Measurement of surface velocity in open channels using a lightweight remotely piloted aircraft system

ABSTRACT In this paper, a low-cost remotely piloted aircraft system (RPAS) technique is proposed for measurement of the surface velocity in rivers or channels with low surface velocity and small discharge. To verify the reliability of the results obtained with the RPAS, we simultaneously measured the surface velocity with other methods based on total stations and close range photogrammetry. The RPAS was used both with ground control points (GCPs) for orientation of the photographic images and without GCPs. The data analysis showed that the RPAS provides valid results even without GCPs. Use of a RPAS without GCPs, relying solely on flight altitude to determine the water velocity, opens the way for its utilization in emergency conditions when it is impossible to access the river banks for the realization and survey of GCPs.


Introduction
River discharge estimation plays a fundamental role in a number of fields: it is essential for planning a rational and responsible use of water resources, ensuring that they are correctly and adequately managed, controlling flood events and mitigating hydraulic risks. In common practice, discharge estimation methods are indirect, since they rely on flow point velocity measurements within the cross-section, whose bathymetry is assumed to be known.
The velocity-area method is one of the most widely used discharge measurement techniques (UNI EN ISO 748 2008): it requires knowledge of the cross-sectional geometry and current meter measurements at different depths along a sufficient number of verticals located within the flow area. While the velocity-area method is particularly reliable, it turns out to be laborious, time-consuming and costly because of the considerable commitment of equipment and personnel, with poor accuracy close to the riverbed due to the presence of vegetation. Moreover, strong currents, which typically occur during exceptional flood events, may cause danger to operators or prevent completion of the velocity sampling.
A valid alternative for discharge estimation is the entropy method: it is based on the principle of entropy maximization and has been used in different fields of research to derive the probability density function of a specific random variable. This approach was applied for the first time to open channel hydraulics by Chiu (1987Chiu ( , 1988 to identify the corresponding (probability) distribution of flow velocity, from which a linear relationship between the mean velocity and the maximum velocity u max in a river cross-section is derived as a function of a dimensionless parameter M (Chiu 1991; CONTACT M. Bolognesi blgmcl@unife.it Xia 1997), i.e.
From a practical viewpoint, the dimensionless parameter M must be preliminarily estimated in order to convert the maximum velocity u max into the mean section velocity U .
In this regard, Farina et al. (2014) proposed a procedure requiring only the maximum surface velocity measurement to estimate the parameter M. Therefore, the possibility of indirectly deriving discharge from the maximum velocity recorded on the surface would not only drastically reduce the measurement times and costs but would eliminate the problems related to monitoring with traditional techniques and instruments (such as current meters), particularly during major floods.
However, the maximum surface velocity must be estimated with sufficient accuracy. The simplest and most practical technique for surface velocity measurement relies on the use of 'non-contact' radar sensors based on the Doppler effect (Costa et al. 2000;Melcher et al. 2002;Cheng et al. 2004;Costa et al. 2006;Fulton & Ostrowski 2008). Although radar sensors are accurate instruments, their application is restricted to velocities exceeding 0.2À0.3 m/s. Thus, we are unable to measure velocity via radar sensors in drainage systems characterized by slow currents.
Alternative 'non-contact' approaches for surface velocity measurement are based on particle image velocimetry (PIV) (Adrian 1991;Adrian 2005). This methodology has been adopted in several hydrological studies to deduce the displacement field of natural tracers (foam, leaves) or artificial tracers added to the surface to carry out measurements with a fixed camera installed on a roof (Creutin et al. 2003), on a bridge (Muste et al. 2008;Tauro et al. 2016), on a telescopic rod (Jodeau et al. 2008) or on a tripod Tauro, Mocio et al. 2012), which allows for surface flow monitoring at a limited number of locations. Recently, significant efforts have been made to extend PIV to manned (Fujita & Hino 2003;Fujita & Kunita 2011) and remotely piloted aircraft systems (Pagano et al. 2014;Tauro, Pagano et al. 2015;Tauro, Petroselli et al. 2015): the main advantage is the ability to rapidly characterize water flow systems in large areas that can be difficult to access by human operators. Because of the low cost of remotely piloted aircraft system (RPAS) and the significant progress in navigation systems and on-board sensors, remote sensing from an RPAS, previously used in cultural heritage surveying (Bolognesi et al. 2014), is now widely used in environmental sciences. There are numerous data acquisition applications: monitoring of aquatic vegetation (Derkx et al. 2015), surveillance of a watercourse (Baroux & Gardes 2015), evaluation of areas suitable for infrastructure construction (Viguier & Forest 2015) and estimation of river discharge (Detert & Weitbrecht 2015).
With regard to river discharge, a remarkable advantage of an RPAS is that it allows non-contact measurements of surface velocity in wide rivers during a flood event with inaccessible areas, which make fixed measurement implementations impractical. Nevertheless, applications of an RPAS to estimate surface water velocity are very limited in number and are typically related to natural rivers with maximum surface speeds of 2À2.5 m/s (Detert & Weitbrecht 2015;Fujita & Kunita 2011).
In this paper, a low-cost RPAS technique is proposed for measurement of the maximum surface velocity in rivers or channels with low surface velocity and small discharge. The measurement technique is based on photogrammetry, in particular the processing of sequences of digital images taken at low altitude, which reflect the different positions of one or more floats in time during their movement along the channel. The data processing is very simple and does not require specialized software.
This method allows reconstruction of the distribution of the surface velocity when several floats are positioned in the channel across the flow width; with only one float, it allows determination of the maximum surface velocity only after prior verification of where the maximum velocity occurs. However, since it is well known that the maximum surface velocity occurs approximately at the centreline of the flow width in a prismatic section (Chiu & Lin 1983;Chiu 1988;Chow et al. 1988;Chiu & Tung 2002), a single float located at the centre of the examined watercourse allows maximum surface velocity estimation.
The technique was applied in two test channels with small cross-sections and low surface velocity. To verify the reliability of the results obtained with the RPAS, we simultaneously measured the surface velocity with three other methods based on total stations, close range photogrammetry and radar gun. Nevertheless, only the first two were used in comparisons because the sensitivity of the radar gun proved inadequate for measurement of such low surface velocity.
The proposed survey technique could easily be used in situations of environmental emergency, when time is limited and access to flooded zones is both difficult and risky. This technique is also advantageous in very wide rivers and in the absence of bridges, when measurement of the maximum speed at the centre is extremely difficult.

