On 17 July 2015, the Alyth Burn, Perthshire, Scotland (324600, 748600 OS BNG), breached its banks as a result of a prolonged period of rainfall over the catchment. While rainfall totals were not in themselves extreme (41 mm over a 6 h period), the prolonged nature of the precipitation event, coupled with the particular catchment configuration upstream of the town, resulted in over 70 properties being flooded and four footbridges in the town centre being destroyed (Perth and Kinross Council et al., 2015). During this flood event, a Phantom Vision 2 UAV equipped with a FC200 camera unit was deployed over the Alyth Burn in manual flight mode by a member of the public at ∼ 11:00 BST. The video footage itself was not collected with the intention of being used for flow reconstruction, but rather to document the impacts of the floods across the inundated area. Footage of the event was collected at 960 × 540 pixel (px) resolution at an acquisition rate of 25 frames per second (FPS).

Ground control points (GCPs) for the area of interest were required to convert the image (px) co-ordinates into geographical co-ordinates (OS BNG m). The deployment of a Leica MS50 multi-station shortly after the flood event enabled the generation of a detailed point cloud with an average point spacing of < 0.002 m from which GCPs could be accurately identified (Fig. 1, Sect. 2.1). These GCPs represented immobile objects that were present during the recording, and which persisted following the clean-up operation (e.g. lamp-posts and wall corners). Individual point clouds were joined using CloudCompare (2015), resulting in an internal error (RMS) of 0.04 m. This point cloud was rectified to real-world co-ordinates through comparison with control point measurements (n= 12) obtained by a Leica GS14 GNSS system. This resulted in an additional three-dimensional error of 0.06 m.

Due to the lack of available navigation data for the UAV, its starting position was modelled using an a priori assumption about its approximate location [Xest, Yest, Zest]. This was based on a visual assessment of the objects within view of the camera; 20 000 co-ordinate solutions were randomly generated (Xest ± 7.5 m; Yest ± 7.5 m; Zest ± 5 m), resulting in 8.9 discrete locations per m3 (Fig. 1, Sect. 2.2). For each of these potential starting positions, a distorted camera model was generated in MATLAB 2016a (cf. Messerli and Grinsted, 2015). For each camera model, the radial distortion coefficients and image centre parameters that define the camera lens were fixed based on the manufacturer's specification. The focal length and view direction (yaw, pitch, and roll) were however free parameters and allowed to vary accordingly. These were optimized to minimize the square projection error of pre-determined GCPs using a modified Levenberg–Marquardt algorithm (Fletcher, 1971). The optimal solution was subsequently defined as the master camera model, which was used as the basis for future projective transformations.

Following generation of the master camera model for the first frame of the video, an updated camera model solution based on updated GCP co-ordinates was generated for each subsequent frame (Messerli and Grinsted, 2015). This enabled UAV movement and changes in view direction to be accounted for. The updated camera model was obtained by randomly generating 1000 new camera positions proximal to the co-ordinates of the optimized camera model for the previous frame (X ± 0.25; Y ± 0.25; Z ± 0.25 m). These camera co-ordinates were then fixed whilst the view direction was perturbed. The optimum camera model for each specific frame was produced by minimizing the difference between the actual and projected GCP co-ordinates. In order for this to be achieved, GCPs were defined and tracked iteratively between each frame using the Kande–Lucas–Tomasi (KLT) algorithm (Shi and Tomasi, 1994). Every tenth frame, the positions of existing GCPs were manually checked and their location manually updated when changes in illumination conditions resulted in poor tracking performance. Additional GCPs were also manually added to account for changes in the camera viewshed (Fig. 1, Sect. 2.3). This ensured that sufficient GCPs were visible throughout the video and that they were still accurately focussed on the object in question. All GCPs were level with the water surface, non-mobile, and clearly visible within the laser scan generated point cloud.

