An Empire's Air Pollution, Measured in Greenland Ice and in Roman Children's Blood

The Drill Comes Up

A core barrel is as wide as a dinner plate.

You lower it on a cable. It cuts a cylinder of ice. You winch it back up and lay the cylinder on a bench in a cold room. Somebody logs the depth it came from. Then you do it again. The ice sheet has been taking snow for a hundred thousand years, so you read down through it, one barrel at a time, until you reach the year you want.

Three cores carry this study. Akademii Nauk on Severnaya Zemlya in the Russian Arctic, then two sites on Greenland: NGRIP2 in the north-centre of the ice sheet and RECAP on the Renland ice cap in the east [1]. They sit at different distances from Europe and catch different amounts of snow each year, so a signal present in all three is unlikely to be a story about any one of them.

At those depths the cores hold lead. The layers run from the last few centuries BCE into the first few CE. Not much of it. Quantities run in picograms per gram of ice, which is parts per trillion. The natural floor from windblown dust and volcanic gas sits well under one part per trillion. Above that floor sits an addition that arrives and departs on a schedule. The schedule is legible.

It rises in the second century BCE. It collapses in the first. It climbs sharply again around 15 BCE and stays high for the better part of two hundred years, then falls in the 160s CE, and does not return to that level until the early second millennium [1, 2].

Nobody layered those dates onto the chemistry afterwards. They come from counting annual layers in the ice, the way you count rings in a tree. Volcanic ash horizons of known date check the count. The ice keeps calendar and chemistry in one cylinder.

What a Deposition Record Cannot Say

A lead concentration in Greenland ice is a deposition record. It reports how much lead fell out of the sky onto one square metre of ice sheet in one year. Nothing else. Laboratories have measured that since the 1990s. Hong and colleagues reported Greek and Roman lead in Greenland ice in 1994, and Rosman and colleagues matched its isotopes to Spanish ore in 1997 [3, 4]. Neither paper claimed to know what any Roman was breathing.

That gap is the whole problem. Greenland sits a long way from a smelter in the Sierra Morena, and between the furnace and the ice lies an atmosphere that lifts some particles and drops others, rains out most of what it lifts, carries the remainder along whatever path the pressure field took that week, and delivers to Greenland a tiny, biased, weather-dependent sample of the original emission.

Going from the sample back to the source demands the sampling function. How much of a kilogram of lead released near Rio Tinto in a given month reaches the snow at NGRIP2? The number is small, and it varies by season and by where in Europe the release happened. Without it a deposition record is a thermometer with no scale. You can watch the reading rise. You cannot say by how much.

The 2025 paper's contribution is the scale on the thermometer.

Running the Weather Backwards

The tool is FLEXPART [1, 6]. A Lagrangian particle dispersion model does not solve equations on a fixed grid. It releases a large number of imaginary particles into a wind field and follows each one until it deposits or leaves the domain. Run forwards, it says where a plume goes. Run backwards from a receptor, and that is the trick here, and it says which parts of the map could have supplied the material arriving at that receptor, and with what efficiency.

The backward run produces an emission sensitivity field. For every grid cell in Europe, it gives the deposition at the ice core site per unit emission from that cell. Divide measured deposition by sensitivity. Out comes an emission estimate. The authors worked at half-degree resolution globally and quarter-degree over Europe. Cells roughly twenty to thirty kilometres across.

Then they ran it the other way. A forward simulation on the recovered emissions maps annual mean air concentrations across the continent. Geography now matters enormously. A person downwind of the Iberian smelting districts breathed something very different from a person in Denmark. The paper reports air lead spanning 0.16 to 157 nanograms per cubic metre under a scenario where Rio Tinto dominates, and a much tighter 0.19 to 12.3 where emissions spread across many smaller districts [1]. Empire-wide averages: near 1 ng/m³ in the northern provinces, 0.5 in the southern.

