**Problem Set #2**
**Ocean 210: Ocean Circulation**
**Assigned: Friday, October 9, 2009**
**Due: Friday, October 16, 2009**
**Problem 1.** Potential temperature along a meridional transect in the Atlantic
a) Figure 1 shows potential temperature with depth along a meridional transect in the Atlantic Ocean. Based on this figure, sketch a plot (depth on the y-axis) with two profiles of potential temperature (x-axis) representing two different points along the transect: 30 N and 30 S (make sure to label your axes). For this question, focus on the differences in potential temperature in the deep ocean (i.e., >3000 m depth). Is the deep ocean colder or warmer in the South Atlantic versus the North Atlantic? What explanation can you think of for this difference in terms of the water masses we have discussed in class so far?
**Problem 2.** Atlantic and Pacific transects (interpreting surface plots).
A useful way to look at oceanographic data can be to look along a “surface” on which some property has a constant value. The objective of this problem is to compare properties on three surfaces: the sea surface (i.e., 0 m), at 3000 m, and on the σ_{θ} = 27.8 kg m^{-3} surface which is an isopycnal (constant density) surface.
We again use real oceanographic data collected during the World Ocean Circulation Experiment (WOCE). We will consider data from two North-South hydrographic survey lines (transects): one in the Atlantic Ocean (Figure 2) and one in the Pacific Ocean (Figure 3). Each figure displays 9 plots; these are the distributions of different ocean properties, such as temperature or salinity, over isosurfaces along the North-South transects. For example, in the first box, each point you see represents Potential Temperature at the surface at different latitudes along a transect. On the x-axis, the negative values (e.g., -50) indicate southern latitudes, zero represents the equator, and positive values (e.g., +50) indicate northern latitudes.
Questions (answer each question in three sentences or so):
Atlantic Ocean:
a) Consider the distribution of potential temperature at the surface (Tpot-0 [°C] on surface) in the Atlantic Ocean between 50°S to 50°N. Explain why the maximum values of potential temperature occur between approximately 25°S and 25°N.
b) Next, examine the surface salinity between 50°S to 50°N. What causes the M-shaped distribution of salinity values (i.e., why are the extremes where they are)?
c) Finally, look at the surface density profile. Based on your answers to parts 1 and 2, explain how temperature and salinity act together to produce the observed density distribution between 50°S to 50°N at the surface.
Comparison between Atlantic and Pacific transects:
d) Compare the distribution and magnitude of surface salinity values in the two oceans. How are the surface patterns similar in the two ocean basins? How are they different? What explanations can you provide for the differences in surface salinity between the ocean basins in terms of the E-P balance between 30°S to 30°N?
e) Notice that at around 3000 m depth at 50°S the temperature, salinity, and potential density are quite similar in the two basins. Why do you think this might be (hint: think of the connectivity of the Atlantic and Pacific Oceans at this latitude)?
f) In contrast, at 3000 m at 50°N, the temperature and the salinity are higher in the Atlantic than in the Pacific. Compare the Sigma-0 values for the two basins at that latitude. What does that tell you about Sigma-0 as a function of potential temperature and salinity at such low temperatures, i.e., which one of the two variables (potential temperature or salinity) is more important in governing the density at such low temperatures (you might also look at page 13 of the Topic1A figures)?
g) How do the depths of the σ_{θ} = 27.8 kg/m^{3} surface compare between the two basins (i.e., which is shallower/deeper) in the northern latitudes? How would the density at a certain depth in the Atlantic compare to the density at the same depth in the Pacific?
Figure 1: Depth in m on y-axis, latitude on x-axis.
Figure 2: Atlantic Ocean
Figure 3: Pacific Ocean
**Problem 3.** Three water samples (X, Y, and Z) were collected during a hydrocast. The X sample is characterized by 2.70°C in situ temperature and 34.46 pss salinity. Sample Y has 2.39°C in situ temperature and 34.40 pss salinity. Sample Z has a temperature of 2.59°C in situ temperature and 34.44 pss salinity.
Given the following formula (a different version of the equation of state than used in Problem Set #1):
*ρ – ρ*_{o}* ≈ α(T – T*_{o}*) + β(S – S*_{o}*)*
where ρ is density and ρ_{o} = 1027 kg m^{-3},
α is the thermal expansion coefficient, -0.15 kg m^{-3} °C^{-1}
T is the temperature and T_{o} = 10 °C
β is the haline contraction coefficient, 0.78 kg m^{-3} pss^{-1}
S is the salinity and S_{o} = 35 pss.
a) Determine the density as a function of T and S of each of the three water masses to two decimal places.
b) Assuming these three samples were taken at different depths what calculation would you need to make to determine if the water column is stable, unstable, or neutral?
A more complete version of the formula takes into account pressure effects on density.
The formula is:
*ρ – ρ*_{o}* ≈ α(T – T*_{o}*) + β(S – S*_{o}*) + k*z*
where all constants remain the same as above and
T is the potential temperature with T_{o} = 10°C
k is a coefficient of compression, 4.5 x 10^{-3} kg m^{-4}.
Now, assume that for the first 1000 meter depth, the rate of in situ temperature increase with depth for seawater is 0.05°C per 1000 meters and the rate of in situ temperature increase with depth for seawater deeper than 1000 meter is 0.15°C per 1000 meters.
c) If sample X was collected at 4500 m, sample Y was collected at 2500 m, and sample Z was collected at 3500 m, calculate the potential temperature of each of the three water masses.
d) Recalculate the in situ and potential density of each of the three water masses and put them in order from the least to most dense; you will use the more complete equation of state which includes the k*z term to calculate in situ density. When calculating the potential density you will use theta instead of T and you will not consider the influence of pressure on density, so ignore the k*z term.
e) Is the water column stable, homogeneous, or unstable? Why?
f) Given that this formula for density has an error of ±0.5 kg m^{-3}, do you think this is accurate enough to calculate density in the real ocean? Why or why not?
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