Every nth and n + 9th frame, where n equals the start of the tracking sequence, the start and finish positions of the successfully tracked GCPs were stored in pixel units representing motion during the previous 0.4 s of video. The start and finish positions of the GCPs (px) are converted to real-world coordinates [NTET] using a two-dimensional transformation (Fujita and Kunita, 2011; Fujita et al., 1998), based on the optimized camera models specific to the nth and n + 9th frames (Messerli and Grinsted, 2015). The degree to which the geo-rectification process is a success is assessed by comparing how the co-ordinates of the surveyed GCPs [N,E] compare to the projected GCP locations [NT,ET]. The residuals [r,s] represent the absolute positional error of the GCPs and provide a direct measure of the accuracy of the geometric transformation from pixel units into geographical co-ordinates (Fig. 1, Sect. 2.4), given by the Euclidean distance between the actual and projected locations REN (Detert and Weitbrecht, 2015): r,s=[NT,ET]-[N,E],REN=(r2+s2)0.5. The degree to which the projection of the GCPs varies over time is assessed by examining the relative changes in the GCP projection locations (m) between the beginning and end of the feature tracking process: uEN,vEN=rn+9-rn,sn+9-sn,UEN=(uEN2+vEN2)0.5. Two-dimensional natural neighbour interpolation of the GCP errors is performed, giving spatially distributed estimates of REN and UEN (Fig. 1, Sect. 2.4).

As with the GCPs, between the nth and n + 9th frames, surface water features are defined and tracked using the KLT algorithm, with their start and finish positions being stored in pixel units. During this process, features were only tracked if they were within the central 90 % of the image. This was necessary to minimize the potential for residual distortion effects to bias measurements, as these were most likely to persist close to the image boundaries (Detert and Weitbrecht, 2015). The start and finish positions (px) of selected surface water features are converted to real-world start and finish co-ordinates, i.e. [Xn,Yn] and [Xn+9,Yn+9] respectively. This is again achieved through two-dimensional transformation (Fujita and Kunita, 2011; Fujita et al., 1998), based on the optimized camera models specific to the nth and n + 9th frames (Messerli and Grinsted, 2015). This method is analogous to the vector correction method (Fujita and Kunita, 2011) whereby stationary objects yield zero or negligible velocity values, with the movement of surface water velocity vectors being corrected for background image displacement. This process enables the calculation of two-dimensional velocities [u,v] following application of a conversion factor k to account for the number of tracked frames I and seconds per frame F: ΔXΔY=Xn+9,Yn+9,-Xn,Yn,k=1FI,[u,v]=[ΔX,ΔY][k], from which the velocity magnitude is obtained: U=u2+v2. Velocity (U) measurements in areas defined as having poor transformation accuracy (i.e. REN≥ 1 m), or significant apparent movement of the GCPs between frames (i.e. UEN≥ 0.3 m), are removed prior to analysis, in addition to tracked features exhibiting minimal displacement (i.e. U≤ 0.3 m). This resulted in 48 % of the original surface water features being eliminated (Fig. 1, Sect. 2.5).

Using the 20 000 potential solutions, the optimized master camera model was selected based on the minimum square projection error of the GCPs (RMSE – root-mean-square error). The minimum RMSE of the 20 000 solutions was 11.4 px (n= 8). Optimization of the initial camera model took 25 min (3.2 GHz CPU, 8 GB RAM) and accounted for 29 % of the total processing time. Following perturbation of geographical and orientation parameters for each frame, the flight path of the UAV was successfully modelled (Fig. 1, Sect. 2.3). The cumulative Euclidean distance travelled by the UAV over the 140 frames was 13.2 m (mean velocity = 2.5 m s-1), whilst the camera rotated on the y axis by 28∘ (Table 1). During the video the RMSE of the optimized camera did not exceed 12.9 px, with a mean μ of 9.6 px and a standard deviation σ of 1.3 px.

Analysis indicates that the precision of the geometric projection REN remains relatively stable throughout the video (Fig. 2a). However, the number of GCPs does exert some influence on the associated REN value. The minimum REN value of 0.4 m is observed at 0.8 s, when six GCPs are within shot. With the removal of GCPs that are difficult to resolve, located close to the upper edge of the frame, REN naturally decreases. The maximum REN value is 0.76 m, which occurs at 1.6 s (13 GCPs). This provides an indication of the minimum spatial scale over which measurements should be averaged and reported. Significant spatial variability in REN values is observed, with median individual GCP REN values ranging from 0.27 to 1.0 m (Fig. 2b). However, the interquartile range of REN for each GCP is relatively small, with a median value of 0.15 m. Furthermore, due to the lack of correlation between geolocation errors and the distance of the GCP from the camera source, we eliminate the potential for significant errors being a function of reduced pixel density per unit area as GCP distance increases (Fig. 2b). These findings indicate that the geo-registration errors are relatively stable and occur as a result of persistent residual distortion effects following image correction, especially close to the image boundaries, due to the specified transformation parameters being sub-optimal.

