Validation against Hiroshima and Nagasaki

The sources disagree by a factor of two on the dead. The disagreement is mostly about what is counted: immediate deaths in June 1946, or acute deaths through the end of 1945.

Reading. At Hiroshima the planar radii for severe blast damage and for fire land within about 10 percent of the record. The 2 psi radius overstates the "all homes destroyed" distance by a third, which says that Japanese wooden houses of 1945 did not survive to 2 psi as the American criterion assumes, not that the pressure was wrong. At Nagasaki the steel-frame radius still matches, but every areal comparison fails by a factor of two: the survey's own explanation is that "the uneven terrain of the city confined the maximum intensity of damage to the valley over which the bomb exploded". A planar model cannot know that. This is the case for the terrain-shock lab.

The British Mission's calculated mortality by distance (MED chapter 10, table C), set against the OTA 1979 blast-only fraction at the same distance for 15 kt:

Area-weighted inside the 5 psi radius of 1.75 km the model gives 65.1 percent and the record 59.9 percent. The step function crosses the recorded slope four times and integrates to roughly the right answer. That is what a calibration looks like: the DCPA curves were fitted to this data, so this is consistency with the source, not independent confirmation.

The MED says 75 percent of Hiroshima's population lived in the 7 square miles that were completely built up. Treating that as a disc of uniform density about the hypocentre and applying the OTA bands:

The blast-only method with the 1946 population figures returns 68,000 to 71,000 dead and 66,000 to 69,000 injured against the 1946 counts of 66,000 to 80,000 dead and 69,000 injured. The fire bound with the same inputs returns 132,000 to 137,000 against the City of Hiroshima's roughly 140,000 by the end of 1945. The two numbers on the readout are, at Hiroshima, the immediate count and the end-of-year count. The 1961 planners were computing the first and calling it the answer.

At Nagasaki the same arithmetic with the MED's 195,000 gives 131,600 blast-only dead against a recorded 35,000 to 40,000. The disc assumption puts the whole city under the bomb; in fact the main city lay behind a mountain spur to the south and the valley took the blast. The model is not wrong about pressure; it is wrong about where people were.

A 5-arc-minute cell at 34°N is 7.6 by 9.3 km. Hiroshima's built-up area was about 18 km², so the city occupies a fraction of one or two cells and the grid spreads it over ten. Within 5 km of the hypocentre HYDE holds half the recorded population; within the 5 psi radius, a small fraction. The grid understates the blast-only dead by seven times. This is the resolution finding: HYDE is adequate for megaton weapons on 1961 cities, where the rings are tens of kilometres across, and not for kiloton weapons on 1945 cities. A finer historical grid or a documented density is needed at that scale, and the lab now says so beside the numbers.

• The planar blast and thermal radii reproduce Hiroshima's recorded damage distances within about 10 percent for severe damage and fire.
• The OTA fatality fractions integrate to the recorded fraction inside the 5 psi radius, because they were derived from it.
• The blast-only method reproduces the immediate counts at Hiroshima and the fire bound reproduces the end-of-1945 count, given the survey's density. This is a check of the arithmetic, on the one city that is close to a uniform disc.
• Nothing here validates the planar model where terrain matters, and Nagasaki shows how much that can be: a factor of two in area and three in deaths.
• Nothing here validates the grid at kiloton scale.

The terrain lab (#/lab/terrain) puts the Nagasaki burst, 21 kt at 503 m, over the AWS terrain tiles resampled to 53 m cells.

Reading. Geometric shadowing does not explain Nagasaki, and Glasstone says as much: §3.36, "shielding from blast effects behind the brow of a large hill is not dependent upon line-of-sight considerations", and §3.37, "little reduction in blast damage to structures may be expected" from terrain, while §3.35 describes the spike at the base of a hill facing the burst and the reduction over the crest, which is the reflection and shadow pattern the acoustic run draws. From a burst 500 m up, hills of 200 to 400 m a kilometre or two away hide only 3 percent of the ground inside the 5 psi radius; the thermal flash reached almost all of it. So the confinement the survey describes is a blast and fire phenomenon, not a line-of-sight one. The acoustic run points the same way: reflections off the valley walls hold the peak inside the valley at about the flat-ground level while the ground beyond the ridges drops to six tenths, which is the survey's sentence drawn as a map. It is not a measurement. The wave is linear, two-dimensional and stopped at the edge of the box; it cannot produce the Mach stem that carries a real shock along a valley floor, and it knows nothing of the wooden houses that burned. The lab's contribution is to rule out the cheap explanation and to show where a real solver would have to work.

