Interesting calculation exercise!
A good starting point for your problem is the formulas given in the classical paper by Roberto Gonfiantini in 1986. In the theory developed there you will see that isotopic evaporation during enrichment depends on the temperature and humidity of evaporation and on the water vapour in the air into which the evaporation takes place.
From the pictures in the article (fig 3-1) you see that the smallest slope for evaporation into dry air has a value of around 3.25. At higher humidity the slope would be higher, until it reaches the 8 of the GMWL at 100% humidity.
Your numbers (-10 for 18O and -100 for 2H) imply that the water has undergone considerable evaporation from the GMWL, because this point is ca. 3.5 per mille enriched in 18O (shifted to the right of the GMWL) already. However, taking your point of -10/-100 as starting point, you can reach a value around -2 in 18O and -60 in 2H with a humidity of around 65% at an evaporation of 18% of the lake volume (assuming here and in the other example below that the water vapour in the wind blowing over your lake has the (-2 in 18O and -60 in 2H) and evaporation happens at a temperature of 20 degrees C). The value of +2 in 18O and -80 in 2H, however, is out of reach, even with evaporation into zero humidity, for this starting point.
Both your hypothetical values can be created from the GMWL (defined as having a slope of 8 and an intercept of 10 as per (Craig, 1961)) with a water starting at -21.25 in 18O and -160 in 2H if you assume either zero humidity (at around 38% evaporation of the original volume) or if you assume a humidity of 65% (at around 29% evaporation) using the temperature and water vapour isotope values above. This corresponds to quite cold areas of the world, so the temperature is probably not realistic…
My hint: try to implement the formulas in Roberto’s paper in an Excel sheet and play around with some values. Or write a program (which is what I have done – it’s in LabData). You can create many points right of the (local or global) meteoric water line with evaporation - but not all.
Craig, H. (1961) Isotopic variations in meteoric waters. Science 133, 1702-1703.
Gonfiantini, R. (1986) Environmental Isotopes in Lake Studies, in: Fritz, P., Fontes, J.-C. (Eds.), Handbook of Environmental Isotope Geochemistry. Vol. 2, The Terrestrial Environment B., pp. 113-168.
Dr. Axel Suckow
Isotope Hydrology, Geochronology
Land and Water
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From: Stable Isotope Geochemistry [mailto:[log in to unmask]] On Behalf Of Leela S
Sent: Friday, 27 January 2017 11:03 AM
To: [log in to unmask]
Subject: [ISOGEOCHEM] Evaporative enrichment
I have been working on oxygen-hydrogen due to evaporation and I am stuck. If we have a sample that falls on the Global Meteoric Water Line originally but due evaporation undergoes enrichment. My understanding is evaporation will affect both oxygen and hydrogen. Let us say there is a water sample originally with a del18 -10 per mil and del D -100 per mil. Because of evaporation, natural or due to poor storage, can it assume values such as del 18 +2 per mil, del D -80 per mil or del18 -2 per mil and del D -60 per mil? In other words the oxygen may show high enrichment not accompanied by enrichment in hydrogen. Any advise will help Leela.