis mine):

Volcanic super-eruptions have been theorized to cause severe global cooling, with the 74 kya Toba eruption purported to have driven humanity to near-extinction. However, this eruption left little physical evidence of its severity and models diverge greatly on the magnitude of post-eruption cooling. A key factor controlling the super-eruption climate response is the size of volcanic sulfate aerosol, a quantity that left no physical record and is poorly constrained by models. Here we show that this knowledge gap severely limits confidence in model-based estimates of super-volcanic cooling, and accounts for much of the disagreement among prior studies. By simulating super-eruptions over a range of aerosol sizes, we obtain global mean responses varying from extreme cooling all the way to the previously unexplored scenario of widespread warming. We also use an interactive aerosol model to evaluate the scaling between injected sulfur mass and aerosol size. Combining our model results with the available paleoclimate constraints applicable to large eruptions, we estimate that global volcanic cooling is unlikely to exceed 1.5°C no matter how massive the stratospheric injection. Super-eruptions, we conclude, may be incapable of altering global temperatures substantially more than the largest Common Era eruptions. This lack of exceptional cooling could explain why no single super-eruption event has resulted in firm evidence of widespread catastrophe for humans or ecosystems.

My notes

I have no expertise in volcanology, but I found McGraw 2024 to be quite rigorous. In particular, they are able to use their model to replicate the more pessimistic results of past studies tweeking just 2 input parameters (highlighted by me below):

  • “We next evaluate if the assessed aerosol size spread is the likely cause of disagreement among past studies with interactive aerosol models. For this task, we interpolated the peak surface temperature responses from our ModelE simulations to the injected mass and peak global mean aerosol size from several recent interactive aerosol model simulations of large eruptions (Fig. 7, left panel). Accounting for these two values alone (left panel), our model experiments are able to reproduce remarkably similar peak temperature responses as the original studies found”. By “reproduce remarkably well”, they are referring to a coefficient of determination (R^2) of 0.87 (see Fig. 7).

  • “By comparison, if only the injected masses of the prior studies are used, the peak surface temperature responses cannot be reproduced”. By this, they are referring to an R^2 ranging from −1.82 to −0.04[1] (see Fig. 7).

They agree with past studies on the injected mass, but not on the aerosol size[2]. Fig. 3a (see below) illustrates the importance of the peak mean aerosol size. The greater the size, the weaker the cooling. I think this is explained as follows:

  • Primarily, smaller particles reflect more sunlight per mass due to having greater cross-sectional area per mass[3].

  • Secondarily, larger particles have less time to reflect sunlight due to falling down faster[4].

According to Fig. 2 (see below), aerosol size increases with injected mass, which makes intuitive sense. So we are lucky big eruptions have less cooling potential per injected mass. For context, the 1815 eruption of Mount Tambora injected 56 Tg of sulphur dioxide (SO2) into the stratosphere (from Table 1 of Wolff 2023), and had a volcanic explosivity index (VEI) of 7.

Past studies have used a small aerosol size for large eruptions, so they estimated much greater cooling than McGraw 2024. This says the following on the relationship between injected mass and aerosol mass:

  • “While a power law scaling (Eqn. 1) is a common assumption, we are aware of only one study that tested this relationship with interactive aerosol models (Aubry et al. 2020), and no study that specifically compared different eruption realizations (rather than different months within simulations) or included injection masses >100 Tg SO2”.

  • “Therefore, to test the validity of the power law functional form we ran GISS ModelE with the MATRIX interactive aerosol model (Bauer et al. 2008, 2020) over a wide range of SO2 injection masses”.

  • “Our results confirm that a power law emerges, with peak global mean effective radius values (green triangles in Fig. 2) closely following a k=1/​4 power law fitting to injected mass (dashed green line in Fig. 2)”.

This green line predicts larger aerosol size than most past studies for large eruptions (see figure just above).

Fig. 10 is pretty crucial to McGraw 2024’s conclusion of 1.5 ºC maximum cooling. In Fig. 10a (see below), they define 4 potential scalings based on the aerosol size of the eruptions of Pinatubo and Samalas:

  • (a) is defined by their upper bounds, so it is optimistic. It overestimates the constant of proportionality, and therefore overestimates aerosol size, and underestimates cooling.

