Multivariate Joint Probability Distribution And Its' Application To Analysis Of Plentiful Or Scanty Runoff Encountering In South-to-North Water Transfer Project (East Areas)

In mathematics, a complete definition and description of hydrological event and calculation of encountering frequency for hydrological variables can be solved by the theory of multivariate joint probability distribution. Arithmetic of the multivariate Pearson-type-three (P-â…¢) joint probability distribution is investigated in this thesis, considering that most hydrological variables, in view of statistics, are characterized by P-â…¢ probability distributions.Five computational methods for multivariate P-â…¢ joint probability distribution are studied, including the Moran method based on normality transform, the EFM method based on empirical frequency analysis, the TAN method based on bi-variate P-â…¢ joint probability distribution, the FEI method of transforming multivariate joint probability distribution into unique variable probability distribution, the FGM method applicable to any distribution. Studies on various characteristics of these methods are carried out by means of Monte-Carlo technique, including comparisons of statistical features on the normality of the transformed samples and the estimation on quantiles through reverse transform between two normalization approaches for Moran method, namely Box-Cox approach and Polynomial normality transforms (PNT); comparisons on quantile estimations between the method of Liner Moments (L-M) and PNT; comparisons among these methods are also presented.These computational methods of multivariate P-â…¢ joint probability distribution are also applied to the analysis of plentiful or scanty runoff encountering among regions within the range of south-to-north water transfer project (east areas), the potential of water transfer is evaluated. At the same time, these methods are compared by observation data and validated by simulated samples, upon which methods are evaluated and recommended. Results indicate that TAN method can offer more reasonable solution if its mathematical constraints are met; otherwise, Moran method is superior; FGM method is applicable to variables with weak correlations; FEI method is unstable in calculating the frequency for a joint probability distribution; EFM method is intensively affected by sample length.Analyses on the encountering frequency of runoff among regions along the south-to-north water transfer project (east areas) are worked out. Results show that synchronous frequency of runoff encountering is smaller than asynchronous frequency, and intense variations of runoff result in the uneven distribution of water resources over the studied regions. It is found that the frequency feasible to transfer water from south to north is relatively high, which implies that there is a nature advantage to make the project a potential measure.