Two scenarios exist because the ice cannot settle where. Lead isotope ratios in the NGRIP2 core point to multiple sources rather than one dominant district, so the authors carry both possibilities instead of picking one. Their emission estimates differ accordingly: about 4.2 kilotons a year concentrated at Rio Tinto, or about 3.0 kilotons a year spread around [1], which over the roughly 175 years of the Pax Romana totals more than 500 kilotons of lead into the air.

Link 1 is a measurement. Links 2 and 3 are physics with known error bars. Links 4 and 5 are epidemiology borrowed from the twentieth century and pointed at the first. Hold that ordering. The uncertainty runs the other way.

Notes From the Club Table

Somebody proposed we redo the ice-core inversion, and four minutes of discussion killed the idea. No cores, no deposition data, no wind field, no dispersion model. Inventing any of those would have made this article a fiction with equations in it. So we drew a line. Emissions are an input, taken from the paper. Everything downstream of emissions we rebuild ourselves.

A standard well-mixed box. Pick an area. Pick a boundary layer height. Put lead in, take lead out by deposition, solve for the steady-state concentration. We argued for a while over whether the boundary layer above Europe averages 800 metres or 1,200. Then one of us wrote the steady-state condition down properly and the argument evaporated.

At steady state, everything emitted is removed. Removal is deposition velocity times concentration times ground area. So

and the height of the box never appears in it, which is the part that stopped the argument dead. A taller box holds more lead at the same concentration. It also takes proportionally longer to fill. The two effects cancel exactly. Twenty minutes, spent on a parameter the model does not contain.

The paper writes the air-to-blood regression as \(\mathrm{BLL} = \exp[1.932 + 0.140 \ln(\text{air concentration})]\), and the published text never spells out the units of that air concentration inside the logarithm. Feed it nanograms per cubic metre and you get 6.9 µg/dL of blood lead, roughly triple what the paper reports. Feed it micrograms and you get 2.6, close to the paper's 2.4. So the units are micrograms. We knew that only because we had the answer to check against. A reader without the answer faces a coin flip and a factor of three.

The paper publishes two sanity checks of its own IQ regression against American data. Children with a geometric mean blood lead of 15.2 µg/dL in 1976 to 1980 should show a 9.2-point deficit, and children at 0.8 µg/dL in 2011 to 2016 should show 1.9 [1]. Our implementation returns 9.23 and 1.95. Exact agreement to rounding, so we hold their functional form, and any disagreement further down is our box. Not our epidemiology. A small thing. It made everything after it much easier to argue about.

The Arithmetic

Plain numbers. The linked script prints every one of them.

The box is the rectangle from 10°W to 40°E and 30°N to 65°N, and on a sphere of radius 6,371 km its area comes to 1.439 × 10¹³ m². Call it 14.4 million square kilometres.

We set the effective bulk removal velocity at 1.5 cm/s. That lumps dry deposition of smelter particles together with wet scavenging by rain. Rain is the larger term for the fine fraction. In a year, 1.5 cm/s sweeps a column 473,000 metres tall. Times the area, the box scrubs 6.81 × 10¹⁸ m³ of air a year.

Emissions enter at 3.5 kilotons a year, the midpoint of the paper's two scenarios. In micrograms, 3.5 × 10¹⁵.

Divide. The air concentration comes out at 5.14 × 10⁻⁴ µg/m³, or 0.514 ng/m³. The paper's domain averages run 0.49 to 1.04. We sit inside their range.

Now the second link. Written as a power law, the air-to-blood regression is

with \(C\) in µg/m³ and \(\Delta\mathrm{BLL}\) the increment above the pre-metallurgy baseline. At \(C = 5.14\times10^{-4}\) that returns 2.391 µg/dL. The paper reports about 2.4.

Add the baseline. Neolithic tooth enamel puts pre-metallurgy European childhood blood lead near 1.0 µg/dL [1]. Total: 3.391 µg/dL. The paper reports about 3.4.

