Estimating the water surface elevation of river systems is one of the most complicated tasks in formulating hydraulic models for flood control and floodplain management. Consequently, utilizing simulation models to calibrate and validate the experimental data is crucial. HEC-RAS is used to calibrate and verify the water surface profiles for various converging compound channels in this investigation. Based on experimental data for converging channels (θ = 5°, 9°, and 12.38°), two distinct flow regimes were evaluated for validation. The predicted water surface profiles for two relative depths (β = 0.25 and 0.30) follow the same variational pattern as the experimental findings and are slightly lower than the observed values. The MAPE for the simulated and experimental results is less than 3%, indicating the predicted HEC-RAS value performance and accuracy. Therefore, our findings imply that in the case of non-prismatic rivers, the proposed HEC-RAS models are reliable for predicting water surface profiles with a high generalization capacity and do not exhibit overtraining. However, the results demonstrated that numerous variables impacting the water surface profile should be carefully considered since this would increase the disparities between HEC-RAS and experimental data.

  • In this article, research was conducted for the non-prismatic compound channel with converging floodplains, utilizing the HEC-RAS software.

  • The findings depict the HEC-RAS models are accurate for forecasting the water surface profile of non-prismatic rivers, have a high capacity for generalization, and do not display any signs of overexertion.

  • The usefulness of HEC-RAS tool for the design of flood control and diversion structures in the non-prismatic rivers.

B

total width of the compound channel

b

width of the main channel

H

flow depth

h

height of the main channel

L

converging length

S

longitudinal bed slope

β

relative flow depth [(Hh)/H]

θ

converging angle

ACRONYMS

2D

two dimensional

ADV

acoustic Doppler velocimeter

ANFIS

adaptive neuro-fuzzy inference system

ANN

artificial neural network

DCM

divided channel method

DEM

digital elevation model

GEP

gene expression programming

GLM

generalized linear model

GMDH

group method of data handling

HEC-RAS

Hydrologic Engineering Centre's – River Analysis System

ISM

independent subsection method

LDM

lateral distribution method

MAE

mean absolute error

MAPE

mean absolute percentage error

MLM

machine learning model

MLPNN

multi-layer perceptron neural network

NF-GMDH

neuro-fuzzy group method of data handling

RF

random forest

RMSE

root mean squared error

SCM

single channel method

SVM

support vector machine

Increased human settlements, buildings, and activities along river floodplains have resulted in severe repercussions during natural river floods due to the global population rise. River floods cause massive human casualties as well as economic damage. Flood catastrophes account for a third of all-natural disaster damages worldwide; flooding accounts for half of all fatalities, with trend analysis revealing that these percentages have dramatically grown (Berz 2000). Flood protection needs to predict the conveyance capacity of natural streams precisely. When the amount of water running through a channel exceeds the waterway's capacity, it results in flooding. Consequently, the requirement for precise flow parameter prediction during flood conditions to limit damage and save lives and property has piqued the interest of academics and engineers in recent years. Various methodologies and procedures have been used to aid precise measurement and forecast of river discharge, velocity distribution, shear stress distribution, and water surface level during overbank flows. Compound channels are the most common river feature during overbank flow. During the course of a river's flow, the geometry of the floodplain changes, resulting in a compound channel that is either converging or diverging. It is more challenging to replicate flow in a non-prismatic compound channel because more momentum is carried from the main channel to the floodplains. Sellin (1964), Myers & Elsawy (1975), Knight et al. (2010), and Khatua et al. (2012) have explored the flow models of straight and meandering prismatic two-stage channels, but little is known about non-prismatic compound channels. A converging channel shape causes the flow on floodplains to rise, while the flow on floodplains expanding is reduced (James & Brown 1977). Compound channels with symmetrically declining floodplains were studied by Bousmar & Zech (2002), Bousmar et al. (2004), Rezaei (2006), and Rezaei & Knight (2009) and found the extra loss of head and transfer of momentum from the main channel to floodplains. Asymmetric geometry with a greater convergence rate was examined by Proust et al. (2006). A greater convergence angle (22°) results in increased mass transfer and head loss. Chlebek et al. (2010) studied the flow behavior of skewed, two-stage converging, and diverging channels. A new experiment on converging compound channels was done by Rezaei & Knight (2011), Yonesi et al. (2013), and Naik & Khatua (2016) that yielded significantly more precise results than previously accessible. In their study, Das et al. (2018) sought to enhance the conventional independent subsection method (ISM) for the estimation of flow magnitudes and velocities in the upper and lower main channels. The calculated results demonstrate the method's ability to accurately forecast the discharge distributions in both the floodplain and main channel. Das & Khatua (2018a) constructed a multivariable regression model that accounts geometric and hydraulic characteristics in order to estimate the Manning's roughness coefficient for non-prismatic compound channels. In their study, Das & Khatua (2018b) explored a numerical approach for estimating water surface elevations in compound channels with converging floodplains, using the momentum balancing concept. The findings derived from the simulation exhibit a strong concurrence with the empirical datasets. Das et al. (2020) used artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) methodologies to forecast the discharge in compound channels with converging and diverging geometries. The discharge is affected by many key input factors, including the friction factor ratio, hydraulic radius ratio, relative flow depth, and bed slope. The ANFIS model has superior performance in comparison to the ANN model. In their study, Das et al. (2022) proposed a non-linear multivariable regression model for estimating discharge distribution in diverging compound channels. This model utilizes geometric non-dimensional factors. The model that has been built demonstrates improved results in terms of statistical analysis when compared to earlier methodologies. Naik et al. (2022) proposed a novel equation by GEP using the non-dimensional variables to predict the water surface profile in converging compound channels. Kaushik & Kumar (2023a) used machine learning methodologies to predict the water surface profile of a compound channel with converging floodplains, using a blend of geometry and flow characteristics. Additionally, the researchers Kaushik & Kumar (2023b) have used gene expression programming (GEP) as a methodology to develop an innovative equation for compound channels with converging floodplains. This equation serves to quantify the boundary shear force transmitted by floodplains. In their study, Kaushik & Kumar (2023c) used the support vector machine (SVM) method to estimate the water surface profile of compound channels with shrinking floodplains. This was achieved by using non-dimensional geometric characteristics. The outcomes of this study suggest that the water surface profile created by the SVM has a significant level of agreement with both the observed data and the results obtained from prior investigations. In their study, Bijanvand et al. (2023) employed various soft computing models, namely the multi-layer perceptron neural network (MLPNN), group method of data handling (GMDH), neuro-fuzzy group method of data handling (NF-GMDH), and SVM, to make predictions on the surface elevation of water in compound channels with converging and diverging floodplains. The findings indicated that all of the used models exhibited satisfactory performance. Nevertheless, the SVM model had the most favorable performance, as shown by its strong statistical indicators. The influence of channel shape and flow characteristics on the water surface profile in non-prismatic compound channels has received little attention. As a result, exact water surface profile modeling is necessary to detect flooded regions, enhancing flood mitigation and risk management studies.

