Note . R² = coefficient of determination; RMSE = root mean square error; n = number of observations

Figure 3. Error metrics for comparison of PIV velocity magnitude vectors against HEC-RAS 2D model predictions at reach A (a) and B (b) using both FFT and Ensemble correlation PIV algorithms.

When comparing the effects of different frame rates on PIV velocities, we consistently obtain the strongest statistical measures against our benchmark 2D model velocity predictions at a frame rate of 0.25 Hz using PIVLab’s FFT correlation algorithm (Table S1). River surface velocities inferred from satellite video via PIV showed acceptable agreement with 2D modelled velocities attaining peak R² values of 0.32 and 0.51 (p < 0.001) at reach A and B when sampling at a frame rate of 0.25 Hz and using the FFT algorithm. RMSE-observations standard deviation ratio (RSR) was 0.98 (A) and 0.79 (B), both greater than the optimal value of zero, indicating that PIV, in general, underestimated velocities as compared to the model.

The measured discharge was 582.01 m³s^-1 at the Tilpa gauge on 5 February 2022 at 23:12 UTC. LSPIV-based discharge estimates were computed at three cross-sections located in each reach (Figure 1) and ranged from 375.9 m³s^-1 (α = 0.7) to 639.9 m³s^-1 (α = 0.9), with median discharges of 536.2 m³s^-1 (reach A) and 483.4 m³s^-1 (reach B). Mean absolute percentage error for LSPIV-based discharge estimates was 10% (reach A) and 19.7% (reach B), with significant variations based on the alpha coefficient used to depth-average PIV-based velocities. Discharge variability was lowest at reach A, with a mean percentage bias of -0.07% as compared to -0.2% at B. Measurements computed at reach B predominantly underestimated the reference discharge value (582 m³ s^-1) by up to 206.11 m³s^-1 while those at reach A tended to overestimate observed discharge by up to 57.89 m³s^-1.