Rainfall isotope distillation

Why does rain falling far inland carry lighter oxygen than the rain that fell near the coast?

Water is water. A molecule built with oxygen-18 instead of the common oxygen-16 is chemically identical and about ten per cent heavier — a difference that should matter to nothing a raindrop does. Yet rain collected a thousand kilometres inland is reliably poorer in oxygen-18 than coastal rain that day, and polar snow poorer still.

So what could a two-neutron difference possibly select on? And why should the selection get stronger the further the air travels?

Begin with the only place mass can bite: escaping a liquid. A heavier molecule is held slightly more tightly in liquid water, so its vapour pressure is slightly lower. At equilibrium near 20 degrees, condensate forms about 9.8 per mil richer in oxygen-18 than the vapour it came from (recalled equilibrium fractionation factor, close to 1.0098). Note how small that is: one per cent.

That number is the whole problem, not the whole answer. A single condensation shifts things by about ten per mil, but inland rain can be twenty per mil below coastal rain, and polar snow far below that. One step cannot do it. So what multiplies a one per cent effect into a large one?

Removal. If the rain simply exchanged with its vapour and stayed put, the system would sit at equilibrium and go nowhere. But rain falls out and leaves. Each event takes with it a sample slightly enriched in the heavy isotope, so the vapour left behind is slightly depleted, and the next event starts from that depleted reservoir. The bias compounds because the population it acts on is being progressively removed.

That is a Rayleigh distillation, and it can be written down. If condensate is removed as fast as it forms, the ratio in the remaining vapour goes as the fraction of vapour remaining, raised to the power (alpha minus 1). Put the numbers in. With alpha minus 1 equal to 0.0098: when half the original moisture has rained out, the exponent gives exp(0.0098 x ln 0.5), which is 0.9932 — the vapour is 6.8 per mil lighter than it started. At eighty per cent rained out, exp(0.0098 x ln 0.2) gives 15.6 per mil lighter. At ninety per cent, 22 per mil.

That is the answer to the puzzle, and notice that nothing exotic was added. The same feeble one per cent preference, applied to a shrinking reservoir, produces tens of per mil — and it explains all four classic patterns at once. Rain gets lighter inland because more has rained out; lighter with altitude, for the same reason over a shorter distance; lighter toward the poles, doubly so because the fractionation factor itself grows as temperature falls; and lighter in heavy tropical downpours, because more of the column is being wrung out.

A second, separate fractionation carries different information. Evaporation into unsaturated air is not an equilibrium process: the heavy molecule also diffuses more slowly through the layer just above the surface, adding a kinetic bias whose size depends on the humidity at the source. Because oxygen and hydrogen respond to that step in different proportions, the combination called deuterium excess survives the later rainout largely intact and reports on where the moisture left the sea.

How would we catch this being wrong? Sample vapour and rain together along an inland transect and compute how much of the original moisture has been removed. Rayleigh makes a quantitative prediction, not a directional one, so the falsifying result is available: rain further inland that is heavier than coastal rain from the same air mass, or a depletion that does not track the rainout fraction. Neither is what the sampling networks show.

But one deviation is real and instructive. Over a large forest such as the Amazon, the inland gradient is much weaker than pure Rayleigh predicts, because roots take up soil water without fractionating and transpiration returns it to the air with essentially the same isotopic ratio. Recycled moisture resets the count. That is not a failure of the mechanism; it is the mechanism being used as a measuring instrument, since the size of the shortfall estimates how much of the interior's rain is recycled rather than imported.

The word "fractionation" invites a misreading: that something happens to the molecules. Nothing does. No atom changes, no bond is transmuted; a population is sorted, and the sorting is visible only in what is left behind. It is the same logical shape as selection anywhere else — a small, repeated, one-way preference acting on a population that is being drawn down.

This is also the complement to what an ice core does with its trapped bubbles. There the gas is the archive and the ice is merely the container; here the water molecules of the ice itself are the archive, and they record the temperature of the air that condensed them, through the two temperature dependencies above. That is the isotope palaeothermometer — and its weak joint should be stated plainly. The calibration usually comes from today's spatial gradient of isotopes against temperature, and there is no guarantee that the slope through space equals the slope through time at one place, since the moisture source and the storm trajectory can change too. Independent checks exist — borehole temperature profiles, and thermal fractionation of gases in the firn at abrupt transitions — and in Greenland they indicated the spatial calibration had understated glacial-to-modern temperature change (recalled, and I give it as a direction rather than a number).

One more separation is needed before any single measurement means much. Individual storms scatter widely, so a year of samples describes storm types rather than climate; the international precipitation-isotope network has run since about 1961 (recalled), and it takes decades of it to separate a trend from that variability.

• Why the tropical amount effect complicates reading speleothem isotopes as a temperature record.

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