Sensitivity Analysis and Predictive Uncertainty Using Inundation Observations for Parameter Estimation in Open-Channel Inverse Problem

The necessity of an improvement of flood risk management has been emphasized by the importance of the damages caused by several disastrous floods in recent years. An obligatory way to better understand and forecast these events is to be able to accurately simulate the water transport in the river. Some parameters embedded in open-channel flow equations are difficult to calibrate in practice and hydraulic models are currently constrained by lack of data. The objective of this study is to test the potential of data typical of remote sensing imagery which may be used together with data assimilation methods to ascertain the value of a set of open-channel model parameters. Indeed, for the modeling of ungauged rivers, it may be necessary to estimate open-channel flow and/or morphological characteristics of the river. The innovation of the proposed methodology is to reconstitute information about the geometry of the river from top sight. A sensitivity analysis using the generalized sensitivity analysis method is carried out, together with an estimation of predictive uncertainty using the generalized likelihood uncertainty estimation, a methodology for calibration and uncertainty estimation of distributed models introduced by Beven and Binley (1992). The study aims at building a framework for parameter optimization in the case of ungauged rivers. The proposed method has been implemented on a reach of the Lèze River, located in the southwest of France.     

Regime Equations for Natural Meandering Cobble- and Gravel-Bed Rivers

Data obtained from 48 stable reaches of upland rivers in the UK were stratified by stream type to develop regime equations specifically for natural meandering cobble- and gravel-bed rivers: C3 and C4 stream types, according to the Rosgen classification. Multiple regression models were applied to derive equations for reach-averaged values of bankfull width, mean depth, slope, meander arc length and sinuosity in bankfull discharge and associated bed-material load, the caliber of the bed material, bank vegetation density, and valley slope. The equations show that their cross-sectional dimensions are primarily determined by the bankfull discharge, bank vegetation, and bed-material size, whereas their profile and plan form are very strongly influenced by the valley gradient. Although bankfull bed-material load only appears to have a minor influence on channel morphology, its effect is implicit in the value of bankfull discharge because this corresponds to the flow that transports most of the bed-material load. Explanations are given for these results on the basis of processes affecting channel geometry. Comparisons with the regime equations derived more than 20?years ago by Hey and Thorne from the same UK data set indicate that stratification by stream type generates equations that are more consistent; for example, bank vegetation affects all aspects of channel morphology rather than simply channel width, and provides significantly better explanations for channel slope and sinuosity because of the inclusion of valley slope as an independent variable. Their potential for designing river restoration schemes is evaluated against North American data. The equations prove to be comparable to the Hey and Thorne equations for predicting width and depth, but provide a significant improvement for the determination of slope and sinuosity. Although bed-material load was shown, statistically, to influence channel dimensions, numerically its influence is trivial. Removing it from the analysis generates equations that provide the best practical point estimates of channel morphology. Predictions with the simplified regime equations are shown to be comparable to the full equations.     

Coupling Bank Stability and Bed Deformation Models to Predict Equilibrium Bed Topography in River Bends

Attempts to include river bank erosion predictors within morphological models are becoming increasingly common, but uncertainty surrounds the procedures used to couple bed deformation and bank erosion submodels in a way that maintains the mass continuity of eroded bank sediment. Herein we present a coupling procedure that comprises two discrete elements. First, immediately following bank failure, the slumped debris comes to rest at the bank toe as a planar surface inclined at an “angle of repose.” Second, we use a fractional transport model to simulate the subsequent erosion and deposition of the failed bank material debris. The method is demonstrated with an example in which an equilibrium bed topography model is combined with a river bank erosion model to predict the morphological response of a river bend to a large flow event.     

Simplified Model for Assessing Meander Bend Migration Rates

This paper describes a simple analytical model for assessing meander bend migration rates. The new model is innovative in that it can be applied directly using output data from one-dimensional hydraulic models. The method is designed as a first approximation that can be applied rapidly to large reaches of river systems, and should not be considered as a replacement for more detailed bank stability assessments. The model is based on a conversion factor for one-dimensional shear stress. Comparison of the conversion factor with existing data sets is presented. Converted shear stresses are translated to bank erosion volumes, which in turn are related to meander bend migration rates, using bank geometry and an appropriate sediment transport law. Results are presented for an evaluation of meander bend migration rates for a restoration feasibility study for a project on the Williamson River, Oregon.     

