A Multivariate Stochastic Flood Analysis Using Entropy
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The principle of maximum entropy (POME) was used to derive a multivariate stochastic model for flood analysis. By specifying appropriate constraints in terms of covariances, variances and cross covariances, multivariate Gaussian and exponential distributions were derived. As a special case, the bivariate process of flood peaks and volumes was investigated for three cases: (1)the peaks and volumes are independent and occur the same number of times; (2)the number of peaks is more than the number of volumes in the same time interval; and (3)peaks and volumes exhibit dependence. Special emphasis was given to the structure of the matrix of Lagrange multipliers in the model. Marginal distributions of flood characteristics were obtained, first with no restrictions imposed, and then with assumptions of independent occurrences and a high threshold value. The conditional distribution of flood volume given the peak was then discussed. Disusses the relationship between this multivariate stochastic model and maximum entropy spectral analysis.