Test sites
The proposed method was verified using data from two channels of the drainage system managed by the Consorzio di Bonifica Pianura di Ferrara: Fossa Masi (Masi Torello) in Figure 1 and Valle Isola (Comacchio) in Figure 2. They were selected because they are easily accessible, have low flow velocity typical of drainage channels, and feature downstream hydraulic devices (gate or pumping station) which allow easy and reliable discharge estimation.
Fossa Masi is a 'mixed-use' channel because its behaviour varies according to the different seasonal uses. While in winter (OctoberÀMarch) the channel is almost empty and used to drain off excess rainwater from surrounding farmland, its capacity inevitably decreases in summer (AprilÀSeptember) because irrigation water is fed into it and several gates located along the channel can be used to maintain the desired water level necessary for irrigation. Being partially water-filled, Fossa Masi has less capacity than in winter, so that if it rains the gates are opened to control the flow, the channel empties and its drainage efficiency increases.
The segment considered for this study is upstream of a gate located near a bridge ( Figure 1). During winter this gate is maintained totally elevated, without intercepting the flow, while in summer it is lowered to maintain the desired volume of water in the channel. During the velocity measurement, the gate was lowered totally and its lower end lay on the cement sill on the channel bottom near the bridge, thus behaving as a gate weir.
Valle Isola collects the water of the whole channel system serving the Valle Isola drainage area adjacent to the Ferrara seaside. This channel flows through the drainage area from north to south and carries the water to the Guagnino pumping station ( Figure 2). This station, located south of the drainage basin, mechanically raises the water to sea level with different groups of pumps and a maximum discharge of 17.9 m 3 /s. The segment considered for this study is located very close to the pumping station, about 60 m upstream. In both channels we identified two cross-sections as parallel to each other as possible and perpendicular to the main direction of the channel in order to delimit a segment where velocity measurements were carried out. The two segments considered for this study are straight and of uniform cross-section and slope, with a stable bed and margins; they are sited far enough from the weir and the Guagnino pumping station, respectively, to avoid unsteady flow conditions during measurements.
In prismatic sections of channels with the characteristics listed above, it has been amply demonstrated that the distribution of surface velocity is approximately symmetric, with the maximum value located more or less at the centreline of the flow width. Therefore, we preliminarily verified the symmetry of the velocity distribution by analyzing the movement of several floats across the whole width of the channels; it was confirmed that the maximum velocity occurred in the centre zone of the flow width. In view of these results, we considered the transit of single floats located at the centreline of the flow width to estimate the maximum surface velocity. Only one velocity measurement was performed for the first site, while two campaigns were carried out for Valle Isola, corresponding to the following configurations of the Guagnino pumping station: configuration C1 with one active pump and discharge of 3.5 m 3 /s; configuration C2 with two active pumps and discharge of 5.1 m 3 /s. Obviously, the higher the discharge the greater the flow velocity. A few days before the tests, the bathymetry was measured at one of the end sections and the value was considered representative of the whole investigated segment. The cross-sections of both channels are shown in Figure 3. The reliability of the measurements of maximum superficial velocity depended on the assumption that the motion of the floating object was as uniform as possible, located in the centre of the channel and directed parallel to the channel's central axis. To ensure that this assumption was achieved we conducted multiple repetitions of the tests and rejected those not meeting the requirements.

