AOSS/GeoSci 321: Earth System Dynamics
2
b) (4 pts) Using the full nonlinear equation of state of seawater, see
http://www.phys.ocean.dal.ca/~kelley/seawater/density.html
at the surface, what is the density of seawater at:
i)
T
= 0
◦
C,
S
= 36 psu
ii)
T
= 0
◦
C,
S
= 33 psu
iii)
T
= 30
◦
C,
S
= 36 psu
iv)
T
= 30
◦
C,
S
= 33 psu
c) (6 pts) Using the linear approximation of the equation of state of sea
water, and assuming
σ
o
=
σ
(30
◦
C
,
33psu) (use
σ
o
in the answer to aiv, and
assume
α
T
= 2
×
10

4
1
/
◦
C,
β
S
= 7
.
6
×
10

4
1
/
psu), calculate
σ
and
ρ
at:
i)
T
= 0
◦
C,
S
= 36 psu
ii)
T
= 0
◦
C,
S
= 33 psu
iii)
T
= 30
◦
C,
S
= 36 psu
d) (8 pts) Using
α
T
and
β
S
corresponding to
σ
o
=
σ
(15
◦
C
,
38 psu) at the
surface (see Table 9.4 in Marshall & Plumb), use the linear approximation
of the seawater equation of state to calculate:
i)
T
= 0
◦
C,
S
= 36 psu
ii)
T
= 0
◦
C,
S
= 33 psu
iii)
T
= 30
◦
C,
S
= 36 psu
iv)
T
= 30
◦
C,
S
= 33 psu
e) (6 pts) What is the diﬀerence in the linear approximations in parts (c)
and (d)? Based on this exercise, what can you conclude about the accuracy
of the linear approximation of the equation of state?
g) (2 pts) Using the full nonlinear equation of state of seawater, see
http://www.phys.ocean.dal.ca/~kelley/seawater/density.html
What is the density of seawater at typical abyss temperature and salinity
(
T
= 2
◦
C,
S
= 34
.
75 psu) at the depth of 1km, and 5km? (HINT: use your
solution to Q1, and 1 decibar = 0.1bar = 100 mbar.)