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Physical Oceanography
Combined Homework and Laboratory Set 9
Due 27 April 2004

Late homework will cost 15 points per week or part of a week it is late.


The goal of this assignment is to learn more about ocean waves and their relation to wind.

First, go to the NOAA Wavewatch web page. It has information needed for the assignment. The maps downloaded from this page were produced from analysis and forecasts by numerical weather models operated by the NOAA Marine Modeling and Analysis Branch of the Environmental Modeling Center. They are responsible for the development of improved numerical weather, marine, and climate prediction modeling and analysis systems within the National Centers for Environmental Prediction/ National Weather Service (NCEP/NWS).

Read the Product Description to learn more about the maps. The Wave Modeling Group also has a very nice Primer on how to use the information and References to published work. You can find information on coastal wave models for the California Coast at: http://cdip.ucsd.edu/cdip_htmls/models.shtml.

Using Wavewatch information:

  • Where in the world are the largest waves today (Note on your write-up the date you are accessing the wave web site)?
  • What is the significant wave height of the largest waves? Note, you can click on the small yellow boxes to get a table of wave information.
  • What is the wind speed at the region of highest waves or just upwind of the region.

Now let's compare these waves with theoretical values calculated from the Pierson-Moskowitz spectrum. Then let's compare the two to see if Pierson-Moskowitz values are useful in this case. In doing the calculations be careful of units.

  1. Use the Pierson-Moskowitz spectrum and calculate the significant wave height that would be produced by the wind in the region of highest waves if the wind blew over a large area for a long time (here large means perhaps 10,000 wave periods and 5,000 wave lengths). Compare this height with the height on the wave map. Are they comparable?
  2. Now we need to determine if the wind blew long enough and far enough to generate the waves in the map. But first, what does NOAA wave group mean by "peak wave frequency"? Hint: see the tutorial.
  3. What is the peak period in the region of highest waves (period of waves at the peak in the wave spectrum)? Using the dispersion relation for deep-water waves, calculate the wavelength of these waves.
    • How long is 10,000 wave periods of waves at the peak of the spectrum?
    • How far is 5,000 wave lengths of the waves at the peak of the spectrum?
    • Estimate the time and distance over which winds blew over the ocean to create the highest waves in the map. How do these values compare to the values needed to create the waves computed from Pierson-Moskowitz spectrum? You may want to look at the wave products from previous model runs. They show wind and wave conditions a day or so before the latest model runs. Did the wind blow long enough over a sufficiently long distance (fetch) to generate the ideal Pierson-Moskowitz waves? Remember the waves are moving downwind as the wind blows on the waves so we must look at wind conditions upwind earlier in time.
    • What is the group velocity of the waves at the peak of the spectrum. How far do these waves travel in 10,000 wave periods? Express this distance in wavelengths of waves at the peak of the spectrum.

  4. What is the wave height, peak wave period, and wind speed in the central Pacific trade-wind region, say at 0° Latitude, 154° W Longitude on the equator?
    • Use the wind speed to calculate significant wave height and period from Pierson-Moskowitz. Compare with the output from the model.
    • Is the agreement better or worse than you found above in the region of highest waves?

Updated on: 5 September, 2004

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