# ESE 102 Problem Set 1 Due Oct 15, 2012 at 5pm 1) Seawater density and water masses For this problem you will need to download the matlab scripts that calculate various physical properties of seawater. You can find them here:

ESE 102

Problem Set 1

Due Oct 15, 2012

at 5pm

1) Seawater density and water masses

For this problem you will need to download the matlab scripts that calculate various
physical properties of seawater. You can find them here:

http://www.cmar.csiro.au/datacentre/ext_docs/seawater.htm

You will notice that there is a large disclaimer at this site that says these scripts are out of
date and that the salinity s
cale of seawater has now changed. This is all true, and you are
welcome to read about it all in depth, but for this problem I would like you to use the old
seawater equation of state (EOS
-
80). I have not vetted the new scripts for myself yet, so
ing you to use the old ones. For bonus points you can do this problem with both
equations of state and compare the differences. You will also need the temperature and
salinity profile from the class web page titled, ‘
CTDProfile_45S_145E
.xls’.

First, cal
culate the potential temperature profile. Next compute the sigma
-
theta and
sigma
-
2 profiles. What, if any, are the differences? What is the mixed layer depth? Are
there any water masses in this profile (it was taken just south of Tasmania in January
20
08.

2
) The strontium cycle: a one
-
box model

(It might help to read: Richter and Turekian, EPSL 119:121(1993))

Sr is essentially conservative in seawater, with a concentration of 90 μmol / kg. The
major Sr input is about 3.3
× 10
10

mol

/ year

from river
s, balanced by sedimentation in
carbonates (hydrothermal cycling is of order 1
× 10
10

mol

/ year and ignored here).
Geochemists are interested in it mostly because
87
Sr is produced
by

the slow decay of
87
Rb, which concentrates in continental rocks, so that

changes in the seawater
87
Sr/
8
6
Sr
ratio over long periods reflect the changing balance between river (continental) and
hydrothermal (basalt) flow. Here, we will calculate the response time of the ocean
87
Sr/
8
6
Sr ratio to a change in the rate of river flow
.

(a) What is the residence time of Sr in the ocean with respect to river input? The
mass M of ocean water is 1.42
× 10
24

kg.

-
state model ocean with a river input F
0

balanced by
sedimentation. Suppose that the river Sr input oscil
lates over some timescale, say because
of climate, sea
-
level, or tectonic oscillations. Let the river input be a sine wave

F(t) = F
0

+ A∙sin(2πt/τ)

(1)

where A is the oscillation amplitude and τ its timescale. Assuming that the removal of Sr
from the o
cean is first
-
order in the Sr concentration, draw the relative fluctuation in ocean
Sr concentration for a given A for τ 5 times less then, about equal to, and 5 times greater
than the residence time.

(c) Plot the amplitude of ocean Sr concentrations C(t)

and the phase shift between
the maximum in C(t) and the maximum in F(t) as a function of the oscillation timescale τ.

(d) River Sr has a mean
87
Sr/
8
6
Sr ratio of 0.711, compared with the modern ocean
ratio of 0.709 (the difference is thought to be due to
hydrothermal exchange with basalt).
Assuming that the river Sr isotopic composition remains the same and that sedimentation
does not fractionate, what is the relative change A/F
0

in the river Sr flux over glacial
-
interglacial time scales (τ =
10
5

year) req
uired for the ocean
87
Sr/
8
6
Sr ratio to oscillate by
3 ×
10

5

(close to the detection limit) over this timescale? Fluctuations of this magnitude
have been reported, though their interpretation remains controversial.

For (b
-
d), you will want to use a one
-
bo
x ocean model, as sketched below.

river flux:
F

sedimen
t
ation:
k
sed
C

ocean
:
M,
C