Over the past several decades, much work has gone into using 2D and 3D modeling to enhance the estimation of water levels and velocities in rivers. Still, minimal work was done on non-prismatic streams. Calculation techniques like single channel method (SCM) and divided channel method (DCM) are incorporated in software like HEC-RAS and MIKE 11. For the whole segment, the SCM uses the same velocity. The DCM divides the cross-section into zones with varied flow characteristics, such as the main channel and floodplains. According to Wormleaton et al. (1982), the SCM underestimates conveyance capacity, whereas the DCM overestimates compound channel capacity. Wormleaton & Merrett (1990) offered a simple change to enhance DCM estimation, while Ackers (1992) experimentally corrected the DCM.

The lateral distribution method (LDM) proposed by Wark et al. (1990) and the approach proposed by Shiono & Knight (1991) were created as alternate and more sophisticated methods. Like a quasi-2D model, these two techniques are based on the same equations and determine the lateral velocity distribution in the cross-section. In natural and artificial channels, HEC-RAS, a widely used hydraulic model developed by the U.S. Army Corps of Engineers, calculates water surface elevation and other flow characteristics in 1D/2D dimensions with progressively altering dimensions for steady and turbulent flow (Brunner 2016). HEC-RAS enables sediment transport/mobile bed calculations and water temperature modeling (Arcement & Schneider 1989; Brunner 2016). The stability of the HEC-RAS modeling was assessed by the use of model verification and validation techniques, which included comparing the model's predictions with experimental findings or actual field data. Stability of a model is determined when the numerical outputs closely align with the experimental findings or actual field data, exhibiting a consistent pattern of fluctuation. River hydraulics and other river-related phenomena have been substantially enhanced by using computer programs in recent years. Leandro et al. (2009) give extensive information on the most often used hydraulic models and their advantages and disadvantages for open channel modeling. Globally, computer hydraulic models are being used for flood defence planning in vulnerable locations to help better understand flood size and frequency trends and prepare for future flood scenarios (Liu & Merwade 2018). The HEC-RAS model was used in various studies to estimate flow characteristics in the main channel and floodplain under different climatic circumstances. Ramesh et al. (2000) estimated roughness for open channel flow using an optimization technique with boundary conditions as constraints. The HEC-RAS model was calibrated using Manning's n roughness coefficient, as reported by Hicks & Peacock (2005) and Kuriqi & Ardiçlioǧlu (2018) when applied to river analysis. Timbadiya et al. (2011) developed an integrated hydrodynamic model with MIKE11 to calibrate Manning's n roughness in assessing the sensitivity of flow resistance for the Tapi River in India. Mowinckel (2011) used the HEC-RAS to increase the flood conveyance capacity of an artificial San Jose Creek in Goleta, California. This assessment allowed us to recommend a revised channel design to accommodate a 100-year flood better while reducing harm to the surrounding region. Parhi et al. (2012) calibrated the channel roughness coefficient along the Mahanadi River in Odisha using the HEC-RAS. Boulomytis et al. (2017) discovered that using Manning's n roughness coefficients for various hydraulic models causes inaccuracies in inflow predictions for the Bashar River. Rivers must be studied since they are often used for agriculture or hydropower generation. An accurate estimation of the water surface elevation is necessary to construct and deploy the appropriate flood control structures and produce proper flow behavior (Kuriqi et al. 2019). In order to lessen the dependence on arbitrary static friction coefficients, Klipalo et al. (2022) conducted research by measuring and presenting actual data collected via quantitative testing. Full-scale field testing was conducted as part of this research to measure the frictional resistance produced between filled polypropylene bulk bags and seven typical bedding surfaces. Coefficients of static friction are used to convey the results of testing each interaction scenario. Three machine learning models (MLMs), including random forest (RF), ANN, and generalized linear model (GLM), were used by Avand et al. (2022) to investigate the impact of the spatial resolution of the DEMs 12.5 m (ALOS PALSAR) and 30 m (ASTER) on the precision of flood probability prediction. The findings show that, regardless of the employed MLM and irrespective of the statistical model used to measure the performance accuracy, resolving the DEM alone cannot substantially impact the accuracy of flood probability prediction. In contrast, the elements that affect floods in this area the most include height, precipitation, and distance from the river. The alterations in the water surface profile and flow velocity brought on by the bridge structural arrangement were studied by Ardiclioglu et al. (2022). For this reason, five flow discharges, four distinct bridge spans' water surface profiles, and flow velocities above and downstream of the bridge were examined. The HEC-RAS model was used to conduct the study both numerically and experimentally. At the bridge's upstream section, the average velocities calculated by HEC-RAS were vastly exaggerated. The average downstream and upstream measured velocities in the various apertures showed linear connections.

