Hysteresis-influenced stage-discharge rating curve based on isovel contours and Jones formula

Considering the hysteresis effect, the stage-discharge rating curve (SDRC) is challenging to measure at gauge stations. Hysteresis also causes uncertainty in SDRC estimations. Therefore, an accurate method to estimate discharge is essential in such conditions. In steady flow conditions, isovel contours can be used to estimate SDRC. However, this method has not been investigated in unsteady conditions. This study uses the Jones formula and isovel contours-based SDRC to consider the hysteresis in Chattahoochee River, USA. First, this method identifies hydro-geometric parameters, such as velocity parameters extracted from isovel contours, to calculate the steady SDRC (SSDRC). Then, it is combined with the Jones formula to estimate loop SDRC (LSDRC). The SSDRC is calibrated using the Markov chain Monte Carlo (MCMC) method. MCMC calibrates model parameters by iteratively selecting parameters that best fit the observed data from the parameter space. Also, uncertainty in model output can be characterized using the posterior distribution of model parameters. The results show that LSDRC is more accurate than SSDRC based on R 2 , mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) metrics. Also, the proposed method outperforms the power function rating curve. The proposed model achieved a maximum MAPE of 6.6%, while the power function rating curve reached 24.6%.