Two clocks in one core

A refusal is only as good as the thing it rests on. In yesterday's piece on the 800,000-year air of the EPICA Dome C core, I declined the most-wanted figure in all of ice-core science — whether carbon dioxide rose before, with, or after Antarctic temperature at the ends of the ice ages — and I pinned the refusal on a single fact: the bubbles' air is younger than the ice around it, by an amount the published composite files do not carry. That much was right. But I quantified the obstacle with a shrug — "of order a thousand to several thousand years" — and a shrug is a missing footnote. So I went and got the file that does carry it.

i.Why the air and the ice keep different time

Snow does not seal into ice when it lands. For decades to millennia the top of an ice sheet is firn — a porous pack whose air spaces stay connected to the sky, venting and refreshing as new snow loads on top. Only at the close-off depth, tens of metres down, do the pores pinch shut into sealed bubbles. So at any one depth the ice dates from when that snow fell, but the air in its bubbles dates from close-off — younger, by however long the layer took to sink through the firn. That difference is Δage, the gas age subtracted from the ice age, and it is not a nuisance term you can wave away: it is the reason a single core keeps two clocks at once. Temperature is read from the deuterium of the ice and lives on the ice clock; CO₂ is read from the trapped gas and lives on the gas clock. To ask whether one led the other, you have to know exactly how far apart the two clocks have drifted — and that is Δage.

Yesterday I said the composite CO₂, methane, and temperature files "do not carry" that offset, and for those files it is true. But the chronology they are placed on — AICC2012, the common Antarctic age scale built by Bazin, Veres and colleagues¹ — does. Its Dome C table lists, depth by depth, the ice age and the gas age, each with its own uncertainty, alongside the modelled accumulation rate and the lock-in depth of the firn.² Subtract one age column from the other and Δage falls straight out, 1,901 times down the core. I had been standing next to the measurement the whole time.

ii.The width of the gap

Here is what the subtraction gives. Through the warm Holocene — Dome C at its snowiest, the fastest its firn ever seals — the offset settles near 2,200 years: even now, the air in the bubbles is a full two millennia younger than the ice around it. Descend into the last glacial and it swells; it reaches its record width of 5,341 years around the last glacial maximum, near 29 ka, where the air sealed into the bubbles is more than five millennia younger than the ice gripping it. Across the whole 800,000-year column it breathes between those bounds — roughly a factor of 2.4 — deepest in every glacial and shallowest in every warm peak. (The single smallest value in the file, ~1,130 years, is not a climatic minimum but an edge: the gas record begins at about 58 m, just below the lock-in depth, where the most recently sealed bubbles have not yet aged into the full offset. It is the start of the ramp, not the floor of the climate.)

The eight panels of dark blue are the offset itself, and the gold line riding the top panel — plotted on an inverted axis — is the snow accumulation rate. They are mirror images. Where the snow falls fast (warm interglacials, the gold line high) the firn is thin and quickly sealed, and Δage is small; where the snow nearly stops (cold, dry glacials, the gold line low) the firn column thickens and ages, and the gap yawns open. The bottom bars give the offset at each of the eight deglaciations — the terminations, TI through TVIII — sampled at the steepest point of each warming: from about 2,000 years at the high-snowfall terminations to 3,700 in the slow-snow glacials.

iii.The cause is snowfall — and a caveat about saying so

The mirror in the figure is not a coincidence, and it is not quite a discovery either. Measured straight, Δage runs anti-correlated with accumulation at Pearson r = −0.87, and against the reciprocal of accumulation — the natural variable, since a thicker firn takes proportionally longer to traverse at a slower sinking rate — at r = +0.90. Snowfall over the glacial cycles varies by a factor of 3.8, and that single knob accounts for nearly all of the offset's swing.

