ESS 201, 2022 Problem Set 3

In class, we derived the following relationship:

Htoday *Ro, today= H(t)*Ro (t) + DSL(t) *Rice_sheet

where R = 18 O/16 O is the isotope mixing ratio, for either the ocean (subscript “o”) or ice sheet (subscript “ice_sheet”).  And H = depth of the ocean, DSL is sea-level change, as a  function of time in the past, t.

Use the definition of (δ18 O = (R/RVSMOW– 1)*1000) and do a bit of algebra to show that we can rewrite the relationship as:

Htoday *d18Oo, today= H(t)* d18Oo (t) + DSL(t) *d18Oice_sheet

In other words, you are showing that you can replace each of the values, “R” in the first equation with the equivalent δ18 O.

Problem 2 (4 points)

Download the data from foram_data.txt (posted on the assignment page alongside this) to create 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 δ18 O, relative to today's value.  The third is the planktonic δ18 O, relative to today’s value.  Note that δ18 O in both cases is given in "per mille" (‰).

i)          Use the equation from problem 1, together with Hnow =H(t)+DSL(t) , and that sea level is equal to DSL(t) to solve for sealevel.

ii)         And use ΔT = -4.2(Δ(δ 18 Oplanktonic - δ 18 Obenthic))) where DT is in K. to calculate the change in surface temperature.

**Note. Assume δ18 Oice_sheet  = – 30‰ (per mille), and that the depth of the ocean today is 4000 m.***

Use only the benthic data to calculate sea level. Choose good axes in your graph thatfit 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.