Snowball Earth Was Flickering: A Planet Stuck in a 56 Million Year Loop

Fifty-six million years is a long time to be cold

Start with the number, because the number is what broke the story.

Rocks laid down by glaciers, full of stones dropped out of floating ice, turn up on almost every continent in sediments of Cryogenian age, and radiometric dating of the ash beds sitting inside those sequences puts the start of the older of the two Cryogenian ice ages, the Sturtian, at about 717 million years ago and the end at about 661 million years ago [5, 6]. Two independent clocks agree on the span, uranium-lead ages from zircon crystals in volcanic ash and rhenium-osmium ages from the black shales above and below, which is the reason nobody has ever managed to argue the number down. Fifty-six million years.

The whole of the Cenozoic, measured from the asteroid to you, runs to 66 million years, so the Sturtian ice lasted very nearly as long as the entire age of mammals.

The standard explanation for how a planet gets into that state is beautiful, and for thirty years it has been taught as though the matter were closed. Joseph Kirschvink named it in 1992: cool the planet far enough that ice reaches low latitudes, and the ice finishes the work on its own, because ice is bright, a brighter planet absorbs less sunlight, and a colder planet grows more ice [2]. The feedback runs away. Within a few thousand years the ocean lies roofed over from pole to pole. Paul Hoffman and colleagues then showed what gets a planet out again: with the continents buried, the chemical weathering that normally scrubs carbon dioxide out of the air stops altogether, volcanoes go on erupting into a sky that has lost its only sink, and carbon dioxide piles up until the greenhouse effect turns violent enough to melt the lid off [3, 4].

That escape route has a timescale, and the timescale is the problem, because estimates of how long a snowball needs in order to accumulate enough carbon dioxide to melt itself back out run from a few million years to about ten million, depending on what you assume about volcanic output and about how much carbon a sealed ocean can hold [13]. Reaching 56 million years then demands either implausibly feeble volcanoes or a deglaciation threshold sitting far above anything most calculations will support, which is why the Sturtian has been a duration problem for exactly as long as its duration has been known.

Two climates, one planet, same sunlight

Before any of the new work makes sense you need one idea, and the idea deserves a slow walk, because the entire paper turns on it.

Write down the simplest possible climate model, in which the planet absorbs sunlight at a rate set by how bright it is and radiates heat away to space at a rate set by how warm it is, so that equilibrium becomes nothing grander than the temperature at which those two rates come out equal. Mikhail Budyko wrote it down in 1969 in almost exactly this form [12].

Now add the one complication that matters, which is that how bright the planet is depends on how cold it is, because cold means ice and ice is white, so the absorption curve never runs straight across temperature but bends instead into an S: nearly flat and low where the planet is frozen solid, nearly flat and high where the planet is ice-free, and steep in the middle where the ice line sweeps across the mid latitudes. The radiation curve, meanwhile, really is close to a straight line.

A straight line can cross an S in three places. The whole argument sits inside that one fact: three crossings mean three temperatures at which the planet balances, and a quick check of the slopes tells you that the outer two are stable, so that a planet nudged off either of them comes back, while the middle one is unstable, so that a planet nudged off it runs away and never returns. A single planet, then, taking in a single amount of sunlight, carries two possible climates inside it, and which of the two you happen to find it wearing depends entirely on where it has already been.

In our reconstruction of the model, at 280 parts per million of carbon dioxide, both climates coexist for solar constants between 1278 and 1472 watts per square metre, a window 194 W/m² wide. Stars brighten as they age, so the sun of 717 million years ago was fainter than the one overhead now, and the standard parameterisation of that brightening [19] puts the Sturtian solar constant at 1281 W/m², or 94.1% of the modern 1361. That value sits inside the window. So does today's, which means that both then and now a frozen Earth stands as a solution the physics allows, and Figure 1 draws the whole business out.

The gap between the two thresholds carries the argument: coming down, the planet freezes at 1277 W/m²; going back up, it will not thaw until 1474, and those two numbers differ by 197 W/m², roughly 15% of the whole solar constant, which is not an amount of sunlight any planet recovers merely by waiting. The word for the lag is hysteresis, from a Greek root meaning to come late, and the lag is why Snowball Earth has been understood for thirty years as a trap rather than as a phase.

A million square kilometres of fresh basalt, at the worst possible moment

Between 719.86 ± 0.21 and 718.61 ± 0.30 million years ago, magma forced its way up through the crust of what is now Arctic Canada and northwest Greenland, and it went on doing so for something over a million years. Out of that came the Franklin large igneous province: a swarm of dykes more than 1,200 kilometres across, sills stacked through the sedimentary pile, and the Natkusiak flood basalts on Victoria Island, which in the north still stand about a kilometre thick after 700 million years of erosion have worked at them. The affected area exceeds a million square kilometres, and precise uranium-lead dates place the end of the main pulse between 0.9 and 1.6 million years before the first Sturtian glacial deposits appear [7].

