Accuracy Improvement of Discharge Measurement with Modification of Distance Made Good Heading

Remote control boats equipped with an Acoustic Doppler Current Profiler (ADCP) are widely accepted and have been welcomed bymany hydrologists for water discharge, velocity profile, and bathymetry measurements.The advantages of this technique include high productivity, fast measurements, operator safety, and high accuracy. However, there are concerns about controlling and operating a remote boat to achieve measurement goals, especially during extreme events such as floods. When performing river discharge measurements, the main error source stems from the boat path. Due to the rapid flow in a flood condition, the boat path is not regular and this can cause errors in discharge measurements. Therefore, improvement of discharge measurements requires modification of boat path. As a result, the measurement errors in flood flow conditions are 12.3–21.8% before the modification of boat path, but 1.2–3.7% after the DMG modification of boat path. And it is considered that the modified discharges are very close to the observed discharge in the flood flow conditions. In this study, through the distance made good (DMG) modification of the boat path, a comprehensive discharge measurement with high accuracy can be achieved.


Introduction
Considering the steadily increasing water demand in Korea, accurate river discharge information is important for sustainable water resources management such as flood control, hydraulic structure design, and hydroenvironment management.Efforts have been made to accurately collect river discharge information by performing systematic measurements and introducing emerging technologies [1].However, it is not easy to measure the river discharge accurately and efficiently.Existing river discharge measurement methods that are most commonly deployed in Korea to date are the floating rod method and current meters.Quick and convenient measurement is the advantage of these methods, but there is a drawback that the uncertainty of velocity and cross section area increases due to the unknown flow route when the floating rod does not flow along the assumed straight line.However, in recent years, the Acoustic Doppler Current Profiler (ADCP), which can probe velocity and bottom changes simultaneously, has been increasingly adopted as an acceptable tool in Korea and is now regarded as the preferred method [2].Because this method measures the change of flow velocity and depth of cross section continuously, this method has an advantage of detailed consideration for the change.
The ADCP was first developed to log ship speed on the ocean.It was subsequently introduced as a method to measure water discharge in the late 1980s.By the 1990s, the use of ADCP equipment gradually increased due to the improvement of accuracy of river measurements and the riverbed tracking function.
The United States Geological Survey (USGS) used the actual measurement results at 12 hydrological stations to examine the application of an ADCP to water discharge measurements and demonstrated that there was more than a 5% error by comparing the existing Price AA current meter and the stage-discharge relationship [3].Mueller [4] evaluated various ADCP models using discharge measurements in the field and analyzed the bias caused with the riverbed tracking function.Oberg [5] examined the existing method and suggested a technique that is able to calculate the deviation of a riverbed tracking function using a differential global positioning system (DGPS).Gartner and Ganju [6] conducted a study to clarify the measurement error of the current velocity near the water surface, which might be physically disturbed by the ADCP's housing with the small blanking distance, as compared with acoustic Doppler velocimetry (ADV).González-Castro et al. [7] noted that the current velocity in the downstream direction had a large bias in representing the time-averaged current velocity and stated that this bias could be reduced by spatial leveling as they compared data of the instantaneous current velocity measured by a mobile ADCP with the measurement result of a fixed ADCP.Adler and Nicodemus [8] developed a method in which the data measured by the ADCP was conducted through postprocessing to calculate an average velocity vector, whereas Muste et al. [9] conducted a study that calculated the velocity vector after postprocessing result measured by the ADCP.Muste et al. [9,10] presented that a turbulent flow could be calculated when an ADCP was deployed at a fixed position and the suggested postprocessing procedure was utilized.In recent years, there have been attempts to measure the bed load movement and concentration of a suspended load using the backscatter intensity of an ADCP [11][12][13].Parsons et al. [14] demonstrated that ADCPs have become multipurpose instruments, demonstrating considerable promise for an improved process-based understanding of geophysical processes in a wide range of hydrological environments [15][16][17][18][19][20][21][22][23][24].
In this study, we improve the discharge measurement using remote-controlled boat with ADCP.However, there is a measurement error due to irregular boat path in flood flow.Therefore, the development of a method to reduce this measurement error will enable the river discharge to be measured more accurately and efficiently and we focused on the method to determine an optimal cross section of an arbitrary path due to a remote-controlled operation in a flood condition.For this, the distance made good (DMG) line by the east-north-up (ENU) coordinate system was used to resolve these issues.