Whilst accurate geometric projection is essential for observed velocities to be assigned an appropriate spatial reference, the precision of the transformation over time is of greatest importance. Unacceptable apparent ground velocities as a result of unstable transformation over time would undermine the value of tracking surface features. This error UEN is quantified by computing the relative movement of reference features across each tracking interval. Unaccounted for movement generally decreases over time, following the maximum UEN of 0.28 m at 1.2 s through to the minimum of 0.05 m at 2.4 s (Fig. 3a). Median UEN values continue to be < 0.15 m throughout the sequence until the final frame when median UEN increases to 0.26 m. Unlike the spatial variability of REN values, UEN values for specific GCPs are observed to be relatively consistent (Fig. 3b). The median of the 15 GCPs ranges from 0.05 to 0.13 m, with no apparent relationship between the distance of the GCP and UEN. These findings illustrate the relative spatial and temporal stability of the geometric transformation. Occasionally however the apparent velocity of fixed targets, and therefore the associated error, is significant (i.e. > 0.3 m). In these instances, features tracked within areas of unaccounted for movement are identified and filtered from subsequent analysis (Fig. 1, Sect. 2.4).

Following the analysis of the 5.2 s video, and the filtering of features tracked from within inaccurately projected regions of the image, a total of 2644 velocity vectors were compiled within a 624 m2 area of the Alyth Burn and the surrounding inundated landscape (Fig. 4). This results in an average of 4.2 at a rate of 508 measurements s-1. Analysis of these vectors provides an insight into the complexity of interactions between flow, sediment load, and debris during flash floods. The bridge in the video (which was ultimately destroyed) was recorded in the imagery as being blocked by coarse woody debris (see Supplement). Due to the turbulent vortices generated by this blockage, surface velocities upstream of the bridge are calculated to be minimal (0.3–0.4 m s-1). This blockage reduced conveyance of the flood waters, with a proportion of channel flow becoming diverted into the adjacent street where surface velocities exceeded 1.2 m s-1 (Fig. 4). Similar breaches of the river defences upstream of the camera frame result in the routing of flood waters along the adjacent street. This routing produces velocities in the region of 0.9 m s-1 before these waters are mixed with those diverted from the main channel at the bridge within the camera shot. Further along the road, flow is disrupted by a partially submerged vehicle. This again results in the visible deflection of flow. In the main channel, immediately downstream of the bridge, large-scale turbulent structures as a result of secondary circulation are detected, with surface velocities progressively increasing to a maximum of 2.14 m s-1 (Fig. 4). The uncertainty attached to all calculated velocities is relatively low, with a spatial average across the area of ±0.15 m s-1. Little difference is observed in the uncertainty attached to out-of-bank velocities (±0.15 m s-1) and within-channel velocities (±0.16 m s-1), illustrating the consistency of the approach.

Application of feature tracking in open channels is dominated by methods operating in the Eulerian frame of reference (e.g. LSPIV). These methods have been widely successful in the characterization of instantaneous and time-averaged velocities for the determination of flood discharges, with deviations from acoustically derived measurements of < 10 % (Jodeau et al., 2008; Muste et al., 2008; Dramais et al., 2011). Measurements made in the Lagrangian frame of reference (e.g. LSPTV), where the paths of individual particles are assessed, have been less widely adopted for monitoring high-magnitude events. This is despite LSPTV replicating hydraulics accurately with improved performance close to boundaries and in areas experiencing high velocity gradients (Admiraal et al., 2004). Enhanced spatial resolution of measurements may also be possible with lower seeding densities (Detert and Weitbrecht, 2015). Our implementation of the KLT algorithm has demonstrated its potential to generate large volumes of temporally consistent data at a distance of up to 50 m. However, feature tracking from non-stationary platforms poses additional challenges in accounting for errors related to sensor movement and orientation. These challenges, which must be addressed for this approach to be beneficial for monitoring flood flows, are discussed in the following sections.

