## 5 Discussion
### Discussion of Interpolated Flow Volumes  
Given that average values resulting from ADCP-measured data are known to be more accurate than individual measurement cells or, in our case, 3D points, spatial interpolation is a good way to remove noise from data and gain a more simple and, possibly, a more accurate and realistic model of the hydrological situation. The 3D interpolation described in Section 3.2 serves to simplify the raw point cloud into a regular grid. This spatial averaging shrinks the conceptual gap between the time-integrated measurements consisting of time-specific snapshots to a time-integrated model consisting of spatially- and time-averaged points. [PERSON] and [PERSON] [7] determined that measurement duration was the most important factor in reducing uncertainty in flow measurements. Even though the interpolation integrates only a relatively small time span into one point, this does increase the measurement duration of the interpolated point data compared to the instantaneous measurements represented in the raw point cloud. Each point in the 3D matrix represents a locally-averaged flow velocity, direction and depth value. This local averaging implicitly introduces short-term time averaging, not just of the previous and subsequent second, but including points from neighboring lines of the zig-zag pattern, which may be close by, but measured over a minute away in time. In a way, the 3D interpolation acts as a low-pass filter that removes small local variation and, therefore, can be considered to remove short-term variability. It has been reasoned [13; 25] that the interpolation of spatially densely measured data reduces uncertainty in velocity measurements. [PERSON] _et al._[13] concluded that the spatial smoothing resulting from interpolation reduces variance in ADCP velocities, but that, at the same time, this elimination of temporal fluctuations may reduce our capacity to capture complex flow fields, while still enabling the mapping of large-scale eddies or turbulence. While no longer representing raw measured data, the 3D-interpolated model is still based exclusively on measured 3D data, as opposed to a computational model. The matrix resulting from the interpolation allows us to express 3D points in terms of volume (voxel), both total volume of water in a certain reach or volumes of water moving at certain velocities. Clearly, the volumes derived in this manner are estimates, since they are based on the number of voxels without taking into account that voxels near the river bed may not be cubic in reality. This inaccuracy is analogous to an irregular 2D polygon represented as a raster, which, at its edge, is only an abstraction of a real line, exhibiting a jaggedness depending on the resolution of the raster. The boundary of an irregular voxelspace, as is the river bed, exhibits the same kind of jaggedness, but on a surface, instead of a line. Considering that the ADCP's ability to measure flow and related parameters accurately in the immediate vicinity of the river bed is limited [40], this voxel space may be in any case the best approximation to be had in that area. The effect of the abstraction of the raw measurements, and the raw shape of the water column, into the 3D voxel space is evident when comparing the histograms of flow velocities of the raw data points (Figure 14) to the interpolated points (Figure 13). The raw flow data contains a considerable amount of low velocity flow measurement points, whereas these are absent in the interpolated point cloud. This is likely due to the above-mentioned edge behavior of the voxels. Much of the edge data that contains the majority of low velocities near the river bed and the shallow areas on the inside of the meander bend gets abstracted into voxels that contain higher velocities. Moreover, since this analysis pertains to measured data, the portion of the river that is not captured by the ADCP, notably the blanking distance near the sensor [40; 41; 42], is excluded from these volumes.