An entropy-based surface velocity method for estuarine discharge measurement

An entropy-based method is developed to estimate estuarine river discharge from surface velocity measurements. A two-dimensional velocity profile based on the principle of maximum entropy is employed to express the mean velocity as a function of average surface velocity. The entropy-based flow profile is parameterized by the location of maximum velocity in the channel and the shape of the velocity distribution. The entropy parameters are quantified over the tidal cycle to account for the unsteady nature of estuarine flow. The method was tested using experiments conducted at the Danshui River, the largest estuarine system in Taiwan. Surface velocities were measured using an Automated River-Estuary Discharge Imaging System (AREDIS), and full-channel velocity profiles were measured with a moving-boat ADP survey. Entropy parameters were calibrated over the tidal cycle and linearly correlated with the average surface velocity to facilitate estimation from AREDIS measurements. The discharge calculated from average surface velocity and entropy relationships exhibits a 7.7% relative error compared to the ADP velocity profiles. The error nearly doubles when the mean values for entropy parameters are used instead of the variable parameters, indicating the importance of accounting for the unsteady nature of estuarine flows. Furthermore, the effects of measurement coverage area, types of entropy distribution, and wind-induced drift current on the surface velocity-based discharge measurement are evaluated and discussed. Overall, surface velocity measurements in conjunction with the entropy profiles well represent the flow in a complex estuarine environment to provide a reliable estimate of discharge.