Divided Channel Method Research Articles

Surface Velocity to Depth-Averaged Velocity—A Review of Methods to Estimate Alpha and Remaining Challenges

The accuracy of discharge measurements derived from surface velocities are highly dependent on the accuracy of conversions from surface velocity us to depth-averaged velocity U. This conversion factor is typically known as the ‘velocity coefficient’, ‘velocity index’, ‘calibration factor’, ‘alpha coefficient’, or simply ‘alpha’, where α=U/us. At some field sites detailed in situ measurements can be made to calculate alpha, while in other situations (such as rapid response flood measurements) alpha must be estimated. This paper provides a review of existing methods for estimating alpha and presents a workflow for selecting the appropriate method, based on available data. Approaches to estimating alpha include: reference discharge and surface velocimetry measurements; extrapolated ADCP velocity profiles; log law profiles; power law profiles; site characteristics; and default assumed values. Additional methods for estimating alpha that require further development or validation are also described. This paper then summarises methods for accounting for spatial and temporal heterogeneity in alpha, such as ‘stage to alpha rating curves’, ‘site alpha vs. local alpha’, and ‘the divided channel method’. Remaining challenges for the accurate estimation of alpha are discussed, as well as future directions that will help to address these challenges. Although significant work remains to improve the estimation of alpha (notably to address surface wind effects and velocity dip), the methods covered in this paper could provide a substantial accuracy improvement over selecting the ‘default value’ of 0.857 for alpha for every discharge measurement.

Modeling unsteady and steady 1D hydrodynamics under different hydraulic conceptualizations: Model/Software development and case studies

The stage-discharge relationship is affected by hysteresis, especially in 1D river cross-sections with very mild slopes, and/or where backwater effects occur. To model these cases, hydraulic property (HP) estimations (e.g., hydraulic radius and conveyance) are usually required as closed-form functions of stage. However, these are typically unavailable for complex cross-sections with overbanks. For no sediment-laden flows, we created the HydroHP - 1D tool to solve the 1D Saint Venant Equations aided by the cross-section HP stored in tables. It also simulates irregular and composite hydraulic cross-sections, allows hydrodynamic simulation using the single-channel method (SCM), and proposes the divided channel method (DCM) for steady and unsteady flow analysis. A wide range of applications in rivers such as the Little Washita River and the Upper Negro River, and comparisons with NOAA normal depth solver, HEC-RAS, and with an analytical solution shows a promising scenario of applying HydroHP - 1D to estimate 1D steady and unsteady hydrodynamics.

Overbank Flow in a Multi-Staged Open Channel: Zonal and Overall Discharge Studies

An improved divided channel method has been proposed by modelling a parameter using the function of depth ratio for a multi-stage compound channel. Experimental data suggest that as the flow depth increases over the second stage floodplain, fractional contribution of the main channel and first stage floodplain under bankfull height plays a pivotal role in shear layer and momentum distribution. Therefore, a new mathematical model has been suggested for estimating the stage-discharge relationship for staged channels of more than one floodplain using the 1D technique of overall roughness correction.

Discharge prediction in partly vegetated channel flows: Adaptation of IDCM method with a curved interface and large-scale roughness elements

This study provides new insight into how to predict flow discharges of partly vegetated channels with emergent vegetation. By adapting for the first time the Interacting Divided Channel Method (IDCM), applied with a curved interface approach and with the presence of large-scale roughness elements (not considered in previous studies), the total and zonal discharges of partly vegetated channels were predicted based on a series of experimental results in this study together with collected data from previous studies. Consideration of transverse momentum transfer in terms of apparent shear stress at curved interface plane showed better performance with IDCM than the Divided Channel Method (DCM) with both curved and classic vertical/diagonal divisions. In this study, we also proposed a series of expressions, easily applicable, to predict the zonal discharges of a partly vegetated channel.Many experiments were carried out in a physical model of a very large rectangular channel with the presence of rows of vertical, rigid, circular, and rough steel cylinders, representing emergent rigid vegetation. The rows of cylinders were partially mounted on the bottom of the channel, leaving lateral areas of free circulation near the walls. The three-dimensional components of the flow velocity were measured using a 3D Acoustic Doppler Velocimeter (ADV)-Vectrino.

