Research On Cost-Effective Algorithm For Unsaturated-Saturated Flow And Its Application

Variably saturated flow modeling is one of most important, but difficult issues in hydrological modeling. A variety of unsaturated-saturated flow models have been developed during the last four decades. Generally these models can be divided into two categories:one based on Richards’equation, and the other based on water budget equation. Richards’equation is derived from the law of mass conservation and Darcy’s law. However, it is crucial to deal with the nonlinear relationships between pressure head, soil moisture and unsaturated hydraulic conductivity in vadose zone. For those models using head as primary variable, mass balance errors are introduced during the temporal discretization. Existing numerical models for solving Richards’equation often own poor stability, especially when the soil is subjected to alternate drying-wetting condition, which is often induced by atmospheric boundary condition. The divergence problem restricts the application of these numerical models. On the other hand, the water budget model is solely based the law of mass conservation, and the consumption and movement of water in the soil are turned into several hydrological processes. Each process is described by an independent conceptual model. However, there are a number of differences between the existing water budget models. It is urgent to make a complete summary and compare the merits and drawbacks of these models.Based on the previous work, the numerical models for different forms of Richards’ equation are derived and proposed in the paper. The stability, mass conservation, computational cost and scope of application for these models under different flow conditions are discussed thoroughly. Afterwards, the iterative models based on different forms of Richards’equation are converted to non-iterative counterparts. Compared to iterative models, non-iterative models own higher efficient and better numerical stability. On the other hand, the conceptual models for the hydrological processes in soil water balance models are summarized. The analytical solutions for soil water redistribution are derived here based on different soil hydraulic conductivity models. Finally, the developed numerical models for variably saturated flow are applied to three problems, i.e., coupled models for regional-scale groundwater modeling, characterization of soil hydraulic properties and evaluation of groundwater recharge. The detailed contents and conclusions are as follows: (1) The iterative models based on different forms of Richards’ equation are derived. The numerical performances of these models are compared. Mass balance error will be introduced when temporal discretization is conducted for head form Richards’ equation. The mixed form Richards’ equation can maintain mass balance given that the solution converges strictly for every time step. These former two models are prone to divergence when simulating infiltration into initially dry soil. Furthermore, the predicted wetting front will be inaccurate if coarse grid is used in the simulation. In the paper, an iterative model based on a modified moisture form Richards’ equation is proposed. This model can be used in heterogeneous soil, and it is inherently mass conservative. This model is preferred in the simulation of flow in dry soil, with regard to accuracy and computational cost. However, this model is restricted to purely unsaturated flow.(2) The non-iterative models can be obtained by linearizing nonlinear terms in the semi-discrete equation sets. Generally, the computational time for non-iterative models can be reduced by50%-75%compared to iterative models, and divergence problem can be avoided. The non-iterative model based on head form Richards’ equation is not capable to maintain global mass balance. The non-iterative model based on moisture form Richards equation inherits all the advantages when soil moisture is used as the primary variable. However, this non-iterative model cannot simulate partially saturated flow. By combining the linearization and the primary variable switching technique, a robust non-iterative model is obtained. This model owns high efficiency as well as excellent mass conservation. Moreover, it can be applied to all kinds of flow conditions.(3) The conceptual modules for the hydrological processes in soil are described. The analytical solutions for soil water redistribution are derived here based on different soil hydraulic conductivity models. Both advantages and disadvantages of soil water balance models are concluded via numerical experiments. Using the same flow conditions, the computational time can approximately be reduced by10times, with absolute stability and mass conservation. The existing soil water balance models does not directly consider the upward flow in soil, which can leads to significant bias for the redistribution of soil water. Furthermore, the oversimplified unsaturated hydraulic conductivity models can also lead to error in the simulation of soil water dynamic and deep percolation. Moreover, the calibrated model parameters vary with the flow conditions when observed data are not sufficient, since the soil water balance models are composed of conceptual modules.(4) By combining the established one-dimensional soil water flow models (i.e., those models based on Richards’ equation or soil water balance equation) and three-dimensional groundwater flow model, two coupled regional-scale groundwater flow models are developed. The simulation results from saturated flow model provide the groundwater table and the lateral flux, which are lower boundary condition and source term for the one-dimensional soil water flow model, respectively. On the other hand, the soil water flow model can provide the groundwater recharge or evaporation, which is essential input for the groundwater model. Using the coupling method described above, the two models can forward using different time step sizes, which can significantly save the computational cost. The coupled model which adopts soil water balance model is more efficient and stable.(5) The established model based on Richards’ equation for variably saturated flow is used in the inverse modeling and stochastic modeling. Using several soil moisture data from infiltration tests, the soil hydraulic parameters can be correctly identified. The a prior information can be used to eliminate the non-uniqueness of the inverted results. Monto Carlo method is adopted to evaluate the uncertainty of groundwater recharge due to the spatial variability of the soil hydraulic parameters. Generally, the computational costs can be reduced by2to10times when the established models are used in the inverse model and stochastic simulation. Moreover, the instability when using the traditional models are completely avoided.Finally, the innovative results in this doctoral thesis are listed, and several suggestions for future work are proposed.