Third link. The IQ regression is

At 3.391 µg/dL the deficit is −4.905 points, and at the 1.0 baseline it is −2.298. The difference, the part attributable to Roman smelting rather than to the world Romans would have had anyway, is 2.607 points. The paper reports 2.5 to 3.

Four numbers, four agreements. Good model, or lucky one. The next two sections separate those.

Where the Curve Is Steep

Two compressions sit in the chain. They do opposite things to your intuition.

The first is the air-to-blood step, and it is remarkably flat. Blood lead goes as air lead to the power 0.140. Multiply the air concentration by ten and blood lead rises by a factor of 10^0.14, which is 1.38, an increase of 38 per cent. Multiply by a hundred and you have not quite doubled it. A physical story sits behind that shape. Airborne lead mostly reaches a child by some route other than the lungs. It settles onto soil, dust, floors and hands, and the pathways carrying it from there into a bloodstream saturate. Doubling what sits in the air does not double what sits on the hands. Nor what reaches the gut.

The second compression is the blood-to-IQ step, and this one runs the other way. The deficit goes as the logarithm of blood lead, so the derivative is

which is steepest at the bottom, and that one property carries most of what follows. The first microgram per decilitre a child acquires costs 3.315 IQ points. The fortieth costs 0.081. A factor of forty-one between them.

No quirk of the regression produces this. The shape is the central finding of lead epidemiology over the last twenty-five years. Establishing it took a long time, because it runs against intuition and because data at low exposure are the hardest to get. In 2003 Canfield and colleagues put that steep region below 10 µg/dL [7]. Lanphear's pooled analysis of seven cohorts confirmed it in 2005 and found lead-related deficits in children whose peak blood lead never exceeded 7.5 µg/dL, with no threshold anywhere [5]. The public health consequence has been enormous. No safe level exists, only lower ones.

Roman children sat exactly where the curve is steep. A blood lead of 3.4 µg/dL would not alarm a modern paediatrician the way 30 would. It does far more than a tenth of the damage.

Which Assumption Drives the Answer

We would defend this part of the exercise hardest, because a reader cannot do it in their head, and because it changes what the headline number means.

Take the central answer of 2.607 IQ points. Move one assumption at a time across the range it could honestly take, hold everything else fixed, and record how far the answer travels. Eight assumptions go into the chain. They do not contribute equally. The ordering is not the one a reader would guess from the paper, where most of the methodological weight sits in the atmospheric transport.

Read the last column. The four at the top are the epidemiology, copied without changing a digit, and we could not have changed them responsibly; the three in the middle are our box, and we could have set those almost anywhere. The invented parameters move the answer least.

The single exponent \(b\) in the air-to-blood power law, moved across one published standard error, shifts the answer by 1.475 IQ points, which is 57 per cent of the whole result and more than five times the span contributed by the paper's entire emission uncertainty. The ice cores, the dispersion model, the volcanic tie points and the annual layer counting, all the difficult apparatus that makes this study a study, together account for 3.3 per cent of the uncertainty in the number everybody quoted.

We then ran all eight together, with 200,000 seeded draws, the coefficients wandering over their published standard errors and our box parameters over their stated ranges. The median comes out at 2.634 IQ points, with a 68 per cent interval of 1.78 to 3.74 and a 95 per cent interval of 1.17 to 5.09. A loss above one point carries probability 98.9 per cent. Above two points, 76.1 per cent. The interval is ours and not the paper's. Theirs comes from a more careful propagation, and they quote a coefficient of variation near 0.9 on the empire-wide average, the same order of looseness.

Three Point Four Micrograms, Against Numbers We Can Check

Alone, 3.4 µg/dL means nothing.

