## 1 Introduction  
The flow characteristics of water in a river influence both the channel morphology and the riverine habitats, which are of great interest to fluvial scientists and engineers alike, for instance in the fields of hydro-power or other in-channel construction, as well as habitat restoration [1] or pollution dispersion [2]. These are complex dynamic processes that have thus far been challenging to map over a continuous spatial extent. The spatial distribution of flow patterns is useful knowledge in studying riverine habitats [3] and geomorphology [4], especially in meander bends, where the distribution of flow velocities is non-uniform, both in the down-stream and the cross-stream direction [5, 6]. Flow field data of high spatial resolution will be beneficial for investigations of fluvial processes--especially in river channels with complex flow structures, such as meandering or braided channels, at confluences or diffluences or around engineered objects, such as dams or bridge pylons, to name but a few--as well as in calibrating and validating computational models over complex river reaches. The use of acoustic Doppler current profilers (ADCP) for measuring streamflow [7] and discharge is becoming increasingly widespread [8]. The principles of the operation of ADCPs are described in great detail, for instance, in [PERSON] _et al._[9] and [PERSON] _et al._[10]. Briefly, ADCP measurements derive flow velocity from the Doppler shift of the measured return of an emitted acoustic signal that is reflected off suspended matter in the water column. The information from a combination of several (usually three or four) acoustic beams is used to calculate the mean velocity and flow direction, based on the assumption that the acoustic scatterers move at the same speed as the water and that flow is homogeneous over the area covered by the beams. These locally-averaged flow measurements are split vertically into cells (bins) that each represent a flow vector at a certain depth. When deployed from a moving vessel, a series of these velocity components measured perpendicular to the cross-section produces a transect of flow vectors across a stream, usually represented in the form of a raster, where each raster cell represents one flow vector. Generally, this series of measurements in a transect is used to calculate discharge. Several researchers have used a series of such transect measurements to analyze flow characteristics in natural streams [11, 12]. Most flow mapping has focused on measurements along a series of transects in a channel measured using either an ADCP [13, 14, 15, 16] or an acoustic Doppler velocimeter (ADV) [17, 18, 19, 20]. [PERSON] _et al._[15] developed a set of software tools that facilitates the analysis and visualization of such transect-based measurements, and they showcase several impressive examples where a series of transects is used to characterize the 3D flow of several river reaches. The transect-based approach gives insight into the flow field in 3D, along the transect and through the water column. This approach is, however, limited in providing information of the areal flow field over a river reach, leaving considerable gaps between the transects. Another approach is to employ sampling trajectories that move beyond the classical transect arrangement towards a more spatial coverage, either surveying a dense pattern of transects intended for spatial interpolation [21] or employing a spatially irregular or continuous survey pattern [22; 23; 24; 25], employing real-time kinematic GPS for accurate positioning of the flow measurements. This approach allows the investigation of the areal flow field by generating, for instance, depth-averaged flow maps along with bathymetry maps. However, the third dimension of flow variation in the water column is not represented in a 2D flow field map. [PERSON] and [PERSON] [22] interpolated ADCP-measured flow vectors onto a 3D grid in order to represent the flow field in three dimensions at the reach scale.