Determination of surface velocity via total stations and close range photogrammetry
To validate the RPAS technique, we applied three alternative measurement methods at both test sites to be carried out at the same time as the RPAS survey; for this we used a 'non-contact' radar sensor (radar gun), two total stations and a couple of cameras. Moreover, we used some small artificial floats made of polystyrene and plastic, with an approximately parallelepiped shape, that met the following requirements: be easily identified on images taken from the RPAS and from the ground and maintain the same speed as the water without being affected by wind.
The method based on total stations is simple and accurate. In correspondence of each of the two cross-sections of the channel, we set-up a total station with the line of sight lying on the vertical plane of the section (Figure 4). Before the start of the survey, several floats were thrown into the channel near the centre so that they could be carried by the stream. To determine the exact moment when the floating object crosses the reference section it is sufficient to observe its passage through the reticule of the total station's telescope. The time interval Dt between the passage of any float from the first to the second total station reference plane was measured with a stopwatch (with an a priori standard error of 0.1 s). Since the distance Ds between the sections is known (with an a priori standard error of 5 mm) the average speed vts of the moving float is computed as follows: vts D Δs Δt (2) Table 1 shows the results of several determinations of the velocity in both channels and the corresponding standard deviation obtained from error propagation for uncorrelated variables. In view of the accuracy of the method, the results obtained with total stations were assumed as reference values for other tests.
At the same time as the total stations measurements, a photogrammetric survey was performed with a device consisting of a bar set parallel to the channel with two cameras (CANON Powershot SX130) with parallel optical axes perpendicular to the axis of the channel ( Figure 5). With two identical cameras with the same focal distance, the field of view (L) is the same (L1 D L2) and the base B (in this case 0.906 m) is constant regardless of the distance between the cameras and the floats (7.9 m in Fossa Masi and 15.8 m in Guagnino). The test procedure is described in Figure 6. In particular, the time Dt that the float takes to travel along the base is where t 0 is the instant in which the object exits the field of view of the left camera (L1) and t 1 is the instant in which the object exits the field of view of the right camera (L2).