Linear-scale models for discharge estimation: asymmetric compound open channel flows

In this study, three recent methods of discharge estimation are evaluated, namely, the interacting divided channel method, the modified divided channel method and the momentum transfer divided channel method, which include momentum exchange on the interface for prediction of discharge. These methods are compared intensively using 22 experimental flume data sets with six river data sets taken from the literature comprising 204 test runs in total. These data sets are categorised as asymmetric compound channels with a wide range of width ratio (B/b), aspect ratio (b/h) and bed slope ([Formula: see text]), where [Formula: see text] is the total width of channel at the bankfull condition, [Formula: see text] is the main channel bed width and [Formula: see text] is the bankfull main channel height. All these three methods are capable of predicting both overall and zonal discharge for small- to large-scale channels, including natural rivers. However, the interacting divided channel method is the least erroneous, with an average percentage error of 5.83%. Further investigations should include in-depth discussion on zonal discharge prediction, particularly for floodplain discharge, which has been an area of concern and interest in the areas of the water environment and sustainable design of rivers.

Gene-expression programming for calculating discharge in meandering compound channels

Computation of flow in natural channels is the key to the solution of numerous engineering problems particularly at the time of flood. Therefore, different approaches have been incorporated for accurate estimation of flow discharge in compound meandering channels. The present work focuses on developing an empirical model for estimating the flow of meandering compound channels using gene-expression programming (GEP) by considering four non-dimensional parameters viz Relative Depth, Sinuosity, Coherence Parameter, and Discharge Ratio (Qvdm/Qbf). The model developed for the meandering compound channels is best suited for sinuosity in the range of 1.04–2. To measure adequacy of the model, the results of the developed model are compared with various discharge estimation methods such as the Single Channel Method (SCM), Divided Channel Method (DCM), Meander Belt Method (MBM), Modified Divided Channel Method (MDCM), Interacting Divided Channel Method (IDCM), and Coherence Method (COHM). Results indicate that the proposed GEP model predicted the ratio of total discharge in compound channel (Qt) to the bank-full discharge (Qbf) in main channel satisfactorily with root mean square error of 0.15 and 0.19 for training and testing dataset, respectively. The developed model is also used to validate with higher sinuous channels having sinuosity exceeding 2.0. Finally, the model was successfully validated with natural flood conditions of River Baitarani, India (sinuosity of 1.334) giving the minimum errors in terms of mean absolute square error of 0.885 and 0.882 for the two overbank flow depths of 7.5 and 8.63 m, respectively.

Prediction of stage-discharge relationship in two-stage channels

Predicting the stage-discharge relationship in two-stage channels is a significant factor, as it determines the discharge and the degree of flood accurately. There are conventional methods, in which they either do not meet the required accuracy or simplicity. In this paper, a new simple model is developed for symmetric compound channels to predict the stage-discharge relationship accurately. The method is proposed by improving the weighted divided channel method (WDCM), which includes the apparent shear force (ASF), wetted perimeters and B/b ratio. It was concluded that the improved weighted divided channel method (IWDCM) is limited to all rigid symmetric compound channels with B/b ratios greater than or equal to 3. The IWDCM led to an absolute percentage error always less than 10% for total discharges for all smooth and rough cases. The proposed IWDCM method will therefore be very helpful to hydraulic engineers to predict the stage-discharge relationship precisely due to its simplicity.

Prediction of stage-discharge relationship in two-stage channels

Predicting the stage-discharge relationship in two-stage channels is a significant factor, as it determines the discharge and the degree of flood accurately. There are conventional methods, in which they either do not meet the required accuracy or simplicity. In this paper, a new simple model is developed for symmetric compound channels to predict the stage-discharge relationship accurately. The method is proposed by improving the weighted divided channel method (WDCM), which includes the apparent shear force (ASF), wetted perimeters and B/b ratio. It was concluded that the improved weighted divided channel method (IWDCM) is limited to all rigid symmetric compound channels with B/b ratios greater than or equal to 3. The IWDCM led to an absolute percentage error always less than 10% for total discharges for all smooth and rough cases. The proposed IWDCM method will therefore be very helpful to hydraulic engineers to predict the stage-discharge relationship precisely due to its simplicity.

