Stream Temperature Dynamics in Upland Agricultural Watersheds

A numerical model to compute the free-surface flow hydrodynamics and stream temperature dynamics by solving the depth-averaged, 1D unsteady flow and heat transport equations is presented. The hydrodynamics model considers the effects of arbitrary stream geometry, variable slopes, variable flow regimes, and unsteady boundary conditions. The thermal transport model accounts for the effects of solar radiation, air temperature, relative humidity, cloud cover, wind speed, heat conduction between water and streambed, subsurface flow, and shading by riparian vegetation. The model is verified with measurements in a stream in an upland agricultural watershed located in Indiana. Diurnal variations in the streamflow and stream temperatures are highly transient. The proposed model predicted well the streamflow and stream temperatures that were measured every 15 min over 25 days. The results of this study demonstrate that the solar (shortwave) radiation and subsurface inflow are the most significant contributors to the stream heat budget.     

Numerical Model for Channel Flow and Morphological Change Studies

In this paper a depth-integrated 2D hydrodynamic and sediment transport model, CCHE2D, is presented. It can be used to study steady and unsteady free surface flow, sediment transport, and morphological processes in natural rivers. The efficient element method is applied to discretize the governing equations, and the time marching technique is used for temporal variations. The moving boundaries were treated by locating the wet and dry nodes automatically in the cases of simulating unsteady flows with changing free surface elevation in channels with irregular bed and bank topography. Two eddy viscosity models, a depth-averaged parabolic model and a depth-averaged mixing length model, are used as turbulent closures. Channel morphological changes are computed with considerations of the effects of bed slope and the secondary flow in curved channels. Physical model data have been used to verify this model with satisfactory results. The feasibility studies of simulating morphological formation in meandering channels and flows in natural streams with in-stream structures have been conducted to demonstrate its applicability to hydraulic engineering research∕design studies of stream stabilization and ecological quality among other problems.     

3D Numerical Modeling of Flow and Sediment Transport in Open Channels

A 3D numerical model for calculating flow and sediment transport in open channels is presented. The flow is calculated by solving the full Reynolds-averaged Navier-Stokes equations with the k ? ε turbulence model. Special free-surface and roughness treatments are introduced for open-channel flow; in particular the water level is determined from a 2D Poisson equation derived from 2D depth-averaged momentum equations. Suspended-load transport is simulated through the general convection-diffusion equation with an empirical settling-velocity term. This equation and the flow equations are solved numerically with a finite-volume method on an adaptive, nonstaggered grid. Bed-load transport is simulated with a nonequilibrium method and the bed deformation is obtained from an overall mass-balance equation. The suspended-load model is tested for channel flow situations with net entrainment from a loose bed and with net deposition, and the full 3D total-load model is validated by calculating the flow and sediment transport in a 180° channel bend with movable bed. In all cases, the agreement with measurements is generally good.     

Case Study: Two-Dimensional Model Simulation of Channel Migration Processes in West Jordan River, Utah

The paper presents the application of a two-dimensional depth-averaged numerical model to simulate the lateral migration processes of a meandering reach in the West Jordan River in the state of Utah. A new bank erosion model was developed and then integrated with a depth-averaged two-dimensional hydrodynamic model. The rate of bank erosion is determined by bed degradation, lateral erosion, and bank failure. Because bank material in the West Jordan River is stratified with layers of cohesive and noncohesive materials, a specific bank erosion model was developed to consider stratified layers in the bank surface. This bank erosion model distinguishes itself from other models by relating bank erosion rate with not only flow but also sediment transport near the bank. Additionally, bank height, slope, and thickness of two layers in the bank surface were considered when calculating the rate of bank erosion. The developed model was then applied to simulate the processes of meandering migration in the study reach from 1981 to 1992. Historical real-time hydrographic data, as well as field survey data of channel geometry and bed and bank materials, were used as the input data. Simulated cross-sectional geometries after this 12-year period agreed with field measurements, and the R2 value for predicting thalweg elevation and bank shift are 0.881 and 0.706, respectively.     