Acoustic Doppler Current Profiler (ADCP).
An ADCP transmits, receives, and processes ultrasonic waves reflected from neutrally buoyant particles inside a small volume and gates them into a specific depth and then produces velocity profiles.An ADCP measures the instantaneous current velocity; this approach is different from that of a general current meter, which only measures point velocity.Therefore, there is a difference between the velocity data obtained from an ADCP and the time-averaged velocity data obtained from continuous measurement over dozens of seconds.Figure 1 illustrates a typical ADCP.There are four independently working acoustic beams with each beam angled 20-30 ∘ from the vertical axis of the transducer assembly [25].
River discharge can be measured by an ADCP mounted on a moving boat.The ADCP autonomously identifies the direction of the boat and the current velocities using a built-in compass.It calculates the discharge by combining the distance moved over a time interval, the shape of a cross section, and the current velocity.The ADCP is able to measure discharge of large rivers.The ADCP calculates discharge using (1).When using ADCP data to measure discharge, the integral in ( 1) is replaced by a summation, and the elements  and  are replaced by Δ and Δ, which are the depth and horizontal resolutions of the ADCP measurements, respectively.The depth resolution Δ corresponds to the range interval.The horizontal resolution Δ depends on the boat speed and is equal to the distance traveled by the boat during the time interval [26].Consider where  is the discharge,  is the position along an arbitrary line across the river,  is the horizontal unit vector normal to the line at ,  is the velocity vector, and  is the water depth.
An ADCP extracts the current velocity elements used in a discharge calculation by subtracting the boat velocity, which is calculated by river bed tracking from the measured velocity and changing from the progress direction of the boat to an element at a right angle.Therefore, when the ADCP movement is faster than the actual flow, errors can easily occur when measuring the current velocity.In particular, the error is known to increase when the current velocity is slow [25].Therefore, the ADCP movement should not exceed three times the current velocity, and ADCP should be employed at a velocity slower than the current velocity to obtain the most optimal data [27].

Instrument Setup.
A remote-controlled boat equipped with an ADCP and RTK (real-time kinematic) GPS (global positioning system) was used to measure the bottom geometry, velocity profile, and river discharge simultaneously.This remote-controlled boat is propelled by twin DC (direct current) brushless motors with a 2.4 GHz RC controller, providing control up to 1 km and operating for 3 hours with a 12 V 30 A DC battery (see more details in Table 1).The positional information of the remote-controlled boat is produced in three ways: bottom tracking, DGPS (differential GPS), and RTK GPS.The bottom tracking is the preferred method when there is no bed load movement.The accuracy of DGPS and RTK GPS is 1-2 m and 2-3 cm, respectively.Three different types of positional information play important roles in reducing the error in the bathymetry measurement.

Distance Made Good (DMG).
A rhumb line is an arc crossing all meridians of longitude at the same angle as shown in Figure 2(a), and that is a path with constant bearing as measured relative to true or magnetic north.On a Mercator projection map, a rhumb line is a straight line as shown in Figure 2(b).Distance made good is the distance between two points on the Earth along a rhumb line connecting the two points.

Site Characteristics.
To evaluate the compatibility and accuracy of the moving boat method in normal and flood flow conditions, discharge measurements were performed at Mokgye site in Korea (Table 2, Figure 3).This site has a welldefined rating curve because of the upstream Chungju regulation dam release.Figure 4 illustrates the flood discharge data from the Chungju regulation dam and the water levels of the Mokgye site from June 28, 2011, to June 30, 2011.As shown in the figure, the Mokgye site is directly influenced by the Chungju regulation dam, and there are very limited or no tributary inflows between the Mokgye site and the Chungju regulation dam, with the controlled discharge data from the dam securing the rating discharge of this site.Table 2 shows the hydrological characteristics of the Mokgye site.

