Application of Cubic Spline Interpolation to Generate River Rating Curve

Abstract

The rating curve represents the relationship between discharge and water level in a water body including rivers. This pair of entities is obtained through the measurement of water depth and velocity and wet cross-sectional area. The water discharge itself is the multiplication of water velocity and wet cross-sectional area. The river perimeter, which is generally irregularly fluctuating, is an obstacle to the accurate calculation of wetted cross-sectional area using numerical integration methods so far. This paper presents the application of cubic spline interpolation to delineate the river cross-sectional perimeter to obtain a continuous mathematical equation that can be used to calculate the river cross-sectional area and the area in each segment of water velocity measurement. Based on the calculated riverwater discharge, the slope of the riverbed is then estimated using Manning's formula. In this paper, the rating curve of several rivers in Indonesia is presented. The algorithm of this method is written using Visual Basic in an interactive MS Excel environment and is open for further development.