Do you mean underestimating? I agree that it’s not that large of an effect.
Thanks! I have now changed “overestimating” to “underestimating”.
The total loss of international food trade would cause 5.2% of all die in Xia 2022. So it seems like attributing this all to the climactic effects would increase your death rate by 5.2 percentage points. But digging in deeper, since you are using the gray dotted line in figure 5B corresponding to no human edible food fed to animals and zero waste, if you plugged in a value of 5 Tg, you would say that that amount of soot would actually decrease mortality relative to no food trade and 0 Tg. So clearly that no trade case is not the scenario of no human edible food fed to animals and zero waste
The BOTEC related to this in my comment had an error[1]. I have now corrected it in my comment above:
For arguably more reasonable assumptions of 50 % loss of international food trade, and 50 % of it being caused by the climatic effects, linearly interpolating, the increase in the death rate would be 25 % (= 0.5^2). So the new death rate would be 5.67 % (= 0.0443 + (0.0940 − 0.0443)*0.25), i.e. 1.28 (= 0.0567/0.0443) times my value.
It is still the case that I would get a negative death rate inputting 5 Tg into my formula. However, I am linearly interpolating, and the formula is only supposed to work for a mean stratospheric soot until the end of year 2 between 14.6 and 24.6 Tg, which excludes 5 Tg. I am approximating the logistic function describing the famine deaths due to the climatic effects as being null up to an injection of soot into the stratosphere of 11.3 Tg.
I couldn’t find quickly what exactly their assumptions were for that [no internationl food trade nor climatic effects] case
The blue line in b shows the percentage of population that can be supported by current food production when food production does not change but international trade is stopped.
So my interpretation is that the blue line corresponds to no livestock grain fed to humans and current household food waste (in 2010), but without international food trade. I have clarified this in the post. Ideally, instead of adjusting the top line of Figure 5b to include international food trade, I would rely on scenarios accounting for both climatic effects and no loss of international food trade, but Xia 2022 does not present results for that.
I understand that you are picking the no human edible food fed animals and zero waste scenario because you think other factors would compensate for this optimism. But I think it is particularly inappropriate for the relatively small amounts of Tg.
I am very open to different views about the famine death rate due to the climatic effects of a large nuclear war. My 95th percentile is 702 times my 5th percentile.
In the expression “1 - (0.993 + (0.902 − 0.993)/(24.6 − 14.6)*(14.5 − 14.6))*0.948”, 14.5 should have been 18.7. The calculation of the death rate in the post was correct, but it had the same typo in the formula, which I have now corrected.
For arguably more reasonable assumptions of 50 % loss of international food trade, and 50 % of it being caused by the climatic effects, linearly interpolating, the increase in the death rate would be 25 % (= 0.5^2). So the new death rate would be 5.67 % (= 0.0443 + (0.0940 − 0.0443)*0.25), i.e. 1.28 (= 0.0567/0.0443) times my value.
Half of the impact of the total loss of international food trade would cause 2.6% to die according to Xia 2022. So why is it not 4.43%+2.6% = 7.0% mortality?
It is still the case that I would get a negative death rate inputting 5 Tg into my formula. However, I am linearly interpolating, and the formula is only supposed to work for a mean stratospheric soot until the end of year 2 between 14.6 and 24.6 Tg, which excludes 5 Tg. I am approximating the logistic function describing the famine deaths due to the climatic effects as being null up to an injection of soot into the stratosphere of 11.3 Tg.
I see how you avoid the negative death rate by not considering 5 Tg. However, this does not address the issue that your comparison is not fair, which is exposed by the fact that if you did put in 5 Tg, you would get negative death rate.
So my interpretation is that the blue line corresponds to no livestock grain fed to humans and current food waste (in 2010), but without international food trade.
I think that is a reasonable assumption, as then the mortality due to 5 Tg alone (no trade in both cases) is ~2% (not a reduction in mortality).
Ideally, instead of adjusting the top line of Figure 5b to include international food trade, I would rely on scenarios accounting for both climatic effects and no loss of international food trade, but Xia 2022 does not present results for that.
One logically consistent way of doing it would be taking the difference between the blue and dark red lines, because they are comparable scenarios. I agree that no reduction in waste or food fed to animals is too pessimistic, but maybe you could do sensitivity on the scenario? Because even though I think that particular scenario is unlikely, I do think that cascading risks including loss of much of nonfood trade could very well increase mortality to these levels.
