Surface and subsurface flow systems are inherently unified systems that are often broken into sections for logical (e.g., time scales) and technical (e.g., analytical and computational solvability) reasons. While the basic physical laws are common to surface and subsurface systems, spatial and temporal dimensions as well as the continuum approach used for the subsurface lead to different formulations of the governing partial differential equations. While in most applications such decoupling of the systems works well and allows a very accurate and efficient description of the individual system by treating the adjacent system as a boundary condition, in the case of water flow over a porous medium, it does not. Therefore coupled models are in increasing use in this field, led mostly by watershed and surface irrigation modelers. The governing equations of each component of the coupled system and the coupling physics and mathematics are reviewed first. Three different coupling schemes are identified, namely the uncoupled (with the degenerated uncoupled scheme being a special case of the uncoupled), the iteratively coupled, and the fully coupled. Next, the different applications of the different coupling schemes, sorted by field of application, are reviewed. Finally, some research gaps are discussed, led by the need to include vertical momentum transfer and to expand the use of fully coupled models toward surface irrigation applications.

Modeling Coupled Surface-Subsurface Flow Processes: A Review

Depth averaged models are widely used in engineering practice in order to model environmental flows in river and coastal regions, as well as shallow flows in hydraulic structures This paper deals with depth averaged turbulence modelling The most important and widely used depth averaged turbulence models are reviewed and discussed, and a depth averaged algebraic stress model is presented A finite volume model for solving the depth averaged shallow water equations coupled with several turbulence models is described with special attention to the modelling of wet-dry fronts In order to asses the performance of the model, several flows are modelled and the numerical results are compared with experimental data

Depth Averaged Modelling of Turbulent Shallow Water Flow with Wet-Dry Fronts

A model is presented for the simulation of shallow water flow and, specifically, flood waves propagating on a dry bed. The governing equations are transformed to an equivalent system valid on a deforming coordinate system and are solved by a dissipative finite-element technique. A second-order difference scheme is employed for the integration in time. The implicit nonlinear equations resulting from the weak formulations are solved by the Newton-Raphson method, and the set of linear algebraic equations generated is solved by a frontal algorithm. A deforming grid generation scheme is introduced in the dissipative finite-element formulation to account for the effects of the propagating or receding wave fronts on dry land. The accuracy and stability of the model is examined by comparing the model results with observed data from an experimental field test. Results of trial runs for the simulation of overland flow are also presented.

Closure of "Model for Flood Propagation on Initially Dry Land"

In the rainfall-runoff process, interaction between surface and subsurface flow components plays an important role, especially in rainwater abstraction and overland flow initiation at the early stage of rainfall events. Coupling of surface and subsurface flow submodels, therefore, is necessary for advanced comprehensive and sophisticated rainfall-runoff simulation. This article presents a conjunctive two-dimensional (2D) surface and three-dimensional (3D) subsurface flow model, which uses the noninertia approximation of the Saint-Venant equations for 2D unsteady surface flow and a modified version of the Richards equation for 3D unsteady unsaturated and saturated subsurface flows. The equations are written in the form of 2D and 3D heat diffusion equations, respectively, and solved numerically. The surface and subsurface flow components are coupled interactively using the common boundary condition of infiltration through the ground surface. The conjunctive model is verified with Smith and Woolhiser’s exper...

Modeling of conjunctive two-dimensional surface-three-dimensional subsurface flows

Problems, Perspectives and Challenges of Agricultural Water Management

Overland flow of water over a porous bed in two spatial dimensions is governed by three partial differential equations accounting for continuity of momentum in the \ix- and \iy-directions and continuity of mass. A leapfrog explicit finite-difference numerical scheme was applied to solve this system of equations for the initial and boundary conditions that characterize level-basin irrigation. The numerical procedure is stable and robust for different applications, and can accommodate three different inflow configurations: line, corner, and fan. These configurations simulate inflow from an overflowing canal on a field boundary and at point sources from a corner or in the middle of a straight boundary, respectively. A numerical test was performed to assess the effect of grid fineness on the results of the simulation and on central-processing-unit time requirement. Data from two field tests were used to validate the model in quasi-one-dimensional and two-dimensional conditions.

/pdf/two-dimensional-simulation-of-basin-irrigation-i-theory-wgyb1tie5b.pdf

Two‐Dimensional Simulation of Basin Irrigation. I: Theory

The development of a two‐dimensional hydrodynamic simulation model of basin irrigation is reported in a companion paper. This article presents four applications of the model. Two hypothetical case studies are used to illustrate the ability of the model to accommodate multiple inflows and irregular field shapes including internal high spots. The model is applied to study the effect of field shape on irrigation performance. The particular case of a rectangular basin irrigated from a corner is considered. Results show that one‐dimensional models can underestimate the time of advance by up to 20%. Finally, the model is applied to explore the effects of spatially varied infiltration on irrigation performance. A series of infiltration observation points is used to estimate the infiltration rate in unmeasured locations. The model is used to simulate a hypothetical case study involving the design of a square level‐basin irrigation field with spatially varied infiltration irrigated from a corner. Results show that...

/pdf/two-dimensional-simulation-of-basin-irrigation-ii-4pp60w1woi.pdf

Two‐dimensional simulation of basin irrigation. II: Applications

Discussion and Closure: Two-Dimensional Simulation of Basin Irrigation. I: Theory

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Two‐Dimensional Simulation of Basin Irrigation. I: Theory

Two‐dimensional simulation of basin irrigation. II: Applications

Discussion and Closure: Two-Dimensional Simulation of Basin Irrigation. I: Theory