A Multivariate Stochastic Flood Analysis Using Entropy

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 that of volumes in the same time interval; and (3) peaks and volumes exhibit dependence Special emphasis was given to the structure of the matrix to Language 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.This multivariate stochastic model was related to maximum entropy spectral analysis (MESA). This relationship was shown by deriving power spectrum from marginal distributions of flood characteristics and cross-spectrum from the bivariate distribution of peaks and volumes. This connection has two useful practical applications: use of the derived distributions in statistical inferences and use of the spectral analysis for predication and reconstruction of historical records.