I am very open to different views about the famine death rate due to the climatic effects of a large nuclear war. My 95th percentile is 702 times my 5th percentile.
That is true, but if you had significant probability mass on the scenarios where people react very suboptimally, then your mean mortality would be a lot higher.
Half of the impact of the total loss of international food trade would cause 2.6% to die according to Xia 2022. So why is it not 4.43%+2.6% = 7.0% mortality?
In my BOTEC with “arguably more reasonable assumptions”, I am assuming just a 50 % reduction in international food trade, not 100 %.
I see how you avoid the negative death rate by not considering 5 Tg. However, this does not address the issue that your comparison is not fair, which is exposed by the fact that if you did put in 5 Tg, you would get negative death rate.
My famine deaths due to the climatic effects are a piecewise linear function which is null up to a soot injection into the stratosphere of 11.3 Tg. So, if one inputs 5 Tg into the function, the output is 0 famine deaths due to the climatic effects, not negative deaths. One gets negative deaths inputting 5 Tg into the pieces of the function respecting higher levels of soot because after a certain point (namely when everyone is fed), more food does not decrease famine deaths. My assumptions of no household food waste and feeding all livestock grain to humans would not make sense for low levels of soot, as I guess roughly everyone would be fed even without going all in these mitigation measures in those cases. In any case, I agree I am underestimating famine deaths due to the climatic effects for 5 Tg. My piecewise linear function is an approximation of a logistic function, which is always positive.
One logically consistent way of doing it would be taking the difference between the blue and dark red lines, because they are comparable scenarios. I agree that no reduction in waste or food fed to animals is too pessimistic, but maybe you could do sensitivity on the scenario? Because even though I think that particular scenario is unlikely, I do think that cascading risks including loss of much of nonfood trade could very well increase mortality to these levels.
I am happy to describe what happens in a very worst case scenario, involving no adaptations, and no international food trade. Eyeballing the bottom line of Figure 5b, the famine death rate due to the climatic effects for my 22.1 Tg would be around 25 %. In this case, the probability of 50 % famine deaths due to the climatic effects of nuclear war before 2050 would be 0.614 %, i.e. 1.87 k (= 0.00614/(3.29*10^(-6))) times as likely as my best guess.
I must note that, under the above assumptions, activities related to resilient food solutions would have cost-effectiveness 0, as one would be assuming no adaptations. In general, I do not think it is obvious whether the cost-effectiveness of decreasing famine deaths due to the climatic effects at the margin increases/decreases with mortality. The cost-effectiveness of saving lives is negligible for negligible mortality and sufficiently high mortality, and my model assumes cost-effectiveness increases linearly with mortality, but I wonder what is the death rate for which cost-effectiveness is maximum.
In my 1st reply, I said “AI and bio catastrophes would also have cascade effects”. Relatedly, how society reacts affects all types of catastrophes, not just nuclear winter. So, if one expects interventions decreasing famine deaths in a nuclear winter to be more cost-effective due to the possibility of society reacting badly, one should also expect interventions mitigating the risks of AI and bio catastrophes to be more cost-effective.
That is true, but if you had significant probability mass on the scenarios where people react very suboptimally, then your mean mortality would be a lot higher.
I would say we have strong evidence that animal consumption would decrease in a nuclear winter because prices would go up, and meat is much more expensive that grain. More broadly, as I said in the post:
It is quite easy for an apparently reasonable distribution to have a nonsensical right tail which drives the expected value upwards.
>Half of the impact of the total loss of international food trade would cause 2.6% to >die according to Xia 2022. So why is it not 4.43%+2.6% = 7.0% mortality?
In my BOTEC with “arguably more reasonable assumptions”, I am assuming just a 50 % reduction in international food trade, not 100 %.
That’s why I only attributed half of the impact of total loss of international food trade. If I attributed all the impact, it would have been 4.43%+5.2% = 9.6% mortality. I don’t see how you are getting 5.67% mortality.
My famine deaths due to the climatic effects are a piecewise linear function which is null up to a soot injection into the stratosphere of 11.3 Tg. So, if one inputs 5 Tg into the function, the output is 0 famine deaths due to the climatic effects, not negative deaths.