The aim of the present study is to validate the experimental results of the water surface profile of a two-stage channel with narrowing floodplains using one-dimensional numerical models. The approach proposed in this article uses the HEC-RAS to enhance numerical modeling. The dataset used in this study effort to complete the simulation effectively was gathered from the work of Naik & Khatua (2016), which was done on a variety of converging compound channels and provided the basis for this work. In order to compare and validate the experimental results, the same boundary conditions, cross-section data, and flow parameters were used. Finally, the simulated water surface level results were analyzed and compared to existing experimental data to evaluate and validate the findings.

Physical modeling

A series of experiments were conducted in a concrete flume 15 m long, 0.9 m wide, and 0.5 m deep with three different converging compound channels. The converging portion of the channel was constructed with the help of the Perspex sheet. The converging angles of the channel were 12.38°, 9°, and 5°, respectively, keeping the geometry constant. The non-prismatic compound channel has converging lengths of 0.84, 1.26, and 2.28 m, respectively. The subcritical flow regime was attained in several conditions of the two-stage channel with a longitudinal bed slope of 0.0011. The main channel and the floodplain subsections of these compound channels exhibit uniform roughness. Manning's n value of 0.01 was selected for smooth main channel and floodplain surfaces with trowel finishes (Subramanya 2015). Based on data collected from in-bank and overbank flows in the floodplains and main channel, Manning's n value variation was estimated in the converging section of the channel. This system recirculates the water supply by pumping it from an underground sump to a reservoir in the experimental channel. The rectangular notch has been surrounded by adjustable vertical gates and flow strengtheners. The removable flume tailgates help maintain a consistent flow over the test reach. A volumetric tank at the end of the channel is fitted with v-notch which has been used to measure the flow rate from the channel. The water collected in the volumetric tank goes back to the underground sump. The experimental channel has a limit of discharge that cannot increase beyond 0.055 m3/s. The geometric characteristics: B is the total width of the compound channel, b is the width of the main channel, h is the main channel depth, H is the flow depth at any discharge, and a cross-section of a two-stage channel are described in Figure 1.
Figure 1

Cross-section of a compound channel.

Figure 1

Cross-section of a compound channel.

Close modal
Figure 2 illustrates the experimental setup from the top. The plan view of non-prismatic cross-sections of Naik & Khatua (2016) channels is shown in Figure 3. Each point on the channel's plan could be accessed for measuring as part of the compound channel design. A moveable bridge could be used to collect the measurements. The research relies heavily on the channel's width ratio and aspect ratio. The flow velocity at the grid locations (shown in Figure 1) was measured using a pitot-static tube with a diameter of 4.77 mm. The order of maximum velocity for a given flow path was determined using a flow detector with a minimum least count of 0.1°. Use a circular scale and pointer configuration on the flow direction sensor to measure the pitot tube leg angle concerning the channel longitudinal direction. When combining the longitudinal velocity plot with the volumetric tank collection, the total discharge computed was within ±3% of the actual data. This study used velocity data and a semi-log plot to predict channel bed and wall shear stresses. The boundary shear stresses were calculated using Patel (1965) relationship and manometer measurements of Preston tube head differences. Shear values were corrected by comparing them to the equivalent values computed using the energy gradient technique.
Figure 2

Experimental setup.

Figure 2

Experimental setup.

Close modal
Figure 3

Plan view of non-prismatic sections.

Figure 3

Plan view of non-prismatic sections.

Close modal

Thus, the results were always within 3% of the actual value. According to laboratory data analysis, the pitot tube calculated tractive stresses are more accurate than ADV. For one thing, measuring velocity at the boundary with ADV is never trustworthy. In addition, ADV has specific limits for measuring the velocity near the bed and top surface. It can penetrate up to 5 cm below the top edge. Consequently, the micro-ADV down probe could not reach a distance of 5 cm from the free surface. It cannot measure the velocity beyond 2 m/s. In order to measure the transient decrease, a pitot tube was used near the bed and top surface. The U-tube manometer fitted along with the pitot tube measures the pressure difference values up to certain values. Verification of the validity of this approach was carried out using the energy gradient methodology (Naik & Khatua 2016).