Depth-Averaged Two-Dimensional Numerical Modeling of Unsteady Flow and Nonuniform Sediment Transport in Open Channels

A depth-averaged two-dimensional (2D) numerical model for unsteady flow and nonuniform sediment transport in open channels is established using the finite volume method on a nonstaggered, curvilinear grid. The 2D shallow water equations are solved by the SIMPLE(C) algorithms with the Rhie and Chow’s momentum interpolation technique. The proposed sediment transport model adopts a nonequilibrium approach for nonuniform total-load sediment transport. The bed load and suspended load are calculated separately or jointly according to sediment transport mode. The sediment transport capacity is determined by four formulas which are capable of accounting for the hiding and exposure effects among different size classes. An empirical formula is proposed to consider the effects of the gravity on the sediment transport capacity and the bed-load movement direction in channels with steep slopes. Flow and sediment transport are simulated in a decoupled manner, but the sediment module adopts a coupling procedure for the computations of sediment transport, bed change, and bed material sorting. The model has been tested against several experimental and field cases, showing good agreement between the simulated results and measured data.     

Modeling of Conjunctive Two-Dimensional Surface-Three-Dimensional Subsurface Flows

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 experimental data (reported in 1971) of initially dry and initially wet soil. Subsequently the model is applied to a hypothetical soil plot of clay or sand to simulate the overland flow, infiltration, and subsurface flow for four different rainfalls. The conjunctive model contributes as a tool for improved detailed simulation of 2D surface and 3D subsurface flows and their interaction.     

Modeling Sediment Transport Using Depth-Averaged and Moment Equations

A 1D mathematical model to calculate bed variations in alluvial channels is presented. The model is based on the depth-averaged and moment equations for unsteady flow and sediment transport in open channels. Particularly, the moment equation for suspended sediment transport is originally derived by the assumption of a simple vertical distribution for suspended sediment concentration. By introducing sediment-carrying capacity, suspended sediment concentration can be solved directly from sediment transport and its moment equations. Differential equations are then solved by using the control-volume formulation, which has been proven to have good convergence. Numerical experiments are performed to test the sensitivity of the calibrated coefficients α and k in the modeling of the bed deposition and erosion. Finally, the computed results are compared with available experimental data obtained in laboratory flumes. Comparisons of this model with HEC-6 and other numerical models are also presented. Good agreement is found in the comparisons.     

Numerical Simulation of Longitudinal and Lateral Channel Deformations in the Braided Reach of the Lower Yellow River

Bank erosion frequently occurs in the Lower Yellow River (LYR), playing an important role in the evolution of this braided river. A two-dimensional (2D) composite model is developed herein that consists of a depth-averaged 2D flow and sediment transport submodel and a bank-erosion submodel. The model incorporates a new technique for updating bank geometry during either degradational or aggradational bed evolution, allowing the two submodels to be closely combined. Using the model, the fluvial processes in the braided reach of the LYR between Huayuankou and Laitongzhai are simulated, and the calculated results generally agree with the field measurements, including the water-surface elevation, variation of water-surface width, and variations of cross-sectional profiles. The calculated average water-surface elevation in the study reach was 0.09?m greater than the observed initial value, and the calculated mean bed elevation for six cross sections was 0.11?m lower than the observed value after 24 days. These errors are attributed to the large variability of flow and sediment transport processes. Sensitivity tests of three groups of parameters are conducted, and these groups of parameters are related to flow and sediment transport, bank erosion, and model application, respectively. Analysis results of parameter sensitivity tests indicate that bank erodibility coefficient and critical shear stress for bank material are sensitive to the simulated bank erosion process. The lateral erosion distance at Huayuankou will increase by 19% as the value of bank erodibility coefficient changes from 0.1 to 0.3, and it will decrease by 57% as the value of critical shear stress for bank increases from 0.6 to 1.2?N/m2. Limited changes of other parameters have relatively small effects on the simulated results for this reach, and the maximum change extent of calculated results is less than 5%. Because the process of sediment transport and bank erosion in the braided reach of the LYR is very complicated, further study is needed to verify the model.     

