The Salty Oceans

Sodium accumulates in the oceans much faster than it leaves. Where, then, is the salt of three billion years?

The world’s oceans are salty. Specifically, by mass, they are roughly 3.5% dissolved salts, of which the dominant cation is sodium and the dominant anion is chloride. There is, in total, on the order of \(1.5 \times 10^{19}\) kg of sodium dissolved in the ocean.¹

That sodium does not stay there forever. Rivers carry sodium into the oceans from weathering of continental rock — about \(4.5 \times 10^{11}\) kg per year, give or take a factor of two. Hydrothermal vents at mid-ocean ridges contribute more. Sodium leaves the ocean by various mechanisms — sea-spray that ends up on land, deposition in salt formations on continental shelves, alteration of basalt at ridge crests, ion exchange in clays — but each of these output mechanisms is small. The current input-minus-output ratio is positive: the oceans are getting saltier over time.

This is a rate-based clock, and it has a problem.

The arithmetic

If we know the current sodium mass in the oceans, and we know the net rate at which sodium is accumulating, we can divide one by the other to get an upper bound on how long the oceans have been collecting salt.

Steven Austin and Russell Humphreys did the careful version of this calculation in 1990.² They surveyed the geochemical literature, identified every input and output mechanism the literature describes, and computed:

• Total sodium input rate (rivers + hydrothermal + atmospheric + smaller sources): about \(4.6 \times 10^{11}\) kg per year.
• Total sodium output rate (sea-spray + salt deposition + basalt alteration + clay ion exchange + smaller sinks): about \(0.6 \times 10^{11}\) kg per year.

Net accumulation: \(4.0 \times 10^{11}\) kg per year.

Total current sodium in the oceans: \(1.5 \times 10^{19}\) kg.

Maximum age (if oceans started with zero sodium):

About thirty-eight million years.

Austin and Humphreys then made their calculation as friendly as possible to the deep-time position: they reduced the input estimates to the lower end of the geochemical literature’s range, and increased the output estimates to the upper end, accepting figures that no honest mass-balance accounting would normally use. With this maximally-generous-to-deep-time set of figures, they get an upper bound of about 62 million years.

The oceans are supposed to be over three billion years old. They are between fifty and eighty times saltier than they should be on a 3 Ga timescale.

What’s missing?

This is sometimes called the missing-salt problem. On the deep- time chronology, the oceans should contain roughly a hundred times more sodium than they actually do. Where did it go?

The standard responses, in order of how often they appear in the literature:

Output rates were higher in the past. Particularly, salt deposition into evaporite basins (large enclosed bodies of water that dried out and left salt formations) is invoked as the missing sink. The Mediterranean’s Messinian salinity crisis, for example, deposited a huge volume of salt around 6 Ma when the Mediterranean dried out.

The problem with this rescue: the cumulative salt deposited in all known evaporites on earth is far less than what would be needed to dispose of three billion years of sodium accumulation. Austin and Humphreys account for evaporite removal already, with a generous estimate.

Input rates were lower in the past. The argument is that weathering rates were slower before continents were exposed, or before plate tectonics established its modern pattern.

The problem here is that lower weathering rates also slow the deposition of evaporites, since evaporites form from the same dissolved load. You cannot lower input without lowering output by roughly the same factor; the ratio that drives the age calculation is roughly preserved.

The oceans started with sodium already in them. Maybe seawater was salty from the beginning, as part of the planet’s primordial chemistry.

This is a coherent move, but it’s a philosophical one rather than an empirical one. It says: we cannot test the initial-condition assumption, so we are free to choose whatever assumption preserves the age we want. It is not an answer; it is an acknowledgment that the rate-based clock cannot constrain the chronology if you allow yourself to set the initial state.

What it does not say

The salt-flux argument does not, by itself, prove the earth is six thousand years old. The upper bound it gives — sixty million years or so, in the most generous case — is still vastly longer than the biblical chronology. The argument is an upper bound, not a fixed estimate.

What it does say is this: if you believe the earth is older than sixty million years, you have to explain the missing salt. The explanations on offer either invoke unmeasurable initial conditions or rely on rate variations that work in one direction but not the other. Neither is satisfying.

The young-earth reader notes that the present input-output ratio, applied honestly, gives a number consistent with a recent ocean — one that has not had time to accumulate the salt that deep time would predict.

A note on style

This kind of argument is sometimes called evidence from absence. The absence of salt is the evidence. Absence arguments are easy to do badly — I don’t see X, therefore X doesn’t exist — and easy to wave away.

But this isn’t I don’t see salt. It’s I don’t see the specific quantity of salt that a specific theory predicts. And the prediction is precise enough — to within a factor of two — that the absence of the predicted quantity is a real datum, not a hand-wave.

It is the same kind of argument that drove the discovery of the neutrino: the missing energy in beta decay was a calculable discrepancy, and the only way to balance the books was to postulate a new particle. The salt-flux problem is asking for a similar honesty about the books.

Next: soft tissue in dinosaur bones, where the problem moves from chemistry to biology.