Structure class is the other half. "All Japanese homes destroyed" at 2.4 km against a 2 psi radius of 3.3 km is the American masonry criterion applied to a wooden city, and the OTA fractions were fitted to these two cities and no others. A structure-class correction belongs beside terrain as the second departure from the planar model.

Glasstone and Dolan §5.53: Japanese-style wooden dwellings "collapsed at distances up to 7,500 feet (1.4 miles) from ground zero, where the peak overpressure was estimated to be about 3 pounds per square inch". The American test houses of 1953 and 1955 collapsed or were damaged beyond repair at 5 psi (§5.57, §5.67), which is the collapse pressure the OTA bands assume. The obvious correction scales the band thresholds by 3/5, so that the Japanese city's people are counted at the pressures at which their houses fell.

The scaled total lands between the RERF and City of Hiroshima end-of-1945 figures, which looks like a success until the mortality-by-distance table is consulted:

Inside the scaled collapse radius of 2.47 km the scaled model gives an area-weighted 64.9 percent dead against a recorded 34.4 percent; the unscaled bands give a figure within a tenth of the record. The correction reaches the right total by killing the wrong people: it doubles the near-field mortality that the record does not support, and the extra deaths it produces are the fire and radiation deaths that the blast-only method cannot see, arrived at by a different route.

The reason is that the DCPA curves were fitted to these two cities. Their pressure labels are labels; the fractions already embed the Japanese houses. A structure correction on top double counts, and the test now asserts that it does. The class remains in the lab as an exploratory control, badged inferred, for building stock the record cannot calibrate, and the readout says when it is off the baseline. For the 1961 Soviet cities of SIOP//62 the honest position is to leave the bands as published and state that their building stock is not in the calibration.

NUKEMAP's casualty method is this engine's: the DCPA bands of 1973 as reprinted in OTA 1979, applied to the overpressure rings, with no shielding and no thermal or radiation count. A difference between the two is therefore a difference of rings, of population data, or of ground zero. NUKEMAP sums LandScan 2011 ambient population; the lab sums GHSL residential population for 2025. The published runs are Newsweek's of 30 October 2025, a W88 of 455 kt air burst over seven cities, and of 16 May 2022, the Tsar Bomba over New York; neither states its ground zero, so the city's geocoded centre stands for it. The lab's numbers are the population lab on the 2025 grid, blast only.

The rings account for most of it. NUKEMAP's report quotes its ring areas, which give its radii; the lab's are Glasstone's optimum-height figures.

The fireball, burn and 1 psi radii agree within ten percent. The 5 psi ring differs by a third in radius and by 73 percent in area, and the 5 to 12 psi band is where the method counts most of its dead, so a lab figure 1.5 to 2 times NUKEMAP's is what the rings alone predict. The lab's 5.46 km is Glasstone's optimum-height 5 psi radius scaled from 1 Mt; NUKEMAP's 4.15 km sits between that and the surface-burst figure of 4.43 km, so its run used a lower burst height than the 5 psi optimum. That is a choice, not an error, on either side, and the lab's panel now shows both sets of rings.

The rest is population and ground zero. New York runs below NUKEMAP because LandScan's ambient count puts Manhattan's daytime workers under the rings where a residential grid does not. London runs four times above, with NUKEMAP's injured fewer than its dead, which no set of bands produces from a centred ground zero; the published London run's ground zero must have been off the centre, or on the river. Beijing has grown since 2011. The Tsar Bomba case, where the rings are tens of kilometres and the population is a whole metropolis, agrees within a fifth, which is the comparison that tests the population data rather than the burst height.