Numerical modeling

To simulate a constantly changing flow, researchers opted for the HEC-RAS model, which works by computing the Saint-Venant equations (Equations (1) and (2)):
(1)
(2)
Equations (1) and (2) represent continuity and momentum equations, respectively, in which H denotes the elevation of water level, t and x indicate temporal and longitudinal coordinates, ql represents lateral inflow, which in our instance is 0; So is the bed slope of channel, and Sf denotes the slope of total energy line or friction slope. These equations were computed with the help of the finite-difference approach based on a four-point implicit box (Brunner 2016). Even though the finite-difference principle has limitations in transitioning between the subcritical and supercritical flow regimes, this procedure necessitates a new solution strategy for each flow state. However, the previous constraint may be avoided by employing the HEC-RAS model's mixed-flow regime option; by doing so, HEC-RAS can propose patching solutions in the river reach's sub-zones (Hicks & Peacock 2005; Timbadiya et al. 2011; Brunner 2016). The HEC-RAS model was calibrated by keeping the same experimental data, such as channel dimensions, boundary conditions, longitudinal bed slope, discharge data, and roughness coefficient values used in the experimental procedure. Manning's n value of 0.011 was inserted at the simulation stage for the main channel and floodplains based on the smooth trowel finish used in the physical modeling. Due to the almost continuous and uniform flow conditions at the study river reach, the downstream boundary condition was reset to its upstream condition. Figures 4 and 5 depict the plan, and 3D views of converging compound channel geometry created in the HEC-RAS with the 1 m resolution DEM was calibrated using measured experimental values within the channel reach. Figure 4 displays stations 900 and 500, which represent the upstream and downstream of the waterway, respectively. In contrast, stations 800, 700, and 600 correspond to the beginning, intermediate, and final segments of the converging section, respectively. Stations 900 and 500 are considered to be stationary; however, stations 800, 700, and 600 are not stationary, for all three converging angles of 5°, 9°, and 12.38°. The variation in distance between stations 800 and 600 is seen to be 2.28, 1.26, and 0.84 m, corresponding to converging angles of 5°, 9°, and 12.38°, respectively. The use of the same nomenclature for stations was implemented in order to mitigate any misunderstanding during the simulation procedure. The remaining stations located in both the straight and converging parts of the two-stage channel are considered interpolated stations. The HEC-RAS estimated water depth was then compared to the experimental water depth to validate the developed non-prismatic model of the compound channel.
Figure 4

Plan view of a converging compound channel in HEC-RAS.

Figure 4

Plan view of a converging compound channel in HEC-RAS.

Close modal
Figure 5

3D view of the converging compound channel in HEC-RAS.

Figure 5

3D view of the converging compound channel in HEC-RAS.

Close modal
Figure 6 illustrates the stage–discharge correlation for a relative depth of β = 0.25 at several locations along the converging section of different channels. These locations include the upstream of the channel, the start, middle, and end of the converging portion. The converging channels have varying degrees of convergence, denoted by θ = 5°, 9°, and 12.38°. The increase in discharge leads to a corresponding rise in flow depth. Nevertheless, a little decrease in the rate of increase occurs beyond the point when the river reaches its maximum capacity, mostly as a result of the interaction and subsequent transfer of momentum between the primary channel and the adjacent floodplains. The reduction in flow depth occurs in the converging section due to the convergence of channel geometry, while maintaining the same discharge. Furthermore, it has been shown that an increase in the angle of floodplain convergence at a given stage is accompanied by a corresponding rise in the flow rate. The empirical evidence obtained from stage–discharge correlations supports the notion that power functions exhibit consistency when applied to datasets containing big values.
Figure 6

Stage discharge relationship for various converging channels: (a) θ = 5°, (b) θ = 9°, and (c) θ = 12.38°.

Figure 6

Stage discharge relationship for various converging channels: (a) θ = 5°, (b) θ = 9°, and (c) θ = 12.38°.

Close modal
Figure 7 demonstrates the changes in velocity as a function of longitudinal distance for different converging channels, specifically at a relative depth β of 0.25. The terms ‘Vel chnl PF’, ‘Vel left PF’, and ‘Vel right PF’ refer to the mean velocities of the whole channel, the floodplain on the right side, and the floodplain on the left side, respectively. The variable ‘PF’ represents the flow depth at which the simulation has been done. The study determined that the average velocity of the channel was greater than the average velocity observed in both the right and left floodplains. The velocities are seen to begin at a uniform channel distance of 15 m, indicating the upstream portion of the compound channel. On the contrary, a numerical value of zero signifies the downstream portion of the compound channel. The commencement of the building of the converging segment of the canal took place at a distance of 6 m. After the start of the converging section, the velocities inside the floodplain zones undergo a decrease due to the convergence of the channel morphology, which enables the transfer of momentum from the floodplains to the main channel. An incremental rise in the velocity of the channel is noted in the prismatic section. However, the velocity experiences a significant spike in the converging section as a result of the abrupt constriction in the channel's shape. An increase in the convergence angle of the non-prismatic compound channel leads to a significant rise in velocity in the converging section.
Figure 7

Variation of velocity with longitudinal distance for relative depth β = 0.25 for various converging channels: (a) θ = 5°, (b) θ = 9°, and (c) θ = 12.38°.

Figure 7

Variation of velocity with longitudinal distance for relative depth β = 0.25 for various converging channels: (a) θ = 5°, (b) θ = 9°, and (c) θ = 12.38°.