My understanding is that you chose this piecewise linear function to be null at 11.3 Tg because that’s where the blue and gray dotted lines crossed, meaning that it appeared that the climate impacts did not kill anyone below 11.3 Tg. But what I’m arguing is that those two lines had different assumptions about feeding food to animals and waste, so the conclusion is not correct that there was no climate mortality below 11.3 Tg. And this is supported by the fact that there are currently under nutrition deaths, and any nonzero Tg is likely to increase those deaths.
I am happy to describe what happens in a very worst case scenario, involving no adaptations, and no international food trade.
There are many ways that things could go worse than that scenario. As I have mentioned, there could be reductions in nonfood trade, such as fertilizers, pesticides, agricultural equipment, energy, etc. There could be further international conflict. There could be civil unrest in countries and a breakdown of the rule of law. If there is loss of cooperation outside of people known personally, it could mean a return to foraging, or ~99.9% mortality if we returned to the last time we were all hunter-gatherers. But it could be worse than this given the people initially would not be very good foragers, the climate would be worse, and we could cause a lot of extinctions during the collapse. The very worst case scenario is if there is insufficient food, if it were divided equally, everyone would starve to death.
I must note that, under the above assumptions, activities related to resilient food solutions would have cost-effectiveness 0, as one would be assuming no adaptations.
I certainly agree that there would be some reduction in human edible food fed to animals and food waste before there will be large-scale deployment of resilient foods. But what I’m arguing is that the baseline expected mortality without significant preparation on resilient foods could be 25% because of a combination of factors listed above. Furthermore, I think that preparation involving planning and piloting of resilient foods would make it less likely that we fall into some of the terrible situations above.
In general, I do not think it is obvious whether the cost-effectiveness of decreasing famine deaths due to the climatic effects at the margin increases/decreases with mortality. The cost-effectiveness of saving lives is negligible for negligible mortality and sufficiently high mortality, and my model assumes cost-effectiveness increases linearly with mortality, but I wonder what is the death rate for which cost-effectiveness is maximum.
As above, even if the baseline expectation were extinction, there could be high cost effectiveness of saving lives from resilient foods by shifting us away from that scenario, so I disagree with “The cost-effectiveness of saving lives is negligible for … sufficiently high mortality.”
That’s why I only attributed half of the impact of total loss of international food trade. If I attributed all the impact, it would have been 4.43%+5.2% = 9.6% mortality. I don’t see how you are getting 5.67% mortality.
I was assuming 50 % reduction in international trade, and 50 % of that reduction being caused by climatic effects, so only 25 % (= 0.5^2) caused by climatic effects. I have changed “50 % of it” to “50 % of this loss” in my original reply to clarify.
My understanding is that you chose this piecewise linear function to be null at 11.3 Tg because that’s where the blue and gray dotted lines crossed, meaning that it appeared that the climate impacts did not kill anyone below 11.3 Tg.
Yes, that is quite close to what I did. The lines you describe intersect at 10.5 Tg, but I used 11.3 Tg because I believe Xia 2022 overestimates the duration of the climatic effects.
But what I’m arguing is that those two lines had different assumptions about feeding food to animals and waste, so the conclusion is not correct that there was no climate mortality below 11.3 Tg. And this is supported by the fact that there are currently under nutrition deaths
I was guessing this does not matter much because I think the famine deaths for 0 Tg for the following cases are similar:
No international food trade, and current food production. This matches the blue line of Fig. 5b I used to adjust the top line to include international food trade, and corresponds to 5.2 % famine deaths.
No international food trade, all livestock grain fed to humans, and no household food waste. This is the case I should ideally have used to adjust the top line, and corresponds to less than 5.2 % famine deaths.
Since the 2nd case has less famine deaths, I am overestimating the effect of having international food trade, thus underestimating famine deaths. My guess for the effect being small stems from, in Fig. 5b, the cases for which there are climatic effects (5 redish lines, and 2 greyish lines) all seemingly converging as the soot injected into the stratosphere tends to 0 Tg:
The convergence of the redish and greyish lines makes intuitive sense to me. If it was possible now to, without involving international food trade, decrease famine deaths by feeding livestock grain to humans or decreasing household food waste, I guess these would have already been done. I assume countries would prefer less famine deaths over greater animal consumption or household food waste.
there are currently under nutrition deaths, and any nonzero Tg is likely to increase those deaths.