What it validates. The method is the same and the large-yield case agrees, so the exposure chain is sound; the disagreement at half a megaton is the burst-height convention, which the lab states on every readout as an optimum-height air burst. A NUKEMAP run at the optimum height for 5 psi with a stated ground zero would settle the remaining difference, and the lab's comparison buttons put the cases one click away for anyone with both tools open.

The burst-height convention, settled

NUKEMAP's FAQ (read 10 September 2026) describes two air-burst modes. "Maximize airburst radii for all effects" draws each ring at the height that maximises that ring, and the FAQ says of it that "it is really showing you a spread of different altitudes." "Optimize for overpressure" and a typed altitude use one height for every ring. The lab's model is the first mode: every ring at its own optimum height, from the Sublette fits to Glasstone and Dolan. The published runs the comparison quotes give a 5 psi radius a third smaller than the lab's, which is what one height for all rings produces, so the difference is the mode and not the fits. A like-for-like check is one setting away: run NUKEMAP at the case's yield with "maximize airburst radii for all effects" and read its 5 psi radius against the lab's; the lab's ring should match within the fits' stated ten per cent. A single-height model for the lab would need the height-of-burst curves (Glasstone and Dolan figure 3.73) as fits, which the engine does not yet carry.

The defence lab's model (src/models/defence.ts) is the bookkeeping every published assessment of missile defence has used in some form: credible objects are warheads plus the decoys the defender cannot discriminate; each receives the doctrine's shots while interceptors in position last; an engaged warhead is killed with probability 1 − (1 − p)^k; shoot-look-shoot spends the next shot only after a miss; a space layer's absentee ratio divides the stock by the fraction overhead. The cost exchange is Nitze's 1985 criterion in numbers. No intercept physics is modelled.

Checks: two shots at the test record's 12 in 21 give 82 per cent, against the film's 61; four give 97, which is the agency's claim exactly, so the claim is the record with independence assumed; forty-four interceptors in salvos of four engage eleven objects and leak the twelfth onward; ten undiscriminated balloons per warhead (UCS 2000) raise the credible objects elevenfold and the leakage to nearly everything. The reference cases' kill probabilities are the test record where one exists and stated assumptions where none does, and the lab says which on every case.

The accuracy lab's model (src/models/lethality.ts) is the standard single-shot kill rule: the warhead kills if it lands within the radius at which the target's overpressure is reached, and the miss distance is circular normal with median CEP, so P = 1 − 0.5^((r/CEP)²). Radii come from the engine's own blast fits: the optimum-height air burst at 5 psi and below, the contact surface burst above. Checks: a CEP equal to the lethal radius gives exactly one half; Atlas D at 1.44 Mt and 3.7 km has better than a 60 per cent chance against a city and under 10 against a 2,000 psi silo; Trident II at 455 kt and 120 m has better than 90 against the silo; no American system before 1966 reaches an even chance against the silo and the first that does enters service between 1970 and 1986. Yields are the Databook's; CEPs are the open literature's estimates and are tiered as such.

The guidance lab's model (src/models/guidance.ts) is the root-sum-of-squares budget every guidance assessment uses: each error source as a per-axis standard deviation at the target, added in quadrature, with CEP = 1.1774 σ for a circular normal miss. Position and alignment errors scale with range and are cut by the star sight; velocity and gravity errors run for the flight; an accelerometer bias and a gyro drift integrate through boost. Checks: the lines' shares sum to one; each of the five presets reproduces its published CEP within a quarter; the CEP grows by more than half over a day without a fix on the 1960 preset and the star sight brings it below the fresh-fix value; and in 1960 the boat's own terms are more than sixty per cent of the variance. The structure is MacKenzie's; the magnitudes are illustrations and are labelled so, since the book could not be read for this build.

The plume is Glasstone and Dolan's idealized unit-time pattern (Table 9.93) revealed downwind at the effective wind speed, with t^-1.2 decay. Its far contours are the least trustworthy part of the instrument: the 1 rad per hour line for 800 kt at 17 mph runs about 1,300 km by the table, and by the time fallout arrives there the H+1 rate has decayed a hundredfold; real patterns bend as the wind veers with height and over the hours, and rain puts hotspots off the axis. Since 10 September 2026 the strike console feeds the model an effective wind averaged over three pressure levels and twelve hours, its directional spread as shear, and a terrain factor of 0.7; the drawn tail fades with dose. The shape at 48 hours is still "order of magnitude and general direction", and the fallout lab and the readouts say so.