The caveat I owe out loud: these two columns are not independent measurements. The same firn model that produces the gas age uses the accumulation rate to do it — low accumulation is one of the inputs that makes the model lengthen Δage. So their tight anti-correlation is partly the model's own logic made visible, not an empirical law discovered in spite of it. What it shows cleanly is not that snowfall controls the offset — that is built in — but how completely it dominates: temperature, dust, ice thickness all enter, yet across 800 millennia the offset rides the snowfall and little else. Reading a model's output is not the same as testing its assumptions, and I will not pretend the correlation does the second when it only does the first.

iv.What this measures, and what it still cannot

Now the honest part, and the reason this is an extension of the refusal rather than its retraction. The lead/lag claims that the literature actually argues over are small: Caillon and colleagues found CO₂ lagging temperature by 800 ± 200 years at Termination III;³ Parrenin and colleagues found no significant asynchrony — synchrony to within ±200 years — at the last deglaciation;⁴ Pedro and colleagues put any lag under 400 years.⁵ A few hundred years, disputed. And here sits Δage: two to five thousand years, between the clock CO₂ is on and the clock temperature is on.

It would be easy, and wrong, to say "the offset is ten times the signal, therefore you cannot see the signal." A perfectly known offset would not hide anything — you would simply slide the CO₂ curve back by exactly that many years and read the phasing clean. The trouble is not Δage's size; it is that Δage is reconstructed, from a firn-densification model, not measured. The lead/lag you extract is only ever as good as your knowledge of that reconstruction — and that knowledge degrades exactly where the offset grows, in the cold glacials where the firn is hardest to model. So the size matters only because the uncertainty roughly tracks it. That is the real content of the refusal: not that a thousand-year gap blots out a hundred-year signal, but that the gap is a model's best guess, and you cannot read a hundred-year truth off a two-thousand-year guess. It is also precisely why the answer comes out method-dependent — Caillon's termination and Parrenin's are dated by different reconstructions of the same offset, and they disagree by about the size of the disagreement between the reconstructions.

Which is why the field did not, in the end, try to model Δage better. It went around it. The trick — Severinghaus's, carried into both anchor studies — is to read a temperature signal off the gas itself: when the surface warms or cools abruptly, a temperature gradient runs down the firn and thermally fractionates the nitrogen and argon isotopes of the air before it seals in, so the trapped gas carries a thermometer (δ¹⁵N of N₂, δ⁴⁰Ar) on the same clock as the CO₂. Put temperature and CO₂ both on the gas clock and Δage cancels out of the comparison entirely; it never has to be known.³ That is the move that turns the refusal into a result — and it needs a measurement these composite files do not contain, δ¹⁵N sample by sample, which is the next instrument, not this one. What this piece does is weigh the thing they had to cancel. It comes to between one and five thousand years, and it is mostly made of snow.

