Physics based, integrated modeling of hydrology and hydraulics at watershed scales

This thesis presents the major findings in the development of the hydrology and hydraulics modules of a first principle, physics-based watershed model (WASH123D Version 1.5). The numerical model simulates water movement in watersheds with individual water flow components of one-dimensional stream/channel network flow, two-dimensional overland flow and three-dimensional variably saturated subsurface flow and their interactions.;Firstly, the complete Saint Venant equations/2-D shallow water equations (dynamic wave equations) and the kinematic wave or diffusion wave approximations were implemented as three solution options for 1-D channel network and 2-D overland flow. The accuracy of the three wave models for 1-D channel flow was evaluated with several non-trivial (trans-critical flow; varied bottom slopes with frictions and non-prismatic cross-section) benchmark problems (MacDonnell et al., 1997). The test examples for 2-D overland flow include: (1) a simple rainfall-runoff process on a single plane with constant rainfall excess that has a kinematic analytical solution under steep slope condition. A range of bottom slopes (mild, average and steep slope) are numerically solved with the three wave models and compared; (2) Iwagaki (1955) overland flow experiments on a cascade of three planes with shock waves; (3) overland flow in a hypothetical wetland. The applicability of dynamic-wave, diffusion-wave and kinematic-wave models to real watershed modeling is discussed with simulation results from these numerical experiments. It was concluded that kinematic wave model could lead to significant errors in most applications. On the other hand, diffusion wave model is adequate for modeling overland flow in most natural watersheds. The complete dynamic wave equations are required in low-terrain areas such as flood plains or wetlands and many transient fast flow situations.;Secondly, issues about the coupling between surface water and subsurface flow are investigated. In the core of an integrated watershed model is the coupling among surface water and subsurface water flows. Generally, there are two cases based on physical nature of the interface: continuous or discontinuous assumption, when a sediment layer exists at the interface, the discontinuous assumption may be justified. As for numerical schemes, there are three cases: time-lagged, iterative and simultaneous solutions. Since modelers often resort to the simplest, fastest schemes in practical applications, it is desirable to quantify the potential error and performance of different coupling schemes. It is concluded that different coupling approaches are justified for flow problems of different spatial and temporal scales and the physical setting of the interface.;Thirdly, The Method of Characteristics (MOC) in the context of finite element method was applied to the complete 2-D shallow water equations for 2-D overland flow. For two-dimensional overland flow, finite element or finite volume methods are more flexible in dealing with complex boundary. We consider the Method of Characteristics (MOC) in the context of finite element method, as a good alternative. We have implemented a numerical scheme that attempts to diagonalize the characteristic equations based on pressure and velocity gradient relationship. This new scheme was evaluated by comparison with other choice of wave characteristic directions in the literature. Example problems of mixed sub-critical flow/super-critical flow in a channel with approximate analytical solution was used to verify the numerical algorithm. Then experiments of overland flow on a cascade of three planes (Iwagaki 1955) were solved by the new method. The circular dam break problem was solved with different selections of wave characteristic directions and the performance of each selection was evaluated based on accuracy and numerical stability. Finally, 2-D overland flow over complex topography in a wetland setting with very mild slope was solved by the new numerical method to demonstrate its applicability.;Finally, the physics-based, integrated watershed model was tested and validated with the hydrologic simulation of a pilot constructed wetland in South Florida. (Abstract shortened by UMI.)...