Close modal
Figure 8 exhibits the fluctuation of shear stress in relation to the longitudinal distance for converging channels with a relative depth β of 0.25. The expressions ‘Shear Chan PF1’, ‘Shear LOB PF1’, and ‘Shear ROB PF1’ are used to refer to the shear stress experienced by the whole channel, the left floodplain (left bank), and the right floodplain (right bank), respectively. The variable ‘PF1’ represents the flow depth, denoted by β = 0.25, at which the simulation was performed. The study determined that the shear stress inside the channel exhibited a larger magnitude compared to the shear stress seen on the right and left floodplains. The initiation of shear stresses is seen at a uniform channel distance of 15 m, indicating the upstream portion of the compound channel. On the other hand, a numerical value of zero signifies the downstream portion of the compound channel. The commencement of the converging section of the canal occurred at a distance of 6 m. After the start of the converging section, the velocities inside the floodplain zones undergo a decrease due to the convergence of the channel morphology. This convergence enables the transfer of momentum, specifically in terms of shear, from the floodplains to the main channel. The magnitude of the channel shear stress exhibits an increasing trend as it progresses throughout the length of the flow. The convergence angle of the non-prismatic half of the channel has a direct impact on the shear stress increment seen in all three converging channels. As the convergence angle rises, the shear stress increment becomes more pronounced, mostly owing to increased resistance from the channel boundaries.
Figure 8

Variation of shear stress with longitudinal distance for relative depth β = 0.25 for various converging channels: (a) θ = 5°, (b) θ = 9°, and (c) θ = 12.38°.

Figure 8

Variation of shear stress with longitudinal distance for relative depth β = 0.25 for various converging channels: (a) θ = 5°, (b) θ = 9°, and (c) θ = 12.38°.

Close modal
Figure 9 displays the longitudinal water surface profile for different relative depths (β = 0.25, 0.30) at various locations along the converging part of channels with different convergence angles (θ = 5°, 9°, 12.38°). The locations include the upstream of the channel, the start, middle, and end of the converging segment. In the prismatic section of the flume, the water surface profile remains constant. However, it should be noted that throughout the converging section of the flume, there is a noticeable decline in the water level. This decline may be attributed to the acceleration of the flow, particularly in the latter half of the transition. In the lower section of the flume, the flow exhibits a mostly consistent pattern, but with occasional fluctuations. The magnitude of flow depth diminishes as the relative distance increases, and this decrease is more noticeable at larger converging angles. The reason for this phenomenon may be attributed to the convergence of the channel geometry inside the non-prismatic part of the compound channel.
Figure 9

Longitudinal water surface profile for different relative depths and converging angles: (a) β = 0.25, θ = 5°; (b) β = 0.30, θ = 5°; (c) β = 0.25, θ = 9°; (d) β = 0.30, θ = 9°; (e) β = 0.25, θ = 12.38°; and (f) β = 0.30, θ = 12.38°.

Figure 9

Longitudinal water surface profile for different relative depths and converging angles: (a) β = 0.25, θ = 5°; (b) β = 0.30, θ = 5°; (c) β = 0.25, θ = 9°; (d) β = 0.30, θ = 9°; (e) β = 0.25, θ = 12.38°; and (f) β = 0.30, θ = 12.38°.

Close modal
In Figure 10, a comparison is made between the empirically obtained flow depth and the flow depth calculated using HEC-RAS for non-prismatic compound channels with converging floodplain angles of θ = 5°, 9°, and 12.38°. The simulated values exhibit a similar pattern of variance to that found in the experimental data. The observed flow depths in the experiment exhibit a modest elevation compared to the values predicted by the HEC-RAS model. This disparity becomes more pronounced as the relative depths increase. The variability in flow depth measurements exhibits an upward trend as the degree of floodplain convergence increases.
Figure 10

Comparison of experimental and HEC-RAS simulated values of flow depth for different converging channels: (a) θ = 5°, (b) θ = 9°, and (c) θ = 12.38°.

Figure 10

Comparison of experimental and HEC-RAS simulated values of flow depth for different converging channels: (a) θ = 5°, (b) θ = 9°, and (c) θ = 12.38°.

Close modal

Different forms of error assessment, including the coefficient of determination (R2), root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), are examined using established equations to conduct further assessments on the precision of the simulated flow depths produced by HEC-RAS. Tables 13 provide a comprehensive investigation of statistical errors pertaining to flow depths in several converging compound channels. The findings indicate that the values of R2 for all three converging compound channels are more than 0.90, while the values of RMSE are less than 0.20. The MAPE for both the simulated and experimental findings is below 3%, suggesting a high level of performance and accuracy in the anticipated HEC-RAS results. Consequently, the HEC-RAS models that have been provided demonstrate a dependable methodology for forecasting the water surface profile in compound channels with converging floodplains. These models possess a notable capacity for adaptation and do not display any signs of excessive exertion.

