Modeling of water surface profile in non-prismatic compound channels

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 [(H − h)/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.

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).

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 1–3 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.

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.