Hence the average surface velocity is
To obtain the necessary images we acquired two videos with a resolution of 1280 £ 720 pixels and a focal length of 5 mm. By analyzing the extracted frame (29 frames/s) we could determine very precisely the two instants when the floaters were out of sight in the two images.
The values obtained with the photogrammetric method and the corresponding standard deviations (with a priori standard error of 0.1 s and 5 mm for the time and distance values, respectively) are listed in Table 2.
This method is valid if some simple assumptions are met: the axes of the cameras must be parallel and, as mentioned at the end of Section 2, the direction of the floating objects must be straight and parallel to the camera bar. To prevent erroneous results, we performed numerous tests and measurements for which the assumptions were not met were rejected.
Many radar gun measurements were made in both channels but reliable results were not obtained due to the low water velocity, below the sensitivity of the Doppler technique.
The results obtained with total stations and photogrammetry were compared. As seen in Table 3, the differences are very small, both in absolute and percentage terms, confirming the reliability of both techniques.

Determination of surface velocity via RPAS
Simultaneously with the measurements by total stations and photogrammetry, we carried out measurements with the remotely piloted aircraft system. For this experiment, we used a DJI S800 RPAS equipped with a calibrated CANON EOS M mirrorless camera with a focal length of 18.688 mm. The camera was mounted on the RPAS with a gimbal that keeps the optical axes nadiral to the ground (Figure 7). The RPAS was maintained at a constant height of 30 m over the first channel (Fossa Masi) and 50 m over the second (Valle Isola), with GSD (ground sample distance) of 8 mm in the first case and 13 mm in the second. The images had a resolution of 5184 £ 3456 pixels. The difference in height between the two tests was due to the need to get both sides of the channel into every digital image in order to orient them on the basis of GCPs (ground control points). All images were corrected for optical distortion by a careful process of self-calibration carried out with the photogrammetric software Photomodeler®. For this measurement technique we employed the same floats used with the total stations and photogrammetry.

Determination of surface velocity with GCPs
Four targets were positioned on the banks of the channel, two on the left and two on the right, at a distance such that all were visible in each photographic image (Figure 8). These targets would then be used as GCPs during orientation of the images. Moreover, their three-dimensional positions were detected in a local reference system with a total station with an estimated standard error about 5 mm lower than the GSD. In the same reference system we measured the height of the water surface with a total station. For each flight, sequences of about 100 images were acquired by setting the camera in the 'time lapse' mode between shots. Time lapses of 2 and 3 s were set for the tests. For each image we used Photomodeler® to determine: the orientation parameters in the local reference system (realized by GCPs), the size of the GSD and the position of any float. Hence the displacement Ds of the float in the direction of the axis of the channel between two successive instants is obtained from the vector whose components are the coordinate differences between two images acquired at time  interval Dt. The value of the average speed is obtained for any pair of images and any float by the ratio between Ds and Dt. Table 4 reports the average values of surface velocity resulting from numerous measurements carried out with all the floats available for the test.

Determination of surface velocity without GCPs
The results obtained in Section 4.1 show that it is possible to detect the water surface velocity as long as GCPs are used for the orientation of frames taken with the RPAS. However, in the case of an environmental emergency or wide rivers/channels, it may be difficult or even impossible to use GCPs. Therefore, at least the flight altitude from which to calculate the scale of the frame must be known. If the RPAS remains still during the test, the flight altitude does not vary over time and the reference system is determined merely by the optical centre of the camera. The measurement of the space travelled by the float does not require an absolute reference system. The RPAS stability is an important aspect to be verified. A first check of the flight stability of the RPAS was carried out by analyzing the change of its coordinates obtained from the external orientation of images (image geo-referencing by GCPs as described in Section 4.1). A data set of 16 images taken from the Valle Isola (C1) test at regular intervals of 3 s for a total of 48 s was analyzed. The coordinate values are reported in Figure 9.
The  water surface. From the focal length (18.668 mm) and pixel size of the camera's sensor (0.0044 mm), we obtained a GSD of 0.0125 m. The position of the float in the image is given by the position of the corresponding pixel in a reference system fixed to the CCD (charged-coupled Device)/ CMOS (complementary metal-oxide-semiconductor) sensor. Thus in each image it is possible to measure the pixel position of the float (using the correct image without distortion) and to easily calculate the distance travelled by the object between two successive times. With these assumptions and not knowing the orientation of the images, it is not possible to evaluate the position of the float in an absolute reference system. Hence its position at each instant was determined from its pixel coordinates on each image. The distance travelled (Ds) was obtained from the difference between these coordinates. It is clear that a possible displacement of the RPAS between one image and the other would lead to a change of scale (for vertical displacement) of the image and an error of the horizontal position of the float (for horizontal displacement). The objective of the simulation was to identify the best procedure for image processing to minimize the effect of the position error of the RPAS on the calculation of the water surface velocity. For the Valle Isola (C1) test, two different calculation methods were used: in the first method (M1) we measured the velocity between images taken every 3 s; in the second method (M2) we calculated the velocity for increasing intervals between the first image and all subsequent ones. With method M1 (see Figure 10) we obtained an average velocity of 0.174 m/s. A result like this involves long data processing because it is necessary to acquire a large number of images and to correct the distortion and make a measurement for each one. As seen in Figure 9, the distances travelled by the float in just 3 s are very small (0.28À1.05 m) and thus fluctuations in the position of the RPAS (comparable with those distances) significantly influence the estimate of the velocity. However, such fluctuations appear to be random and tend to compensate each other, as demonstrated by the fact that the average velocity is in line with the one obtained by the other techniques. This suggests that larger measuring intervals would tend to minimize the influence of the RPAS fluctuations with respect to the motion of the float. To confirm this, we performed measurements with progressively larger intervals (method M2) and observed the respective velocity results.
With method M2 (see Figure 11) the average velocity was 0.153 m/s. As the measurement interval increases, the estimated velocity approaches the calculated average value. This means that both methods can be used for the velocity estimation, although the second (M2) is more practical because reliable results can be obtained with only two images, one at the start and one at the end of the test.

