EN330 – Probability & Statistics with Ocean Applications
Random Waves – Probability Distributions
1. Consider a severe storm in which the standard deviation of the water surface is 10 ft.
Assume the mean water surface elevation to be zero.
a. What are the probabilities of the water surface exceeding elevations of 0 ft? 10 ft?
20 ft? 30 ft?
b. What is the probability of the water surface being less than -15 ft?
c. Plot the Gaussian PDF (f(η) vs. η).
2. Consider the sea surface elevation in fairly calm seas where the standard deviation is 4 ft.
a. Plot the Gaussian PDF for this case on the same graph as 1(c) above. Observe the
effect of changing the standard deviation.
b. Based on the new PDF, what are the probabilities of the water surface exceeding
elevations of 10 ft? 20 ft?
3. Plot the Rayleigh distribution (f(Η) vs. Η) for storm waves with a significant wave height
of 4.75 m. Note H1/100, Hrms, and Hs on the diagram.
4. What percentage of the waves in a Rayleigh distribution will exceed the average height,
the rms height, and H1/10?