Soft Bedrock Erosion Modeling with a Two-Dimensional Depth-Averaged Model

Many rivers in Taiwan have steep slopes, are subject to typhoon-induced flood flows, and contain soft bedrock that is exposed at many locations and easily erodible. The occurrence of extensive bedrock erosion has been a major threat to river infrastructure at many locations. Soft bedrock erosion, therefore, is an important process to consider for river projects in Taiwan. In this study, bedrock erosion models are reviewed. A specific model is proposed by combining two existing models incorporating both the hydraulic and abrasive scour mechanisms. The proposed bedrock erosion model is incorporated into a two-dimensional mobile-bed model, and the integrated model is tested by simulating bedrock erosion downstream of the Chi-Chi weir on the Choshui River in Taiwan. A calibration study is performed to determine appropriate values of the model parameters based on two and a half years of measured data. The model is then assessed based on a verification study that compares model predictions of bedrock erosion of the same reach to two additional years of measured data. The bedrock erosion model is found to be suitable for the river reach studied. Further improvement, however, is still necessary, which points to potential future research.     

淮河流域水文随机方法的径流图化

Theoretical difficulties for mapping and for estimating river regime characteristics in a large-scale basin remain because of the nature of the variable under study:river flows are related to a specific area, I.e. The drainage basin, and are hierarchically organized in space through the river network with upstream-downstream dependencies. Another limitation is there are not enough gauge stations in developing countries. This presentation aims at de-veloping the hydro-stochastic approach for producing choropleth maps of average annual runoff and computing mean discharge along the main river network for a large-scale basin.The approach applied to mean annual runoff is based on geostatistical interpolation proce-dures coupled with water balance and data uncertainty analyses. It is proved by an applica-tion in the upstream at Bengbu in the Huaihe River Basin, a typical large-scale basin in China.Hydro-stochasitic approach in a first step interpolates to a regular grid net and in a second step the grid values are integrated along rivers. The interpolation scheme includes a con-straint to be able to account for the lateral water balance along the rivers. Grid runoff map with 10 km x 10 km resolution and the discharge map along the river with the 1 km basic length unit are the main results in this study. This kind of statistic approach can be widely used be-cause it avoids the complexity of hydrological models and does not depend on the meteoro-logical data.     

Analytical Approach to Calculate Rate of Bank Erosion

Bank erosion consists of two processes: basal erosion due to fluvial hydraulic force and bank failure under the influence of gravity. Because bank resistance force varies with the degree of saturation of bank material, the probability of bank failure is the probability of the driving force of bank failure being greater than the bank resistance force. The degree of saturation of bank material increases with river stage; therefore, the frequency of bank failure is correlated to the frequency of flooding. Consequently, the rate of bank erosion is due to both basal erosion and bank failure, and bank failure is a probabilistic phenomenon. In this paper, for cohesive bank material experiencing planar bank failure, a deterministic approach was adopted for basal erosion analysis, whereas the probability of bank failure was included in the analysis of bank failure. A method for calculating the rate of bank erosion was derived that integrates both basal erosion and bank failure processes, and accounts for the effects of hydraulic force, bank geometry, bank material properties, and probability of bank failure.     

Procedure to Calibrate and Verify Numerical Models of Estuarine Hydrodynamics

In most hydrodynamic models, friction and turbulent diffusion∕dispersion coefficients are the important calibration parameters affecting the calculation of surface elevation, velocity and salinity distribution. This paper presents a rational approach to calibrate and verify a hydrodynamic model of partially stratified estuaries. The calibration procedures and verification requirements are demonstrated with the application of a vertical (laterally averaged) two-dimensional model to a branched estuarine river system. The friction coefficient is calibrated and verified with model simulation of barotropic flow, and the turbulent diffusion and dispersion coefficients are calibrated through comparison of salinity distributions. The overall model verification is suggested to be achieved with comparisons of Eulerian residual circulation and salinity distribution. In the case of the Tanshui River system, the available prototype current records are too short to calculate slowly varying residual currents. The snapshots of the model-computed and field-measured residual currents are provided to qualitatively agree with theoretical analysis. The overall performance of the model is verified with an additional set of salinity data.     

Role of Resistance Coefficient in Seasonal Adjustments in Alluvial Rivers

Using the river, canal, and flume data, it is found that the role played by the seasonal variation in the Manning rugosity coefficient, n, equalizes the sediment transporting capacity with sediment supply in the dune bed-form regime. Aggradation/degradation in a sand-bed river is thus avoided on a seasonal basis. A relation between the dimensionless rugosity coefficient and the dimensionless ratio of stream power to sediment concentration exists in sand-bed rivers for any specific gauge height. Once field measurements of the sediment transport rate are made and such a relationship is worked out, thereafter, it may be possible to estimate the sediment concentration for each observed flow discharge merely by applying this relationship adopting the data of velocity, depth, slope, and bed material size which are routinely observed at a stream-gauging site.     

