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Question 1 Generate a random series of 100 data points pertaining to the wave height (H) and wave period (T) for a site where the mean wave height is Hm = 2 m. The wave height should be sampled from a Rayleigh distribution with the shape parameter set to σ = √2/π and the period should be sampled from a uniform distribution between 3 and 10 s. NOTE: If you are using MS Excel to generate your data points, the following commands may be used to obtain the wave heights and periods: • . Wave height: =2*SQRT(2/PI())*SQRT(-2*LN(RAND())). This command is equivalent to H = Hmov-2 In U where U is a random number between 0 and 1. Wave period: =3+7*RAND() Question 2 For the wave series generated in Question 1: a) What is the highest wave (Hmax and Tmax), the mean wave (Hm and Tm), and the significant wave (H, and Ts)? b) What are your Hs/Hm and Hmax/Hs ratios? How do these ratios compare to what might be expected in real data? c) Plot a histogram of the wave height H (i.e., number of waves vs. wave height), the histogram of H/Hm, and a histogram of the wave period T d) Assume we have a record of 200 waves that have Hs = 6 m. What is Hmax such that there is only a 5% chance it will be exceeded?

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