Predicting discharge capacity of vegetated compound channels: uncertainty and identifiability of one-dimensional process-based models

Abstract. Despite the development of advanced process-based methods for estimating the discharge capacity of vegetated river channels, most of the practical one-dimensional modeling is based on a relatively simple divided channel method (DCM) with the Manning flow resistance formula. This study is motivated by the need to improve the reliability of modeling in practical applications while acknowledging the limitations on the availability of data on vegetation properties and related parameters required by the process-based methods. We investigate whether the advanced methods can be applied to modeling of vegetated compound channels by identifying the missing characteristics as parameters through the formulation of an inverse problem. Six models of channel discharge capacity are compared in respect of their uncertainty using a probabilistic approach. The model with the lowest estimated uncertainty in explaining differences between computed and observed values is considered the most favorable. Calculations were performed for flume and field settings varying in floodplain vegetation submergence, density, and flexibility, and in hydraulic conditions. The output uncertainty, estimated on the basis of a Bayes approach, was analyzed for a varying number of observation points, demonstrating the significance of the parameter equifinality. The results showed that very reliable predictions with low uncertainties can be obtained for process-based methods with a large number of parameters. The equifinality affects the parameter identification but not the uncertainty of a model. The best performance for sparse, emergent, rigid vegetation was obtained with the Mertens method and for dense, flexible vegetation with a simplified two-layer method, while a generalized two-layer model with a description of the plant flexibility was the most universally applicable to different vegetative conditions. In many cases, the Manning-based DCM performed satisfactorily but could not be reliably extrapolated to higher flows.

Evaluation of Flow Resistance Models Based on Field Experiments in a Partly Vegetated Reclamation Channel

This study presents a methodology for improving the efficiency of Baptist and Stone and Shen models in predicting the global water flow resistance of a reclamation channel partly vegetated by rigid and emergent riparian plants. The results of the two resistance models are compared with the measurements collected during an experimental campaign conducted in a reclamation channel colonized by Common reed (Phragmites australis (Cav.) Trin. ex Steud.). Experimental vegetative Chézy’s flow resistance coefficients have been retrieved from the analysis of instantaneous flow velocity measurements, acquired by means of a downlooking 3-component acoustic Doppler velocimeter (ADV) located at the channel upstream cross section, and by water level measurements obtained through four piezometers distributed along the reclamation channel. The main morphometrical vegetation features (i.e., stem diameters and heights, and bed surface density) have been measured at six cross sections of the vegetated reclamation channel. Following the theoretical assumptions of the divided channel method (DCM), three sub-sections have been delineated in the reference cross section to represent the impact of the partial vegetation cover on the cross sectional variability of the flow field, as observed with the ADV measurements. The global vegetative Chézy’s flow resistance coefficients have been then computed by combining each resistance model with four different composite cross section methods, respectively suggested by Colebatch, Horton, Pavlovskii, and Yen. The comparative analysis between the modeled and the experimental vegetative Chézy’s coefficients has been performed by computing the relative prediction error (εr, expressed in %) under two flow rate regimes. Stone and Shen model combined with the Horton composite cross section method provides vegetative Chézy’s coefficients with the lowest εr.

Estimation of water surface profiles using rating curves

ABSTRACT Water surface profiles (WSPs) are among the most valuable information in artificial and natural open channels. Most of the conventional methods for computing the WSPs in compound channels are based on the water surface calculated by the divided channel method (DCM) which is used by HEC-RAS. However, this approach cannot predict the water surface with good accuracy when dealing with compound channels. Therefore a new approach is implemented to calculate the WSP. This approach consists of two steps. In the first step, the rating curve is computed based on the newly proposed method by Maghrebi et al. In the second step, based on the governing equations for gradually varied flow including energy equation, the WSP is computed. The experimental results reported for three sets of measured WSPs in compound channels and WSP measurements of the Main River are used to evaluate the accuracy of the proposed method. The results show that the proposed technique can predict the WSP with better accuracy in comparison to the HEC-RAS and CES models.

Prediction of discharge in converging and diverging compound channel by gene expression programming

ABSTRACT Discharge estimation in rivers is the most important parameter in flood management. Predicting discharge in the converging and diverging compound open channel by analytical approach leads to solving a system of complex nonlinear equations. In this study, the gene expression programming (GEP) is used for modeling and predicting of flow discharge in the non-prismatic compound open channel. Existing approaches on discharge estimation are surveyed in order to carry out a comparison among them and the proposed GEP model. Comparison of results showed that the divided channel method with vertical division lines with the coefficient of determination (0.74) and root-mean-square error (0.0093) is accurate among the analytical approaches. The non-dimensional parameters like friction factor ratio, area ratio, hydraulic radius ratio, bed slope, width ratio, relative flow depth, angle of converging or diverging, relative longitudinal distance, and flow aspect ratio have been taken as input parameters for predicting discharge. Gamma test has been performed and provided the best combination of input parameters as friction factor ratio, hydraulic radius ratio, relative flow depth, and bed slope which influence the discharge significantly. Results demonstrate that the conveyance capacity computed by the GEP model gives far better outcomes than the customary models. The GEP model with a coefficient of determination greater than 0.80 and mean absolute percentage error less than 15% for the testing stage has a suitable performance for predicting the discharge in the non-prismatic compound open channel.

