After falling into disrepute for some years, the nuclear winter hypothesis has enjoyed something of a renaissance over the past decade. In the January 2010 edition of

*Scientific American*, two of the principal proponents of the hypothesis, Alan Robock and Owen Brian Toon, published an article summarising recent work. This article focused on the hypothetical case of a regional nuclear war between India and Pakistan, in which each side dropped 50 nuclear warheads, with a yield of 15-kilotons each, on the highest population density targets in the opponent's territory.
Robock and his colleagues assumed that this would result in at least 5 teragrams of sooty smoke reaching the upper troposphere over India and Pakistan. A climate model was developed to calculate the effects, as Robock and Toon report:

"

These claims seem to have been widely believed within the scientific community. For example, in 2017

But is there any way of empirically testing the predictions made by Robock and his colleagues? Well, perhaps there is. In 1945, the Americans inflicted an incendiary bombing campaign on Japan prior to the use of nuclear weapons. Between March and June of 1945, Japan's six largest industrial centres, Tokyo, Nagoya, Kobe, Osaka, Yokohama and Kawasaki, were devastated. As military historian John Keegan wrote, “Japan's flimsy wood-and-paper cities burned far more easily than European stone and brick...by mid-June...260,000 people had been killed, 2 million buildings destroyed and between 9 and 13 million people made homeless...by July 60 per cent of the ground area of the country's sixty larger cities and towns had been burnt out,” (

This devastation created a huge amount of smoke, so what effect did it have on the world's climate? Well Robock and Brian Zambri have recently published a paper, 'Did smoke from city fires in World War II cause global cooling?', (

Robock and Zambri use the following equation to estimate the total mass of soot $M$ injected into the lower stratosphere:

$$

M = A*F*E*R*L \;.

$$ $A$ is the total area burned, $F$ is the mass of fuel per unit area, $E$ is the percentage of fuel emitted as soot into the upper troposphere, $R$ is the fraction that is not rained out, and $L$ is the fraction lofted from the upper troposphere into the lower stratosphere. Robock and Zambri then make the following statements:

"

But then something strange happens at this point, because the authors make no attempt to quantify the uncertainty, or to place confidence intervals around their estimate of 0.5 teragrams.

I'll come back to this shortly, but for the moment simply note that 0.5 teragrams is one-tenth of the amount of soot which is assumed to result from a nuclear exchange between India and Pakistan, a quantity of soot which Robock and his colleagues claim is sufficient to cause a worldwide nuclear winter.

Having obtained their estimate that 0.5 teragrams of soot reached the lower stratosphere in 1945, Robock and Zambri examine the climate record to see if there was any evidence of global cooling. What they find is a reduction in temperatures at the beginning of 1945, before the bombing of Japan, but no evidence of cooling thereafter: "The injection of 0.5–1 Tg of soot into the upper troposphere from city fires during World War II would be expected to produce 0.1–0.2 K global average cooling...when examining the observed signal further and comparing them to natural variability, it is not possible to detect a statistically significant signal."

Despite this negative result, Robock and Zambri defiantly conclude that "Nevertheless, these results do not provide observational support to counter nuclear winter theory." However, the proponents of the nuclear winter hypothesis now seem to have put themselves in the position of making the following joint claim:

Unfortunately, their analysis doesn't even entitle them to make this assertion, precisely because they failed to quantity the uncertainty in that estimate of 0.5 teragrams. The omission rather stands out like a sore thumb, because there are well-known, routine methods for calculating such uncertainties.

Let's go through these methods, starting with the formula $M = A*F*E*R*L \;.$ The uncertainty in the input variables here propagates through to the uncertainty in the output variable, the mass $M$. It seems reasonable to assume that the input variables here are mutually independent, so the uncertainty $U_M$ in the output variable can be inferred by a simple formula from the uncertainties attached to each of the input variables:

$$

U_M = \sqrt{(U_A^2 + U_F^2+U_E^2+U_R^2+U_L^2)} \;.

$$ $U_A$ is the uncertainty in the total area burned, $U_F$ is the uncertainty in the mass of fuel per unit area, $U_E$ is the uncertainty in the percentage of fuel emitted as soot into the upper troposphere, $U_R$ is the uncertainty in the fraction that is not rained out, and $U_L$ is the uncertainty in the fraction lofted from the upper troposphere into the lower stratosphere.