Table 1

Statistical error analysis for converging channel, θ = 5°

ParametersConverging channel, θ = 5°
Relative depth, β = 0.25
Relative depth, β = 0.30
Experimental flow depth, HHEC-RAS flow depth, HExperimental flow depth, HHEC-RAS flow depth, H
Range 0.1379–0.1203 0.1352–0.1178 0.1466–0.1286 0.1431–0.1251 
R2 0.946 0.954 0.932 0.932 
RMSE 0.183 0.183 0.195 0.195 
MSE 0.0335 0.0335 0.038 0.038 
MAE 0.131 0.128 0.139 0.136 
MAPE 2.10 2.10 2.52 2.52 
ParametersConverging channel, θ = 5°
Relative depth, β = 0.25
Relative depth, β = 0.30
Experimental flow depth, HHEC-RAS flow depth, HExperimental flow depth, HHEC-RAS flow depth, H
Range 0.1379–0.1203 0.1352–0.1178 0.1466–0.1286 0.1431–0.1251 
R2 0.946 0.954 0.932 0.932 
RMSE 0.183 0.183 0.195 0.195 
MSE 0.0335 0.0335 0.038 0.038 
MAE 0.131 0.128 0.139 0.136 
MAPE 2.10 2.10 2.52 2.52 
Table 2

Statistical error analysis for converging channel, θ = 9°

ParametersConverging channel, θ = 9°
Relative depth, β = 0.25
Relative depth, β = 0.30
Experimental flow depth, HHEC-RAS flow depth, HExperimental flow depth, HHEC-RAS flow depth, H
Range 0.1380–0.1203 0.1355–0.1178 0.1443–0.1262 0.1408–0.1227 
R2 0.952 0.952 0.940 0.940 
RMSE 0.183 0.183 0.191 0.191 
MSE 0.0335 0.0335 0.0365 0.0365 
MAE 0.131 0.128 0.137 0.133 
MAPE 1.92 1.92 2.56 2.56 
ParametersConverging channel, θ = 9°
Relative depth, β = 0.25
Relative depth, β = 0.30
Experimental flow depth, HHEC-RAS flow depth, HExperimental flow depth, HHEC-RAS flow depth, H
Range 0.1380–0.1203 0.1355–0.1178 0.1443–0.1262 0.1408–0.1227 
R2 0.952 0.952 0.940 0.940 
RMSE 0.183 0.183 0.191 0.191 
MSE 0.0335 0.0335 0.0365 0.0365 
MAE 0.131 0.128 0.137 0.133 
MAPE 1.92 1.92 2.56 2.56 
Table 3

Statistical error analysis for converging channel, θ = 12.38°

ParametersConverging channel, θ = 12.38°
Relative depth, β = 0.25
Relative depth, β = 0.30
Experimental flow depth, HHEC-RAS flow depth, HExperimental flow depth, HHEC-RAS flow depth, H
Range 0.1381–0.1204 0.1355–0.1178 0.1444–0.1263 0.1408–0.1227 
R2 0.953 0.953 0.940 0.940 
RMSE 0.183 0.183 0.191 0.191 
MSE 0.0335 0.0335 0.0365 0.0365 
MAE 0.131 0.128 0.137 0.133 
MAPE 1.99 1.99 2.63 2.63 
ParametersConverging channel, θ = 12.38°
Relative depth, β = 0.25
Relative depth, β = 0.30
Experimental flow depth, HHEC-RAS flow depth, HExperimental flow depth, HHEC-RAS flow depth, H
Range 0.1381–0.1204 0.1355–0.1178 0.1444–0.1263 0.1408–0.1227 
R2 0.953 0.953 0.940 0.940 
RMSE 0.183 0.183 0.191 0.191 
MSE 0.0335 0.0335 0.0365 0.0365 
MAE 0.131 0.128 0.137 0.133 
MAPE 1.99 1.99 2.63 2.63 

In the present study, one-dimensional models have been made to simulate the water surface profile of a compound channel with converging floodplains using the HEC-RAS. Two relative depths (β = 0.25 and 0.30) and three converging angles (θ = 5°, 9°, and 12.38°) were investigated. Flow depth rises as discharge increases up to bankfull depth, but beyond bankfull depth, a modest decrease in depth was seen at all converging angles owing to interaction and momentum transfer between the main channel and floodplains. Due to the convergence of the channel geometry, the flow depth decreases with the length of the channel, and the same tendency has been seen for greater relative depths and varied floodplain convergence angles. The velocity and boundary shear stress followed the same trend of variation and observed a sharp rise in the converging portion of the compound channel. The flow regime is subcritical for both prismatic and non-prismatic reaches of a compound channel. The HEC-RAS projected water surface profile is slightly lower than the experimental values but follows the same trend as the observed water surface profile. The MAPE for flow depth computed experimentally, and HEC-RAS simulated is less than 3% for all three converging channels, showing the model's high performance and accuracy. It was observed that the estimated results are affected by bed slope, velocity distribution, flow resistance, secondary currents, and shear stress distribution. Localized variations in channel shape and 2D effects due to the curvature of a channel may also affect the water surface profile. The models developed in the study can have a practical application to non-prismatic rivers such as the River Main in Northern Ireland, the Brahmaputra River in India, and other similar rivers. The findings of the study will be useful in the design of flood control and diversion structures and thereby reducing economic as well as human losses. The present study was focused on non-prismatic compound channels with smooth floodplains. In terms of future study, it would be interesting to investigate the water surface profile under overbank flow circumstances with rough floodplains to improve the comprehensive flood defence plans.