Since 10 September 2026 every ballistic flight in the engine has a powered phase. The trajectory model had been the textbook minimum-energy ellipse with an impulsive burn at the surface, which understated flight times by the burn (three to five minutes on a thirty-minute ICBM flight) and drew the arc rising at full speed from the pad. Now a boost profile by class and propellant, round figures from the open literature stated as reconstructed, carries the missile to a burnout point (a solid ICBM or SLBM: 180 s, 200 km up, 400 km downrange; a liquid heavy: 300 s, 250 km, 600 km; intermediate, medium and short-range classes shorter), and the coast is the minimum-energy ellipse over the rest of the range. The bus releases ninety seconds after burnout. Burnout is marked on the trail in amber. The window study's SS-18 flight to Minot is now about thirty-four minutes rather than twenty-nine; the 72-minute timeline keeps the book's minutes-to-impact and launches the missile earlier to match. WOPR's evaluator uses the flight time only and is unaffected in kind. The boost phase is the only window a boost-phase interceptor has, and the strike console says how long it is.

src/models/boost-intercept.ts is deliberately simple: detection at 60 s and decision at 30 s after launch, an interceptor closing at 5 km/s from a shell at 500 km, the reach as a cap of that shell, the constellation spread evenly, and the chance of at least one inside the reach as one minus the Poisson zero. It ignores orbital geometry (inclination bands leave the poles and equator unevenly covered), the interceptor's own boost and divert, and countermeasures, all of which cut the chance further; and it credits every interceptor within reach with a kill, which the defence lab's kill probability of 0.7 would reduce. It is meant to show the shape of the problem, that the window is a few minutes over the adversary's own territory and the constellation must be large, not to size a system. The American Physical Society's 1987 study and the 2003 APS boost-phase study are the references.

Until 10 September 2026 a study's fallout casualties appeared in one step, computed once when the clock passed the end of the plume's deposition, so the reader watched a plume spread for two days beside a figure that did not move and then jumped. The count is now carried forward at stages, 1, 2, 4, 8, 16, 24, 36, 48, 72 and 96 hours after each burst: the plume is recomputed for the part it has reached and for the dose accumulated from arrival to that hour, the per-target figure is re-summed, and the union's dose map keeps the worst dose each person has taken, so re-adding a plume at a later hour raises their dose rather than counting them twice. The readout says which hour the figure has been carried to and marks it as still rising in amber until the last stage.

What the literature supports, and what it does not

Two assumptions sit under the count, and they are not equally well founded. The readouts now separate them.

That nobody moves is supported. It is what the governments assumed of themselves. British policy from the 1970s was to stay at home and use an inner refuge, on the reasoning that the roads would be needed and that movement into an unknown plume was worse than shelter in a known place; the Home Office's own casualty work assumed a stay-at-home population. American crisis relocation planning, by contrast, assumed several days of warning in which to move the population of the risk areas, and the Office of Technology Assessment's The Effects of Nuclear War (1979) treated that warning as the condition on which the whole scheme rested. In an attack that begins with a strike, it is not available.

That nobody shelters is a bound, not a case. Glasstone gives protection factors of about two for an ordinary house, five for a ground-floor inner room, ten to forty for a basement and a hundred or more for a purpose-built shelter. A sheltered population takes a fraction of the dose in the open, so the figures here are an upper bound on the acute fallout dead. This is the largest single uncertainty in any such estimate and it is why official and academic figures for the same attack differ by millions: for Square Leg the Home Office and Openshaw, Steadman and Greene reach very different totals largely on shelter and its assumed effectiveness, which the Britain study already sets side by side. The fallout lab now carries the protection factor as a control so the sensitivity can be seen rather than argued about.

