Smoothing River Discharge Time Series Computed Using the Velocity-Area Method

Abstract

Early warning systems for flood disaster mitigation involves hydrological and hydraulic models. These models require the discharge series as input and calibration. The indirect measurement of discharge, derived using the velocity-area method, presents errors, and thus, uncertainty. The associated uncertainty is mainly caused by the error in estimation since the direct measurement of discharge is neither feasible nor cost-efficient. Smoothing is employed to address the issue. Three smoothing techniques are proposed, i.e. Fourier smoothing, kernel smoothing using the Gaussian Density function, and LOESS Curve Fitting. Two river basins located in Davao del Sur, Lipadas and Padada, were evaluated. The Nash-Sutcliffe Efficiency (NSE) and RMSE-Observations Standard Deviation Ratio (RSR) were used to evaluate smoothing performance. Results showed that the Gaussian kernel smoothing technique outperformed both Fourier method and LOESS for both river discharge series. The values for both NSE and RSR indicated that the technique produced very good performances. The quality of smoothed discharge series was studied using two quality functions, Quality of Discharge (QOD) and BALANCE. Results showed that a more appropriate method would result in a better discharge quality regardless of the smoothing parameter chosen. Therefore, the smoothed discharge series is affected by the choice of smoothing technique and the method of choice is crucial. This study suggests that Gaussian kernel smoothing is a promising technique in smoothing discharge, with bandwidth at around 2 to 10. A very good quality of smoothed discharge is to be expected when the Gaussian kernel technique gives a very good smoothing performance.

Keywords: Smoothing · Fourier smoothing · Gaussian Kennel smoothing · LOESS Curve Fitting · NSE · RSR · discharge series · discharge quality