Next, to infer confidence intervals, we can follow the prescriptions of the IPCC, the Intergovernmental Panel on Climate Change. The 2010

First we note that because $M$ is the product of several variables, its distribution will tend towards a lognormal distribution, or at least a positively skewed distribution resembling the lognormal. The IPCC figure below depicts how the upper and lower 95% confidence limits can be inferred from the uncertainty in a lognormally distributed quantity. The uncertainty $U_M$ corresponds to the 'uncertainty half-range' in IPCC terms.

*The model calculated how winds would blow the smoke around the world and how the smoke particles would settle out from the atmosphere. The smoke covered all the continents within two weeks. The black, sooty smoke absorbed sunlight, warmed and rose into the stratosphere. Rain never falls there, so the air is never cleansed by precipitation; particles very slowly settle out by falling, with air resisting them...**"The climatic response to the smoke was surprising. Sunlight was immediately reduced, cooling the planet to temperatures lower than any experienced for the past 1,000 years. The global average cooling, of about 1.25 degrees Celsius (2.3 degrees Fahrenheit), lasted for several years, and even after 10 years the temperature was still 0.5 degree C colder than normal. The models also showed a 10 percent reduction in precipitation worldwide...Less sunlight and precipitation, cold spells, shorter growing seasons and more ultraviolet radiation would all reduce or eliminate agricultural production.*," (*Scientific American*, January 2010, p78-79).These claims seem to have been widely believed within the scientific community. For example, in 2017

*NewScientist*magazine wrote a Leader article on the North Korean nuclear problem, which asserted that: "those who study nuclear war scenarios say millions of tonnes of smoke would gush into the stratosphere, resulting in a nuclear winter that would lower global temperatures for years. The ensuing global crisis in agriculture – dubbed a “nuclear famine” – would be devastating," (*NewScientist*, 22nd April 2017).But is there any way of empirically testing the predictions made by Robock and his colleagues? Well, perhaps there is. In 1945, the Americans inflicted an incendiary bombing campaign on Japan prior to the use of nuclear weapons. Between March and June of 1945, Japan's six largest industrial centres, Tokyo, Nagoya, Kobe, Osaka, Yokohama and Kawasaki, were devastated. As military historian John Keegan wrote, “Japan's flimsy wood-and-paper cities burned far more easily than European stone and brick...by mid-June...260,000 people had been killed, 2 million buildings destroyed and between 9 and 13 million people made homeless...by July 60 per cent of the ground area of the country's sixty larger cities and towns had been burnt out,” (

*The Second World War*, 1989, p481).This devastation created a huge amount of smoke, so what effect did it have on the world's climate? Well Robock and Brian Zambri have recently published a paper, 'Did smoke from city fires in World War II cause global cooling?', (

*Journal of Geophysical Research: Atmospheres*, 2018, 123), which addresses this very question.Robock and Zambri use the following equation to estimate the total mass of soot $M$ injected into the lower stratosphere:

$$

M = A*F*E*R*L \;.

$$ $A$ is the total area burned, $F$ is the mass of fuel per unit area, $E$ is the percentage of fuel emitted as soot into the upper troposphere, $R$ is the fraction that is not rained out, and $L$ is the fraction lofted from the upper troposphere into the lower stratosphere. Robock and Zambri then make the following statements:

"

*Because the city fires were at nighttime and did not always persist until daylight, and because some of the city fires were in the spring, with less intense sunlight, we estimate that L is about 0.5, so based on the values above, M for Japan for the summer of 1945 was about 0.5 Tg of soot. However, this estimate is extremely uncertain.*"But then something strange happens at this point, because the authors make no attempt to quantify the uncertainty, or to place confidence intervals around their estimate of 0.5 teragrams.

I'll come back to this shortly, but for the moment simply note that 0.5 teragrams is one-tenth of the amount of soot which is assumed to result from a nuclear exchange between India and Pakistan, a quantity of soot which Robock and his colleagues claim is sufficient to cause a worldwide nuclear winter.

