Figure 2. Discharge estimation workflow
Water depths were estimated by intersecting the flood extent limits in the satellite imagery with a DEM. Depths at each vertical are computed by subtracting the local bed elevation from the maximum water elevation along a cross-section (Figure 2b) from a 1 m resolution LiDAR DEM with a vertical and horizontal accuracy of 0.3 m and 0.8 m respectively (Geoscience Australia, 2022). The DEM was acquired when the river channel was dry, effectively incorporating bathymetry. Since PIVLab provides discrete velocity measurements at specific vector locations, interpolation was necessary to obtain continuous velocity maps. Here we used inverse distance weighting, a spatial interpolation approach where sample points are weighted based on their distances from the unknown location being interpolated. LSPIV-derived surface velocities along cross-sections are converted to depth-averaged using a specified coefficient α . Hauet et al . (2018) and Le Coz et al . (2010) constrain α between 0.8 – 1 for deep natural channels experiencing flood discharges.
Results
LSPIV velocity accuracy
Stabilization and georectification of images used in PIV are subject to errors that propagated uncertainty to computed velocity estimates. Maximum, minimum, and mean displacement errors associated with stabilization of extracted frame sequences were 0.42, 0.055, 0.237 and 0.442, 0.15, 0.261 pixels for reach A and B respectively, all less than a single pixel width. Total georectification root mean square error (RMSE) was 0.5 and 0.77 m at reach A and B, respectively, and was uniform for all frames since all our stabilized images relied on a single affine transformation matrix. Since our smallest search area was 8 pixels, equivalent to a distance of 9.8 m, our residual georeferencing errors were 5.1% and 7.9% of the spacing between our PIV velocity vector maps. Figures 3 and S1 (in the supplementary material) summarize the results of the quantitative velocity accuracy assessment of LSPIV (processed using both FFT and Ensemble correlation PIV algorithms at frame rates of 0.25, 0.5 and 1 Hz) against calibrated HEC-RAS 2D model predictions.