Laurentia, the ancient core of North America, sat in the tropics.

Two consequences follow, on very different timescales, and both of them push the planet the same way. The first arrives across the first few thousand years, when a very large eruption throws sulfur into the stratosphere, where it forms reflective aerosol and cools the planet sharply, and Francis Macdonald and Robin Wordsworth showed that sulfur injection from a tropical province of this size is enough on its own to tip a marginally cool Earth over the ice-albedo edge [9]. Across the following million years, with the sulfur long gone from the sky, something far slower takes the job over.

Fresh basalt weathers fast. The second consequence rests on that, and it is the one that matters here, because chemical weathering of silicate rock removes carbon dioxide from the atmosphere on geological timescales along a chain that has not altered once since the Archean: rain dissolves carbon dioxide, the resulting weak acid attacks the rock, calcium and magnesium ions wash down to the sea, and carbonate minerals settle onto the seafloor with the carbon shut inside them. How fast the chain runs depends on what rock lies available to it. Basalt, rich in calcium and magnesium silicates and freshly broken, dissolves several times faster than the old granitic crust that makes up most continents, so a million square kilometres of it laid down in the wet tropics raises the planet's capacity to strip carbon dioxide out of the air, at every temperature, for as long as the basalt lasts, which is the argument Grant Cox and colleagues made in 2016 about how the Sturtian began [8].

Here is the step the new paper takes. Should the Franklin basalts have triggered the first freeze by drawing carbon dioxide down, then most of that basalt was still sitting there when the freeze arrived, buried under ice, doing nothing, waiting out the glaciation with every gram of its reactivity intact. Come the eventual thaw, the rock stands exposed again, in the tropics, under rain carrying a hundred times the modern load of acid in it, and it goes straight back to work [1].

From the club table

We spent the first forty minutes not understanding the phrase limit cycle, and the reason was a bad assumption none of us had noticed we were making. We kept hunting for the equilibrium. Where does it settle. What temperature does it end at. Somebody drew the S-curve on the board, marked the two stable branches, and asked which of them the Sturtian had been sitting on.

The answer, which took an embarrassingly long time to arrive, is neither. Should the carbon cycle want to balance at a temperature lying on the unstable middle branch, it cannot get there, because nothing whatever can sit there. So the planet does the only thing left to it and goes round.

We wrote a toy. Two ordinary differential equations. The first is the energy balance above, with a smooth ice-albedo feedback. The second is a single box of exchangeable carbon, gaining from volcanoes at a constant rate and losing to silicate weathering at a rate that depends on temperature, on carbon dioxide, and on how much ice-free land the planet still has.

The script is linked at the top of this page. Three hundred lines or so, printing its own reasoning as it goes. Nothing in it pretends to be the paper's model. The paper's authors run a coupled box model of Neoproterozoic climate, carbon and oxygen, with reservoirs and fluxes ours does not have [1]. Our version exists so that we could watch the mechanism turn over in something small enough to hold in your head.

We had a bug. The routine that finds the critical weatherability does a bisection, and the two branches of the bisection sat the wrong way round, because the test it bisects on is true below the threshold and false above it, which runs backwards from the usual convention. It printed a critical value of 20.0 while the table printed directly above it plainly showed the transition happening between 3.50 and 3.75. Two numbers in the same block of output disagreeing with each other is the cheapest bug you will ever catch, and the only reason we caught it is that the script prints both.

Fixed, it prints 3.59. Every number below rests on that one.

The oscillation survives handling. The period does not. We ran 200 draws with five parameters jittered by up to ten per cent each, and the planet cycled in the great majority of them, with periods spread over a range considerably wider than the differences between any two rows of our headline table. We take that as the correct level of confidence: the loop is a real consequence of the equations, and the numbers hung on it are illustrative.

The arithmetic

Two state variables. Global mean temperature \(T\) in kelvin, and atmospheric carbon dioxide \(p\) in bar.

Energy:

Carbon:

The albedo \(\alpha\) runs from 0.30 ice-free to 0.50 fully glaciated, through a hyperbolic tangent centred on 262 K with a width of 9 K. The ice-free land fraction \(g(T)\) uses the same tangent, so weathering switches off the moment the planet freezes. The weathering form comes from Walker, Hays and Kasting, 1981 [11]. The multiplier \(f_W\) is the weatherability: 1 is modern, and raising it is what a flood basalt province does.

