Three different models to evaluate water discharge: An application to a river section at Vinh Tuy location in the Lo river basin, Vietnam

This study presents three different models, namely power-law rating curve, one-dimensional lateral distribution method (1D–LDM), and gated recurrent network (GRU) model that can be applied to evaluate water discharge from water surface elevation time-series in a river cross-section for a long time period. A river section at Vinh Tuy location on the Lo river basin (Vietnam) is used to demonstrate the models. Appropriate values of modelling parameters are carefully determined using (i) the daily observed discharge values collected in the period from 2012 to 2018 and (ii) five error estimates for quantitatively assessing the agreement between estimated and observed water discharges. The results showed that all three models reproduced very well the observed discharge values, with root mean square error and mean absolute error, as well as mean error of discharge, are only about 5.5% of the maximum value of discharge monitoring in the studied cross-section, while Nash–Sutcliffe efficiency and Pearson’s correlation coefficient are greater than 0.89. The models are then applied to evaluate discharge values in the studied cross-section for the period from 1972 to 2011, revealing that statistical indicators, i.e. mean value, standard derivation, and covariance of estimated water discharge, are consistent with those obtained from the observations. Among three investigated models, the GRU model was finally proved to be the best one, providing even better results than the 1D-LDM and power-law rating curve.