That the dying is front-loaded is not a supposition at all. It follows from the decay law the model already uses: the dose rate falls as t^-1.2, so it drops roughly tenfold in the first seven hours and a hundredfold in two days, the seven-ten rule of Glasstone chapter IX. Most of the dose anyone ever takes is taken early, which is what the staged figures show and why an evacuation begun after arrival would not help those already under the heavy contours.

The accumulation also shows where the deaths fall in time, which the single figure hid. On the demolition belt, fifteen surface bursts of one and ten kilotons over the 1983 grid: 6,500 acute fallout deaths by two hours, 13,000 by eight, 18,000 by forty-eight, against 230,000 people under the plumes at two hours and 3.1 million at eight. Two thirds of the dying is done in the first eight hours, while the plume is still spreading over people who are not yet under it. Movement, had any been possible, would have had to happen before the plume arrived, not after.

The engine draws a plume for a surface burst and none for an air burst, which follows Glasstone §9.48, and the reason is worth stating because "an air burst produces no fallout" is only half true.

Local fallout needs something to fall. In a surface burst the fireball touches the ground, vaporises and melts soil, and that soil is drawn up into the rising cloud; as the cloud cools the fission products condense onto particles tens to hundreds of microns across, which are heavy enough to fall out within minutes to hours and near enough to make a plume. In an air burst there is no soil in the cloud, so the fission products condense onto each other into sub-micron particles that are carried into the upper troposphere or the stratosphere and come down over weeks to years, worldwide, after much of the short-lived activity has decayed. The activity is the same; where and when it lands is not. What the engine omits is therefore delayed global fallout, which is real and is not anybody's local dose, and the readout says so on every air-burst study.

Whether the fireball touches is a matter of burst height, and the coincidence the user asked about is real but not a definition. A burst is set at the height that maximises the area covered by the overpressure the planner wants, and for the overpressures used against soft targets that height is comfortably above the fireball. At 335 kt the fireball's maximum radius is about 620 m and the height that maximises the 5 psi area is about 2,100 m. The margin closes as the overpressure rises: the same weapon burst for 20 psi sits about 620 m up, which is one fireball radius, so a strike for very high overpressures is on the edge of scooping up its own crater. Below that, against a hard target, the weapon is burst on the surface deliberately, because cratering and ground shock are what is wanted, and the fallout is accepted. fireballTouchesGround and optimumBurstHeightMetres in the blast model make the comparison and are covered by tests.

A metropolitan attack of ten or more surface bursts a few kilometres apart makes one contaminated area, not ten separate ones, and the dose at a point downwind is the sum of what every plume puts there. Until this date the union kept the highest dose any plume gave a sample rather than the total. Within a single plume that is right, because its contours nest and the innermost should win; across plumes it was wrong, and it understated the dose wherever plumes overlapped.

How much it understated, for ten 335 kt surface bursts laid down over one city on the atlas's own sunflower spacing, wind 15 mph:

Near the aim points the correction changes nothing, because one plume already delivers a certainly fatal dose and the rest add nothing that matters. It changes the picture entirely in the middle distance, which is where the population is: at 50 km the dose goes from a quarter of the median lethal dose to well past it, and at 100 km from a dose that does nothing to one that causes radiation sickness across a whole region. The far field is where a metropolitan strike does its widest killing, and taking the maximum had hidden it.

The union now keeps each burst's contribution separately and sums them, so a re-add at a later hour raises that burst's own contribution rather than repeating it. applyGroupDose in the exposure model does the bookkeeping and the union tests cover both properties: three plumes of 200 rads each kill most of those under them, while one of 200 rads alone kills nobody.

A forty-eight hour window is not where the dying stops; it is where the model used to stop looking. Two additions, on 10 September 2026, say how much was being left out.

The dose a window captures. The decay integral converges, because t^-1.2 falls faster than 1/t, so there is a finite dose that someone who never leaves eventually takes: from an arrival at one hour it is five times the unit-time reference rate. Against that, forty-eight hours captures about 54 per cent, a week 64, a month 72. So a study that stops at two days has counted a little over half the dose its own model says the ground delivers. When a study's clock reaches its end the count is now carried out to a month and the readout says if nobody leaves for a month, which nobody would, and that is the point of showing it. On the demolition belt the acute figure goes from 18,000 at forty-eight hours to 27,000 at a month. The t^-1.2 law is good to within about a quarter for two weeks and is an extrapolation beyond that, so the month figure is a bound.