  • (b) is defined by the means of their aerosol size (their best guess). “As scaling (b) traverses the mean of both our Pinatubo and Samalas Reff bounds, we treat this as our best estimate for how aerosol size scales with injection mass”.

  • (c) is defined by their lower bounds, so it is pessimistic. It underestimates the constant of proportionality, and therefore underestimates aerosol size, and overestimates cooling.

  • (d) is defined by the upper bound of Pinatubo (smaller eruption), and lower bound of Samalas (larger eruption), so it is very pessimistic. It underestimates the exponent of the power law, and therefore greatly underestimates aerosol size, and greatly overestimates cooling.

Figure 10b (see below) shows the cooling for the various levels of scaling. The maximum cooling is:

  • 0.5 ºC for their optimistic aerosol size (a).

  • 1 ºC for their best guess aerosol size (b).

  • 1.5 ºC for their pessimistic aerosol size (c). This is the number they mention in the abstract.

  • 5 ºC for 2 k Tg of SO2 and their very pessimistic aerosol size (d). 2 k Tg is the mass injected into the stratosphere in the Toba eruption (see Table 1), which some argue almost caused human extinction.

Extinction risk from supervolcanoes

Calculations

I calculated a nearterm annual extinction risk from supervolcanoes of 3.38*10^-14 (= 3.38*10^-8*10^-6). By nearterm annual risk, I mean that in a randomly selected year from 2025 to 2050. I got my estimate multiplying:

  • 3.38*10^-8 (= 2.5*10^-3*1.35*10^-5) annual probability of an eruption causing a maximum surface cooling of at least 5 ºC. I computed this from the product between[5]:

    • 0.25 % (= 0.05^2) chance of a more pessimistic relationship between injected mass and aerosol size than the suggested by curve (d) of Fig. 10b of McGraw 2024, assuming a probability of 5 % of the power law being defined by:

      • Greater aerosol mass than the upper bound of Pinatubo.

      • Smaller aerosol mass than the lower bound of Samalas.

    • 0.00135 % (= 1/​(74*10^3 + 2)) annual chance of an eruption worse than Toba’s, which was 74 k years ago. I just applied Laplace’s rule of succession, but I guess there is research estimating the probability of an eruption as a function of the minimum injected mass of sulphur dioxide into the stratosphere.

  • 10^-6 probability of human extinction given a maximum surface cooling of at least 5 ºC:

    • I have assumed before a probability of 10^-6 of human extinction given insufficient calorie production, considering 1 M years is the typical lifespan of a mammal species[6]. I defined insufficient calorie production as less than 1.91 k kcal/​person/​d, and I guess the aforementioned maximum surface cooling would result in a similar calorie production.

      • Eyeballing Figure 3 of Toon 2014, a maximum surface cooling of 5 ºC corresponds to a nuclear winter involving 63.1 Tg (= 10^1.8) of soot injected into the stratosphere.

      • Supposing the net effect on calorie production of all the adaptation measures is similar to assuming equitable food distribution, consumption of all edible livestock feed, and no household food waste, linearly interpolating the data of Fig. 5a of Xia 2022, 63.1 Tg leads to a calorie consumption of 2.18 k kcal/​person/​d (= 2.38 - (2.38 − 1.08)/​(150 − 47)*(63.1 − 47)), which is 1.14 (= 2.18*10^3/​(1.91*10^3)) times the threshold for insufficient calorie assumption.

    • For context, the aforementioned maximum surface cooling would result in temperatures similar to those of the last ice age temperatures. From NOAA, “the latest ice age peaked about 20,000 years ago, when global temperatures were likely about 10°F (5°C) colder than today”.

Discussion

Relative to what I obtained for other risks, my nearterm annual extinction risk from supervolcanoes of 3.38*10^-14 is:

  • 1.54 (= 3.38*10^-14/​(2.20*10^-14)) times mine for asteroids and comets.

  • 0.570 % (= 3.38*10^-14/​(5.93*10^-12)) of mine for nuclear war.

  • 3.38*10^-9 (= 3.38*10^-14/​10^-5) of mine for artificial intelligence (AI).

