An Integrated Regression Model for Estimating the Velocity Index in Non-Contact River Discharge Measurements

Non-contact river discharge measurement techniques, such as radar-based surface velocity sensors, are increasingly applied in hydrological observations due to their advantages in operational safety and accessibility during flood events. However, these sensors directly measure only surface velocity, and reliable discharge estimation therefore requires conversion to depth-averaged velocity using an accurately estimated velocity index (α). In practice, α is often treated as a constant or determined empirically, which can lead to substantial uncertainty, particularly under unsteady flow conditions. 

This study proposes a regression-based framework to quantify the velocity index as a function of hydraulic and flow variability characteristics, using field observations from natural rivers. Both Acoustic Doppler Current Profiler (ADCP) measurements and radar-based surface velocity data are employed. First, reliable depth-averaged velocities and velocity profiles are obtained from ADCP observations, from which reference velocity index values are derived. Subsequently, corresponding α values for radar observations are generated using stage–discharge relationships, and the regression dataset is expanded by integrating both ADCP- and radar-based cases.

The velocity index is formulated using a hybrid multiplicative regression model incorporating water surface slope, channel aspect ratio, and the rate of water level change (dH/dt). In particular, the inclusion of the water level change rate explicitly accounts for unsteady flow effects occurring during rising and falling stages of flood events. Model performance and robustness are comprehensively evaluated using adjusted coefficient of determination, root mean square error, mean absolute percentage error, and variance inflation factor to assess both predictive accuracy and multicollinearity.

Results indicate that the three-variable model consisting of water surface slope, channel aspect ratio, and water level change rate achieves the most favorable balance, exhibiting the lowest prediction errors while maintaining low multicollinearity. The incorporation of dH/dt is shown to effectively represent hysteresis effects in the relationship between surface velocity and depth-averaged velocity during flood conditions, significantly improving model stability.

The regression model proposed in this study is developed based on an integrated dataset combining ADCP and radar observations and provides a velocity index formulation that is applicable across a wide range of hydraulic conditions, including unsteady flood flows, without dependence on a specific sensor type. The results confirm that the proposed model contributes to improving the reliability and consistency of depth-averaged velocity estimation in non-contact river discharge measurements.

Keywords : Non-contact river discharge measurement, Velocity index (mean velocity conversion coefficient), Surface velocity, Unsteady flow conditions, Regression model

 

Acknowledgements 

This work was supported by Korea Environment Industry & Technology Institute (KEITI) through Research and development on the technology for securing the water resources stability in response to future change Program, funded by Korea Ministry of Climate, Energy and Enviroment (MCEE)(RS-2024-00336020)