Arabian Journal for Science and Engineering https://doi.org/10.1007/s13369-018-3161-y RESEARCH ARTICLE - CIVIL ENGINEERING Numerical Method to Compute Water Surface Profile for Converging Compound Channel Bhabani Shankar Das 1 · Kishanjit Kumar Khatua 1 Received: 6 September 2017 / Accepted: 12 February 2018 © King Fahd University of Petroleum & Minerals 2018 Abstract Water surface profile prediction is an important task in flood risk management in the urban area. In the present research, based on the principle of the momentum balance a numerical method is investigated to predict the water surface elevations in compound channels with converging floodplains. Experimental data series are collected from literature on converging compound channels for different geometry and flow conditions to test the present model. The developed method requires the percentage of flow in the main channel. To deal with it, various existing flow distributions model is used in the developed numerical method to estimate the water surface elevation. The flow distribution model which provides less error in water surface profile computation for converging part of the compound channel is selected. Finite difference method is used to solve the numerical model using MATLAB tool. The results obtained from the simulation show a good agreement with the experimental datasets. Statistical error analysis has been performed to verify the strength of the present model and the other prevailing water surface profile models. The present model found to provide the minimum error in terms of mean absolute error, mean absolute percentage error and root mean square error. Keywords Water surface profile · Converging compound channel · Flow distribution model · Finite difference method · MATLAB Notations n Manning’s roughness coefficient B Width of the channel g Acceleration due to gravity H Total flow depth h Bank full depth W r Width ratio D r Relative flow depth θ Converging angle χ Relative longitudinal distance δ Aspect ratio S 0 Longitudinal bed slope U Mean velocity R Hydraulics radius of the channel Q Total discharge B Bhabani Shankar Das bsd.nitrkl@gmail.com Kishanjit Kumar Khatua kkkhatua@yahoo.com 1 Department of Civil Engineering, N.I.T. Rourkela, Rourkela, India Q mc Discharge in the main channel A Cross-sectional area x Position of channel section Abbreviation Cv3.81 Converging compound channel with converging angle 3.81 ◦ Cv5 Converging compound channel with converging angle 5 ◦ Cv9 Converging compound channel with converging angle 9 ◦ Cv11.31 Converging compound channel with converging angle 1.91 ◦ Cv12.38 Converging compound channel with converging angle 12.38 ◦ LGA Line of good agreement MAE Mean absolute error MAPE Mean absolute percentage error RMSE Root mean square error NITRF National Institute of Technology Rourkela flume UBF University of Birmingham flume UCLF University of Catholic de Louvain flume 123