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.     

Downstream Hydraulic Geometry of Clay-Dominated Cohesive Bed Rivers

Empirical downstream hydraulic geometry equations for consolidated clay-dominated cohesive bed (nonalluvial) natural streams are presented using data from six rivers in eastern Ontario, Canada and four rivers from other regions. The width exponent (0.57) was comparable to the exponents reported for previous studies; however, the depth exponent (0.52) was greater for clay-dominated cohesive bed than for typical alluvial gravel-bed and sand-bed rivers. The width to depth ratio of smaller channels (Qbf<20?m3/s) was greater for consolidated clay bed than for either sand-bed or gravel-bed channels. This study suggests that the concept of hydraulic geometry and bankfull (channel forming) discharge can be extended to nonalluvial consolidated clay-bed channels.     

USGS Streamflow Data and Modeling Sand-Bed Rivers

United States Geological Survey streamflow data are commonly used for hydraulic model calibration and boundary conditions. The transitory nature of sand-bed rivers’ bathymetry is problematic for the traditional automated stream gauging methods used by the USGS. This note seeks to assess the limitations of streamflow measurements for use in hydraulic models. An overview of USGS rating-curve development and use is presented with a focus on the specific challenges of sand-bed rivers. Measurements from three consecutive USGS gauges for a storm event on the Rio Grande in Albuquerque, New Mexico, illustrate the outlined problems with rating curves. These gauges are utilized to study the impact of uncertainty in rating-curve discharges on hydraulic model results. A one dimensional hydraulic model of the study reach indicates up to 25% reduction in the calculated flow depth if questionable rating-curve discharges are used as model input. Recommendations for using USGS streamflow data in hydraulic models are outlined.     

Hydraulic and Sedimentological Characterizations of a Reach on the Anaktuvuk River, Alaska

Rivers located on the North Slope of Alaska’s Brooks Range are typically not well characterized with respect to basic hydraulic and sedimentological data. In order to obtain basic hydrosedimentological information on the Anaktuvuk River, a pristine stream located in the Colville River basin, we conducted an extensive field campaign from late May to early June 2009. The study reach was located at N69°27.785′, W151°09.858′, latitude and longitude, respectively. The Anaktuvuk River flows north from the Brooks Range to the Colville River, drains an area of 7,058?km2, and encompasses 2,063 m of vertical relief. During the field campaign, the field crew measured discharge and water-surface slope, collected water samples, and characterized bed sediment. As a result of fieldwork and laboratory work, we present an initial rating curve for the Anaktuvuk River, as well as the calculated roughness coefficient and suspended sediment concentrations. In addition, we compare the observed bankfull discharges with the bankfull discharge predicted by a recently published model.     

Unobstructed and Obstructed Turbulent Flow in Gravel Bed Rivers

An acoustic Doppler velocimeter was used to characterize turbulence in two gravel bed rivers. Data were collected in unobstructed flow and compared to recent investigations. Additional data collected in the wake of emergent boulders indicate that mean flow velocity, turbulent kinetic energy, gradients in the streamwise velocity, and Reynolds stress downstream from large rocks deviate from unobstructed flow results, but similar turbulence patterns are found behind each boulder. Results of this study are discussed with regard to natural channel design and fish habitat.     

Flow Resistance and Suspended Load in Sand-Bed Rivers: Simplified Stratification Model

New methods are presented for the prediction of the flow depth, grain-size specific near-bed concentration, and bed-material suspended sediment transport rate in sand-bed rivers. The salient improvements delineated here all relate to the need to modify existing formulations in order to encompass the full range of sand-bed rivers, and in particular large, low-slope sand-bed rivers. They can be summarized as follows: (1) the inclusion of density stratification effects in a simplified manner, which have been shown in the companion paper to be particularly relevant for large, low-slope, sand-bed rivers; (2) a new predictor for near-bed entrainment rate into suspension which extends a previous relation to the range of large, low-slope sand-bed rivers; and (3) a new predictor for form drag which again extends a previous relation to include large, low-slope sand-bed rivers. Finally, every attempt has been made to cast the relations in the simplest form possible, including the development of software, so that practicing engineers may easily use the methods.     

Downstream Hydraulic Geometry of Alluvial Channels

This study extends the earlier contribution of Julien and Wargadalam in 1995. A larger database for the downstream hydraulic geometry of alluvial channels is examined through a nonlinear regression analysis. The database consists of a total of 1,485 measurements, 1,125 of which describe field data used for model calibration. The remaining 360 field and laboratory measurements are used for validation. The data used for validation include sand-bed, gravel-bed, and cobble-bed streams with meandering to braided planform geometry. The five parameters describing downstream hydraulic geometry are: channel width W, average flow depth h, mean flow velocity V, Shields parameter τ*, and channel slope S. The three independent variables are discharge Q, median bed particle diameter ds, and either channel slope S or Shields parameter τ* for dominant discharge conditions. The regression equations were tested for channel width ranging from 0.2 to 1,100?m, flow depth from 0.01 to 16?m, flow velocity from 0.02 to 7?m/s, channel slope from 0.0001 to 0.08, and Shields parameter from 0.001 to 35. The exponents of the proposed equations are comparable to those of Julien and Wargadalam (1995), but based on R2 values of the validation analysis, the proposed regression equations perform slightly better.     

