In short, even the most civilised nations may burn with passionate hatred of
each other. We may see from this what a fallacy it would be to refer the war
of a civilised nation entirely to an intelligent act on the part of the
government, and to imagine it as continually freeing itself more and more from
all feeling of passion in such a way that at last the physical masses of
combatants would no longer be required; in reality, their mere relations
would suffice - a kind of algebraic action.
I fear nuclear war and I can imagine the horrors it entails, but I can only
write about it in a detached way. Please do not be offended by my style. You
probably have some conception of nuclear war and fear it too. Some things I
write might increase your own fear and some might alleviate it. My goal is to
fight the wishful thinking combined with fatalism surrounding the topic, which
I consider dangerous. Rest assured that I do not want to paint nuclear war as
something you can plan for and be safe. No matter how well you are prepared,
survival is a matter of luck.
So let's start with the first myth:
"The risk of nuclear war is low"
Estimating the risk of nuclear war is
extremely difficult. But all experts will agree, that:
For a short time interval like a month or a year, the probability of nuclear war - even in peacetime - is above 0.
For arbitrarily long time intervals, the probability approaches 1.
If you do something that can go wrong over and over again, it will eventually
go wrong - no matter how low the probability. This is why a long term goal
of worldwide abolishment of nuclear weapons is so important. I am in no way
implying that past luck or misfortune will affect present probabilities -
this is a common misconception. But if you commit yourself to never give
up nuclear weapons, you commit to nuclear war sometime in the future.
As long as the situation does not allow worldwide abolishment, it seems to
make sense to reduce the severity and probability of nuclear war with
arms control and careful choice of nuclear doctrine and posture. At this
point, the disagreements already start: Wouldn't reducing the severity make
nuclear war more acceptable and therefore more probable?
Let's have a look at the persistent cliche of how it would look like:
"All buttons are pressed simultaneously, humanity goes extinct"
This is how some non-proliferation activists like
Daniel Ellsberg like to think of it. As soon as the taboo of nuclear
weapon use is broken, the situation immediately and automatically escalates
into a spasm war, all buttons are pressed and then the surviving
military staff goes home to die with the rest of humanity.
This situation is exactly like with a
doomsday device - the ultimate deterrent where nuclear war can only happen
by accident. Building a doomsday device would be foolish and I guess this
is the point. But this view of the current state of deterrence is in many ways
wishful thinking: Deterrence is not guaranteed and never absolute, nuclear war
can start intentionally, it has distinguishable outcomes and current
arsenals do not threaten all of humanity - arguably not even the survival of
the nations involved.
"Cities are military targets"
Not really. Better think of cities as the hostages of nuclear war.
Strategic bombing - like in WWII - has the goal of destroying enemy morale
and/or economic ability to sustain its forces. Unless you plan a prolonged
conventional war after a nuclear exchange, both is not
very relevant in a nuclear war due to its short duration (hours to weeks).
Only the direct and immediate effect on leadership morale is important.
Furthermore, any desired effect will be negated as soon as you are unable to
continue destruction.
This is why, in a nuclear war, the first attack with the intent to maximize
civilian casualties ("countervalue targeting") - if it happens at all - will
likely be exemplary - and forces have to be held back for effective
blackmail.
The first priority for attacker and defender is to limit damage to the own
country. The defender may give punishment priority over limiting damage -
but that is a bit irrational. There is an incentive for both sides not to
cross the "no cities"
treshold first and this
seems to be current US policy. Both sides may have a
different perception of that treshold though. The precision and the yield
options of modern nuclear weapons make it easier to reduce collateral damage
but there is of course no such thing as a "clean" nuclear war and
military targets can be in urban areas.
Limiting damage also entails targeting the military of the enemy ("counterforce
targeting"). A first strike might take out many enemy weapons before they can
be used. In a second strike, it makes sense to at least attack weapon
stockpiles, bomber bases and submarine ports to deny restocking.
It is not very credible.
If the attacker has taken care to minimize civilian damage and holds your
cities hostage with the rest of his force, would you attack his cities with
what you have left? Minimal deterrence can work because the attacker may never
be sure about your reaction beforehand or how well things are under control
and correctly perceived on your side.
It gives an attacker a free ride.
In the extreme, no counterforce means not
even trying to stop enemy bombers and submarines with conventional forces
before they finish delivering their load and return to their intact bases for
another round. Civil defense is a more general form of counterforce and
therefore also usually opposed in minimal deterrence.