Comparison
The comparison of the measurements made with the RPAS, with total stations and with photogrammetry is shown in Table 5.
The surface velocity estimation carried out with the RPAS with GCPs is in good agreement with those obtained with total stations for the Valle Isola 1 and 2 tests (Dv < 10%), while there is a remarkable difference in percentage with respect to the Fossa Masi test (Dv D 26.5%). However, this result is probably due to the very low water velocity. In fact the difference between the absolute values of the estimated velocity is only 0.009 m/s. Table 6 compares the results obtained only with the RPAS. The velocity estimation can be performed with both calculation schemes, i.e. even without the use of GCPs, as long as there is a sufficient number of velocity determinations. In conclusion, both proposed methods seem reliable and the fluctuations of the RPAS position are considered acceptable for the purpose of the measurement.

Conclusions
The use of an RPAS to determine the maximum water surface velocity, for the purpose of estimating its flow, was tested in two channels with small cross-sections and low water velocity. To validate the results obtained with the RPAS we also determined the surface velocity via total stations and a photogrammetric survey from the ground carried out with a special device. In particular, the RPAS method was carried out both with GCPs for orientation of the photographic images and without GCPs. The use of a RPAS provides satisfactory results even without GCPs (with minor differences of 10%) as long as there are appropriate numbers of separate velocity determinations.
In this experiment we made use of special floats, although natural objects such as driftwood could be used provided they are not affected by wind. The action of wind is particularly important when the water velocity is very low.
The use of an RPAS without GCPs, relying solely on telemetry to determine the water velocity, opens the way for its utilization in emergency conditions when it is impossible to access the river banks for the realization and survey of GCPs.
As regards the hydraulic aspect, measurement of the maximum surface velocity allowed estimation of the discharge by means of the method proposed by Farina et al. (2014). This method allows estimation of the discharge based only on the maximum water surface velocity since the channel cross-section is known. It is noteworthy that, in both case studies, a ca. 10% uncertainty in the measurement of the maximum water surface velocity leads to a similar 10% uncertainty in the estimation of the discharge. However, this uncertainty value is acceptable for practical purposes and is not significantly higher than the uncertainty that typically characterizes discharge measurements, even when much more time-consuming approaches (e.g. the velocity-area method) are used (UNI EN ISO 748 2008; Alvisi et al. 2014). Therefore, a clear advantage can be derived from using the Farina et al. (2014) method to monitor channel discharge given that RPAS data are now available and suitable for the measurement of water surface velocities. This procedure reduces the times and costs of taking measurements and ensures the maximum safety of personnel.