Investigating the Role of Clasts on the Movement of Sand in Gravel Bed Rivers

The bed morphology of mountain rivers is characterized primarily by the presence of distinguishable isolated roughness elements, such boulders or clasts. The objective of this experimental study was to provide a unique insight into the role of an array of clasts in regulating sand movement over gravel beds for low relative submergence conditions, H/dc<1, and flow depth, H, to the diameter of the clast, dc, a process that has not been studied thoroughly. To assess the role of clasts in controlling incoming sand movement, detailed flume experiments were conducted by placing 40 equally spaced clasts atop a well-packed glass bead bed for replicating the isolated roughness flow regime. The experiments were performed for moderate ( ～ 2.50τcr* where τcr* is the critical dimensionless bed shear stress) and high ( ～ 5.50τcr*) applied bed shear stress conditions, representative of gravel bed rivers. For comparison purposes, experiments were also repeated for nearly identical flow conditions but without the presence of clasts to discern the potential effects that clasts may have on sediment movement and hydraulics within the clast array region and also in the upstream section of the clast region where few observations exist. The experimental results revealed the formation of two distinguishable bed morphological features, namely a funnel shaped “sand ridge” upstream from the clast array region and small depositional “sand patches” around individual clasts. The sand patches were formed in the stoss region of the clasts, which contradicted previous observations of depositional patterns around clasts under high relative submergence conditions (H/dc>1) where, in this case, depositional patches were observed to have formed in the clast wake region. Furthermore, most of the incoming sand was found to be intercepted by the evolving sand ridge upstream from the clast array region with implications in the amount of sand entering the clast array region. The exiting bed-load rate was found to be reduced by a factor of ～ 5.0–20, depending on the prevailing flow conditions when experiments with and without clasts were compared under nearly identical flow conditions. The findings of this research, although limited to the isolated roughness regime, may have significant ramifications in stream restoration projects for the design of engineered riffle sections, which typically consist of an array of clasts installed to improve degraded waterways and aquatic habitat.     

Exact Discontinuous Solutions of Exner’s Bed Evolution Model: Simple Theory for Sediment Bores

Determining the evolution of the bed of a river or channel due to the transport of sediment was first examined in a theoretical context by Exner in 1925. In his work, Exner presents a simplified bed evolution model derived from the conservation of fluid mass and an “erosion” equation that is commonly referred to as the sediment continuity or Exner equation. Given that Exner’s model takes the form of a nonlinear hyperbolic equation, one expects, depending on the given initial condition of the bed, the formation of discontinuities in the solution in finite time. The analytical solution provided by Exner for his model is the so-called classical or genuine solution of the initial-value problem, which is valid while the solution is continuous. In this paper, using the general theory of nonlinear hyperbolic equations, we consider generalized solutions of Exner’s classic bed evolution model thereby developing a simple theory for the formation and propagation of discontinuities in the bed or so-called sediment bores.     

High-Resolution Method for Modeling Hydraulic Regime Changes at Canal Gate Structures

A method for modeling flow regime changes at gate structures in canal reaches is presented. The methodology consists of using an approximate Riemann solver at the internal computational nodes, along with the simultaneous solution of the characteristic equations with a gate structure equation at the upstream and downstream boundaries of each reach. The conservative form of the unsteady shallow-water equations is solved in the one-dimensional form using an explicit second-order weighted-average—flux upwind total variation diminishing (TVD) method and a Preissmann implicit scheme method. Four types of TVD limiters are integrated into the explicit solution of the governing hydraulic equations, and the results of the different schemes were compared. Twelve possible cases of flow regime change in a two-reach canal with a gate downstream of the first reach and a weir downstream of the second reach, were considered. While the implicit method gave smoother results, the high-resolution scheme—characteristic method coupling approach at the gate structure was found to be robust in terms of minimizing oscillations generated during changing flow regimes. The complete method developed in this study was able to successfully resolve numerical instabilities due to intersecting shock waves.     