It will not deter conventional conflict in a symmetrical situation.
The more nuclear war (and only nuclear war) is deterred, the safer it is to
engage in conventional conflict. This is the
Stability-instability paradox. A no-first-use policy will always loose
credibility in an intense crisis - which is good because this will be the only
thing that limits the conventional conflict: The fear of the adversary that you
might use nuclear weapons first despite your assurances not to.
It will not protect your allies (extended deterrence).
Would you "commit suicide" to avenge your allies? NATO has fought with this
credibility problem of US extended deterrence since its inception. With minimal
deterrence, credibility is so low that your allies have a strong incentive
to develop nuclear weapons of their own.
This is why the US has a
nuclear posture that includes counterforce and flexible response options.
How this came about historically can be read in
this very interesting article (BTW I do not share its optimism over missile
defense). The drawback of counterforce is that it makes arms control more
difficult.
There are several tresholds that might be respected or crossed in nuclear war
and they are all older than the no-first-use taboo:
Demonstration
Real attack
Foreign territory
Homeland
Military
Civilian
Property
People
Limited
Unlimited
These tresholds show up in Herman Kahn's
famous escalation ladder.
What your tresholds are and where exactly you draw the lines depends on your
views. The escalation ladders of two adversaries might look quite different
and that will complicate things. The higher a situation is on the
escalation ladder, the higher the risk tends to be that things will
unintentionally get out of control. This is a desired effect, as your opponent
might back down out of fear even if he can match your escalation. Thus
rungs 4-9 are labelled "rocking the boat". It's the boat both you and your
opponent are in.
Despite this, the idea that any nuclear war,
regardless of circumstances, would quickly reach the topmost rung seems
untenable to me. People who say otherwise will often cite war games that
went horribly wrong like
Proud Prophet. I doubt that people under the extreme stress of a real
situation would simply enact the standard policy like in Proud Prophet. It
would be nice to know the number of war games that did not escalate out of
control vs. the number of those that did.
"Nuclear war is unthinkable"
It is May 2022 and media is full about speculation about nuclear war. Why?
Because Putin has made it more thinkable in order to deter NATO countries
from helping Ukraine - with some success. The escalation ladder linked above
in fact has a "Nuclear war is unthinktable" treshold and Putin is playing with
it.
It would be dangerous to assume that nuclear war is always unthinkable for
potential adversaries or that they will always think "it cannot be won".
Nuclear weapon countries have to work hard for these goals. Maintaining
stability of deterrence in a changing world includes permanent thought about
nuclear war.
"Nuclear weapons are useless"
They have been used numerous times since the end of WWII to deter what one
side or the other regarded as major or minor provocation. Deterring nuclear
war is just the basic function.
One cannot be 100% sure what the outcome would have been without them and
whether a counterfactual conventional war between NATO and the Soviet Union
would have been worse than all the factual proxy wars taken together.
But the fact that so many countries regard nuclear weapons as desireable -
either their own or those of their allies - speaks for itself.
The dilemma is that the more risk a state is willing to take, the
more useful nuclear weapons can be. Minimal deterrence will just barely cover
the basic deterrence from nuclear attack. The other extreme is a posture
that suggests to your adversary that even a minor provocation might cause a
first strike from you. It's quite obvious that this is very dangerous and
at the same time very tempting for states with lacking conventional
forces and/or revanchist attitudes. In the first phase of the cold war,
this role of brinkmanship fell to the US with its
massive retaliation policy and tactical nuclear war capability in Europe.
These days, North Korea, Russia and
maybe soon China are playing with fire to gain political advantage.
If we want to distinguish between "defensive deterrence" and
"aggressive deterrence", Russia's recent threats accompanying a war of
aggression seem to cross that line.
"Nuclear winter"
The science of nuclear winter is
extremely contested and ridden with politically motivated worst case
assumptions. A
typical paper will assume that:
All deployed weapons are used and only cities are targeted by both sides.
I have already explained how this makes no sense at all.
Every weapon causes a
firestorm on an area that is a function of weapon yield only.
Hiroshima had a firestorm, Nagasaki did not - probably due to different
city layout. The population density of the affected area in Hiroshima was
high (>22700 per square mile). Also "experts suggest that
differences in modern US city design and construction make a raging firestorm
unlikely" (cited from
this government report).
