SIO 210 Problem Set 1

October 3, 2016

Due October 17, 2016 (2 weeks)

If you work together on these, please make sure that you understand the concepts and use your group discussion to help with the understanding.

  1. (a) Explain briefly the usefulness of the non-dimensional parameter ‘aspect ratio’. The aspect ratio is the ratio of the height H to the length scale L. It tells us if a fluid motion will have similar or very different vertical and horizontal scales. If they are similar (H/L ~1), then vertical velocities and horizontal velocities might be the same order of magnitude. If the aspect ratio is small (H/L < 1), then vertical velocities would be very small compared with horizontal.

For the following, estimate the Rossby number

The Rossby number is 1/(fT), where T is the time scale. Estimate 1/f ~ 1day.

Using the scales from the Introductory lecture:

(b) Tsunami T = minutes to hours. Ro = 1 day/(minutes, hours) > 1

(c) Diurnal tide T = 24 hours. Ro = 1 day/1day = O(1)

(d) Global overturning circulation T = 100s to 1000s years. Ro = 1 day/(100s years) < 1

(e) Bubbles T = 0.01 sec. Ro = 1 day/ (0.01 sec) > 1

2. Use the Mindanao Trench temperature and potential temperature graphical comparison from class (properties of seawater second lecture) and the textbook:

(a) Estimate from the graph the temperature and potential temperature at 5000 m depth, and the difference between them.

T ~ 1.5°C.  ~ 1.0°C. (T - ) ~ 0.5 C.

(b) Use this estimated value of potential temperature and calculate the heat content if this value is correct for a layer that is 1000 m thick and over a region that is 10,000km x 5,000 km. For density, look at other graphs or vertical sections online and estimate the density. Use a specific heat of cp = 3850 J/kg °C. Express your answer in Joules.

This was really not quite the right question. It should have been specified in terms of a change in temperature.

Q =  cp ( + 273.16) (V) = 1040 kg/m3 (3850 J/kg°C)(274.16)(1000m)(10x103x103m)(5x103x103m) = 5.48 x1026J

(c) Calculate the difference between your heat content and a heat content that would be calculated from the temperature. Express your answer in Joules.

Same calculation but just 0.5°C instead of 274.16. Q = 1.00x1024J.

Aside: there is a unit, the ZetaJoule. 1 ZJ = 1021 J.

Ocean heat content changes are being expressed in ZJs. The total change in deep ocean heat content since 1955 is about 80 ZJ, for comparison with the number that is being calculated here.

  1. Use your web browser and look at an online SST anomaly animation produced by NOAA, using satellite data.

Site:

(a)Explain what an anomaly is. How was it calculated for this animation? (Look for the information on the website: you are most welcome to critique what you find if it’s inadequate.)

Anomaly is the difference between the actual observation and the mean, however the mean is defined. What’s important in description of method is to clearly define how the mean was constructed.

(b)Describe the overall structure of the field that you find. (You do not need to learn all about the climate phenomenon – we will do this later. Please just describe what you see.)

Any nice general description of this field and what one sees through having an animation will likely be a good answer.

(c)Pick one local feature and describe how it evolves with time.

Any nice general description of this field and what one sees through having an animation will likely be a good answer.

  1. A computer file that is a time series of water temperature at the end of the Scripps pier is now linked on the course website.

SIO pier data are found on several sites. Data set provided here is in csv (ascii) format, easy to use with excel and other programs. I retrieved it from:

Another way in to the SIO pier data sets is here, with lots of plots available, but data not easily accessed:

Use this file and compute the

  1. mean
  2. variance
  3. standard deviation
  4. standard error

Use whatever plotting capability you have (matlab, R, python, etc), plot the time series and then plot its anomaly relative to the record mean (i.e. the mean value over the entire record).

  1. (a) On the attached vertical section, from the Pacific Ocean at 160°E, find at least one location that has a strong halocline. What is a halocline?

A halocline is depth range through which salinity changes very rapidly in the vertical. It is usually associated with fresh water above salty water, hence increase stability of the water column

In the figure, there is a halocine between 100 and 150 m in the north.

There is another halocline, much stronger, in the tropics, about 4°N to 15°N, with weaker halocline also extending to the southern end of the section at about 4°S. The 4°N-15°N halocline is due to the ITCZ excess precipitation in the warm pool region.