The collective dose, and the cancers in it. The union now carries person-rads among those the blast and fire left alive, and the readout gives latent fatal cancers at the nominal coefficient of about five and a half per cent per sievert. On the demolition belt that is 910,000 person-sieverts and about 50,000 latent deaths, against 27,000 acute: the tail is larger than the head. The coefficient is contested for exactly this use, and the commission that publishes it advises against multiplying a population's collective dose by it; it is given because leaving the long tail at zero is further from the truth than giving it with the caveat attached.

What is still missing is larger than either. Between the acute deaths and the cancers lie the injured who die because there is no hospital, the people who die of a winter without heat or water, the crops that fail and the famine that the atmospheric work of the last decade puts above every prompt effect combined. The studies of consequence, from the Office of Technology Assessment in 1979 to the crop-model work of the 2020s, are mostly about that gap. This engine does not model it and now says so on every surface-burst readout.

The third-degree burn radius has always been Sublette's closed form, 0.67 · Y^0.41 km, which is a fit to Glasstone and not Glasstone. Both editions are now to hand, and the fit holds.

The 1977 edition gives the mechanism in §7.96: a target receives Q ≈ 3.07 f W τ / D² calories per square centimetre, so a fixed exposure would put the radius at the square root of the yield. The exponent is below a half because the thermal pulse lengthens with yield and a longer pulse needs more energy to do the same damage to skin. The 1962 edition tabulates the outcome directly, in Table 12.31:

The tabulated second-degree ranges scale as Y^0.423 against this model's Y^0.41, and the model's radius sits inside them across four decades, which is where a third-degree burn belongs. §12.66 of the 1977 edition puts 4.5 to 6 cal/cm² at nine to ten miles for a megatonne, which is the same place.

The check is in blast.test.ts, with the table as data, so the fit cannot drift away from the source it was fitted to.

Two more numbers checked against the 1977 edition rather than against a fit of it.

The initial radiation. §8.32 has the dose falling as the inverse square of the distance and then again by absorption in the air, which over the range that matters is what a fixed distance per factor of ten amounts to. The doses themselves are curves in Figure 8.33, not a table, but §8.34 works one case in the text: a 50 kt fission air burst gives "somewhat less than 300 rads" at 2,000 yards, which the book interpolates at about 250. This model puts 250 rads at 1,922 yards, four per cent inside the book's own figure. The book's curves carry a stated reliability factor of one half to two, so four per cent is well inside the source's own uncertainty.

The crater, which was not modelled at all until now. §6.09 gives a one-kilotonne surface burst on dry soil an apparent radius of 60 feet and a depth of 30, every dimension scaling as the yield to the power 0.3, and works its own example: a hundred kilotonnes gives 240 feet and 120 feet. §6.71 puts the lip crest at 1.25 times the radius, and §6.09 separately says the crest stands 15 feet beyond a 60-foot crater — the same lip, stated twice, and the model reproduces both from one constant. §6.74 puts continuous ejecta at 2.15 times the radius.

For the 335 kt surface burst the strike console fires most often, that is a hole 105 metres in radius and 52 deep, ejecta to 225 metres, and 1.4 million tonnes of soil lifted. Which is the point of computing it: that soil is what the fission products condense onto, and the plume the fallout model draws is this material coming down again. The console now says so on every surface burst.

Water-saturated soil gives a wider and shallower crater and hard rock a smaller one. The book gives neither a number, so neither is given one here.