Population centers contain 11 tons of flammable material per person.
The author divided an estimate of the total flammable material in the
developed world by the total population. Also a linear relationship between
population density and amount of flammable material seems questionable.
But if one goes along with it, areas with a population density below
9400 per square mile should not be considered part of the firestorm
(40 kg/m2
has been suggested as the minimum fuel load).
Within the area of firestorms, all the available flammable material is
consumed.
Even when buried under rubble?
80% of the emerging soot reaches the upper troposphere, where it can have
a global long term effect.
This is contested and subject to intense debate between scientists.
A
simulation by Reisner et al. suggests that soot production scales
nonlinear with regard to fuel load and only a small fraction reaches an
altitude above weather systems.
Nuclear winter cannot be ruled out and some kind of "nuclear autumn" causing
famine might even be likely. So what would be the worst case?
This paper
from 2019 posits 150 teragrams of soot injected into the upper troposphere
for a full city exchange between the US and Russia. This number of 150 teragrams
has come up again and again in papers since the 1980s - with completely
different underlying war scenarios (e.g. including China) and contemporary
arsenals. Based on
figure 2 of the paper I linked earlier, one could argue for 70 teragrams
of soot for a US/Russia exchange with 2022 nuclear arsenals.
But let's assume
150 teragrams and sound modelling. One would have to expect below freezing
temperatures over much of the northern hemisphere during summer for years.
If not
prepared for, this could kill a majority of humankind due to famine -
but some people would be able to survive even in the worst affected areas and
civilization would not be seriously threatened in the southern hemisphere.
Why is it dangerous to buy into nuclear winter uncritically?
Assuming all involved parties buy into it, it will increase deterrence and
decrease the risk of nuclear war. This will make limited conventional conflict
more acceptable (Stability-instability paradox).
Also, it will cause fatalism - increasing the severity of nuclear war due to
missing preparedness. If one party does not buy into nuclear winter, deterrence
becomes asymmetric and the risk of escalation due to miscalculation
increases. The best case may be when all parties have doubts about
nuclear winter.
Fallout
No scare quotes here because
fallout is real - but probably not as scary as you imagine:
When targeting cities, it is more effective to detonate the weapon in an air
burst, such that the nuclear fireball is not near the ground and the
fallout becomes negligible in terms of casualties because it is
distributed mostly globally and delayed instead of locally and early.
A surface or ground burst instead will diminish the range of
thermal and blast effects (e.g. 40% less casualties) but add
potentially lethal fallout over a range of up to hundreds of kilometers
downwind. Whether the added casualties from fallout compensate the diminished
thermal and blast effects depends on variables difficult to predict - like
wind direction and speed, population density downwind, how many people seek
which protection how fast and how long their supplies will last before they
have to leave shelter. The planner targeting a city will usually
prefer the more calculable air burst option.
Any "nuclear winter" targeting scenario from above assumes air bursts only
and has negligible local fallout casualties compared to the direct effects of
the weapons. Global life expectancy would shrink due to increased cancer and
mutation risk. The additional risk of birth defects would be lower than the
additional cancer risk - possibly by an order of magnitude.
This study from
1986 suggests an average additional global cancer risk around 1%, but uses
contemporary arsenals and assumes no protection from time spent inside
buildings.
Annex A contains a calculation of cancer
risk based on data from atmospheric testing and more realistic modelling.
The average additional cancer risk seems to be between 0.1 and 0.3% in the
northern hemisphere for a full exchange of NATO+Russia deployed arsenals
using air bursts only. The average impact in the southern hemisphere would be
at least an order of magnitude lower.
The 1986 study also separately examines targeting of nuclear facilities to make
the fallout worse and more durable. That would dramatically affect the local
situation and at least triple the global numbers, but it would not be able to
dramatically change the global situation. The doomsday scenario from the
Novel/Movie
On the Beach is not on the table.
What is the cause of the residual radiation of [thermo]nuclear
weapons? The radioactive fission and fusion products of the weapon and
any radioactive isotopes created by
neutron capture.
Neutrons do not travel far in the atmosphere
- this is why
neutron bombs
are small bombs suitable for attacking enemy troops - not cities.
Above 10 kiloton yield, the thermal and blast effects always
reach further than any prompt radiation. With modern high yield weapons,
almost all isotopes created by neutron capture will share the fate of the
other fallout or stay near
ground zero.