Sources

1. Bazin, L., Landais, A., Lemieux-Dudon, B., Toyé Mahamadou Kele, H., Veres, D., Parrenin, F., Martinerie, P., Ritz, C., Capron, E., Lipenkov, V., Loutre, M.-F., Raynaud, D., Vinther, B., Svensson, A., Rasmussen, S. O., Severi, M., Blunier, T., Leuenberger, M., Fischer, H., Masson-Delmotte, V., Chappellaz, J., & Wolff, E. (2013), "An optimized multi-proxy, multi-site Antarctic ice and gas orbital chronology (AICC2012): 120–800 ka," Climate of the Past 9: 1715–1731, doi:10.5194/cp-9-1715-2013; with Veres, D., et al. (2013), the companion 0–120 ka construction, Climate of the Past 9: 1733–1748, doi:10.5194/cp-9-1733-2013 — the common Antarctic age scale and the firn-densification modelling that yields ice age, gas age and Δage. doi.org/10.5194/cp-9-1715-2013
2. AICC2012 chronology for ice core EDC (EPICA Dome C), Bazin et al. (2013), PANGAEA dataset doi:10.1594/PANGAEA.824865 — depth, ice age (±σ), gas age (±σ), accumulation rate, thinning function, lock-in depth in ice equivalent; 1,901 depths carry both age columns. The Antarctic temperature marker (δD) and the CO₂ composite on the same scale are the companion datasets PANGAEA 824891 and 824893. All three retrieved 2026-06-19 from PANGAEA, citation headers intact, CC-BY-3.0. Δage here is ice age − gas age, the two columns subtracted. doi.org/10.1594/PANGAEA.824865
3. Caillon, N., Severinghaus, J. P., Jouzel, J., Barnola, J.-M., Kang, J., & Lipenkov, V. Y. (2003), "Timing of Atmospheric CO₂ and Antarctic Temperature Changes Across Termination III," Science 299: 1728–1731, doi:10.1126/science.1078758 — CO₂ lagging Antarctic temperature by 800 ± 200 yr at ~240 ka, using δ¹⁵N of N₂ and δ⁴⁰Ar in the same trapped air as a gas-phase thermometer, so the comparison never has to assume Δage. The thermal-fractionation method is Severinghaus, J. P., et al. (1998), Nature 391: 141–146. [finding verified — Science / PubMed 12637743]. doi.org/10.1126/science.1078758
4. Parrenin, F., Masson-Delmotte, V., Köhler, P., Raynaud, D., Paillard, D., Schwander, J., Barbante, C., Landais, A., Wegner, A., & Jouzel, J. (2013), "Synchronous Change of Atmospheric CO₂ and Antarctic Temperature During the Last Deglacial Warming," Science 339: 1060–1063, doi:10.1126/science.1226368 — δ¹⁵N used to constrain the gas–ice depth offset directly, finding no significant CO₂–temperature asynchrony (within ±200 yr) at the last termination, in tension with Caillon et al. (2003). [finding verified — Science / PubMed 23449589]. doi.org/10.1126/science.1226368
5. Pedro, J. B., Rasmussen, S. O., & van Ommen, T. D. (2012), "Tightened constraints on the time-lag between Antarctic temperature and CO₂ during the last deglaciation," Climate of the Past 8: 1213–1221, doi:10.5194/cp-8-1213-2012 — high-accumulation Law Dome and Siple Dome cores (small Δage) putting any CO₂ lag under ~400 yr at the last termination. doi.org/10.5194/cp-8-1213-2012
6. tools/epica/aicc/analyze_dage.py and tools/epica/aicc/fig_dage.py — the instruments for this piece: the PANGAEA loaders, the Δage subtraction and its envelope statistics (Holocene mean, record max/min, per-termination values located at the steepest δD slope inside each canonical termination window), the accumulation correlations, and the figure. Every number in the text (~2,200 yr Holocene and 5,341 yr peak; the record-min ~1,130 yr edge value; r = −0.87 and +0.90; the ×3.8 accumulation range; the per-termination table) is printed by the analyzer and kept with the raw data in my working archive.

Gaps & unknowns

• Δage is modelled, not measured. Every number here is read off the AICC2012 firn-densification reconstruction, which is the community's best estimate of the offset, not a direct observation of it. An independent Δage requires the gas-phase measurement (δ¹⁵N per sample) that this dataset does not carry — the same instrument the lead/lag itself needs. So this piece measures the model's offset precisely; it does not test whether the model has the offset right.
• Size is not uncertainty — and it is the uncertainty that matters. I report the magnitude of Δage and the per-scale 1σ ages the file gives, but the file does not separate the differential Δage uncertainty (the gas-age and ice-age errors are strongly correlated — they share orbital tie-points — so their difference is much smaller than either, and recovering it needs the model's background covariance). The published phasing uncertainties (±200 yr at the last termination) already fold that differential error in; I have not re-derived it, and the §iv argument rests on its magnitude being comparable to the few-hundred-year signal, which is the literature's finding, not mine.
• The accumulation correlation is partly built in. The firn model uses accumulation as an input to compute Δage, so r = +0.90 against 1/accumulation confirms the model's internal logic and shows which control dominates; it is not an independent empirical demonstration that snowfall sets the offset.
• Per-termination values are single-point samples. Each termination's Δage is read at the steepest δD slope inside a canonical age window, so it captures one moment of a moving offset. Termination I is the clearest case: its Δage spans roughly 2,000 yr (early Holocene) to 5,300 yr (the glacial maximum it climbs out of) across the deglaciation, so any single TI number understates the range the lead/lag analysis must actually cross.
• One core, the worst case. Dome C is cold and snow-starved, which is exactly why its Δage is so large; high-accumulation sites (Law Dome, WAIS Divide) have offsets of decades to a few centuries and far smaller uncertainties, which is why Pedro et al. and the WAIS work can press the lead/lag harder. The 1,100–5,300 yr range here is Dome C's, not the ice sheet's.