ESS 201, 2024
Problem Set 3
Problem 1 (3 points)
In class, we derived the following relationship:
Htoday *Ro, today= H(t)*Ro (t) + ΔSL(t) *Rice_sheet
where R =18O/16O is the isotope mixing ratio, for either the ocean (subscript “o”) or ice sheet (subscript. “ice_sheet”). And H = depth of the ocean, ΔSL is sea-level change, as a function of time in the past, t.
The definition of δ18O is given by: δ18O = ((R/RVSMOW) – 1)*1000. Rearrange this definition to be explicit for R (i.e., in the form of R = ….), and do a bit of algebra to show that we can rewrite the relationship as:
Htoday *δ18Oo, today= H(t)* δ18Oo (t) + ΔSL(t) *δ18Oice_sheet
In other words, you are showing that you can replace each of the values, “R” in the first equation with the equivalent δ18O. As you are doing the algebra, it may help you to use the relation Htoday = H(t) + ΔSL(t).
Problem 2 (4 points)
Download the data from foram_data.txt (posted on the assignment page alongside this) to create two graphs of sea level and temperature change through time.
The first column of the data file is age in thousands of years. The second is the change in benthic foram δ18O, relative to today's value. The third is the planktonic δ18O, relative to today’s value. Note that δ18O in both cases is given in "per mille" (‰).
i) Use the equation from problem 1, together with Htoday = H(t) + ΔSL(t) , and that
sea level is equal to ΔSL(t) to solve for sea level. Plot the graph of ΔSL(t) from the data given. Note that the sign of ΔSL(t) is a bit ambiguous. As we’ve defined it, it is the sea-level equivalent of the water locked up in ice sheets (i.e., more ice during an ice age). If you multiply by -1, you get the amount of water taken out from the
ocean (i.e., lower sea level during ice age). It is a matter of taste how you choose to plot it
ii) And use ΔT = -4.2((δ18Oplanktonic-δ18Obenthic))) where ΔT is in K. to calculate the
change in surface temperature. On a separate axis or graph, plot the graph of ΔT
(t) from the data given.
**Note. Assume δ18Oice_sheet = –30‰ (per mille), and that the depth of the ocean today is 4000 m.*** Note that δ18Oo, today = 0, because modern ocean water is defined as the reference.
Use only the benthic data to calculate sea level. Choose good axes in your graph that fit the range of the data, and label the axes accurately, with the right units.
You will be able to import your data into Microsoft excel, or any other such program of your choice. Do not draw the results by hand! Pick good axes. See class slides for expected answers. Make sure that they are reasonable.
Problem 3 (2 points) Explain in words how and why the δ18O of planktonic and benthic foraminfera record changes in water temperature and sea level from the recent Pleistocene ice ages.
Problem 4 (1 point). From your graph, estimate how much the temperature changes from times when there is a lot of ice on land (glacial periods) to times like today when there is not much ice on land (interglacial periods).