Development of Stage – Distance – Discharge Relationship and Rating Curve using Least Square Method

Abstract

For any river, besides the importance of stage – discharge relationship (rating curve), a stage-discharge- distance relationship is of more significance.  The accurate estimation of both relationships along a river reach is considered a key point for various applications of water resources engineering such as operation and management of water resources projects, designing of hydraulic structures, and sediment analysis.  In this paper, both relationships were established for the Shatt Al – Hillah river reach by applying multiple linear regression and simple linear regression using least square method for determining regression equations. Twelve gauging stations including three primary and nine secondary stations were considered for this method. Moreover, for evaluating the performance of both regressions, statistical measures such as coefficient of determination, root mean square error, mean square error, and Thiel's factor were used. The study results generally indicate a superior performance of both modeling techniques. MLR model was able to predict and mimic the stage-discharge-distance relationship with a coefficient correlation of about 0.932, while SLR model was able to predict three rating curves for the three primary stations with coefficient correlation of about 0.960, 0.943, and 0.924 respectively.