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.
Discharge accuracy
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.