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.     

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.     

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.     

Reduction of Bend Scour by an Outer Bank Footing: Flow Field and Turbulence

River bank protection is a costly but essential component in river management. Outer banks in river bends are most vulnerable to scour and erosion. Previous laboratory experiments illustrated that a well-designed horizontal foundation of a vertical outer bank protruding into the cross section, called a footing, can reduce the scour depth and thereby protect the bank. This paper provides detailed experimental data in a reference experiment without footing and an experiment with footing carried out under similar hydraulic conditions, which suggest a delicate interaction between bed topography, downstream and cross-stream velocity, and to lesser extent turbulence. The presence of the outer bank footing modifies this delicate interaction and results in a more favorable configuration with respect to bank stability including: reduced maximum scour depth, more uniformly distributed downstream velocity, and weaker cross-stream circulation cells.     

Coupled and Decoupled Numerical Modeling of Flow and Morphological Evolution in Alluvial Rivers

Existing numerical river models are mostly built upon asynchronous solution of simplified governing equations. The strong coupling between water flow, sediment transport, and morphological evolution is thus ignored to a certain extent. An earlier study led to the development of a fully coupled model and identified the impacts of simplifications in the water-sediment mixture and global bed material continuity equations as well as of the asynchronous solution procedure for aggradation processes. This paper presents the results of an extended study along this line, highlighting the impacts on both aggradation and degradation processes. Simplifications in the continuity equations for the water-sediment mixture and bed material are found to have negligible effects on degradation. This is, however, in contrast to aggradation processes, in which the errors purely due to simplified continuity equations can be significant transiently. The asynchronous solution procedure is found to entail appreciable inaccuracy for both aggradation and degradation processes. Further, the asynchronous solution procedure can render the physical problem mathematically ill posed by invoking an extra upstream boundary condition in the supercritical flow regime. Finally, the impacts of simplified continuity equations and an asynchronous solution procedure are shown to be comparable with those of largely tuned friction factors, indicating their significance in calibrating numerical river models. It is concluded that the coupled system of complete governing equations needs to be synchronously solved for refined modeling of alluvial rivers.     

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.     

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.     

Oxygen Sag Models for Multiorder Biochemical Oxygen Demand Reactions

The empirical biochemical oxygen demand (BOD) equation is expressed as a multiorder reaction equation of order n, then is combined with the dissolved oxygen mass balance equation to give the differential form of an oxygen sag equation for small rivers and streams for which dispersion can be neglected. The value of n in the BOD reaction is restricted to values that are larger than one (first order). The dissolved oxygen sag equation is verified with two published dissolved oxygen sag models by setting n equal to 3/2 (three-halves order BOD reaction), and n equal to 2 (second order BOD reaction). The proposed dissolved oxygen sag equation may be applied to test the BOD and dissolved oxygen models in large, complex numerical models, such as models used in developing total maximum daily load recommendations. Examples show how the BOD reaction order affects the dissolved oxygen sag characteristics of a river.     

Case Study: River Training and Its Effects on Fluvial Processes in the Lower Yellow River, China

More than 50?years’ river training practices in the Lower Yellow River provide valuable experience in river management for flood control in rivers having rapid flow changes, silting beds, and active channel migrations and are of importance in understanding the fluvial processes in regulated rivers with high sediment loads. Planned channel alignments for river training in the Lower Yellow River usually consist of a series of consecutive moderate bends representing the natural tendency of flows. Flow guide works, namely spur dikes, were constructed on the concave banks of the planned bends to protect the channel against scouring and migration by deflecting the current away from bends and further guiding the main flow from one bend to the next one. As a result, well-planned flow guide works can play a crucial role in limiting channel shifting and migration and in establishing a relatively stable channel. Enough flow guide works, on both sides together reaching about 80% of the channel length, may change the transitional and braided channel patterns to a confined meandering pattern.     

Dispersion in Varying-Geometry Rivers with Application to Methanol Releases

Most analyses of turbulent mixing in rivers assume constant hydraulic geometry (width, depth, and velocity), despite the fact that in natural rivers these variables typically increase downstream. A comprehensive set of data for the rivers and streams in the United States is used to derive generalized equations for variations in hydraulic geometry. As a preliminary investigation of the importance of these variations, an approximate analytical solution to the one-dimensional advective-dispersion equation is derived for rivers with variable velocity, cross-sectional area, and dispersion coefficient. The solution compares well with previous analyses, and is used to assess the potential environmental impacts of methanol releases into a hypothetical river. The resulting downstream concentrations of methanol are considerably lower than those calculated assuming constant hydraulic geometry.