The authors would like to express their most profound appreciation to the anonymous reviewers for their time spent on this paper.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

Ackers
P.
1992
Hydraulic design of two-stage channels
.
Proceedings of the Institution of Civil Engineers – Water, Maritime and Energy
96
(
4
),
247
257
.
Arcement
G. J.
&
Schneider
V. R.
1989
Guide for Selecting Manning's Roughness Coefficients for Natural Channels and Flood Plains
, Vol.
I
.
United States Government Printing Office
,
Washington, DC
.
https://doi.org/10.3133/wsp2339
.
Ardiclioglu
M.
,
Hadi
A. M. W. M.
,
Periku
E.
&
Kuriqi
A.
2022
Experimental and numerical investigation of bridge configuration effect on hydraulic regime
.
International Journal of Civil Engineering
20
(
8
),
981
991
.
https://doi.org/10.1007/s40999-022-00715-2
.
Avand
M.
,
Kuriqi
A.
,
Khazaei
M.
&
Ghorbanzadeh
O.
2022
DEM resolution effects on machine learning performance for flood probability mapping
.
Journal of Hydro-Environment Research
40
,
1
16
.
https://doi.org/10.1016/j.jher.2021.10.002
.
Berz
G.
2000
Flood disasters: lessons from the past – worries for the future
.
Proceedings of the Institution of Civil Engineers – Water, Maritime and Energy
142
(
1
),
3
8
.
Bijanvand
S.
,
Mohammadi
M.
&
Parsaie
A.
2023
Estimation of water's surface elevation in compound channels with converging and diverging floodplains using soft computing techniques
.
Water Supply
23
(
4
),
1684
1699
.
https://doi.org/10.2166/ws.2023.079
.
Boulomytis
V. T. G.
,
Zuffo
A. C.
,
Dalfré
F. J. G.
&
Imteaz
M. A.
2017
Estimation and calibration of Manning's roughness coefficients for ungauged watersheds on coastal floodplains
.
International Journal of River Basin Management
15
(
2
),
199
206
.
https://doi.org/10.1080/15715124.2017.1298605
.
Bousmar
D.
&
Zech
Y.
2002
Periodical turbulent structures in compound channels
. In
River Flow International Conference on Fluvial Hydraulics
,
Louvain-la-Neuve, Belgium
, pp.
177
185
.
Bousmar
D.
,
Wilkin
N.
,
Jacquemart
J. H.
&
Zech
Y.
2004
Overbank flow in symmetrically narrowing floodplains
.
Journal of Hydraulic Engineering
130
(
4
),
305
312
.
Brunner
G. W.
2016
HEC-RAS River Analysis System (Trans: Center HE)
, 5.0 edn.
U.S. Army Corps of Engineers
,
Davis, CA
.
Chlebek
J.
,
Bousmar
D.
,
Knight
D. W.
&
Sterling
M. A.
2010
Comparison of overbank flow conditions in skewed and converging/diverging channels
. In
River Flows International Conference
, pp.
503
511
.
Das
B. S.
&
Khatua
K. K.
2018a
Flow resistance in a compound channel with diverging and converging floodplains
.
Journal of Hydraulic Engineering
144
(
8
),
04018051
.
https://doi.org/10.1061/(ASCE)HY.1943-7900.0001496
.
Das
B. S.
&
Khatua
K. K.
2018b
Numerical method to compute water surface profile for converging compound channel
.
Arabian Journal for Science and Engineering
43
(
10
),
5349
5364
.
https://doi.org/10.1007/s13369-018-3161-y
.
Das
B. S.
,
Devi
K.
,
Proust
S.
&
Khatua
K. K.
2018
Flow distribution in diverging compound channels using improved independent subsection method
. In
River Flow 9th International Conference on Fluvial Hydraulics
. Vol.
40
, No.
05068
, p.
8
.
https://doi.org/10.1051/e3sconf/20184005068
.
Das
B. S.
,
Devi
K.
,
Khuntia
J. R.
&
Khatua
K. K.
2020
Discharge estimation in converging and diverging compound open channels by using adaptive neuro-fuzzy inference system
.
Canadian Journal of Civil Engineering
47
(
12
),
1327
1344
.
https://doi.org/10.1139/cjce-2018-0038
.
Das
B. S.
,
Devi
K.
,
Khuntia
J. R.
&
Khatua
K. K.
2022
Flow distributions in a compound channel with diverging floodplains
.
River Hydraulics: Hydraulics, Water Resources, and Coastal Engineering
2
,
113
125
.
Hicks
F. E.
&
Peacock
T.
2005
Suitability of HEC RAS for flood forecasting
.
Canadian Water Resources Journal
30
(
2
),
159
174
.
https://doi.org/10.4296/cwrj3 002159
.
James
M.
&
Brown
R. J.
1977
Geometric parameters that influence floodplain flow. U.S. Army Engineer Waterways Experimental Station. Vicksburg Miss, June, Research report H-77
.
Kaushik
V.
&
Kumar
M.
2023a
Assessment of water surface profile in nonprismatic compound channels using machine learning techniques
.
Water Supply
23
(
1
),
356
378
.
https://doi.org/10.2166/ws.2022.430
.
Kaushik
V.
&
Kumar
M.
2023b
Sustainable gene expression programming model for shear stress prediction in nonprismatic compound channels
.
