Maximum Entropy Estimation of n-Year Extreme Waveheights
摘要
A new method for estimating the n (50 or 100) -year return-period waveheight, namely, the extreme waveheightexpected to occur in n years, is presented on the basis of the maximum entropy principle. The main points of the method are as follows: ( 1 ) based on the Hamiltonian principle, a maximum entropy probability density function for the extreme waveheight H, f(H)= αHγe-βΗ4 is derived from a Lagrangian function subject to some necessary and rational constraints; (2) the parametersα,β, andγin the function are expressed in terms of the mean H, variance V = ( H - H)2and bias B = ( H- H)3; and (3) with H, V and B estimated from observed data, the n-year return-period wave height Hn is computed in accordance with the formula 1/1 - F(Hn) = n, where F(Hn) is defined as F(Hn) =n Hn Of(H)dH.Examples of estimating the 50 and 100-year retum period waveheights by the present method and by some currently used method from observed data acquired from two hydrographic stations are given. A comparison of the estimated results shows that the present method is superior to the others.