The dissertation focuses on the application of entropy theory in hydrologic analysis and simulation, namely, rainfall analysis, streamflow simulation and drought analysis. The extreme value distribution has been employed for modeling extreme rainfall values. Based on the analysis of changes in the frequency distribution of annual rainfall maxima in Texas with the changes in duration, climate zone and distance from the sea, an entropy-based distribution is proposed as an alternative distribution for modeling extreme rainfall values. The performance of the entropy based distribution is validated by comparing with the commonly used generalized extreme value (GEV) distribution based on synthetic and observed data and is shown to be preferable for extreme rainfall values with high skewness. An entropy based method is proposed for single-site monthly streamflow simulation. An entropy-copula method is also proposed to simplify the entropy based method and preserve the inter-annual dependence of monthly streamflow. Both methods are shown to preserve statistics, such as mean, standard deviation, skenwess and lag-one correlation, well for monthly streamflow in the Colorado River basin. The entropy and entropy-copula methods are also extended for multi-site annual streamflow simulation at four stations in the Colorado River basin. Simulation results show that both methods preserve the mean, standard deviation and skewness equally well but differ in preserving the dependence structure (e.g., Pearson linear correlation). An entropy based method is proposed for constructing the joint distribution of drought variables with different marginal distributions and is applied for drought analysis based on monthly streamflow of Brazos River at Waco, Texas. Coupling the entropy theory and copula theory, an entropy-copula method is also proposed for constructing the joint distribution for drought analysis, which is illustrated with a case study based on the Parmer drought severity index (PDSI) data in Climate Division 5 in Texas.

Streamflow forecasting is a fundamental component of various water resources management systems, ranging from flood control and mitigation to long-term planning of irrigation and hydropower systems. In the context of floods, a probabilistic forecasting system is required for proper and effective decision-making. Therefore, the primary goal of this research is the development of an advanced ensemble-based streamflow forecasting framework to better quantify the predictive uncertainty and generate enhanced probabilistic forecasts. This research started by comprehensively evaluating the performances of various lumped conceptual models in data-poor watersheds and comparing various Bayesian Model Averaging (BMA) modifications for probabilistic streamflow simulation. Then, using the concept of BMA, two novel probabilistic post-processing approaches were developed to enhance streamflow forecasting performance. The combination of the entropy theory and the BMA method leads to an entropy-based Bayesian Model Averaging (En-BMA) approach for enhanced probabilistic streamflow and precipitation forecasting. Also, the integration of the Hydrologic Uncertainty Processor (HUP) and the BMA methods is proposed for probabilistic post-processing of multi-model streamflow forecasts. Results indicated that the MACHBV and GR4J models are highly competent in simulating hydrological processes within data-scarce watersheds, however, the presence of the lower skill hydrologic models is still beneficial for ensemble-based streamflow forecasting. The comprehensive verification of the BMA approach in terms of streamflow predictions has identified the merits of implementing some of the previously recommended modifications and showed the importance of possessing a mutually exclusive and collectively exhaustive ensemble. By targeting the remaining limitation of the BMA approach, the proposed En-BMA method can improve probabilistic streamflow forecasting, especially under high flow conditions. Also, the proposed HUP-BMA approach has taken advantage of both HUP and BMA methods to better quantify the hydrologic uncertainty. Moreover, the applicability of the modified En-BMA as a more robust post-processing approach for precipitation forecasting, compared to BMA, has been demonstrated. / Thesis / Doctor of Philosophy (PhD) / Possessing a reliable streamflow forecasting framework is of special importance in various fields of operational water resources management, non-structural flood mitigation in particular. Accurate and reliable streamflow forecasts lead to the best possible in-advanced flood control decisions which can significantly reduce its consequent loss of lives and properties. The main objective of this research is to develop an enhanced ensemble-based probabilistic streamflow forecasting approach through proper quantification of predictive uncertainty using an ensemble of streamflow forecasts. The key contributions are: (1) implementing multiple diverse forecasts with full coverage of future possibilities in the Bayesian ensemble-based forecasting method to produce more accurate and reliable forecasts; and (2) developing an ensemble-based Bayesian post-processing approach to enhance the hydrologic uncertainty quantification by taking the advantages of multiple forecasts and initial flow observation. The findings of this study are expected to benefit streamflow forecasting, flood control and mitigation, and water resources management and planning.