EPSc 484/584 Problem set 4. Due Tues Mar 30, 5 pm
Stable Isotopes
Some basic calculations
Temperature in kelvins:
Kelvins= °C + 273
Conversion between SMOW and PDB
18OSMOW = 1.03091*(18OPDB) + 30.91
Calcite-water fractionation as a function of temperature (calcite and water on same scale)
1000ln[(1000 + 18Oc)/(1000 + 18Ow)]=18.03(103T-1) - 32.42
Equilibrium fractionation
  1000
 vl  l
 v  1000
Temperature dependence of equilibrium fractionation (water liquid/vapor):
1.534  10 6 3.206  10 3
10 3 ln  

 2.644
T2
T
Global meteoric water line:
D = 8.13*18O + 10.8
♦(1) Calculate 18O of water vapor in equilibrium with liquid water at 10°C assuming that 18Ol
= -10.0 ‰ SMOW and lv = 1.0105
♦(1) Calculate 18O of liquid water that is condensing from vapor at 10°C having 18O = -25%
assuming that lv = 1.0105
♦(1) Calculate the 18O value of meteoric water whose D = -70‰
♦(1) Use the calculator at
http://wateriso.eas.purdue.edu/waterisotopes/pages/data_access/oipc.html to determine what the
modern isotopic composition of rainfall in Kharga Oasis, Western Desert, Egypt is (25.5 deg. N,
30.5 deg E, 100 m) (note which standard is being used)
♦(2) The average 18O of calcite in spring deposits (formed from groundwater during humid
climatic phases) in Kharga Oasis is -10‰ (PDB). If the groundwater had the same isotopic
composition as modern rainfall, what would be the temperature at which the calcite was formed?
♦(1) If the carbonate actually formed at 20°C, what would the 18O of the water from which it
formed have been?
♦(2) What might explain the difference between the water from which the carbonate formed and
modern rainfall?
Part 2. Speleothems.
You have been given an excel file with stable isotope data from two Holocene speleothems in
Minnesota.
(2 pts) Create two graphs; both with age on the x axis, one which plots carbon isotope data for
both speleothems on the y axis, and one which plots oxygen isotope data for both on the Y axis.
(4 pts). Discuss, in general, the discrepancies within the isotopic data from two speleothems in
the same cave. Specifically, please address: over what time period are the speleothem records
most different? Are the differences between the speleothems the same in timing and magnitude
for both carbon and oxygen? What might explain the differences between two speleothems in the
same cave, and what do you think is the most likely explanation for the differences you observe
here, and why?
(2 pts) Over time (use data for both speleothems), do carbon and oxygen isotope ratios covary?
Give the r2 for the relationship.
(3 pts) Suggest a reason for this covariance (or lack thereof). Note: controls on isotopic variation
across time (like the dataset you have here) are not likely to be the same as those which would be
important at any one given time (isotopic variation within one speleothem growth band).
(2 pts) The carbon which ends up in speleothem carbonate comes principally from dissolution of
bedrock and from soil CO2.
Given the following information:
Bedrock contributes 1/3 of the carbon in your speleothem, the rest is from the soil.
13C of bicarbonate (HCO3-) dissolved from limestone bedrock= -2‰ (PDB)
C3 organic matter= -27‰
C4 organic matter= -13‰
Fractionation between soil organic matter and soil respired CO2= 4.4‰ (soil CO2 heavier)
Fractionation between soil CO2 and speleothem carbonate (note: this is temperature dependent,
but we’re not going to worry about that; this value is for ~20 C) = speleothem carbon heavier
than CO2 by 10‰
Fractionation between dissolved bedrock carbonate (HCO3--) and speleothem carbonate=
speleothem= 1‰ heavier
Write an equation that represents speleothem carbonate 13C as a function of the % C3 plants
growing in the soil of the cave’s recharge area.
(2pts) What important things does the above equation ignore?
(1pt) For speleothem SVC-1, use the equation you derived above to calculate % C3 vegetation
using the given speleothem 13C data, and plot on a graph vs. time (on x axis).
(2 pts) There should be an obvious problem with your numbers- what is it, and what do you think
is the most likely cause? (This answer may be similar to your answer for the last question. Here,
please discuss what specifically may have caused the particular problem you’re having; e.g., your
numbers may be too small because you underestimated x, y, or z, not just, “my numbers are crazy
because there are a lot of unknowns”)
(3 pts). Discuss your results with reference to this figure:
http://esp.cr.usgs.gov/info/lite/midcontinent/fig1.gif
Your cave is in southern Minnesota; what can you say about the migration of vegetation
communities and/or potential complications with using carbon isotopes in this location during the
Holocene?