MAST667-010 Coastal Oceanography: From Physics to Fish
Spring 2001
Instructor Andreas Münchow
Homework #4 (due Mar. 19, 2001)
I. (50 pts) Estimate the correlation coefficient of sealevel oscillations of two time series x1(t) and x2(t) representing
(a) Lewes and Reedy Point,
(b) Lewes and Philadelphia,
(c) Reedy Point and Philadelpia
for the 8-day long time series from March 1-9, 2001 at temporal lag times t from 0-7 hours in increments of D t=30 minutes, that is, compute
r12(t j) = [ S i x1(ti)*x2(ti+t j) ] / [( S i x1(ti)*x1(ti) )*( S i (x2(ti)*x2(tI) )]1/2 i=1,2,...,N
with t j=j*D t where D t=0.5 hours. Write a set of .awk and .bat programs that will accomplish this task. Please include your code in the returning this homework.
II. (25 pts) Graph the results, that is, show the cross-correlation function r12(t ) and interpret its meaning physically. How could you use the results to predict sealevel in Philadelphia based on measurements in Lewes? How could you use the result to predict sealevel under the Delaware Memorial Bridge?
III. (25 pts) Based on the time lag of maximum correlation, estimate the average water depth H between the two stations. Assume that the tidal wave is the major signal that causes this maximum correlation. Assume further that the tidal wave is a linear Kelvin wave that propagates its phase at c=(gH)1/2 m/s.