The bomb remains will be vaporized and spread over the fireball. As the
fireball expands and cools, the bomb remains condense to particles so small
(10nm-20µm) that they are lifted up and carried away with the fireball
if it does not come near the ground. This is the case in an air burst. If the
fireball is near or at the ground, bigger fallout particles (up to
milimeter size) will form due to the increased concentration of vaporized
matter and condensation on unvaporized matter drawn into the fireball. These
particles will reach the ground in a matter of hours instead of weeks and
months. They simply fall out of the moving mushroom cloud - with bigger
particles hitting the ground earlier. This is the early fallout (up to 24h).
The delayed fallout (24h up to years) occurs for the small particles
(10nm-20µm). A mushroom cloud is a
pyrocumulus cloud like those from firestorms but will rise much quicker.
The higher the bomb yield the faster it will rise and the higher it will
settle. This is why fallout due to rain within the first 24h is unlikely
for modern high yield weapons (source).
The black rain falling 20-30 minutes after
the Hiroshima air burst was caused by the
firestorm cloud (often confused with the mushroom cloud) and it is
contested whether it contained fallout from the
mushroom cloud (note the disconnect between top and stem typical
for an air burst).
Delayed fallout will happen via two mechanisms:
Tropospheric fallout due to precipitation, which is irregular and can
cause local hotspots. Half of the particles will typically reach the ground
within 30 days, which is enough time for them to travel once around the earth.
Stratospheric fallout due to exchange of air with the troposphere. This
causes more regular fallout mainly over the temperate latitudes. Half of the
particles will typically reach the ground within 10 months.
It is dangerous to fear fallout to the point of fatalism. If target planners
can assume that many people will not seek shelter, they might choose more
ground bursts to increase fallout. But even if you live
downwind of a ground burst, you are not necessarily doomed.
This is a simulation by
NUKEMAP of a 100 kiloton ground burst at Büchel
air base in Germany, where the
B61 gravity bombs that are
shared with Germany are kept. A ground burst makes sense here to destroy
the runway and the bunkers with the bombs (no, they will not add to the yield
and my guess is they won't contribute to fallout).
Let's assume you are ca. 35km downwind in the middle of the 100 rads per hour
fallout contour in the district Kell of Andernach. Wind speed is 12mph
(19.31 km/h), so the fallout will start to arrive at your location ca. 1.8
hours after detonation. Click on the button "Probe location" and drag the
icon with the question mark near ground zero into Kell. On the right, look
for the "Information at sample point" section.
In the first 6 months, fallout exposure/dose rates will approximately follow
the equation R * t-1.2 once no new fallout arrives (t=0 is the time
of detonation). This means that for every 7-fold increase in time after
detonation, there is
approximately a 10-fold decrease in the exposure rate (seven-ten rule).
After 6 months, fallout decays even faster.
The H+1 dose of ca. 203 rads per hour given by NUKEMAP is the normalized dose
rate at Kell one hour after detonation. At that time, the fallout has not even
arrived but with that trick, we know know R for Kell
(203 = R * 1-1.2 = R). After 1.8 hours - when the fallout
arrives - the equation gives 203 * 1.8-1.2 = 100 rads per hour.
That number is too high because not all of the fallout has settled but let's
be on the safe side. 48 hours after detonation, you would measure
1.95 rads per hour and two weeks after detonation, it would be 0.19 rads per
hour. These are the recommended times to stay sheltered: At least 48 hours,
optimally two weeks. The outside accumulated dose between 1.8 hours and t hours
can be estimated by:
5 * R * ( 1.8-0.2 - t-0.2 )
This is 434 rads in the first 48 hours - a dose that would cause
radiation sickness and might kill you if you are unlucky. After two weeks,
this would climb to 585 rads. A common goal for fallout shelters is a
protection factor of 1000 - reducing those doses to 0.434 and 0.585 rads, but
even a protection factor of 10 would save you from radiation sickness.
Let's assume a protection factor 10, no relocation and no cleanup - not even
due to rain. Accumulated dose in the first two weeks is 58.5 rads. If you
leave shelter after two weeks and spend your time unprotected until 6 months
have passed, you would accumulate an extra 127 rads.
You can estimate your additional cancer risk in percent by multiplying your
accumulated long term rad dose by 0.055 (source).
