Isotope Rainout: Rayleigh Distillation of δ¹⁸O

Air-Mass Journey

Sea-surface temperature 20 °C

Rainout rate (continental effect) 0.60 %/km

Mountain height (orographic effect) 1400 m

Air-mass speed 1.0×

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Vapor remaining f

100%

Distance inland

0 km

δ¹⁸O vapor

0.0‰

δ¹⁸O precip (now)

0.0‰

Local temperature

20.0 °C

α (equilibrium)

1.0000

How it works

A moist air parcel forms over the ocean and travels inland, losing water to precipitation as it goes. Each condensation event preferentially removes the heavier isotope (H₂¹⁸O) from the vapor, so the remaining vapor — and every raindrop after it — becomes progressively more depleted. This is Rayleigh distillation:

R_v / R_v0 = f^(α−1)
δ_v(‰) = [(1+δ_v0/1000)·f^(α−1) − 1]·1000
δ_p(‰) = [(1+δ_v/1000)·α − 1]·1000   (precip in equilibrium with local vapor)

where f is the fraction of the original vapor still airborne and α is the liquid–vapor equilibrium fractionation factor, which itself depends on local temperature (Majoube, 1971):

1000·ln(α) = 1.137×10⁶/T² − 0.4156×10³/T − 2.0667   (T in kelvin)

Because α varies with T along the path, the model integrates the distillation step by step rather than using a single closed-form α — exactly how real isotope-hydrology "rainout" models work.

Sea-surface temperature — sets the starting vapor isotope ratio and how strongly α starts out.
Rainout rate — how fast the air mass loses moisture per kilometre inland (the "continental effect": rain gets isotopically lighter the farther inland it falls).
Mountain height — orographic lift over the range steepens cooling and rainout locally (the "altitude effect").
Vapor cloud colour shifts from light blue (isotopically heavy, near ocean) to deep violet (strongly depleted); falling raindrops are tinted the same way — this is literally what a mass spectrometer reads off a rain sample.

Real-world relevance: this is the physical basis for dating groundwater, reconstructing paleoclimate from ice cores, and tracing where a river's water actually recharged.

Vapor (isotopically heavy) Vapor (depleted) Falling precipitation

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