A new apparent shear stress-based approach for predicting discharge in uniformly roughened straight compound channels

Accurately predicting flow discharge in a compound river channel becomes increasingly important when in river eco-environment design and flood risk management, in which the conventional methods, such as divided channel method (DCM) and single channel method, do not meet precision requirement. In the present paper, a new approach is proposed to improve the prediction of flow based on the concept of the apparent shear stress at the diagonal interface between main channel and floodplains. The new approach is compared with a wide range of the author's experimental data and the data available in the literature. The 27 datasets used in this study cover homogenous symmetric channels (22 datasets) and asymmetric channels (5 datasets), which have various width ratios [channel total width (B) at bankfull / main channel bottom (b) = 1.5 ~ 15.8] and bed slopes (So = 2.6 × 10−4 ~2.5 × 10−3). It was found that the new approach can significantly improve the accuracy of flow prediction compared with the conventional DCM for all the datasets, particularly for relatively low flow depths of floodplain (e.g. Dr < 0.15) where the flow discharge was very difficult to predict correctly. The new approach predicts the total discharge well for straight homogeneously symmetric and asymmetric channels, within a mean absolute percentage error (MAPE) of 5%. Furthermore, compared with the DCM, the new approach can also have a better prediction of zonal discharge percentage and it has less variation of discharge prediction error over the flow depth.

Identification of vegetation parameters for compound channel discharge as inverse problem

Abstract In recent years many sophisticated models for discharge capacity of compound channels with vegetation have been developed. Despite the mature state of knowledge in this field, in a practice the simplest methods prevail and most of hydraulic models are based on the Manning formula. One of the reasons is that more complex methods require detailed characteristics on vegetation. The present study demonstrates that this issue can be solved by treating all such necessary variables as parameters to be identified in a sense of an inverse problem, using techniques of optimization. With a flume experiment as a case study, four models of a uniform flow were identified: Pasche, Mertens as complex methods, divided channel method (DCM) with Manning and Darcy–Weisbach equations as techniques used in a practice. Results showed that parameters for all methods can be found on the basis of minimization of model residuals, with the restriction that because of the larger number of parameters in complex methods, more observations are required. Methods of Pasche and Mertens with identified parameters provided a much better explanation of water depths than the Manning or Darcy–Weisbach based on the DCM. It is surprising that significant discrepancies between identified parameters and their real measured values were recorded. Even more, an almost perfect fit was obtained for different parameter sets.

Stage–discharge estimation in straight compound channels using isovel contours

AbstractFor various hydrological applications such as flood control projects, a knowledge of stage–discharge relationship is of particular interest to river engineers. Stage–discharge curves in compound channels cannot be easily predicted in comparison with single channels due to their 3D characteristics of flow. In this paper, the concept of cross‐sectional isovel contours is used for estimation of stage–discharge curves in compound channels. The multivariate Newton's method is applied to the difference between the observed and estimated data to optimize the exponent values of the governing parameters. The accuracy of the proposed model is tested successfully against available experimental results, which are taken from the Flood Channel Facility (FCF) laboratory. Then the results are compared with the Single and Divided Channel Methods (SCM and DCM, respectively), the Weighted Divided Channel Method (WDCM), the exchange discharge method (EDM), and the Coherence Method (COHM). The average values of mean absolute percentage error (MAPE) and normalized root mean square error (NRMSE) in discharge estimation based on each referenced section at any level for 6 sections of the experimental cases are within 3.1% and 0.023, respectively. The biggest advantage of the proposed method is its inherent simplicity, which does not need any calibration.

An improved method for predicting discharge of homogeneous compound channels based on energy concept

Accurate estimation of flow discharge in a compound river channel is increasingly important in river management and hydro-environment design. In this paper, a new model is developed to improve the prediction of flow based on Energy Concept Method (ECM) and Weighted Divided Channel Method (WDCM) along with the apparent shear stress at the interface between main channel and floodplain. The new model is compared with a wide range of our experimental data and the data available in the literature. The 27 datasets used include homogenous symmetric channels (22 datasets) and asymmetric channels (5 datasets) with various aspect ratios [channel total width (B) at bankfull / main channel bottom (b) =1.5–15.8], and bed slopes (So = 4.3 × 10−4–1.3 × 10−2). It was found that the new model has significantly improved the accuracy of flow prediction compared with the traditional Divided Channel Method (DCM), and has also considerably better results than the ECM and WDCM methods against all the datasets, particularly for relatively low flow depths of floodplain where the flow discharges are most difficult to predict correctly. The new model predicts the total discharge well for both symmetric and asymmetric channels, within an averaged relative error of about 5%.