That's an extra 10% chance of getting cancer - which might need decades
to develop and might not be fatal. Not nice but not "envy the dead" territory
either.
How do you achieve a protection factor of 1000? With a shielding of ca.
25cm of steel or 84 cm of concrete or 122cm of earth (these numbers will
vary with the density of the material). If you have less shielding, your protection
factor for thickness d will be approximately e6.91*d/D - where D is
the thickness for factor 1000. If you have several layers of shielding
(e.g. different walls in a building), the individual protection factors will
multiply. In many situations, a windowless basement
will provide sufficient protection - so the most important advice is:
Get inside, stay inside, stay tuned (to emergency advice via radio).
Here are some additional points:
The above scenario, simulation, calculations and numbers should be
regarded as a crude approximation.
Only gamma radiation is considered, because it is the most dangerous.
Alpha particles will not travel more than 3cm in air and cannot penetrate
your skin. Beta particles will not travel more than 3m in air and cannot
penetrate your clothing. The main risk from them is when fallout touches
your skin or radioactive isotopes are ingested/inhaled.
Do not worry too much about fallout entering your shelter. The very
small fallout particles (10nm-20µm) are not part of the early fallout
described here. Once the fallout has settled and no wind is blowing dust into
your shelter, passive ventilation is safe. If your shelter is small, the
danger from overheating and oxygen-depletion is far greater than any danger
from active ventilation.
Do not worry too much about inhaling fallout. Particles above 10µm
will not reach your lung and leave your body soon through mucus. A
FFP2/N95 mask will filter anything above 0.3µm. If you don't have one,
cover your nose and mouth when outside.
Drinking water will be your main problem as the water supply may be broken
or contaminated. Better address this before fallout arrives or even before
a crisis breaks out.
Any food that has not been in direct contact with fallout should be safe
(alpha, beta and gamma radiation will not make it radioactive).
Don't forget that fallout collects on roofs. If there is no suitable
basement, the middle floors of tall buildings will be best.
Geometry is your friend, but do not forget that gamma rays get
scattered in air.
This quote is attributed to Nikita Khrushchev, but
nobody seems to be able to tell where and when he said that.
The Day After
shows only the immediate aftermath of those who are worst affected by a worst
case scenario. The more powerful movie
Threads instead follows events in the UK until 13 years after an attack and
includes a nuclear autumn/winter scenario. This illuminates the definition
problem of the term "survivor" in time and place: Would it be those alive 1
hour after an explosion, 1 month 1 year or 10 years? Would it include people
from countries not participating in the war?
Herman Kahn tried to translate that quote into a more meaningful question:
"Is a normal happy life precluded for the majority of survivors?". He obviously
had a broad definition of "normal". His outlook
was mid to long term (starting 1-3 months after the war) and
geographically restricted to a country directly affected (the US). I think
these qualifications of the question make sense. His answer was cautiously
optimistic but the only answer can be: It depends. On the timing and outcome
of the war, the preparations made before the war, the attitude of the
people and other factors. Let's try to break down the problem - with the basic
assumption that problems not listed here will be less relevant:
Breakdown of logistics causing famine.
Long-term breakdown of economy causing famine and exceptionally low
living standards.
Breakdown of social order.
Effects of food and water contamination from fallout.
The first two problems dominate. If they cannot be solved,
the other problems will not matter much and if they can be solved, the other
problems will likely be alleviated to a tolerable degree.
If the attack timing is not too bad, it seems that
stored grain in the US could feed 300 million americans for more than a
year. The problem is tending these stockpiles and getting them to where they
are needed after an attack. This will be very difficult
without some pre-war planning and training. Perhaps the most important factor
will be the availability of radiation meters to overcome any reluctance of
key personnel to leave shelter within the first days or weeks. An all-out
attack shortly before harvest would be the worst timing. With current policies,
stockpiles would be low and harvesting would be limited by radiation hazard
(crops would be mostly undamaged though as they did not have time to
accumulate fallout internally and can be cleaned from adhesive fallout).
In a worst case scenario, reestablishing a sustainable "economy" before
stockpiles run out is a race against time.
It involves salvaging of resources, relocation of people, decontamination of
important areas, appropriate sheltering during work and free time,
establishment of currency and more. Whether this problem is tackled centrally
or decentralized, it will require good leadership.