Two-Dimensional Nonequilibrium Noncohesive and Cohesive Sediment Transport Model

The purpose of this paper is to develop an unsteady 2D depth-averaged model for nonuniform sediment transport in alluvial channels. In this model, the orthogonal curvilinear coordinate system is adopted; the transport mechanisms of cohesive and noncohesive sediment are both embedded; the suspended load and bed load are treated separately. In addition, the processes of hydraulic sorting, armoring, and bed consolidation are also included in the model. The implicit two-step split-operator approach is used to solve the flow governing equations and the coupling approach with iterative method are used to solve the mass-conservation equation of suspended sediment, mass-conservation equation of active-layer sediment, and global mass-conservation equation for bed sediment simultaneously. Three sets of data, including suspension transport, degradation and aggradation cases for noncohesive sediment, and aggradation, degradation, and consolidation cases for cohesive sediment, have been demonstrated to show the rationality and accuracy of the model. Finally, the model is applied to evaluate the desilting efficiency for Ah Gong Diann Reservoir located in Taiwan to show its applicability.     

Simulation of Flow and Mass Dispersion in Meandering Channels

This paper reports the development of an enhanced two-dimensional (2D) numerical model for the simulation of flow hydrodynamics and mass transport in meandering channels. The hydrodynamic model is based on the solution of the depth-averaged flow continuity and momentum equations where the density of flow varies with the concentration of transported mass. The governing equation for mass transport model is the depth-averaged convection and diffusion equation. The dispersion terms arisen from the integration of the product of the discrepancy between the mean and the actual vertical velocity distribution were included in the momentum equations to take into account the effect of secondary current. Two laboratory experimental cases, flow in mildly and sharply curved channels, were selected to test the hydrodynamic model. The comparison of the simulated velocity and water surface elevation with the measurements indicated that the inclusion of the dispersion terms has improved the simulation results. A laboratory experiment study of dye spreading in a sine-generated channel, in which dye was released at the inner bank, centerline, and outer bank, respectively, was chosen to verify the mass transport model. The simulated concentration field indicated that the Schmidt number can be used as a calibration parameter when dispersion is computed using a 2D approach with a simplified turbulence model.     

Flow Structure at Different Stages in a Meander-Bend with Bendway Weirs

Streambank erosion is an important management issue, particularly for meandering rivers. Recently, bendway weirs have become popular control measures for bank erosion along small meandering streams in the agricultural Midwest. Although these structures have successfully mitigated bank erosion in some cases, there is evidence that the weirs do not always perform as anticipated. Scientific understanding of how bendway weirs influence flow dynamics, streambank erosion, and aquatic habitat is limited. Current design criteria are based primarily on expert judgment rather than a formalized technical design procedure. At field-scale studies, the present paper represents a first step toward an integrated geomorphological and engineering evaluation of the performance of bendway weirs in rivers. To accomplish this initial phase, three-dimensional (3D) velocity data were collected on Sugar Creek at Brookside Farm, Ill., and 3D numerical simulations for low-flow conditions were performed to validate the computational fluid dynamic model. Overall results show good agreement between measured and simulated data for streamwise velocities and turbulence kinetic energy. The model is less accurate at predicting the velocity and turbulence kinetic energy in the shear layer immediately downstream from the weir tips. Based on the validation for low-flow condition, 3D simulations were carried out for medium and high flows where the bendway weirs are completely submerged. These simulations indicate that 3D patterns of flow, especially flow near the outer bank, change dramatically with changes in flow stage. Flow patterns at high-flow condition indicate that bank retreat over the tops of weirs is associated with locally high-shear stresses, thus producing a “shelf” along the base of the outer bank as observed in the field.     