Incorporating a machine learning technique to improve open-channel flow computations

The objective of this study is to employ support vector machine as a machine learning technique to improve flow discharge predictions in compound open channels. Accurate estimation of channel conveyance is a major step in prediction of the flow discharge in open-channel flow computations (e.g., river flood simulations, design of canals, and water surface profile computation). Common methods to estimate the conveyance are highly simplified and are a main source of uncertainty in compound channels, since popular river/canal models still incorporate 1-D hydrodynamic formulations. Further, the reliability of using a specific method (e.g., vertical divided channel method, the coherence method) over other methods for different applications involving various geometric and hydraulic conditions is questionable. Using available experimental and field data, a novel method was developed, based on SVM, to compute channel conveyance. The data included 394 flow rating curves from 30 different laboratory and natural compound channel sections which were used for the training, and verification of the SVM method. The data were limited to straight compound channels. The performance of SVM was compared with those from other commonly used methods, such as the vertical divided channel method, the coherence method and the Shiono and Knight model. Additionally, SVM estimations were compared with available data for River Main and River Severn, UK. Results indicated that SVM outperforms traditional methods for both laboratory and field data. It is concluded that the proposed SVM approach could be applied as a reliable technique for the prediction of flow discharge in straight compound channels. The proposed SVM can be potentially incorporated into 1-D river hydrodynamic models in future studies.

Mathematical expression of discharge capacity of compound open channels using MARS technique

In this paper, analytical methods, artificial neural network (ANN) and multivariate adaptive regression splines (MARS) techniques were utilised to estimate the discharge capacity of compound open channels (COC). To this end, related datasets were collected from literature. The results showed that the divided channel method with a coefficient of determination (R 2) value of 0.76 and root mean square error (RMSE) value of 0.162 has the best performance, among the various analytical methods tested. The performance of applied soft computing models with R 2=0.97 and RMSE = 0.03 was found to be more accurate than analytical approaches. Comparison of MARS with the ANN model, in terms of developed discrepancy ratio (DDR) index, showed that the accuracy of MARS model was better than that of MLP model. Reviewing the structure of the derived MARS model showed that the longitudinal slope of the channel (S), relative flow depth (H r ) and relative area (A r ) have a high impact on modelling and forecasting the discharge capacity of COCs.

Optimal prediction of lateral velocity distribution in compound channels

ABSTRACTMany rivers have deep main channels in the centre with one or two adjoining floodplains. Prediction of the lateral velocity distributions over the entire river cross-section is necessary for solving many river-related and hydro-engineering problems. Using Genetic Algorithm (GA), this paper proposes a simple model with two separate equations for predicting the lateral velocity distribution in the main channel and floodplains of straight compound channels. The proposed model is based on two key parameters of compound channels, i.e. depth ratio and the coherence parameter. The constants and exponents of the model are obtained by using a GA based on both experimental data of several compound flumes and measurements of the river Severn in the UK. Using several statistical measures, it is shown that the predictions of lateral velocity distribution and stage-discharge by the model agree well with the observed laboratory data and natural river measurements used for calibration and validation. Moreover, the model is shown to outperform the conventional vertical divided channel method with 11.2% less error on average in predicting the velocity distribution.

Evaluation of interacting length in prediction of over bank flow

Study of interaction mechanism in compound channels consisting of main channel with adjoining floodplains is very important for environmental, ecological and design issues. The flow structures at junction between main channel and floodplain are rigorous due to the complex exchange of momentum. It leads to the imprecise quantification of the discharge in compound channel. Many investigators have proposed various discharge prediction methods among which divided channel method is widely acceptable. This current study approaches a simple way to predict discharge in a compound channel by incorporating an interacting length at the interface between the main channel and adjoining flood plains. From the experimental results of NITR channel data and Flood Channel Facility of UK data, the interacting lengths have been estimated for different combinations of flow depths and width ratios. The functional relationships of the interacting length with the non-dimensional hydraulic and geometric parameters have been found out and a multi linear regression model is developed. The performance of present approach has also been evaluated with other standard approaches. The strength of the current model is successfully tested with natural river data.