The whole of this work is now written up as a background document, Sixty Feet at One Kilotonne: every prompt-effect formula traced to its section, with the computed values beside the handbook's own worked examples, and the gaps stated as gaps. Two results in it come from putting the book's sections beside each other rather than from any one of them, and both are now assertions in blast.test.ts:

• The prompt radiation ring falls inside the 5 psi ring above about 2.2 kt (and the 1,000-rad ring above 0.91). Blast goes as W^(1/3) and thermal as W^0.41, but initial radiation as W^0.19, because the air absorbs the extra gammas before they arrive. Below the crossing, radiation reaches people the blast does not; above it, everyone who would have taken a fatal dose was already inside a radius where the buildings came down.
• At the height that maximises the 20 psi area, the fireball reaches the ground above about 323 kt. The fireball grows as W^0.4 and the height as W^(1/3). At 300 kt the fireball reaches 597 m and the burst sits at 600; at 335 kt it reaches 624 and the burst sits at 622. So a burst placed against a hard target is, above that yield, a fallout-producing burst whether it was meant to be or not — and the 335 kt W78 the console fires two to a silo is just over the line. At the 5 psi height it never happens at any yield. The heights are the engine's own fraction rule rather than the handbook's figure 3.73 curves, so this is a modelled crossing; the direction of the result does not depend on the rule.

The classifier's inputs were the geocoder's tag and the population density. Adding OpenStreetMap's land-use polygons, measured by shoelace within two and a half kilometres, changes what the console makes of a place. Two live checks:

Fairford is the case that justifies the whole thing: three thousand people, tagged place=village, and an airbase under it. The synthetic tests in landuse.test.ts check the areas, the classes and the precedence — tag first, then ground, then density — and the fallback when Overpass does not answer.

The winter chain (src/models/soot.ts, winter.ts, harvest.ts, famine.ts, ozone.ts) is a fit and is stated as one. Its structure is physical; the coefficients inside that structure were chosen so that the whole chain reproduces the published results of the three-dimensional models at both ends of the range. What follows is what it gives, against what they give.

The chain, case by case

Against the published figures, at the same population Xia used, 6.70 billion:

Eighteen published numbers, most within a tenth. Three places where it is not, and they are stated rather than tuned away: it runs cool at five teragrams, about a third under the ModelE figure; it is heavy in the middle of the famine range, where its ten-degree bands cannot see that a band is a dozen countries which would not share a harvest; and its land-against-ocean contrast is milder than the published one at the same global mean, −12 against −18 over land, because a zonal band averages a continental interior with the coast beside it and the published maps do not.

The growing-season row is the one worth noting, because nothing was fitted to it. The harvest model was set against Xia's crop losses and Xia's famine totals; the season length is a different quantity, computed from the monthly temperatures by interpolation, and it lands on Mills's published range on its own. At a hundred and fifty teragrams the same calculation gives no growing season at all between forty and sixty north, for four years running, which is Robock's Iowa and Ukraine staying below freezing for more than a year.

What the fit had to be told twice

Two structural errors were found by the fit refusing to work, and both are worth recording because the corrected version is the physics.

The land stops evaporating and the sea does not. The first version assumed the sunlight deficit was more strongly compensated over the ocean, on the reasoning that a warm ocean holds its air up. The fit inverted it, and the fit was right: a field that loses its sunlight also stops lifting water, and the heat it is no longer losing offsets about half the deficit, while a sea surface goes on evaporating into the cold air above it and takes the whole of it. What keeps the sea warm is not the surface budget but the two hundred and fifty metres of water under it.

A tropical continent cannot decouple from the sea beside it. The first version froze the Congo and the Amazon, which no published run does. Deep convection over warm water sets the temperature of the whole tropical troposphere and the free troposphere will not hold a horizontal gradient against it, so tropical land is tied to tropical sea in a way that northern land is not. With that coupling in, the tropics cool by five degrees where the northern continents cool by twenty, which is what the maps show.

A third error was arithmetic rather than physical: the monthly step went unstable once the coupling was strong enough to be right, and the month is now walked in twelfths.

The number the whole thing hangs on

The fuel loading is not a parameter, it is the argument, and this is what it does to the northern-hemisphere case with everything else held fixed:

Above about ten grammes per square centimetre the cooling saturates near ten and a half degrees, because the sunlight is already gone and more soot has nothing left to take. The interesting part of the range is all below the firestorm threshold, where the answer swings by a factor of a hundred.

Which is to say: the difference between the two positions in the literature is the difference between a bad year and the end of agriculture, and it rests on a quantity that has been measured for exactly one city, where the published values differ by a factor of four.