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Thread: Probability of storm surge given parameters for hurricanes.

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    Probability of storm surge given parameters for hurricanes.




    I've been working through some statistics problems and could use a little guidance on how to arrive at the right answer (and more importantly, why that is the right answer.)

    I've detailed the problem below

    "4. You are tasked with assessing the risk of damage due to hurricanes at a coastal city whose total exposed assets (e.g. building stock) are valued at 100 billion USD. The city is hit by two storms per year on average. For simplicity, you assume that each storm is independent and at landfall may have an intensity of Vmax = {30, 40, 60} m/s with probabilities of 0.5, 0.3, 0.2, respectively, and a translation speed of Vtrans = {1, 5, 10} m/s with probabilities of 0.1, 0.7, 0.2, respectively. Assume that Vmax and Vtrans are independent.

    (a) Suppose storm surge depth, hsurge, depends simply on the maximum wind speed according to the following equation: hsurge = (hsurge,0)*(Vmax/30 m/s)^1.5 [m], where hsurge,0 = 1 m. However, the city is protected by a 2 m tall sea wall, and thus there is no surge at all unless hsurge exceeds this height. If the wall is breached, though, then water flows over and the wall does not reduce the surge at all. Calculate the probability that the sea wall will be breached at least once in a given year."

    What I have done so far is calculated probabilities for each of the possible hsurge values using the Vmax values (30, 40, and 60).


    hsurge,30 = 1m --> Probability = .5
    hsurge,40 = 1.54m --> Probability = .3
    hsurge,60 = 2.83m --> Probability = .2

    Given that hsurge,60 is the only case in which there is any storm surge in the city, due to the surge wall, it is the only case that counts right? (I'm fairly confident that all other points are not being considered since we were given the sample space for Vmax)

    What do I do with this now? There are two storms per year on average but I'm fairly certain I can't just multiply .2 by 2. Any guidance would be greatly appreciated.

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    Re: Probability of storm surge given parameters for hurricanes.

    You could look at the Poisson distribution.

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    Re: Probability of storm surge given parameters for hurricanes.

    hi,
    this looks like a binomial distribution example to me. Two experiments per year, probability of "success" of 0.2.

    regards

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    Re: Probability of storm surge given parameters for hurricanes.

    Two storms a year on average. So we will have more than two storms some years. Or three perhaps, or even more.

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    Re: Probability of storm surge given parameters for hurricanes.


    Quote Originally Posted by katxt View Post
    Two storms a year on average. So we will have more than two storms some years. Or three perhaps, or even more.
    Ouch, you are right. This would make it a nice exercise : P(S) =Sum(P(S|n)*P(n)) where n is the number of storms hitting the city and S is a surge. P(n) being Poisson and P(S|n) binomial.

    regards

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