Sediment and Metals Modeling in Shallow River

It is a challenge to apply coupled hydrodynamic, sediment process, and contaminant fate and transport models to the studies of surface water systems. So far, there are few published modeling studies on sediment and metal transport in rivers that simulate storm events on an hourly basis and use comprehensive data sets for model input and model calibration. The United States Environmental Protection Agency (USEPA) in 1997 emphasized the need for credible modeling tools that can be used to quantitatively evaluate the impacts of point sources, nonpoint sources, and internal transport processes in 1D/2D/3D environments. A 1D and time-dependent hydrodynamic, sediment, and toxic model, within the framework of the 3D Environmental Fluid Dynamics Code (EFDC), has been developed and applied to Blackstone River, Mass. The Blackstone River Initiative (USEPA) in 1996, a multiyear and multimillion-dollar project, provided the most comprehensive surveys on water quality, sediment, and heavy metals in the river, and served as the primary data set for this study. The model simulates three storm events successfully. The river flow rates are well calculated both in amplitude and in phase. The sediment transport and resuspension processes are depicted satisfactorily. The concentrations of sediment and five metals (cadmium, chromium, copper, nickel, and lead) during the three storm events are also simulated very well. Numerical analyses are conducted to clarify the impacts of contaminant sources and sediment resuspension processes on the river. While point sources are important to sediment contamination in the river, other sources, including nonpoint sources from watershed and bed resuspension, were found to contribute significantly to the sediment and metals in the river. Point sources alone cannot account for the total metals in the river. The model presented in this paper can be a useful tool for studying sediment and metals transport in shallow rivers and for water resource management.     

Efficient Solution of the Coupled One-Dimensional Surface—Two-Dimensional Subsurface Flow during Furrow Irrigation Advance

Physically based modeling of the coupled one-dimensional surface and two-dimensional (2D) subsurface flow during furrow irrigation advance often causes numerical instabilities and nonconvergence problems. This is particularly the case for low irrigation advance rates when infiltration consumes a predominant part of the inflow volume. The proposed furrow advance phase model (FAPS) further develops the concepts of a previous study. An analytical zero-inertia surface flow model is iteratively coupled with the 2D subsurface water transport model HYDRUS-2. In contrast to the previous study, the flow domain is discretized using fixed space increments and the resulting set of nonlinear flow equations is solved using the Newton method. The complexity of the model was reduced by process adequate simplifications. FAPS exhibited better convergence, numerical stability, and less computational time than the original fixed time interval solution. The new solution converged rapidly for a number of model tests with various inflow rates including runs with very slow irrigation advance. Simulation model predictions agree very well with advance times measured in laboratory and field tests.     

Physically Based Modeling of Interacting Surface–Subsurface Flow During Furrow Irrigation Advance

Surface–subsurface flow during furrow irrigation is analyzed employing both a laboratory experiment and a surface–subsurface flow model. The proposed model overcomes the restrictions of traditional furrow irrigation models by rigorously describing the subsurface flow at computational nodes using the physically based two-dimensional (2D) model Hydrus-2D. Surface flow is portrayed by an analytical zero-inertia model. In order to couple both models efficiently, an iterative procedure was developed. Using a sensitivity analysis we investigated the space interval separating 2D infiltration computations. This variable showed little effect on model performance, thus permitting the selection of rather generous distances. Due to the similarity of the hydrographs at neighboring cross sections we investigated transferring the results of Hydrus-2D computations to the next downstream location. This was performed by interpolating cumulative infiltration using infiltration opportunity times. This procedure uncovered other dependencies, making the interpolation strategy unattractive. To validate the coupled surface–subsurface model, an irrigation furrow was set up in a 26.4 m long, 0.88 m wide, and 1.0 m deep tank, filled with 50 t of sandy loam soil and equipped with surface and subsurface measurement devices. Although the model results compared favorably with the observed data, the study also showed an important impact of surface cracking and preferential flow during the irrigation experiments.     