I guess famine deaths due to the climatic effects are described by a logistic function, which is a strictly increasing function, so I agree with the above. However, I guess the increase will be pretty small for low levels of soot.
There are many ways that things could go worse than that scenario. As I have mentioned, there could be reductions in nonfood trade, such as fertilizers, pesticides, agricultural equipment, energy, etc. There could be further international conflict. There could be civil unrest in countries and a breakdown of the rule of law. If there is loss of cooperation outside of people known personally, it could mean a return to foraging, or ~99.9% mortality if we returned to the last time we were all hunter-gatherers. But it could be worse than this given the people initially would not be very good foragers, the climate would be worse, and we could cause a lot of extinctions during the collapse. The very worst case scenario is if there is insufficient food, if it were divided equally, everyone would starve to death.
There arereasons pointing in the other direction too. In general, I think further more empirical investigation usually leads to lower risk estimates (cf. John Halstead’s climate change and longtermism report). I am trying to update all the way now (relatedly), such that I do not (wrongly) expect risk to decrease (the rational thing is expecting best guesses to stay the same, although this is still compatible with higher than 50 % chance of the best guess decreasing).
As above, even if the baseline expectation were extinction, there could be high cost effectiveness of saving lives from resilient foods by shifting us away from that scenario, so I disagree with “The cost-effectiveness of saving lives is negligible for … sufficiently high mortality.”
I just meant the cost-effectiveness of saving lives tends to 0 as the expected population loss (accounting for preparation, response and resilience) tends to 100 %. An expected population loss of exactly 100 % means extinction with 100 % probability, in which case there is no room to save lives (nor to avoid extinction). Of course, this is a very extreme unrealistic case, but it illustrates cost-effectiveness will start decreasing at some point, so “I wonder what is the death rate for which cost-effectiveness is maximum”. On way of thinking about it is that, although importance always increases with mortality, the decrease in tractability after a certain point is sufficient for cost-effectiveness to decrease too.
I was assuming 50 % reduction in international trade, and 50 % of that reduction being caused by climatic effects, so only 25 % (= 0.5^2) caused by climatic effects. I have changed “50 % of it” to “50 % of this loss” in my original reply to clarify.
That makes sense. Thanks for putting the figure in!
I guess famine deaths due to the climatic effects are described by a logistic function, which is a strictly increasing function, so I agree with the above. However, I guess the increase will be pretty small for low levels of soot.
If it were linear starting at 10.5 Tg and going to 22.1 Tg, versus linear starting at 0 Tg and going to 22 Tg, then I think the integral (impact) would be about four times as much. But I agree if you are going linear from 10.4 Tg versus logistic from 0 Tg, the difference would not be as large. But it still could be a factor of two or three, so I think it’s good to run a sensitivity case.
If it were linear starting at 10.5 Tg and going to 22.1 Tg, versus linear starting at 0 Tg and going to 22 Tg, then I think the integral (impact) would be about four times as much.
You are right about that integral, but I do think that is the relevant BOTEC. What we care about is the mean death rate (for a given input soot distribition), not its integral. For example, for a uniform soot distribution ranging from 0 to 37.4 Tg (= 2*18.7), whose mean matches mine of 18.7 Tg[1], the middle points of the linear parts would be:
If the linear part started at 10.5 Tg, 7.27 % (= ((10.5 + 37.4)/2 − 10.5)/(18.7 − 10.5)*0.0443).
If the linear part started at 0 Tg, 10.1 % (= ((0 + 37.4)/2 − 0)/(18.7 − 10.5)*0.0443).
So the mean death rates would be:
If the linear part started at 10.5 Tg, 5.23 % (= (10.5*0 + (37.4 − 10.5)*0.0727)/37.4).
If the linear part started at 0 Tg, 10.1 %.
This suggests famine deaths due to the climatic effects would be 1.93 (= 0.101/0.0523) times as large if the linear part started at 0 Tg.
