Dear all,
Rayleigh condensation model is described as δ=(1+δ_0 )*∂*f^(∂-1)-1
where δ stands for the isotopic composition of the liquid phase at the given stage, δ_0 is the initial isotopic composition of the vapour, f is the fraction of the initial moisture content remaining in the given air mass and ∂ is the isotopic fractionation factor.
Traditionally, f is assumed as a constant. In fact, f exponentially depends on temperature. Would you please give me an equation between f and temperature or some relative references?
Thanks a lot!!!
Typically the Rayleigh condensation model is (oxygen isotopes as an example):
δ18O = (δ18O0 + 1000) * f (∂-1) - 1000 (‰)
where δ18O and δ18O0 are isotopic compositions of the liquid phase at any time and the beginning, respectively; f is the fraction of moisture content remaining in the give air mass; ∂ is the isotopic fractionation factor during condensation of water. How can you get an equation different from this?
The f depends on temperature by the Clausius-Clapeyron Equation, calculating saturation vapor pressure at different temperatures. The saturation vapor pressure of water can be converted to moisture content in the air.
Yes, I agree with Xinming Chen, the Rayleigh distillation equation is the one he wrote.
f is not really traditionally kept constant. Actually, Rayleigh type models usually evaluate the variation of isotopic composition along the air masses trajectory while f decreases. The link between f and temperature is obtained for the saturated vapour pressure: everytime the partial pressure of water vapour of the air masses is above the saturated vapour pressure at the temperature T, condensation occurs, and thus, you can estimate f as the ratio between the saturated vapour pressure at the temperature T and the initial vapour pressure of the air masses.
I recommend you to read the book 'Principles of Stable Isotope Distribution' from Robert Criss. The description in this book is very thorough.
Many thanks for Xinming Chen and Mathieu Casado. Let's number my equation as Eq.1, and Xinming's equation as Eq.2.
Eq.2 gives the relation between the isotopic compositions of the liquid phase at any time and the beginning. Assuming temperature (T) is constant, substituting (δ18O0 + 1000) = ∂*(δ18Ov + 1000) (Eq.3) into Eq.2 will get Eq.1, where δ18Ov is the initial isotopic composition of the vapour, and ∂ is the isotopic fractionation factor depending on T. Eq.3 describes the first small amount of condensation from the vapor. Assuming δ18Ov is constant (isolated air mass in Rayleigh model), then δ18O0 also depends on T. Am I right? I am really confused.
Looking forward to your reply.
How do you get the Eq. 3? That equation is not right.
Isotope fractionation factor is: ∂liquid-vapor= Rliquid/Rvapor.
In Eq.3, (δ18O0 + 1000) = ∂*(δ18Ov + 1000) , δ18O0 should be oxygen isotopic composition of the liquid phase at any stage, δ18Oliquid. You can read the book 'Principles of Stable Isotope Distribution' from Robert Criss to figure out the derivation process.
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