The handout for this lab is available in pdf format here: waves.pdf. Below, you may find the section of the handout which includes the exercises.

Go to the following web site:
http://storm.rsmas.miami.edu/~cook/Surf/maps.html

1. What is the main feature charted on surface weather maps?
 
 

2. In the Northern Hemisphere, what direction does air move around low pressure and high pressure centers?
 
 

3. What phenomena is responsible for this circulation?
 
 

4. Draw a simple diagram of this phenomenon.
 
 

5. What is the pressure gradient?
 
 

6. How does the pressure gradient relate to the speed of the wind?
 
 

7. What does an isobar indicate?
 
 

8. If you see tightly packed isobars on a surface weather map, will there be light or strong winds in that area?
 
 

Please now go to the following website and read about symbols used on surface weather charts:
http://www.meteor.wisc.edu/~hopkins/aos100/sfc-anl.htm

What do the following symbols mean?

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Please now take a look at the following example of a North Pacific weather chart for January 1998 and answer the following questions:
http://ilikai.soest.hawaii.edu/HILO/jan28/jan26w.gif

15. Observe the atmospheric system centered at 30^o N, 163^o E. How would you describe this system?
 
 

16. Observe the system centered at 45^o N, 180^o E. How would you describe this system?
 
 

17. Does the wind direction show the theoretical wind direction we discussed in Question 2?
 
 

Using the weather charts provided, we are going to now track a potent winter storm that blew up off Japan during January 1998. Using the skills that we learned in the first section of the lab, we will determine central pressures and wind speeds of the storm as it moves across the North Pacific over a 4-day period. Knowing the times that the observations were made, we can come up with the first three pieces of information used to make a surf forecast.

Using the maps, please fill out the following table:
 
 

Date/Time1	Center of Storm	Central Pressure (mb)	Wind Speed towards Hawaii (knots)2	Estimated Fetch Length Pointed at N. Shore, Oahu
Jan24 1200Z	38o N152o E
Jan25 1200Z	43o N168o E
Jan26 1200Z	45o N179o W
Jan27 0000Z	45o N166o W
Jan271200Z	44o N163o W

Table Notes:
1 The maps are given by date and Greenwich Mean Time. This time is 10 hours ahead of the time in Hawaii. For example, 1200Z is 2 AM in Hawaii.)
2 To estimate the fetch pointed at the North Shore, overlay the surface weather charts with the Great Circle charts. Look for areas in the storm where the winds (isobars) are parallel or roughly parallel to the Great Circle routes.

18. Using data from the table you just completed, estimate the significant wind velocity, duration, and fetch for the January 1998 storm.

a) Significant wind velocity in mph (1 knot = 1.15 mph)
 

b) Duration of maximum winds in hours
 

c) Fetch in nautical miles
 
 

19. Using the attached graph, derive the height of the seas using the wind velocity, duration of wind, and fetch from above.

Now we know the initial sea heights pointed toward the North Shore. The next factor we need to take into consideration is wave decay. These waves will have to travel a very long distance across the open ocean before they arrive at Outer Log Cabins on the North Shore. As these waves move out of the storm area, they decrease greatly in size. This decay is due to 3 main factors:
1) short period waves and chop dissipation outside of storm area,
2) directional spreading of waves as they move away from the storm, and
3) separation of waves as they travel forward at different speeds after leaving the storm area.

20. Estimate the travel distance in nautical miles from the storm location at its peak (Jan 27 0000Z) to the North Shore (use a ruler and convert).
 
 

21. Assuming a swell period of 23 seconds (massive swells such as this generally, after decay, have periods of 20-25 seconds), we need to calculate the amount of time necessary for the swell to reach Oahu.

a) First, calculate the speed of the wave trains:
Speed (mph) = 1.70 * swell period (sec)
 

b) Next, using the speed from part a, calculate the amount of time necessary for the swell to reach the North Shore:
Travel time (hrs) = Distance (miles) / Speed (mph)
 
 

We will utilize an often-used and simple relationship to account for decay. We will assume that for every 1 day of travel time the height of the swell will decrease by 30%. Thus, if the swell leaves the storm with a height of 10 ft, after one day of travel the height is then 7ft. At the end of the 2 nd day of travel, the height is 5 ft and so on.

22. What will the swell height be as it arrives on the N. Shore of Oahu?
 

23. Since you know the time of the peak intensity of the storm and the time it will take for the swell to reach Oahu, estimate the date and time that the peak of this swell will hit the North Shore.
 
 

Now, we can use actual buoy observations from the January 1998 storm to confirm and fine-tune our forecast. We can look at Buoy 51001 that sits 250 miles northwest of Kauai. This buoy is very useful to surfers and navigators and it can let us know the exact swell heights expected in the next several hours.

Please go to the following website and click on “51001”:
http://www.ndbc.noaa.gov/Maps/Hawaii.shtml

24. Give the current swell height and period at Buoy 51001.
 

Now, we will look at the archived buoy readings at 51001 for our January ’98 swell. Please visit
http://ilikai.soest.hawaii.edu/HILO/jan28/buoy.txt.
This is a list of the buoy readings for several days before and after our swell event.

25. When does the swell hit Buoy 51001?
 

26. When will the swell be expected to arrive on the North Shore? Give date and time.
 

27. Give the swell size and period for the peak of the swell at Buoy 51001.
 

As the surf actually approaches the North Shore, we need to take into account the effects of shoaling. As any wave train moves from deep open-ocean water into shallower coastal areas, the wave energy below the surface of the ocean is pushed upward, causing the waves to increase in height. Longer period waves, like our swell, will be affected more by shoaling than shorter period waves (e.g., trade wind swell) because longer period waves have more energy that is under the water. We will utilize a shoaling coefficient of 1.4 for our calculations.

29. Calculate the wave height after shoaling:
 

The last thing we need to take into account is refraction. Refraction is the process by which waves bend as they travel over an uneven ocean floor. Imagine a large open-ocean swell coming upon a large shallow reef on the North Shore. The portion of the wave passing over the reef will drag and slow down while the portions outside the reef are still traveling relatively faster. The parts of the wave over deeper water begin to wrap and bend in toward the shallower water. This multiplies the energy in the shallow part of the wave, causing it to grow into a larger breaking wave as it nears shore. The actual effect of refraction depends largely on the ocean bottom topography as well as the wave period. The longer the swell period, the more the waves will be affected by the ocean floor bathymetry. We will utilize a simple refraction coefficient of 1.5 to finish our forecast for the surf at Outer Log Cabins (final wave height = 1.5 X wave height after shoaling effect).

30. Calculate the final wave face height.
 

31. Estimate the actual wave face heights from watching the video.
 

32. Explain any differences you may have found.