The last two problems 3. and 4. will be greatly alleviated by the availability
of stocked (likely uncontaminated) food and good leadership. They also
depend on attitude. If you think the situation will only get worse,
you are more likely to subscribe to "might is right". If you expect pre-war
radiation safety and living standards, you will be disappointed.
Compared to overall casualty numbers, the long term threat from contaminated
food and water is small, if not insignificant - and there are possible
precautions to reduce it.
The web of interdependency in modern societies and its vulnerability to
nuclear war is the main theme of the movie Threads. Many countries depend
on food imports and the efficiency of agriculture may well drop by 50% without
modern high-tech, fertilizers and pesticides. This can be offset by abandoning
livestock and biofuels - but would countries like the United States do that and
keep exporting crop after fighting a nuclear war?
In summary: The secondary effects of nuclear war can be massive - just like
the positive effects of precautions. "The living will envy the dead" should
not become a self-fulfilling prophecy. More resilience to supply chain shocks
is already a popular theme that should be pursued. I also would not worry
about degrading an adversaries nuclear forces due to (comparably low amounts
of) money spent for civil defense. Nuclear war is horrible enough even with
some preparation.
"Nuclear overkill"
You can look up the status of nuclear forces in the world at the
FAS.
As for the US and Russia the
New START treaty from 2010 currently limits the number of deployed
strategic weapons to ca. 1550 for each side. When I use the phrase "current
arsenals" in this article, I assume that tactical weapons do not play a big
role and that stockpiled strategic weapons are not used in a conflict. This may
not be the case in a prolonged tactical nuclear war or in a prolonged crisis
where the treaty is broken and there is enough time to match stockpiled
warheads with delivery vehicles.
With unreasonable assumptions about the course of a war and arbitrary other
assumptions, one can construct an "overkill capacity". Let's look at
current Russian nuclear forces and assume the deployed and reserve
strategic warheads are all fired with 100% success rate at the 331
US cities (population 96,598,047 / area 76,630 km2). The area
to which those weapons can inflict at least 5 psi overpressure ("most
residential buildings collapse, injuries are universal, fatalities are
widespread" according to NUKEMAP) is 146,038 km2 - 1.9 times
the total area of the cities. Make of that what you want.
Final thoughts
There is no deterrence without risk. If you do not want to risk nuclear war
with a revanchist nuclear power, you basically have to surrender. Even when
you escalate in a crisis, you usually hope that the increased risk of things
getting out of control will force the opponent to back down.
The best deterrent is a threat that the other side believes you can
and will carry out (capability and credibility) and that it thinks will hurt
more than any possible gains. If this is not possible or desireable, doubt
about how things may play out still can be a deterrent. In practice, crisis
and nuclear war have so many uncertainties that doubt will play a central role.
A balance has to be sought between looking like a bluffer and an imminent
danger that has to be preempted. This balance will have to be reevaluated
permanently - the world does not stand still.
It may happen that an adversary looks like a danger that has to be preempted
at any cost. We may go into nuclear war fully aware - it's not like there
is no historical precedent of all sides eagerly going to war.
If such a fight has to be fought out, it seems desireable to me that it
would happen conventionally or by some other means that
requires more effort and is slower.
Ultimately, we want to continually reduce the risk of nuclear
war - that is probability and severity - until we have found a better
system that prevents mass slaughter without the risk of mass slaughter.
Until this - admittedly utopian looking - future has arrived, I advise
everyone neither to assume the worst nor the best outcome, not to be totally
unprepared and to join the conversation on nuclear policy.
Annex A - Possible global fallout doses from UNSCEAR data
543 atmospheric nuclear detonations have been reported due to atmospheric
testing and combat use. The United Nations Scientific Committee on the
Effects of Atomic Radiation (UNSCEAR) has estimated the 100-year average
accumulated radiation dose from 1945 to 2099 in the northern hemisphere due
to global delayed fallout to be 0.506 mSv (external only) and 1.340 mSv
(total including ingestion and inhalation).
See Table 16 from annex C of the 2000 report).
This estimate is based both on measurements of actual deposition and modelling.
