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[Display omitted] • Two widespread despiking algorithms implemented on Fluvial Acoustic Tomography (FAT) data. • Discharge measurement accuracy improved significantly using data despiking methods. • 3D-Rousseeuw Phase-Space, recognized as the best method for despiking FAT data. Streamflow is an important hydrological factor in water resources management. The Fluvial Acoustic Tomography (FAT) as a cutting-edge river monitoring technology measures the flow velocity using the travel time of the acoustic signals. The velocity is then multiplied by the river cross-section to obtain accurate and continuous streamflow data. Similar to all acoustic instruments, the FAT output velocity contaminated by spike data. Standard deviation (STD) as a simple method of spike removing, was used in previous FAT studies. The disadvantages of the STD method are that it not only does not replace the identified spikes with the appropriate values and therefore results in measurement discontinuity, but it also requires engineering judgment that may increase the measurement error. In this study, two despiking methods, i.e., Phase-Space Thresholding (PST) and three-dimensional Rousseeuw Phase-Space thresholding (3D-RPS) are applied to detect/modify outliers of a 6-day FAT velocity signals. The results showed that the 3D-RPS method has the best performance with a Nash-Sutcliffe efficiency coefficient (NSC) of 0.731 compared to 0.572 and 0.44 NSC values of STD and PST methods, respectively. The FAT-based streamflow data were also compared with the reference streamflow obtained from the Rating-Curve method. The results reveal that the streamflow measurement accuracy improves significantly, where the relative errors decrease from ± 40% for the STD method to ± 15% for the 3D-RPS approach. As a result, the 3D-RPS approach appears to be an effective method for improving the accuracy of the FAT-acquired streamflow data. [ABSTRACT FROM AUTHOR]