Put it beside the American twentieth century, where the measurements are real and abundant. Between 1976 and 1980, when tetraethyl lead was still in petrol and the exhaust of every car was an aerosol generator, the geometric mean blood lead of American children stood at 15.2 µg/dL [11]. By 2011 to 2016, after the phase-out, 0.8. On the same regression the paper uses, that fall recovers 7.28 IQ points per child, one of the largest public health returns ever documented, and almost nobody thinks about it.

Now the Roman number. 3.391 µg/dL, of which 2.39 is the airborne Roman contribution. The Roman figure reaches 22 per cent of the American leaded-petrol peak and 4.2 times the modern American level, and the cognitive burden of 2.61 points comes to 36 per cent of what leaded petrol cost American children.

One comparison stopped the table for a minute when it printed. Since 2021 the CDC has used a blood lead reference value of 3.5 µg/dL, the level at which a child is flagged for follow-up and a case is opened [12]. Our modelled Roman average is 3.391. Ratio: 0.969.

The average child in the Roman Empire sat about three per cent below the threshold at which a modern American clinic starts a file.

Not a dramatic exceedance. Not a poisoning. A population sitting at the edge of the line a wealthy modern state draws for intervention, for two centuries, across a continent, with no line and no intervention.

The third column computes every deficit against zero blood lead. No real population has ever had zero. Compare the rows against each other. Do not read them as absolute claims about anybody's score.

The Best Case Against

Take the reviewer's chair. The job is to find the world in which every measurement is right and the conclusion is still wrong. What follows is the strongest version we can build. We think it is strong.

The dose-response function has almost no dynamic range at these concentrations, and that is fatal to the specificity of the claim, whatever the ice cores say.

We found this objection ourselves, by running our own model somewhere the paper does not go. Set emissions to 0.05 kilotons a year, the Iron Age background before Rome existed, essentially no industry at all, and the chain returns a total blood lead of 2.32 µg/dL and a decrement of 1.68 IQ points. Set emissions to the Pax Romana value, seventy times higher: 3.39 and 2.61.

Seventy times the industry. Fifty-five per cent more harm.

Take the Sullan trough in the 80s BCE, when the ice shows lead output collapsing back toward background during the civil wars. Our model puts that year at 2.19 IQ points against the Pax Romana's 2.61. If the reconstruction is right that emissions fell by a factor of six, the modelled cognitive difference between an empire at full industrial output and a republic tearing itself apart is under half an IQ point. A function that flat cannot distinguish causes. It ranks them gently, and that is all.

A sharper version of the complaint follows. The power law is calibrated on modern children breathing air lead of order 0.01 to 1 µg/m³, most of whose blood lead came from paint, soil, dust and water rather than from the air at all. Our Roman air concentration is 5.1 × 10⁻⁴ µg/m³, twenty to two thousand times below that calibration range, and Richmond-Bryant and colleagues showed that these slope factors are themselves unstable, shifting as air lead falls [8]. Most fields catch that kind of extrapolation in peer review.

A second objection, from the archaeology. A recent review of Roman lead exposure by Simpson and Garvie-Lok argues that the literature has consistently overstated Roman lead impacts, and that the bioarchaeological record, meaning actual lead measured in actual Roman skeletons, does not support the strong claims often made from documentary sources [15]. That review covers wine and plumbing rather than air, so it does not target this paper directly. It does remind us that this field has a long history of exciting conclusions that did not survive, from Nriagu's 1983 argument that lead poisoning helped bring down the empire [16] through Scarborough's rebuttal the following year [17].

A third, on the physics. The FLEXPART runs use twentieth-century meteorology as a stand-in for antiquity. The authors state that plainly [1]. Two thousand years is short in climate terms, and the general circulation was not obviously different, so the substitution is probably fine, though the assumption cannot be checked.

Now the answers, because a steelman nobody replies to is just a hedge.