Parameters. Solar constant 1281 W/m², from the Gough parameterisation at 717 Ma [19]. Outgoing radiation slope \(B = 1.30\) W/m²/K, which corresponds to 2.85 K of warming per doubling of carbon dioxide. Outgassing \(V = 7.5\times10^{12}\) mol C per year, balanced at present day by an equal weathering sink. Buffer factor 2.5. Ocean plus atmosphere holds \(1.182\times10^{20}\) mol of carbon dioxide per bar.

Figure 2 plots the equilibria of this system against carbon dioxide at the fixed Sturtian sun. Everything below describes that picture. The folds sit where the slope of absorbed sunlight against temperature equals \(B\), a condition that never involves \(p\) at all, which is why the fold temperatures come out fixed at 252.2 K for the cold-branch fold and 271.8 K for the warm-branch fold. Their carbon dioxide levels follow:

Published estimates of the deglaciation threshold span roughly 0.01 to 0.1 bar [13]. Our 0.030 bar lands inside that range. Call the agreement order-of-magnitude rather than precise, because the logarithmic form of the greenhouse forcing was calibrated near 280 ppmv and we are applying it a hundred times higher.

Turning the basalt up until the thermostat breaks

Now the question the paper is really about. Where does the carbon cycle want to put the planet, and can it get there?

A steady climate needs weathering to equal outgassing at a temperature lying on one of the two stable branches, and our script solves that condition along the ice-free branch across a range of weatherabilities, whereupon the answer changes character partway up the range.

At \(f_W = 0.5\), the balance sits at 3,400 ppmv and +14.1 °C. At \(f_W = 1\), at 1,130 ppmv and +9.2 °C. At 2, at 422 ppmv and +4.1 °C. At 3, at 279 ppmv and +0.7 °C. At 3.5, at 259 ppmv and −0.8 °C, almost exactly on the fold. At 3.75 the ice-free branch offers no solution at all. Bisecting between those gives a critical weatherability of 3.59.

What has happened is easy to state and slightly startling: turning weathering up pushes the balance point to lower carbon dioxide and lower temperature, which is exactly what a thermostat ought to do, but the ice-free branch runs out at 257 ppmv, and a balance point shoved past that would have to live on the unstable middle branch, where nothing lives. Call it a strange kind of failure. The thermostat went on working correctly right up to the moment the ground it stood on ran out from under it.

How plausible is 3.59? Basalt weathers something like five to ten times faster than granite under the same conditions, and the Franklin province laid a very large amount of it down in the wet tropics, so crossing the line asks for nothing exotic whatsoever. The uncomfortable part of the result is exactly that.

So we integrated the two equations forward for 140 million years from a warm start, with an implicit solver, because the system is stiff: the climate relaxes in about thirteen years and the carbon cycle in about a million. The table below is the whole sweep. Figure 3 is the part of it that matters.

Read the period column again, because it is the most interesting column in the table and because it surprised us: going from four times modern weatherability to sixteen times, a factor of four, moves the period from 1.33 to 1.36 million years, which is to say the period gets slightly longer. All that extra weathering does is compress the warm interval, from 0.109 down to 0.023 million years, while the frozen interval refuses to budge.

The reason is arithmetic. To carry itself from the freeze threshold to the thaw threshold, the ocean and atmosphere together must take on \(8.886 \times 10^{18}\) moles of carbon, and at \(7.5\times10^{12}\) moles per year that takes 1.185 million years, a figure no amount of weatherability can shorten, because weathering is switched off for the whole of it. Volcanoes alone set the frozen half of every cycle. The floor holds, and the planet cannot flicker faster than the floor.

One turn of the loop, slowly

Set the weatherability to five, which is a plausible Franklin figure, and watch one turn.

The planet is frozen. Sea ice several hundred metres thick covers the ocean, the global mean temperature sits around −40 °C, and nothing anywhere weathers, because no liquid water reaches the rock surface to weather it with. Volcanoes keep erupting, as volcanoes do. Every year they add another seven and a half trillion moles of carbon to a system that has lost every means of taking it back out. The carbon dioxide climbs, slowly at first and almost imperceptibly against the enormous buffering capacity of the ocean, then faster and faster as the total in the system rises toward the threshold. This phase lasts 1.225 million years.

The planet warms as it goes, from −45.6 °C at the moment of freezing to about −21 °C by the end, because carbon dioxide is a greenhouse gas whether or not the ocean beneath it lies roofed over. At 30,328 ppmv, roughly 3% of the atmosphere by volume, the ice-albedo feedback finally loses, and the frozen branch has no equilibrium left anywhere along it.