Having obtained their estimate that 0.5 teragrams of soot reached the lower stratosphere in 1945, Robock and Zambri examine the climate record to see if there was any evidence of global cooling. What they find is a reduction in temperatures at the beginning of 1945, before the bombing of Japan, but no evidence of cooling thereafter: "The injection of 0.5–1 Tg of soot into the upper troposphere from city fires during World War II would be expected to produce 0.1–0.2 K global average cooling...when examining the observed signal further and comparing them to natural variability, it is not possible to detect a statistically significant signal."

Despite this negative result, Robock and Zambri defiantly conclude that "Nevertheless, these results do not provide observational support to counter nuclear winter theory." However, the proponents of the nuclear winter hypothesis now seem to have put themselves in the position of making the following joint claim:

*'5 teragrams of soot would cause a global nuclear winter, but the 0.5 teragrams injected into the atmosphere in 1945 didn't make a mark in the climatological record.'*Unfortunately, their analysis doesn't even entitle them to make this assertion, precisely because they failed to quantity the uncertainty in that estimate of 0.5 teragrams. The omission rather stands out like a sore thumb, because there are well-known, routine methods for calculating such uncertainties.

Let's go through these methods, starting with the formula $M = A*F*E*R*L \;.$ The uncertainty in the input variables here propagates through to the uncertainty in the output variable, the mass $M$. It seems reasonable to assume that the input variables here are mutually independent, so the uncertainty $U_M$ in the output variable can be inferred by a simple formula from the uncertainties attached to each of the input variables:

$$

U_M = \sqrt{(U_A^2 + U_F^2+U_E^2+U_R^2+U_L^2)} \;.

$$ $U_A$ is the uncertainty in the total area burned, $U_F$ is the uncertainty in the mass of fuel per unit area, $U_E$ is the uncertainty in the percentage of fuel emitted as soot into the upper troposphere, $U_R$ is the uncertainty in the fraction that is not rained out, and $U_L$ is the uncertainty in the fraction lofted from the upper troposphere into the lower stratosphere.

Next, to infer confidence intervals, we can follow the prescriptions of the IPCC, the Intergovernmental Panel on Climate Change. The 2010

*Scientific American*article boasts that Robock is a participant in the IPCC, so he will surely be familiar with this methodology.First we note that because $M$ is the product of several variables, its distribution will tend towards a lognormal distribution, or at least a positively skewed distribution resembling the lognormal. The IPCC figure below depicts how the upper and lower 95% confidence limits can be inferred from the uncertainty in a lognormally distributed quantity. The uncertainty $U_M$ corresponds to the 'uncertainty half-range' in IPCC terms.

The IPCC figure "illustrates the sensitivity of the lower and upper bounds of the 95 percent probability range, which are the 2.5th and 97.5th percentiles, respectively, calculated assuming a lognormal distribution based upon an estimated uncertainty half-range from an error propagation approach. The uncertainty range is approximately symmetric relative to the mean up to an uncertainty half-range of approximately 10 to 20 percent. As the uncertainty half-range, U, becomes large, the 95 percent uncertainty range shown [in the Figure above] becomes large and asymmetric, "(

*IPCC**).**Guidelines for National Greenhouse Gas Inventories - Uncertainties*, 3.62
So, for example, given the large uncertainties in the input variables, the uncertainty half-range $U_M$ for the soot injected into the lower stratosphere in 1945 might well reach 200% or more. In this event, the upper limit of the 95% confidence interval would be of the order of +300%. That's +300% relative to the best estimate of 0.5 Tg. Hence, at the 95% confidence level, the upper range might well extend to the same order of magnitude as the hypothetical quantity of soot injected into the stratosphere by a nuclear exchange between India and Pakistan.

Thus, the research conducted by Robock and Zambri fails to exclude the possibility that the empirical data from 1945 falsifies the nuclear winter hypothesis for the case of a regional nuclear exchange.

In a sense, then, it's clear when Robock and Zambri refrained from including confidence limits in their paper. What's more perplexing is how and why this got past the referees at the

*Journal of Geophysical Research...*