Depth-Averaged Model of Open-Channel Flows over an Arbitrary 3D Surface and Its Applications to Analysis of Water Surface Profile

A new set of depth-averaged equations is introduced to study the flow over an arbitrary three-dimensional (3D) surface. These equations are derived based on a generalized curvilinear coordinate system attached to the 3D bed surface, therefore it allows us to include the effect of centrifugal force due to the bottom curvature. These general equations make it possible to analyze flows over complex terrain without the limitation of mild slope assumption used in conventional depth-averaged models. This new model is then applied to calculate the water surface profiles of (1) flow over a cylindrical surface; (2) flow over a circular surface; and (3) flow with an air-core vortex at a vertical intake. A simple hydraulic experiment is conducted in the laboratory to observe the water surface profile of flow over a circular surface. The results obtained from the model are in good agreement with experimental measurements and calculation by an empirical formula. Consequently, it demonstrates the applicability of the model in cases of flow over a highly curved bottom.     

Role of Artificial Dissipation Scaling and Multigrid Acceleration in Numerical Solutions of the Depth-Averaged Free-Surface Flow Equations

A numerical model is developed for solving the depth-averaged, open-channel flow equations in generalized curvilinear coordinates. The equations are discretized in space in strong conservation form using a space-centered, second-order accurate finite-volume method. A nonlinear blend of first- and third-order accurate artificial dissipation terms is introduced into the discrete equations to accurately model all flow regimes. Scalar- and matrix-valued scaling of the artificial dissipation terms are considered and their effect on the accuracy of the solutions is evaluated. The discrete equations are integrated in time using a four-stage explicit Runge–Kutta method. For the steady-state computations, local time stepping, implicit residual smoothing, and multigrid acceleration are used to enhance the efficiency of the scheme. The numerical model is validated by applying it to calculate steady and unsteady open-channel flows. Extensive grid sensitivity studies are carried out and the potential of multigrid acceleration for steady depth-averaged computations is demonstrated.     

Coupled Surface–Subsurface Solute Transport Model for Irrigation Borders and Basins. I. Model Development

Surface fertigation is widely practiced in irrigated crop production systems. Lack of design and management tools limits the effectiveness of surface fertigation practices. The availability of a process-based coupled surface–subsurface hydraulic and solute transport model can lead to improved surface fertigation management. This paper presents the development of a coupled surface–subsurface solute transport model. A hydraulic model described in a previous paper by the writers provided the hydrodynamic basis for the solute transport model presented here. A numerical solution of the area averaged advection–dispersion equation, based on the split-operator approach, forms the surface solute transport component of the coupled model. The subsurface transport process is simulated using HYDRUS-1D, which also solves the one-dimensional advection–dispersion equation. A driver program is used for the internal coupling of the surface and subsurface transport models. Solute fluxes calculated using the surface transport model are used as upper boundary conditions for the subsurface model. Evaluation of the model is presented in a companion paper.     

Flow Velocity and Pier Scour Prediction in a Compound Channel: Big Sioux River Bridge at Flandreau, South Dakota

The two-dimensional (2D) depth-averaged river model Finite-Element Surface-Water Modeling System (FESWMS) was used to predict flow distribution at the bend of a compound channel. The site studied was the Highway 13 bridge over the Big Sioux River in Flandreau, South Dakota. The Flandreau site has complex channel and floodplain geometry that produces unique flow conditions at the bridge crossing. The 2D model was calibrated using flow measurements obtained during two floods in 1993. The calibrated model was used to examine the hydraulic and geomorphic factors that affect the main channel and floodplain flows and the flow interactions between the two portions. A one-dimensional (1D) flow model of the bridge site was also created in Hydrologic Engineering Centers River Analysis System (HEC-RAS) for comparison. Soil samples were collected from the bridge site and tested in an erosion function apparatus (EFA) to determine the critical shear stress and erosion rate constant. The results of EFA testing and 2D flow modeling were used as inputs to the Scour Rate in Cohesive Soils (SRICOS) method to predict local scour at the northern and southernmost piers. The sensitivity of predicted scour depth to the hydraulic and soil parameters was examined. The predicted scour depth was very sensitive to the approach-flow velocity and critical shear stress. Overall, this study has provided a better understanding of 2D flow effects in compound channels and an overall assessment of the SRICOS method for prediction of bridge pier scour.