Long-Term Distribution of Hurricane Characteristics

Abstract Based on analysis of hurricane data, this paper shows that frequencies of hurricane occurrence along the U.S. East and Gulf coasts agree with the Poisson distribution, and the hurricane central pressure, wind velocities, wave heights and storm surge agree with the Waybill distribution, a Poisson-Waybill compound extreme value distribution is presented to compute the long term distribution of hurricane central pressure wind velocities, wave heights and storm surge. Introduction Hurricane waves and storm surge are important design factors for offshore structures along the Atlantic and Gulf coasts of the United States. Therefore, long term distribution of hurrican induced maximum winds, wave heights and storm surges directly influence the safety of structures and indirectly dictate the cost of constructions. Based on a previous study concerning extreme wave and wind along the China coast(7), this paper shows that frequencies distributions of hurricane occurence along the U.S. east and gulf coasts agree with the Poisson distribution, and the hurricane central pressure, wind velocities, wave heights and storm surge agree with the Weibull distribution, a PoissonWeibull compound extreme value distribution is presented to compute the long term distributions of hurricane central pressure, wind velocities, wave heights and storm surge. Sources of data duration 1900-1970 are taken from references, (1, 2, 4 and 8) and some monthly Weather Reviews Poisson-Waybill Compound Extreme Value Distribution By checking the chi-square distribution x2, it is found that frequencies of hurricanes in the seven regions of U.S. coasts agree well with the Poisson distribution. This can be seen from Fig. 1. The seven regions division along the U.S. gulf and east coasts was given in reference (3) and reproduced in Fig. 2. Hurricane central pressure, maximum wind velocities, wave heights and storm surge, on the other hand, are to be shown here to agree with the Waybill distribution. The frequency of occurrence of hurricanes is denoted as n (n = 0, I, 2, 3, .. k,..) and their probability is p (n = k) = Pk, (Pn = Po, Pi, 'Pk, ...). Initial distribution of hurricane central pressure (or maximum wind velocity, wave height, storm surge) is denoted as G(x). According to (7), a discrete distribution (Pk) with a continuous distribution G(x) can form a compound extreme value distribution, that is(MATHEMATICAL EQUATION AVAILABLE IN FULL PAPER) where b, r are parameters of Waybill distribution,(MATHEMATICAL EQUATION AVAILABLE IN FULL PAPER) A is mean value of Poisson distribution.(MATHEMATICAL EQUATION AVAILABLE IN FULL PAPER)