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
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
- 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?
- 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
mean by "peak wave frequency"? Hint: see the tutorial.
- 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
- How far is 5,000 wave lengths of the waves at the peak of
- 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
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
enough over a sufficiently
long distance (fetch) to generate
the ideal Pierson-Moskowitz waves? Remember the waves are moving
the wind blows
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.
- What is the wave height, peak wave period, and wind speed in the
central Pacific trade-wind region, say at 0° Latitude,
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?
5 September, 2004