Physical Basis for Quasi-Universal Relationships Describing Bankfull Hydraulic Geometry of Sand-Bed Rivers

Empirical data indicate that hydraulic geometry relationships for single-thread sand-bed rivers (i.e., rivers with median bed-material size between 0.062 and 0.50?mm) can be delineated such that bankfull width, bankfull depth, and channel slope are related in consistent ways to bankfull discharge. Such relationships ought to be the external expression of physical relationships intrinsic to sand-bed river dynamics. In this study, a back-calculation is performed to identify parameters (exponents and coefficients) for three relationships taken to be intrinsic to sand-bed rivers: (1)?a generalized Manning-Strickler resistance relationship; (2)?a relationship for channel-forming Shields number; and (3)?a relationship for sand yield at bankfull flow. To back-calculate parameters for the physical relationships, first the hydraulic geometry relationships are expressed in suitable dimensionless form. Second, the physical relationships are expressed with coefficients and exponents that are analytically related to parameters in the hydraulic geometry relationships. Third, parameters from the hydraulic geometry relationships are used to calculate parameters for the physical relationships. The analysis yields the following results for the sand-bed rivers: (1)?no physical basis exists for using an exponent of 1/6 in the resistance relationship; (2)?channel-forming Shields number decreases with particle Reynolds number, and thus grain size, in a consistent way; and (3)?sand concentration at bankfull flow must decline with increasing bankfull discharge. Although each of these relationships could have been established independently on its own, in this study they have been obtained as the only conclusions consistent with the observed hydraulic geometry relationships and the proposed physical framework. The analysis also yields a useful, dimensionally homogeneous predictive relationship for bankfull discharge as a function of bankfull width, bankfull depth, bed slope, and bed-material median grain size.     

Outer Scaling for Open Channel Flow over a Gravel Bed

Similarity analysis is performed for hydraulically rough open channel flow over a gravel bed to provide mixed outer scaling of the mean-velocity profile. The analysis is based on equilibrium turbulent boundary-layer theory derived using the asymptotic invariance principle. Outer scaling based on the similarity theory is validated with velocity measurements from the laboratory and field, having a Reynolds number range that includes 1×104, 1×105, and 1×106 and a Froude number range from 0.26 to 0.83. The results show that the free-stream velocity is an appropriate outer scale for gravel-bed river flows at moderate and bankfull stage. The results agree well with the velocity measurements and collapse laboratory and field data, which allow an important connection between open channel research in the laboratory and the applications for which the research is performed in the field. The results show that the R/aD84 roughness parameter is consistent with the mixed scale used in boundary-layer velocity scaling. This is in agreement with the consistent turbulent structure of the flow for both flat plate boundary-layer and open channel flow scenarios. While R/D84 has been used empirically with depth-averaged velocity and roughness laws for many years, this roughness parameter is shown in a theoretical context due to its influence on the turbulent structure of the flow. The results are applicable to modeling the velocity distribution under fundamental gravel-bed flow cases that span to the bankfull flow regime, which provides a contribution to stream engineering.     

Numerical Model for Sediment Transport and Bed Degradation in the Yangtze River Channel Downstream of Three Gorges Reservoir

This paper presents a two-dimensional morphological model for unsteady flow and both suspended-load and bed-load transport of multiple grain size to simulate transport of graded sediments downstream from the Three Gorges Reservoir. The model system includes a hydrodynamic module and a sediment module. The hydrodynamic module is based on the depth-averaged shallow water equations in orthogonal curvilinear coordinates. The sediment module describing nonuniform sediment transport is developed to include nonequilibrium transport processes, bed deformation, and bed material sorting. The model was calibrated using field observations through application to a 63-km-long alluvial river channel on the middle Yangtze River in China. A total of 16 size groups and a loose layer method of three sublayers were considered for the transport of the nonuniform bed materials in a long-term simulation. Predictions are compared with preliminary results of field observations and factors affecting the reliability of the simulated results are discussed. The results may be helpful to the development of more accurate simulation models in the future.     

Riparian Vegetation Mapping for Hydraulic Roughness Estimation Using Very High Resolution Remote Sensing Data Fusion

For detailed hydraulic modeling, accurate spatial information of riparian vegetation patterns needs to be derived in automatic fashion. We propose a supervised classification for heterogeneous riparian corridors with a low number of spectrally separate classes using data fusion of a Quickbird image and LIDAR data. The approach considers nine land cover classes including three woody riparian species, brush, cultivated areas, grassland, urban infrastructures, bare soil and water. The classical “stacked vector” approach is adopted for data fusion, while the nonparametric weighted feature-extraction method and the pixel-oriented maximum likelihood algorithm are used for feature-reduction and classification purposes, respectively. We test the approach over a 14-km stretch of the Sieve River (Tuscany Region, Italy). A one-dimensional river modeling is applied over the study reach comparing the results of a classification-derived hydraulic roughness map and a traditional ground-based approach. Despite the complex study reach, the classification method produced encouraging accuracies (OKS = 0.77) and represents a useful tool to delineate application domains of flow resistance models suited to different hydrodynamic patterns (e.g., stiff/flexible vegetation). Hydraulic modeling results showed that the remotely derived floodplain roughness parameterization captures the equivalent Manning coefficient over 20 test cross sections with uncertainty distributions described by low mean and standard deviation values.     