Note supervolcanoes might have cascade effects which lead to civilisational collapse, which could increase longterm extinction risk while simultaneously having a negligible impact on the nearterm one I estimated. I do not explicitly assess this in the post, but I guess the nearterm annual risk of human extinction from supervolcanoes is a good proxy for the importance of decreasing volcanic risk from a longtermist perspective:

  • Supervolcanoes might have cascade effects, but so do other catastrophes.

  • Global civilisational collapse due to supervolcanoes seems very unlikely to me. There would be global impacts via volcanic ash, but I guess infrastructure loss would be more significant for a similarly likely nuclear war.

  • Even if a volcanic eruption causes a global civilisational collapse which eventually leads to extinction, I guess full recovery would be extremely likely. In contrast, an extinction caused by advanced AI would arguably not allow for a full recovery.

  • Appealing to cascade effects or other known unknowns feels a little like a regression to the inscrutable, which is characterised by the following pattern:

In any case, I believe interventions to decrease deaths from supervolcanoes should be assessed based on standard cost-benefit analysis (CBA):

  • Having in mind my astronomically low nearterm annual extinction risk from supervolcanoes, it is unclear to me whether interventions to decrease deaths from supervolcanoes decrease extinction risk more cost-effectively than broader ones, like the best interventions to boost economic growth or decrease disease burden (e.g. GiveWell’s top charities).

  • I expect extinction risk can be decreased much more cost-effectively by focussing on AI risk rather than supervolcanoes risk (relatedly). So I would argue interventions to decrease deaths from supervolcanoes can only be competitive under an alternative worldview, like ones where the goal is boosting economic growth or decreasing disease burden.

Moreover, I would propose using standard CBAs not only in the political sphere, as argued by Elliott Thornley and Carl Shulman, but also outside of it. In particular, volcanic risk would be significantly more prioritised by grantmakers aligned with effective altruism if it is concluded that the best interventions to decrease it save lives more cost-effectively than GiveWell’s top charities.

Comparison between Toby Ord’s existential risk and my extinction risk

I collected in the table below Toby Ord’s annual existential risk from 2021 to 2120 from AI, nuclear war, supervolcanoes, and asteroids and comets based on his guesses given in The Precipice. I also added my estimates for the nearterm annual extinction risk from the same 4 risks, and the ratio between Toby’s values and mine. The values are not directly comparable, because Toby’s refer to existential risk and mine to extinction risk. Nonetheless, I still have the impression Toby greatly overestimated tail risk. This is in agreement with David Thorstad’s series exaggerating the risks, which includes subseries on climate, AI and bio risk, and discusses Toby’s book The Precipice.

Risk[7]

Toby’s annual existential risk from 2021 to 2120[8]

My nearterm annual extinction risk

Ratio between Toby’s value and mine

AI

0.105 %

0.001 %

105

Nuclear war

1.00*10^-5

5.93*10^-12

1.69 M

Supervolcanoes

1.00*10^-6

3.38*10^-14

29.6 M

Asteroids and comets

1.00*10^-8

2.20*10^-14

455 k

Acknowledgements

I did the initial investigation for this post as part of a project funded by Nuño Sempere’s research consultancy Shapley Maximizers, for which I worked as a contractor to assess the impact of The Centre for the Study of Existential Risk (CSER); thanks Nuño. Thanks to Anonymous Person 1 and Anonymous Person 2 for feedback on the draft.

  1. ^

    Note the R^2 can be arbitrarily negative because one can make arbitrarily bad predictions.

  2. ^

    “An aerosol is a suspension of fine solid particles or liquid droplets in air or another gas”.

  3. ^

    The cross-sectional area of a sphere is proportional to its radius to the power of 2, whereas its mass is proportional to its radius to the power of 3, so its cross-sectional area per mass is inversely proportional to its radius.

  4. ^

    Drag is proportional to area, and mass is proportional to volume, so the deceleration from drag is inversely proportional to the size (holding the drag coefficient and speed constant). In turn, this means larger particles will tend to be less decelerated by air, and therefore fall faster. In a vacuum, falling time does not depend on mass nor shape.

  5. ^

    For reference, McGraw 2024 “deem cooling beyond 5°C highly unlikely”.

  6. ^

    Humans are a mammal species.

  7. ^

    Ordered from the largest to the smallest.

  8. ^

    “Annual risk” = 1 - (1 - “total risk”)^(1/​“duration of the period in years”). The period has a duration of 100 years (= 2120 − 2021 + 1).