Another way of running the BOTEC is considering an effective soot level, equal to the soot level minus the value at which the linear part starts. My effective soot level is 8.20 Tg (= 18.7 − 10.5), whereas it would be 18.7 Tg if the linear part started at 0 Tg, which suggests deaths would be 1.78 (= 18.7/10.5) times as large in the latter case. Using a logistic function instead of a linear one, I think the factor would be quite close to 1.
But I agree if you are going linear from 10.4 Tg versus logistic from 0 Tg, the difference would not be as large. But it still could be a factor of two or three, so I think it’s good to run a sensitivity case.
The challenge here is that the logistic function f(x) = a + b/(1 + e^(-k(x—x_0))) has 4 parameters, but I only have 3 conditions, f(0) = 0, f(18.7) = 0.0443, f(+inf) = 1. I think this means I could define the 4th condition such that the logistic function stays near 0 until 10.5 Tg.
Ideally, I would define the logistic function for f(0) = 0 and f(+inf) = 1, but then finding its parameters fitting it to the 16, 27, 37, 47 and 150 Tg cases of Xia 2022 for international food trade, all livestock grain fed to humans, and no household food waste. Then I would use f(18.7) as the death rate. Even better, I would get a distribution for the soot, generate N samples (x_1, x_2, …, and x_N), and then use (f(x_1) + f(x_2) + … + f(x_N))/N as the death rate.
Thanks! I have now changed “overestimating” to “underestimating”.
The BOTEC related to this in my comment had an error[1]. I have now corrected it in my comment above:
It is still the case that I would get a negative death rate inputting 5 Tg into my formula. However, I am linearly interpolating, and the formula is only supposed to work for a mean stratospheric soot until the end of year 2 between 14.6 and 24.6 Tg, which excludes 5 Tg. I am approximating the logistic function describing the famine deaths due to the climatic effects as being null up to an injection of soot into the stratosphere of 11.3 Tg.
From the legend of Figure 5:
So my interpretation is that the blue line corresponds to no livestock grain fed to humans and current household food waste (in 2010), but without international food trade. I have clarified this in the post. Ideally, instead of adjusting the top line of Figure 5b to include international food trade, I would rely on scenarios accounting for both climatic effects and no loss of international food trade, but Xia 2022 does not present results for that.
I am very open to different views about the famine death rate due to the climatic effects of a large nuclear war. My 95th percentile is 702 times my 5th percentile.
In the expression “1 - (0.993 + (0.902 − 0.993)/(24.6 − 14.6)*(14.5 − 14.6))*0.948”, 14.5 should have been 18.7. The calculation of the death rate in the post was correct, but it had the same typo in the formula, which I have now corrected.
Half of the impact of the total loss of international food trade would cause 2.6% to die according to Xia 2022. So why is it not 4.43%+2.6% = 7.0% mortality?
I see how you avoid the negative death rate by not considering 5 Tg. However, this does not address the issue that your comparison is not fair, which is exposed by the fact that if you did put in 5 Tg, you would get negative death rate.
I think that is a reasonable assumption, as then the mortality due to 5 Tg alone (no trade in both cases) is ~2% (not a reduction in mortality).
One logically consistent way of doing it would be taking the difference between the blue and dark red lines, because they are comparable scenarios. I agree that no reduction in waste or food fed to animals is too pessimistic, but maybe you could do sensitivity on the scenario? Because even though I think that particular scenario is unlikely, I do think that cascading risks including loss of much of nonfood trade could very well increase mortality to these levels.
That is true, but if you had significant probability mass on the scenarios where people react very suboptimally, then your mean mortality would be a lot higher.
In my BOTEC with “arguably more reasonable assumptions”, I am assuming just a 50 % reduction in international food trade, not 100 %.
My famine deaths due to the climatic effects are a piecewise linear function which is null up to a soot injection into the stratosphere of 11.3 Tg. So, if one inputs 5 Tg into the function, the output is 0 famine deaths due to the climatic effects, not negative deaths. One gets negative deaths inputting 5 Tg into the pieces of the function respecting higher levels of soot because after a certain point (namely when everyone is fed), more food does not decrease famine deaths. My assumptions of no household food waste and feeding all livestock grain to humans would not make sense for low levels of soot, as I guess roughly everyone would be fed even without going all in these mitigation measures in those cases. In any case, I agree I am underestimating famine deaths due to the climatic effects for 5 Tg. My piecewise linear function is an approximation of a logistic function, which is always positive.
