Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Civil and Environmental Engineering

First Advisor

Vijay P. Singh


This dissertation discusses the multivariate hydrologic analysis by the entropy theory. It is divided into two major parts. The first part (Volume I) examines hydrologic frequency analysis, specifically rainfall-runoff modeling and the design of rainfall networks. The second part (Volume II) develops two flood forecasting models: the univariate streamflow model, and the bivariate rainfall-runoff model. The hydrologic frequency analysis focuses on three topics: multivariate normal distribution, multivariate exponential distribution and multivariate exponential distribution and multivariate mixed distributions. Many forms of univariate, bivariate and multivariate normal distributions are derived by using the principle of maximum entropy (POME), emphasizing the serial dependency of rainfall and runoff process, and the variable dependency among rainfall and runoff processes. The importance of the variables in the partial duration series model dependent on the cutoff level is examined by entropy and transinformation. Several entropy criteria exist in spacetime design of rainfall networks. Multivariate forms of the Marshall-Olkin exponential distributions are also derived using POME. The bivariate exponential distribution is compared with the bivariate normal distribution in the space design of rainfall networks. By combining exponential and discrete distributions, the multivariate mixed distributions are constructed. These distributions are tested on partial and annual duration series models. The flood forecasting models are developed by adjustment of equations from the maximum entropy spectral analysis. The univariate streamflow model for a long-term (monthly and seasonal) flood forecasting is developed and tested on five climatologically different watersheds, and then compared with the established time series models (ARIMA and state-space). The bivariate rainfall-runoff model, theoretically extending the univariate case, is developed for real-time forecasting, tested on five different climatological areas, and compared with the state-space model. Extensive parameter analyses for both models are given and some intriguing conceptual connections between developed models and time series models are established. Finally, comprehensive guidelines and recommendations for the future work are given.