OC4213 LAB 2

Refraction

 

OBJECTIVE: To use an interactive version of the Dobson refraction model to shoal and refract offshore (CDIP) waves into the nearshore region, then compare refracted results to local (ADCP) measurements.

 

PROCEDURE:

 

1.       After logging in to the linux workstation, copy the appropriate files to your oc4213 directory by typing in the command window:

 

cp   ~orzech/oc4213/Refrac/*   ~/oc4213


(Or on a PC, go to the main oc4213 page, choose "Programs for download to PC", and download lab2pc.tar, then extract its contents with WinZip.)

 

2.       Change to your oc4213 directory and open a Matlab window.

 

3.       Run the refraction program by typing "refrac" at the Matlab prompt.

 

4.       You will initialize the "refrac" program with four different sets of offshore conditions, as detailed in step "c" below. At the beginning of each run you will be asked for the target location (lat-long), depth, and the offshore wave direction and period. Use the information in "a" and "b" for all four runs (coordinates of the Acoustic Doppler Current Profiler (ADCP) off Sand City):

 

a.        Location (lat/long) of desired target:

Latitude = 36o 37' 7", Longitude = 121o 51' 26"

(Type: 36 37 7 121 51 26 )

 

b.       Depth in fathoms where you want the refraction coefficient:

Depth = 5 - 10 fathoms

(Type, e.g.: 5 )

 

c.        Deep water wave angle (in degrees, positive clockwise from true North) from which the waves are coming:

 

For this input, you will use four different initializing scenarios. For your first run, visit the ADCP website as described in the Lab 2 Supplement. The data shown were recorded between 0600 hr on January 3, 2005, and 2000 hr on January 5, 2005. Select a date and time from the x-axis on this page and record the wave height, Hs, and a peak period, Tp, at that time (note that wave heights are in FEET on the left side and METERS on the right side). Also estimate and record the corresponding value for peak wave direction, Dp. Then visit the CDIP website's model archive page (again, see lab supplement) and use the menus to obtain a map image for the same date and time. Make sure you pick a time when the map image has positive wave heights from both the north AND the south. (Print out your final map image for inclusion in your lab writeup). You will need to run the "refrac" program four times, each time entering a different one of the options below.

i.   Tp and Direction for North Pacific swell.

ii.   Tp and Direction for South Pacific swell. (NB: Sometimes, may not be possible to hit target. If not, set Kr and Ks to zero for this case.)

iii.   Use the North Pacific data, but change the wave period by 2 - 4 seconds (keep Tp between 8 - 22 seconds) and wave direction by 10 - 20 degrees in your model inputs.

iv.   Use the South Pacific data, but change the wave period by 2 - 4 seconds (keep Tp between 8 - 22 seconds) and wave direction by 10 - 20 degrees in your model inputs. (If you were unable to hit the target using the original S. Pac. values, adjust the wave direction so that it is at least 220 degrees but less than 270 degrees.)

Note that the values of Tp and Direction actually printed on the CDIP web page may not completely reflect their full ranges as shown on the spectrum. Also, the value of Tp for S. Pac. waves may not accurately represent the specific waves that will actually reach your target. Be sure to record the wave heights (Hs,CDIP,N and Hs,CDIP,S) listed at the CDIP site.


5.       After you enter the wave data in step "c", contour plot of Monterey Bay will be created. The little yellow box is your ADCP target location. Either type "0" to exit the program or just hit ENTER to begin creating refraction rays, then move the mouse arrow into the Matlab command window. (Later, you can also type "1" to clear the rays you've plotted.) The program will allow you to initiate as many refraction rays as you like (up to 100). Next, move the mouse arrow into the contour plot and with the crosshairs, choose the deepwater coordinates where the refracted ray will begin. Click the mouse. A refracted ray will be calculated and its path plotted toward the shoreline. The goal is for the ray to hit the yellow target box, at which point "refrac" will calculate the shoaling and refraction coefficients - Ks and Kr - associated with the successful ray path.


6.       Each time you "HIT TARGET!", the program will inform you of your total hits and store the Ks value and Kr value corresponding to the successful refraction path. Try to get at least 2 hits for each different set of input parameters entered in step 4. When you exit the program, an average of all the collected "hit" values will be computed. Your individual Ks and Kr results, along with the average value, will be saved (appended) to a text file called "refract.output". After your four repetitions with the Sand City ADCP target, you should have at least eight sets of Ks and Kr values stored in your "refract.output" file, along with their averages.


 

REPORT:


1.   Turn in a printout of the "refract.output" file and the CDIP model image with your report.


2. Construct a table of computed and observed values of significant wave heights. Use only your AVERAGED Kr and Ks results. Your table should have 4 rows (one for each of your averaged Kr and Ks results) and 6 columns for trial number, offshore wave direction, wave period, Kr, Ks, and Hs,offshore. Also indicate separately the values you found for Hs, Dp, and Tp at the ADCP, as well as the time and date for which you found them.


3. In using the "refrac" model, we have already substituted a single wave at a single frequency for an entire spectrum of waves. Now, we will assume that the average wave recorded at the ADCP is simply the sum of one shoaled and refracted wave from the SOUTH ( < 270 deg) and one shoaled and refracted wave from the NORTH ( > 270 deg). Using the four sets of averaged Kr and Ks values from your table together with the corresponding Hs,CDIP values, calculate predicted values for wave height at the ADCP location as follows:

Hs,pred=[(Kr,NKs,NHs,CDIP,N )2 + (Kr,SKs,SHs,CDIP,S )2]1/2


(WHY do we use the above equation to calculate a predicted wave height at the ADCP? Because if waves come from two separate directions, you must combine the wave heights by adding their ENERGY. Thus we first shoal and refract each single wave with Kr and Ks, then add their energies -- proportional to the square of their heights -- then take the square root to find an averaged wave height.)

For these results, you should be able to mix and match the Kr and Ks values from North and South in four different combinations, leading to a total of four Hs,pred estimates. Make sure you also list the peak wave periods you found at the CDIP and ADCP websites. Hand in the table, the Hs,pred values, and the peak period data with your report (If you were unable to hit the target using the original southern wave data from CDIP, set Kr,S and Ks,S to zero in the calculations for that case).


4. Your predicted wave heights at the ADCP will probably differ from the actual values you retrieved from the ADCP website. Did the CDIP deepwater values result in the better match of Hs,ADCP to Hs,pred, or did your "adjusted" inputs yield the better fit? Speculate as to why predicted and actual wave heights might differ.


5. Assume that by the time the waves reach the ADCP, they have fully refracted and are coming directly in toward the shore. Based on this assumption, use the peak direction data from the ADCP website to estimate the heading of the "shore normal" (i.e., a line perpendicular to the shoreline) close to the ADCP location. Explain how you arrived at your answer.