I am happy to describe what happens in a very worst case scenario, involving no adaptations, and no international food trade. Eyeballing the bottom line of Figure 5b, the famine death rate due to the climatic effects for my 22.1 Tg would be around 25 %. In this case, the probability of 50 % famine deaths due to the climatic effects of nuclear war before 2050 would be 0.614 %, i.e. 1.87 k (= 0.00614/(3.29*10^(-6))) times as likely as my best guess.
I must note that, under the above assumptions, activities related to resilient food solutions would have cost-effectiveness 0, as one would be assuming no adaptations. In general, I do not think it is obvious whether the cost-effectiveness of decreasing famine deaths due to the climatic effects at the margin increases/decreases with mortality. The cost-effectiveness of saving lives is negligible for negligible mortality and sufficiently high mortality, and my model assumes cost-effectiveness increases linearly with mortality, but I wonder what is the death rate for which cost-effectiveness is maximum.
In my 1st reply, I said “AI and bio catastrophes would also have cascade effects”. Relatedly, how society reacts affects all types of catastrophes, not just nuclear winter. So, if one expects interventions decreasing famine deaths in a nuclear winter to be more cost-effective due to the possibility of society reacting badly, one should also expect interventions mitigating the risks of AI and bio catastrophes to be more cost-effective.
I would say we have strong evidence that animal consumption would decrease in a nuclear winter because prices would go up, and meat is much more expensive that grain. More broadly, as I said in the post:
That’s why I only attributed half of the impact of total loss of international food trade. If I attributed all the impact, it would have been 4.43%+5.2% = 9.6% mortality. I don’t see how you are getting 5.67% mortality.
My understanding is that you chose this piecewise linear function to be null at 11.3 Tg because that’s where the blue and gray dotted lines crossed, meaning that it appeared that the climate impacts did not kill anyone below 11.3 Tg. But what I’m arguing is that those two lines had different assumptions about feeding food to animals and waste, so the conclusion is not correct that there was no climate mortality below 11.3 Tg. And this is supported by the fact that there are currently under nutrition deaths, and any nonzero Tg is likely to increase those deaths.
There are many ways that things could go worse than that scenario. As I have mentioned, there could be reductions in nonfood trade, such as fertilizers, pesticides, agricultural equipment, energy, etc. There could be further international conflict. There could be civil unrest in countries and a breakdown of the rule of law. If there is loss of cooperation outside of people known personally, it could mean a return to foraging, or ~99.9% mortality if we returned to the last time we were all hunter-gatherers. But it could be worse than this given the people initially would not be very good foragers, the climate would be worse, and we could cause a lot of extinctions during the collapse. The very worst case scenario is if there is insufficient food, if it were divided equally, everyone would starve to death.
I certainly agree that there would be some reduction in human edible food fed to animals and food waste before there will be large-scale deployment of resilient foods. But what I’m arguing is that the baseline expected mortality without significant preparation on resilient foods could be 25% because of a combination of factors listed above. Furthermore, I think that preparation involving planning and piloting of resilient foods would make it less likely that we fall into some of the terrible situations above.
As above, even if the baseline expectation were extinction, there could be high cost effectiveness of saving lives from resilient foods by shifting us away from that scenario, so I disagree with “The cost-effectiveness of saving lives is negligible for … sufficiently high mortality.”
I was assuming 50 % reduction in international trade, and 50 % of that reduction being caused by climatic effects, so only 25 % (= 0.5^2) caused by climatic effects. I have changed “50 % of it” to “50 % of this loss” in my original reply to clarify.
Yes, that is quite close to what I did. The lines you describe intersect at 10.5 Tg, but I used 11.3 Tg because I believe Xia 2022 overestimates the duration of the climatic effects.
I was guessing this does not matter much because I think the famine deaths for 0 Tg for the following cases are similar:
No international food trade, and current food production. This matches the blue line of Fig. 5b I used to adjust the top line to include international food trade, and corresponds to 5.2 % famine deaths.
No international food trade, all livestock grain fed to humans, and no household food waste. This is the case I should ideally have used to adjust the top line, and corresponds to less than 5.2 % famine deaths.