Then the fast part. In our model the jump takes a few thousand years, which is what the heat capacity of a hundred-metre ocean mixed layer gives you once the ice-albedo feedback has taken the books over. The ice retreats from the tropics and keeps retreating, because every kilometre of dark ocean exposed absorbs more sunlight and melts more ice. The planet passes through zero and does not stop, arriving at +23.3 °C with 3% carbon dioxide in the air and no ice left anywhere on it.

The rain that falls on the Franklin basalts is carbonic acid at a hundred times modern strength, falling at tropical temperatures, onto rock that has spent more than a million years under ice doing nothing at all. Weathering runs far above the modern global rate. Carbon dioxide falls off a cliff. The entire ice-free interval lasts 0.081 million years: eighty-one thousand years of hothouse, set against 1.2 million years of snowball, which comes to six per cent of the cycle.

At 257 ppmv the ice-free branch ends and the planet falls back. Down 68.8 K, to −45.6 °C, and the recharge starts again. Figure 4 shows three of these turns in a row, which was the first thing that made the shape of the cycle obvious to us: the hothouses are slivers.

What the rocks would have to show

A model that says the planet thawed forty-odd times is making a prediction about sedimentary rocks, and the argument will be won or lost down there in the sediment rather than up here in the equations.

Each thaw in the paper's scenario is a full deglaciation, and every full deglaciation should leave a cap carbonate behind it: a distinctive layer of limestone or dolostone precipitated out of an ocean suddenly loaded with weathering products beneath a hothouse sky. Marinoan cap carbonates are famous and unmistakable. Sturtian ones come patchier and thinner, and no measured section anywhere in the world stacks forty of them, which is the most awkward single fact the flicker hypothesis has to face.

Two things soften that, though neither settles it, and the first is that Sturtian glacial successions are frequently condensed, which is to say that long intervals of time lie compressed into very little rock, and in places the successions are missing altogether because the ice removed whatever came before them. Eighty-one thousand years of hothouse is a thin thing to preserve when the following million years of glacier stand ready to grind it away.

The second softening is that the Sturtian record already reads less uniform than the textbook version suggests, since carbonates that precipitated during glaciation have been described from Sturtian sections, and those require open water and active chemistry in places the hard-snowball picture would have kept sealed [16]. From the Marinoan, meanwhile, Benn and colleagues documented ice sheets advancing and retreating repeatedly through a snowball on orbital timescales, which is evidence that these glaciations carried internal structure even where they never fully deglaciated [17].

So the honest position is this. The repeated-thaw model predicts something the rock record does not obviously show, and the rock record is in no state to rule it out either, which makes for an uncomfortable place for a hypothesis to live and also for exactly the place where the next decade of field geology gets interesting.

The best case against it

Suppose you are the referee who wants to reject this. Your job is to find the world in which the model is competent, the mechanism is real, and the Sturtian still was not a flicker, because mere scepticism is worthless here. Here is the strongest version we can build.

Objection one, and the big one: the cycle may be an artefact of leaving out the middle. Both the paper's model and ours treat the planet as a single point carrying a single temperature, which leaves it exactly two options, fully frozen or fully ice-free. Real planets have latitudes. Add them and a third state appears: a waterbelt, with ice reaching down to the subtropics and a strip of open ocean left along the equator, held steady by the way tropical ocean heat transport and bare sea ice behave [4, 15]. That state stays stable across a wide range of carbon dioxide, and it never shuts weathering off, because open ocean survives at the equator and ice-free land may well survive with it. A planet that can reach a waterbelt has no need to cycle. It parks. Our model cannot represent that state at all, by construction, and the assumption is the first one we would attack were we sitting on the other side of the table.

Objection two: the cycle period fights the geochronology. Uranium-lead and rhenium-osmium dating now brackets the Sturtian at both ends with uncertainties of well under a million years [5, 6], and our period is 1.31 million years. Forty-three complete deglaciations, each one dumping a hothouse ocean's worth of weathering products into the sea, amount to a great deal of chemical and sedimentary signal to hide inside a record that dating has already resolved this finely. Something should have turned up by now.

Objection three: the trigger is load-bearing and the trigger is uncertain. Everything depends on the Franklin basalts staying weatherable for 56 million years, and flood basalt provinces get buried, get eroded, drift out of the tropics and armour themselves in clay. Should the weatherability fall back below the critical value at any point (our figure is 3.59 times modern, and the paper's threshold will differ) the cycling stops and the planet parks on whichever branch it happens to be riding. Making the oscillation last exactly as long as the glaciation requires the basalt to stay reactive for exactly as long as the glaciation, and nobody has shown that it did.