Transformation from pixel to world co-ordinates is one of the greatest challenges in generating accurate velocity estimates, even when measurements are conducted in controlled conditions from sensors of known, fixed locations (Lewis and Rhoads, 2015). Specific error associated with rectification can be controlled by ensuring the camera lens is (i) orthogonal to the water surface (e.g. Lewis and Rhoads, 2015); (ii) corrected for distortion (e.g. Le Boursicaud et al., 2015); and (iii) accurately calibrated using stable GCPs throughout the field-of-view (e.g. Dramais et al., 2011). Unfortunately it is not always possible to maintain the camera lens orthogonal to the water surface whilst capturing flow processes at the scale of interest, which often necessitates oblique image capture. Such oblique image capture may pose methodological difficulties due to far-field objects being poorly resolved relative to those in near-field. Secondly, lens distortion must be removed prior to the implementation of traditional plan-to-plan perspective projection (Le Boursicaud et al., 2015). This can be achieved based on the manufacturer's specifications (e.g. Detert and Weitbrecht, 2015), or through manual calibration (e.g. Tauro et al., 2015a); however, residual distortion may persist close to image boundaries. Finally, following internal camera calibration, the success of the transformation depends on the three-dimensional distribution of GCPs. Distribution of at least four GCPs is required for a two-dimensional transformation (Fujita et al., 1998; Fujita and Kunita, 2011), or a minimum of six GCPs distributed across the region of interest for a three-dimensional plan-to-plan perspective projection (Jodeau et al., 2008; Muste et al., 2008). For accurate transformation, elevation errors can be minimized by ensuring GCPs are similar to or located parallel to the water surface elevation (Jodeau et al., 2008; Fujita and Kunita, 2011). However, an implicit assumption of this approach is that the planar free surface is horizontal and that free-surface undulations are negligible across the frame. Due to the often negligible water surface slopes across the area of interest, errors are typically assumed to be insignificant (Hauet et al., 2008), with previous research indicating that water level errors of ± 0.3 m result in velocity deviations of < ±5 % (Le Boursicaud et al., 2015). A second source of elevation error may be induced by local water level variability as a result of standing waves created by hydraulic jumps, or obstacles. However, previous research (e.g. Dramais et al., 2011) has demonstrated that local variability of up to 1 m may still have an insignificant impact on stream-wise velocity measurements when images are collected perpendicular to flow.

In addition to oblique image capture, camera motion can greatly diminish the precision of any calibration and transformation process. In the case of monitoring fluvial flash floods from UAV platforms, camera motion is inevitable (Tauro et al., 2015a, b), and this movement should be corrected for on a frame-by-frame basis. This may be achieved through the utilization of on-board GPS systems (e.g. Bolognesi et al., 2016) or fixed reference points (e.g. Lewis and Rhoads, 2015). In the approach reported on here, we adopt a methodology to account for these uncertainties and their impacts on subsequent velocity measurements whereby fixed control points are manually selected and automatically tracked between frames using the KLT algorithm. Automatic tracking of GCPs is enabled by the distinct image textures of the water surface and the built environment, enabling the precision of the rectification process to be quantified and uncertainty in velocity measurements to be established. Whilst this procedure requires some supervision, in future deployments, purpose-built GCPs will be installed across the area of interest with distinct optical characteristics so that (semi-)automatic registration would be possible. However, in areas where naturally existing GCP features do not exist, or where installation of purpose-built GCPs would be problematic, a different approach would be required. Therefore, future research should seek to assess the potential for on-board GPS systems, ranging tools (e.g. lasers), and calibrated cameras to enable UAVs to be utilized. This will also open up the possibility of real-time capture of hydraulic properties of flow.

Due to the responsive nature of this survey of the July 2015 Alyth flood event, the distribution of GCPs was not pre-determined, so despite a total of 15 linear structures within the urban landscape that intersected the water surface being identified as GCPs, spatial coverage is incomplete and availability is temporally variable. While rapid response deployment of UAVs during floods may therefore introduce errors in the projection that would otherwise be accounted for in planned deployments, the majority of surveys at high discharge will naturally be “unplanned” and the result of rapid field deployment. Despite this, and the technical challenges of flying surveys during periods of heavy rainfall associated with floods, the relatively stable transformations achieved throughout the duration of the July 2015 Alyth video presented here demonstrate the utility of the approach.