The flatness objection is real, the best of the three, and we would not have found it without building the model. It does not touch the ice cores. The emission history remains an unusually well-dated industrial record, interesting whatever the health inference does. What flatness damages is the attribution: the claim that this particular emission history caused this particular decrement, rather than the weaker and safer claim that a population at 3.4 µg/dL carries a burden of a few IQ points. The paper is careful here. McConnell has said explicitly that he leaves it to historians to decide whether these levels were enough to change anything.

The archaeological objection cuts in a direction that helps rather than hurts. Skeletal lead lower than the documentary tradition implied argues against the wine-and-pipes story. It says nothing about a diffuse atmospheric background, which is exactly what an ice core detects well and what a skeleton from a single site resolves badly.

The meteorology objection is small in the sensitivity ranking. It sits inside the emission estimate, and the emission estimate contributes 3.3 per cent.

What survives is this. The emission record is solid. The map is plausible. The health number is an extrapolation with honest error bars, and those bars happen to be wider than the difference between the historical scenarios it gets used to compare.

What Would Change Our Minds

Falsifiable is a word people use loosely. Four things would move us, in the order we would want them.

Skeletal lead with dates and places attached. The blood lead figure is a model output with no direct evidence behind it. Lead accumulates in bone and in tooth enamel. Enamel locks in a chemical record of early childhood that does not remodel afterwards. A large series of Roman-era skeletons from provinces at very different modelled air concentrations, with lead concentrations and isotope ratios measured in each, would put a real number where a modelled one now sits. Equal body burdens across high-exposure and low-exposure provinces would sink the atmospheric map.

Isotopes matched province by province. Lead from different ore bodies carries different isotope ratios. Rosman and colleagues already showed that the Greenland lead of this period matches Spanish ore [4]. If the isotope signature in the ice tracks the rise and fall of specific mining districts whose operating dates archaeology already knows, the inversion gains a witness it did not have.

A fourth and fifth core, from somewhere other than the Arctic. Three cores rule out a local artefact. Three cores do not map a hemisphere. Alpine ice and peat bogs both record atmospheric deposition, and both sit inside the modelled domain rather than four thousand kilometres downwind of it, so agreement between an Alpine record and the Arctic inversion would test the transport model properly.

A modern natural experiment on the exponent. The weakest link is the air-to-blood power law at very low concentrations. Somewhere in the world, populations have watched their air lead drop through the 0.001 to 0.01 µg/m³ range with blood lead measured before and after. Those data would tell us whether the exponent of 0.140 holds down there or steepens. The entire Roman IQ figure hangs on the answer.

None of that is out of reach. The first item is already underway in various forms, and the third is a matter of somebody funding the drilling.

The Size of the Claim

Go back to the bottom of the rail, to the layer from around 500 BCE. Lead sits in it. Not much: a fraction of a picogram per gram, Greek silver from Laurion and Phoenician work in Iberia, the earliest industrial signal any ice anywhere has recorded. Below it the record goes quiet.

Everything here happened between that layer and the one six hundred years above it. An empire organised silver production at a scale nothing matched again for a thousand years, and silver comes out of galena, which is lead sulphide, and the smelting of galena puts lead into the air whether or not anybody wants it there. Roughly thirty parts of lead were lost to the atmosphere for every part of silver recovered. The pollution was a by-product of coinage, which is to say of the money supply, which is to say of the thing that held the empire together.

What the ice adds is a number and a date. Not an opinion about the fall of Rome, which this paper does not offer and which we would not repeat if it did. Just this: here is how much, and here is the year it stopped.

The health inference on top is softer, and two sections here say how much softer. Our own chain says 2.61 IQ points with a 95 per cent range from 1.17 to 5.09. The honest summary reads: a few points, probably, empire-wide, for two centuries. Not a precise claim. A claim about the right order of magnitude, made about people who left no medical records, and it can be made at all only because the pollution left a receipt in a place nobody was looking.

An ice sheet is a poor witness. It sits four thousand kilometres downwind, it caught a small and biased fraction of what happened, it cannot be cross-examined, and it has no idea what it recorded. But it wrote down the date.

References