Sensitivity Analysis for Hydraulic Models

Sensitivity analysis is well recognized as being an important aspect of the responsible use of hydraulic models. This paper reviews a range of methods for sensitivity analysis. Two applications, one to a simple pipe bend example and the second to an advanced Shallow Water Equation solver, illustrate the deficiencies of standardized regression coefficients in the context of functionally nonlinear models. Derivatives and other local methods of sensitivity analysis are shown to give an incomplete picture of model response over the range of variability in the model inputs. The use of global variance-based sensitivity analysis is shown to be more general in its applicability and in its capacity to reflect nonlinear processes and the effects of interactions among variables.     

Real-Time Hydraulic and Hydrodynamic Model of the St. Clair River, Lake St. Clair, Detroit River System

The Huron-Erie Corridor serves as a major waterway in the Great Lakes and is the connecting channel between Lake Huron and Lake Erie. The system consists of the St. Clair River, Lake St. Clair, and the Detroit River, and serves as a recreational waterway, source of drinking water for Detroit and surrounding cities, as well as the only shipping channel to Lakes Huron, Michigan, and Superior. This paper describes a three-dimensional unsteady model of the combined system and its application to real-time predictions of physical conditions over the corridor. The hydrodynamic model produces nowcasts eight times per day and 48 h forecasts twice a day. Comparisons between model simulations and observed values show average differences of 3 cm for water levels and 12 cm/s for along-channel currents in the St. Clair River (compared to mean current values of 1.7 m/s) for the period of September 2007 to August 2008. Simulations reveal a spatially and temporally variable circulation in Lake St. Clair as well as significant changes in flow rate and distribution through the St. Clair Delta not accounted for in previous models.     

Hydraulic Complexity Metrics for Evaluating In-Stream Brook Trout Habitat

A two-dimensional hydraulic model (River2D) was used to investigate the significance of flow complexity on habitat preferences of brook trout (Salvelinus fontinalis) in the high-gradient Staunton River in Shenandoah National Park, Virginia. Two 100-m reaches were modeled where detailed brook trout surveys (10–30-m resolution) have been conducted annually since 1997. Spatial hydraulic complexity metrics including area-weighted circulation and kinetic energy gradients (KEG) were calculated based on modeled velocity distributions. These metrics were compared to fish density in individual habitat complexes (10–30-m subreaches) to evaluate relationships between fish location and average flow complexity. In addition, the fish density was compared to additional habitat variables including percent cascade (CS), pool (PL) and riffle, and in-stream (ISCN) and riparian cover. There were negative correlations between modeled mean velocity (VEL) and maximum depth (MAXD) and fish density; however, there were no statistically significant correlations between KEGs or area-weighted circulation and fish density. Fish density was negatively correlated to ISCN and positively correlated to the percent of the channel dominated by protruding boulders (BD) and CS. The structural complexity of cascade habitat and areas with protruding boulders creates complex flow patterns indicating that flow complexity plays an important role in brook trout habitat preferences at the local scale. Linear discriminate analysis was used to further investigate the relationships between habitat variables and fish density. Using backward stepwise variable selection, the final explanatory model contained the BD, ISCN, MAXD, PL, and VEL variables. These observations indicate that at a coarse spatial scale hydraulic complexity may be an important component in fish habitat preferences; however, other habitat variables cannot be ignored and the hydraulic complexity metrics calculated using 2D modeling results were not explanatory. While spatial hydraulic complexity metrics provide quantifiable measures for evaluating stream restoration project impacts on in-stream habitat quality, the relationships between fish density and hydraulic complexity were not straightforward. This is likely due in part to modeling limitations in this high-gradient complex stream. Further research is needed at a range of spatial scales, stream types, and fish species to fully investigate the use of hydraulic complexity metrics to quantify in-stream habitat.     

Contractor Performance Prediction Model for the United Kingdom Construction Contractor: Study of Logistic Regression Approach

An accurate prediction of contractor potential is of vital importance during contractor selection and evaluation process. Such prediction enables identification and classification of contractor performance to ease the selection process. This paper outlines the use of clients' tender evaluation preferences for predicting a contractor performance via a logistic regression (LR) approach. A total of 31 clients’ tender evaluation criteria were selected to develop a LR model for predicting contractor performance. The proposed model was developed based on 48 of United Kingdom public and private construction projects and validated in 20 independent cases. It was found that 75% of the cases correctly and the model statistically accurate for contractor performance prediction, where the input variables consist of nominal and interval data. The paper summarized techniques and advantages of LR analysis and discussed literature findings of contractor selection and evaluation methodologies undertaken by construction researchers and commentators from the United Kingdom and Northern America.