Table 6 of the UNSCEAR report lists the "partitioned" fission yield causing
global fallout in the northern hemisphere to be 144 Mt. The fission yield of
currently deployed NATO+Russian arsenals is ca. 520 Mt. A simple scaling of
the dose is not enough though, as the yield mix of the NATO+Russian arsenals
will inject a higher fraction of the fallout into the troposphere and lower
stratosphere instead of the upper stratosphere. This leads to faster
deposition on the ground and thus a higher dose. Another factor is the
latitude mix of the atmospheric tests vs. targets in a NATO/Russian conflict -
due to the limited latitudinal spread of tropospheric fallout and varying
population density.
I assume the following simplified model for global fallout dose in the
northern hemisphere:
D = C * ( MT0-20 * 0.17 + MT20-40 * 0.53 + MT40-60 * 0.3 + ML / 10 + MU / 50 )
D is the 100 year accumulated radiation dose
C is a constant with the unit mSv / Mt
MTa-b is the partitioned fission yield in Mt injected into the
troposphere of the band from a to b degrees latitude.
0.17, 0.53 and 0.3 is the northern hemisphere population fraction in the
three latitude bands From table 8 of UNSCEAR annex C.
ML is the partitioned fission yield in Mt injected into lower stratosphere.
Relative contribution is assumed to be 1/10 due to later deposition.
MU is the partitioned fission yield in Mt injected into upper stratosphere.
Relative contribution is assumed to be 1/50 due to later deposition.
To calculate C from UNSCEAR data, I set:
D = 1.340 mSv (total) / 0.506 mSv (external)
MT0-20 = 6.462 Mt
Derived from table 2 of UNSCEAR annex C (Bikini, Enewetak, Pacific,
Johnston Island and half of Malden Island and Christmas Island)
MT20-40 = 0.796 Mt
Derived from table 2 of UNSCEAR annex C (Algeria, New Mexico, Japan and
half of Nevada and Lop Nor)
MT40-60 = 2.06 Mt
Derived from table 2 of UNSCEAR annex C (Kapustin Yar, Semipalatinsk, Totsk,
Aralsk and half of Nevada and Lop Nor)
ML = 55.5 Mt
From table 6 of UNSCEAR annex C.
MU = 72.7 Mt
From table 6 of UNSCEAR annex C.
This establishes C at 0.147 mSv / Mt for the total dose and 0.055 mSv / Mt
for the external dose.
What would this model predict for scenario A in the
1986 study from Shapiro et al.? The numbers provided in the study are
MT = 226 Mt, ML = 1234 Mt, MU = 571 Mt and a resulting average 50-year
external dose around 15 rads in the northern hemisphere. Assuming the
tropospheric fallout spreads uniformly between 20 and 60 degrees latitude, my
model predicts an average 12.57 mSv 100-year external dose in the northern
hemisphere. UNSCEAR assumes 0.7 Sievert per Gray and a shielding factor of
0.36, while Shapiro et al. assume no shielding - but this still separates both
predictions by a factor of 3. For now, I cannot explain this discrepancy and
will treat the predictions of my amateur model as a lower bound with the upper
bound being 3 times the lower bound.
Now to a scenario with currently deployed NATO+Russian arsenals according to
the
FAS Nuclear Notebook. The sources provide some leeway so some of the
numbers have been chosen rather arbitrarily:
The yield partitioning is derived from table 5 of UNSCEAR annex C:
Total yield in kt
Troposphere
Lower stratosphere
Upper stratosphere
100
80
20
0
200
140
60
0
300
170
130
0
500
160
340
0
700
80
620
0
Partitioning of yields not in the table will be done according to the
relative fractions of the best match, which is found as follows:
Yields below 100kt will use the 100kt partitioning
Other yields will use the the partitioning from the next lower yield
in the table.
The fission fraction of all warheads is assumed to be 0.5. Again, it is
assumed that the tropospheric fallout spreads uniformly between 20 and 60
degrees latitude. The model predicts an external 100-year average dose of
6.93 mSv and a total dose of 18.53 mSv in the northern hemisphere for a full
exchange with air bursts (source code).
The total dose amounts to an additional cancer risk of 0.10%.
Changes to this document
2022-06-15 Added comments section, corrected miscalculation of "overkill factor" from 1.5 to 1.9.
2022-06-30 Added Clausewitz quote
2022-07-14 Added link to 2013 US report on nuclear employment strategy
2022-09-15 Added minimum fuel load considerations for firestorms
2022-09-19 Added link to paper/comment by Reisner et al.
2022-09-20 Added some words about interdependency and resilience to supply chain shocks