Since the 2nd case has less famine deaths, I am overestimating the effect of having international food trade, thus underestimating famine deaths. My guess for the effect being small stems from, in Fig. 5b, the cases for which there are climatic effects (5 redish lines, and 2 greyish lines) all seemingly converging as the soot injected into the stratosphere tends to 0 Tg:
The convergence of the redish and greyish lines makes intuitive sense to me. If it was possible now to, without involving international food trade, decrease famine deaths by feeding livestock grain to humans or decreasing household food waste, I guess these would have already been done. I assume countries would prefer less famine deaths over greater animal consumption or household food waste.
I guess famine deaths due to the climatic effects are described by a logistic function, which is a strictly increasing function, so I agree with the above. However, I guess the increase will be pretty small for low levels of soot.
There are reasons pointing in the other direction too. In general, I think further more empirical investigation usually leads to lower risk estimates (cf. John Halstead’s climate change and longtermism report). I am trying to update all the way now (relatedly), such that I do not (wrongly) expect risk to decrease (the rational thing is expecting best guesses to stay the same, although this is still compatible with higher than 50 % chance of the best guess decreasing).
I just meant the cost-effectiveness of saving lives tends to 0 as the expected population loss (accounting for preparation, response and resilience) tends to 100 %. An expected population loss of exactly 100 % means extinction with 100 % probability, in which case there is no room to save lives (nor to avoid extinction). Of course, this is a very extreme unrealistic case, but it illustrates cost-effectiveness will start decreasing at some point, so “I wonder what is the death rate for which cost-effectiveness is maximum”. On way of thinking about it is that, although importance always increases with mortality, the decrease in tractability after a certain point is sufficient for cost-effectiveness to decrease too.
That makes sense. Thanks for putting the figure in!
If it were linear starting at 10.5 Tg and going to 22.1 Tg, versus linear starting at 0 Tg and going to 22 Tg, then I think the integral (impact) would be about four times as much. But I agree if you are going linear from 10.4 Tg versus logistic from 0 Tg, the difference would not be as large. But it still could be a factor of two or three, so I think it’s good to run a sensitivity case.
You are right about that integral, but I do think that is the relevant BOTEC. What we care about is the mean death rate (for a given input soot distribition), not its integral. For example, for a uniform soot distribution ranging from 0 to 37.4 Tg (= 2*18.7), whose mean matches mine of 18.7 Tg[1], the middle points of the linear parts would be:
If the linear part started at 10.5 Tg, 7.27 % (= ((10.5 + 37.4)/2 − 10.5)/(18.7 − 10.5)*0.0443).
If the linear part started at 0 Tg, 10.1 % (= ((0 + 37.4)/2 − 0)/(18.7 − 10.5)*0.0443).
So the mean death rates would be:
If the linear part started at 10.5 Tg, 5.23 % (= (10.5*0 + (37.4 − 10.5)*0.0727)/37.4).
If the linear part started at 0 Tg, 10.1 %.
This suggests famine deaths due to the climatic effects would be 1.93 (= 0.101/0.0523) times as large if the linear part started at 0 Tg.
Another way of running the BOTEC is considering an effective soot level, equal to the soot level minus the value at which the linear part starts. My effective soot level is 8.20 Tg (= 18.7 − 10.5), whereas it would be 18.7 Tg if the linear part started at 0 Tg, which suggests deaths would be 1.78 (= 18.7/10.5) times as large in the latter case. Using a logistic function instead of a linear one, I think the factor would be quite close to 1.
The challenge here is that the logistic function f(x) = a + b/(1 + e^(-k(x—x_0))) has 4 parameters, but I only have 3 conditions, f(0) = 0, f(18.7) = 0.0443, f(+inf) = 1. I think this means I could define the 4th condition such that the logistic function stays near 0 until 10.5 Tg.
Ideally, I would define the logistic function for f(0) = 0 and f(+inf) = 1, but then finding its parameters fitting it to the 16, 27, 37, 47 and 150 Tg cases of Xia 2022 for international food trade, all livestock grain fed to humans, and no household food waste. Then I would use f(18.7) as the death rate. Even better, I would get a distribution for the soot, generate N samples (x_1, x_2, …, and x_N), and then use (f(x_1) + f(x_2) + … + f(x_N))/N as the death rate.
18.7 Tg is the mean stratospheric soot until the end of year 2 corresponding to an initial injection of 22.1 Tg.