Sustainable Energy Technologies and Assessments
57
,
103229
.
https://doi.org/10.1016/j.seta.2023.103229
.
Kaushik
V.
&
Kumar
M.
2023c
Water surface profile prediction in non-prismatic compound channel using support vector machine (SVM)
.
AI in Civil Engineering
2
,
6
.
https://doi.org/10.1007/s43503-023-00015-1
.
Khatua
K. K.
,
Patra
K. C.
&
Mohanty
P. K.
2012
Stage-discharge prediction for straight and smooth compound channels with wide floodplains
.
Journal of Hydraulic Engineering
138
(
1
),
93
99
.
Klipalo
E.
,
Besharat
M.
&
Kuriqi
A.
2022
Full-scale interface friction testing of geotextile-based flood defence structures
.
Buildings
12
(
7
),
990
.
https://doi.org/10.3390/buildings12070990
.
Knight
D. W.
,
Tang
X.
,
Sterling
M.
,
Shiono
K.
&
McGahey
C.
2010
Solving open channel flow problems with a simple lateral distribution model
.
River Flow
1
,
41
48
.
Kuriqi
A.
&
Ardiçlioǧlu
M.
2018
Investigation of hydraulic regime at middle part of the Loire River in context of floods and low flow events
.
Pollack Periodica
13
(
1
),
145
156
.
https://doi.org/10.1556/606.2018.13.1.13
.
Leandro
J.
,
Chen
A. S.
,
Djordjević
S.
&
Savić
D. A.
2009
Comparison of 1D/1D and 1D/2D coupled (Sewer/surface) hydraulic models for urban flood simulation
.
Journal of Hydraulic Engineering
135
(
6
),
495
504
.
https://doi.org/10.1061/(ASCE)HY.1943-7900.0000037
.
Liu
Z.
&
Merwade
V.
2018
Accounting for model structure, parameter and input forcing uncertainty in flood inundation modeling using Bayesian model averaging
.
Journal of Hydrology
565
,
138
149
.
https://doi.org/10.1016/j.jhydr ol.2018.08.009
.
Mowinckel
E.
2011
Flood Capacity Improvement of San Jose Creek Channel Using HEC-RAS
.
Calif Polytech State Univ
, California.
Myers
W. R. C.
&
Elsawy
E. M.
1975
Boundary shears in channel with flood plain
.
Journal of the Hydraulics Division ASCE
101
(
7
),
933
946
.
Naik
B.
&
Khatua
K. K.
2016
Water surface profile computation for compound channels with narrow flood plains
.
Arabian Journal for Science and Engineering
42
(
3
),
941
955
.
doi:10.1007/s13369-016-2236-x
.
Naik
B.
,
Kaushik
V.
&
Kumar
M.
2022
Water surface profile in converging compound channel using gene expression programming
.
Water Supply
22
(
5
),
5221
5236
.
https://doi.org/10.2166/ws.2022.172
.
Parhi
P. K.
,
Sankhua
R. N.
&
Roy
G. P.
2012
Calibration of channel roughness for Mahanadi River, (India) using HEC-RAS model
.
Journal of Water Resource and Protection
04
(
10
),
847
850
.
https://doi.org/10.4236/jwarp.2012.410098
.
Patel
V. C.
1965
Calibration of the Preston tube and limitations on its use in pressure gradients
.
Journal of Fluid Mechanics
231
,
85
208
.
Proust
S.
,
Rivière
N.
,
Bousmar
D.
,
Paquier
A.
&
Zech
Y.
2006
Flow in the compound channel with abrupt floodplain contraction
.
Journal of Hydraulic Engineering
132
(
9
),
958
970
.
Ramesh
R.
,
Datta
B.
,
Bhallamudi
S. M.
&
Narayana
A.
2000
Optimal estimation of roughness in open-channel flows
.
Journal of Hydraulic Engineering
126
(
4
),
299
303
.
https://doi.org/10.1061/(ASCE)0733-9429(2000)126:4(299)
.
Rezaei
B.
2006
Overbank Flow in Compound Channels with Prismatic and Nonprismatic Floodplains
.
PhD Thesis
,
University of Birmingham
,
UK
.
Rezaei
B.
&
Knight
D. W.
2011
Overbank flow in compound channels with non-prismatic floodplains
.
Journal of Hydraulic Engineering
137
,
815
824
.
Shiono
K.
&
Knight
D. W.
1991
Turbulent open channel flows with variable depth across the channel
.
Journal of Fluid Mechanics
222
,
617
646
.
Subramanya
K.
2015
Flow in Open Channels
, 4th edn.
McGraw Hill
,
India
.
Timbadiya
P.
,
Patel
P. L.
&
Porey
P.
2011
Calibration of HEC-RAS model on prediction of flood for lower Tapi River, India
.
Journal of Water Resource and Protection
03
(
11
),
805
811
.
https://doi.org/10.4236/jwarp.2011.311090
.
Wark
J. B.
,
Samuels
P. C.
&
Ervine
D. A.
1990
A practical method of estimating velocity and discharge in compound channels
.
Proc. River Flood Hydraulics
, pp.
163
172
.
Wormleaton
P. R.
,
Allen
J.
&
Hadjipanos
P.
1982
Discharge assessment in compound channel flow
.
Journal of Hydraulics Division ASCE
108
(
9
),
975
994
.
Yonesi
H. A.
,
Omid
M. H.
&
Ayyoubzadeh
S. A.
2013
The hydraulics of flow in nonprismatic compound channels
.
Journal of Civil Engineering and Urbanism
3
(
6
),
342
356
.
https://doi.org/10.1061/(ASCE)0733-9429(2000)126:4(299)
.
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