(b)Go online to find this section (in - follow links until you find it.)

Find the potential density section. Identify the pycnocline that goes with this (these) haloclines.

I’ve attached the figure, from

Northern halocline: shallow pycnocline that matches the halocline depth

Equatorial halocline: the strong halocline is within the <22.0 kg/m3 layer, which apparently doesn’t have enough contour intervals to delineate the halocline’s contribution to density.

(d)Find the potential temperature section. Describe the vertical potential temperature structure that goes with the halocline(s).

I’ve attached the potential temperature section.

In the northern halocline, there is a temperature minimum. A T minimum can be sustained only if its water is relatively fresh. The T minimum and halocline coincide, so here the halocline is accompanied by and stabilizes the cold water, which is a remnant of winter cooling that is vertically stable because the surface water is so fresh.

In the tropical halocline, the surface water is very warm, with no hint of a temperature minimum. Here there is actually uniform temperature through the halocline, a so-called ‘barrier layer’, although that is beyond the scope of this question.

(e)Back on the salinity section above: identify the Subtropical Underwater and explain what created it.

The STUW is the subsurface salinity maximum between about 10°N and 17°N. It is created through subduction from the surface salinity maximum water.

(There is also an STUW at the southern boundary of the section, which is subducted from the South Pacific’s surface salinity maximum, which is closer to the equator than the North Pacific’s maximum, as the atmospheric forcing ‘equator’ is in the ITCZ which is north of the equator.)

To see the surface sources of these STUWs, look at the maps of salinity on the same website in

(f)Locate the low salinity intermediate water on this section (it’s called North Pacific Intermediate Water). Explain why there is a salinity minimum.

The NPIW salinity minimum lies between 4°N and 42°N although it is most strongly developed north of about 15°N. Its source is fresher surface waters in the subpolar North Pacific. We do not need more detail here than this.

6. In the vertical profile of density shown in the figure, the arrow points to the

(a) Thermostad

(b) Mode water

(c) Abyssal ocean

(d) Pycnocline

(circle one).

(Identified as pycnocline because density changes rapidly with depth. There is also a seasonal pycnocline very close to the surface, but we know that d is the righ answer because this feature is not a thermostad, mode water, or the abyssal ocean.)

(e) explain why this feature exists.

At any given location in the ocean, the water we see at different depths comes from different sea surface locations. Pycnocline water comes from subduction of sea surface waters in the subtropics and higher latitudes and subsequent advection to the location of our measurement. The density range reflects the densities that outcrop at the sea surface. The intensity of the pycnocline, how rapidly its density varies with depth, is more subtle. It involves the amount of water that is subducted in each isopycnal outcrop at the sea surface, and also involves vertical velocity and mixing that can intensify the vertical gradient of density.

7. Two volumes of water with different properties are mixed together. The potential temperature and salinity of volume A are 17°C and 36 psu. The potential temperature and salinity of volume B are 4°C and whatever salinity is required for the potential density of A and B to be the same.

a. Estimate the salinity for Volume B from the graph.

Plotting as attached: salinity is about 33 psu for the 4°C water.

Could double check this if one already had a subroutine to computer density.

b. If Volumes A and B are the same, what are the potential temperature and salinity of the mixture?

Mixing must be on a straight line between two points in T,S. I did not mention of emphasize this in class. This could be a point to raise in tutorial.

Mixing is proportional: T = (4 + 17)/2 = 10.5°C; S = (33+36)/2 = 34.5 psu.

c. If both volumes cover the same horizontal surface area, but Volume A is 500 m thick and Volume B is 2000 m thick, what are the potential temperature and salinity of mixture?

Now need to weight the mixing by the volume, just use thickness:

T = (2000*4 + 500*17)/2500 = 6.6°C; S = (2000*33+500*36)/2500 = 33.6 psu

d. Using the plot, what is the potential density for mixture (b)?

Mixing along straight line: density is about 26.5 kg/m3

e. Compare this with the potential density mixture (a) would have if the equation of state were linear.

Mixing would retain original density of about 26.2 kg/m3

f. On the figure, sketch the potential density contours that you would have if referencing to 4000 dbar rather than 0 dbar.

Sketch in flattened and rotated isopycnal curves.