Objection four, which is against our own work rather than the paper's. Our deglaciation threshold of 0.030 bar comes from extrapolating a logarithmic greenhouse formula, one calibrated near 280 ppmv, all the way out to the 30,000 ppmv the model demands. At those pressures the absorption bands saturate, the water vapour continuum starts to matter, and collision-induced absorption by carbon dioxide itself begins to contribute, so that our number, though it sits inside the published range [13], sits there by luck as much as by physics.

Now the rebuttal, because a steelman left standing is just a hedge. Objection one is genuine, and it is the reason the paper's claim stands as a hypothesis rather than as a result, though the waterbelt states in the literature also tend to require particular assumptions about sea-ice dynamics and cloud behaviour that are themselves contested [14]. Objection two is the strongest empirical challenge of the four, and it will be answered in the end by drilling and by dating rather than by argument. Objection three names a real constraint on the scenario, and a testable one. Testing it means reading the weathering history of the Franklin basalts out of the rocks of Arctic Canada. Objection four is ours to own, which is the reason every number in this article is quoted as an illustration of a mechanism rather than as a measurement.

Oxygen, and why anybody outside paleoclimate should care

There were animals on the other side of this. Not many of them and not complicated ones, but the molecular clocks and the first unambiguous animal fossils both sit close enough to the Cryogenian that whatever happened during it happened to somebody's ancestors. So did the diversification of eukaryotic algae. The interval was survived.

Surviving it required oxygen, and oxygen is the part of the problem a hard snowball handles worst, since atmospheric oxygen is maintained by the burial of organic carbon in marine sediments, which depends on photosynthesis in the surface ocean, which depends in its turn on sunlight reaching open water. Roof the ocean over for 56 million years and you have removed the source while leaving every sink running: oxidative weathering of sulfides and organic matter carries on across the land surface, and volcanic reduced gases keep arriving from below. The residence time of oxygen in the Proterozoic atmosphere, at levels well below modern, was probably short compared with tens of millions of years [18]. Run the sums for a continuous 56-million-year snowball and the atmosphere should have been scrubbed clean of oxygen, which leaves the survival of anything aerobic very hard indeed to explain.

A flickering planet changes that completely. In our version the ocean lies open for 6.2% of the time, and that 6.2% arrives in eighty-thousand-year instalments spread evenly through the interval, never more than about 1.2 million years apart. Each hothouse is a burst of extraordinary productivity: a warm, ice-free, nutrient-saturated ocean receiving the weathering products of a whole continent that has spent a million years under a glacier. Organic carbon burial goes up sharply, oxygen is resupplied, and then the lights go out again for a while, and the paper's own model, tracking oxygen through the whole sequence, finds it staying within survivable bounds through the cycling, which is the part of the result its authors describe as explaining how aerobic life persisted [1].

That lesson runs wider than the Cryogenian. A system that sits in one extreme state for 56 million years and a system that oscillates between two extremes for 56 million years share the same average, and they are completely different places to try to be alive.

What would settle this

Three kinds of evidence would move this, and they are of very different quality.

The weakest is more modelling, since running the same idea in a general circulation model with real latitudes would tell you only whether the loop survives contact with a waterbelt. Worth doing, and the first thing the field will do, and still not decisive, because the answer will hang on exactly those sea-ice and cloud parameterisations that are already the substance of the disagreement.

The strongest is geochronology inside the glacial interval. The Sturtian is currently dated at its ends. Ash beds or datable shales from within the glacial package, recovered from enough sections to correlate between them, would say directly whether the ice ran continuously or not, and should someone find a Sturtian section with three cap carbonates stacked in it, separated by glacial diamictite, the argument is over in one afternoon.

The third is the outgassing rate, because our model says the frozen half of every cycle is nothing but volcanic recharge time, and Adriana Dutkiewicz and colleagues, reconstructing mid-ocean-ridge outgassing across the Neoproterozoic from plate models, concluded that it ran exceptionally low at 717 Ma [10]. We ran that. At 40% of the modern rate our period stretches from 1.31 to 3.31 million years and the number of cycles inside the Sturtian falls from 43 to 17. At 60% the period comes out at 2.16 million years and 26 cycles. The prediction is sharp and it runs the right way, since the same evidence that made the Sturtian long in the old story makes each flicker long in the new one.

None of which is what we expected to be writing when we picked this paper up. The interesting thing about Snowball Earth used to be the trap. The interesting thing now might be the pendulum, and the whole difference between the two comes down to one rock formation that happened to be lying in the tropics at the wrong moment in deep time.

References