Measurements under Normal and Flood Flow Conditions.
In this study, field measurements for two events (event 1: May 18, 2012; event 2: June 28, 2011) were performed to assess discharge in normal and flood flow conditions.The measurements were repeated five and two times, respectively.Table 3 provides the actual observed water level and discharge at the Mokgye site, and the maximum water levels and discharges for events 1 and 2 are el.52.87 m and el.54.86 m and 127.63 m 3 /s and 2,020.62m 3 /s, respectively.
Under flood flow conditions, the maximum flow speed reached 4 m/s, and the boat meandered along the path as its maximum speed was 2 m/s.Despite these unfavorable conditions, the remote-controlled boat measured flood discharge successfully, and the discharges were 1,771.13m 3 /s   4.Under normal flow conditions, the measured discharges were in the range of 122.92-129.83m 3 /s.

Operational Challenge for the Measurements.
The USGS provides guidelines to measure the average river sectional discharge by four consecutive measurements with the same water level condition in a moving boat [25].However, for remote-controlled ADCP measurements there is an operational challenge for the flood discharge measurements.It is maintaining the boat track to match the desired cross section under fast flow conditions [28,29].The problem can be solved by adopting the DMG line by the east-northup (ENU) coordinate velocity projections on the track line under normal flow conditions [28].However, under flood flow conditions, the DMG heading of a moving boat cannot easily be fixed because the actual measured cross section changes constantly.Therefore, the DMG heading cannot be determined physically during the measurement.DMG heading is determined based on the postprocessed measured path from the data set.The RiverSurveyor Live program can only provide the starting edge and ending edge setup for the DMG calculations.However, in the moving boat method, particularly under flood flow conditions, the starting and ending points are not clear because the user cannot fix the cross section due to the reasons provided above.The boat movement changes continuously from a straight line because there is no sufficient amount of thrust to maintain a highspeed flow.The changing streamline does not match a straight DMG line that corresponds to the conventional tag line idea.The straight DMG line should be processed after the measurement to obtain the optimum DMG heading.

Evaluation and Modification.
The differences between the first measurement and the rating for events 1 and 2 are presented in Table 5.Under flood flow conditions, the differences were 249.49(12.35%) and 431.31 m 3 /s (21.82%) for Cases 6 and 7, respectively.Under normal flow conditions, however, the differences were relatively very small in the 0.89-4.71m 3 /s (0.70-3.69%) range.Consequently, the measured discharges   under normal flow conditions were very close to observed (rating) discharge while there were relatively large differences under flood flow conditions.
As previously discussed, main source of errors is from the DMG heading judgment because the boat was allowed to drift downstream.So as to maintain the cross section alignment until the end point, the boat sailed to the upstream direction for some distance.To resolve this issue, the DMG line must be modified.In steady and straight flows, the cross section is simply the shortest path between the two banks.The flow streamline meets the cross section line perpendicularly, and the DMG line should be the cross section line.As unsteady and nonuniform flows occur frequently in meandering rivers, the cross section can be changed depending on the streamline changes, and therefore, the cross section line changes as the water level changes.Thus, the DMG line should be a line that produces the largest discharge under the possible cross sections because the flow vectors should remain perpendicular to the DMG line.
Following this assumption, the DMG headings of the data sets in flood flow cases were modified to find the maximum discharge via trial and error.For this, the repetition calculation is applied to get the maximum discharge by changing the DMG heading direction at discharge measuring section.The discharge is recalculated by changing arbitrarily the heading direction, and it is repeated until the maximum discharge is found.As a result, the maximum discharges for flood flow condition were calculated at 8.6 and 231.0 (deg.) of the heading direction, and therefore, these heading lines were chosen for the river cross section.Figure 5 the   discharge modification using the DMG heading modification for Cases 6 and 7.As shown in Table 6, the modified discharges were estimated by setting the DMG heading to reflect the actual cross-sectional flow direction.

Results and Discussions.
The modified discharge estimates according to the above aspects are shown in Table 7 and the differences are 24.9-73.2m 3 /s (1.2-3.7%).Table 7 demonstrated that the differences decrease by 11.1-18.1% in flood flow conditions.Figures 6 and 7 illustrate the final vertically averaged velocity profile with the final discharge for the river cross section of two cases.In Figures 6 and 7, the units of the and -axes are transformed to display the position in universal transverse Mercator (UTM) coordinates, and the axis is the water depth.The red line is the river bed along the boat's route, the black dotted line is the DMG line, and the color scale legends are the vertically averaged velocity in the flow direction.

Conclusion
In this study, the river velocity profiles and discharge under normal and flood flow conditions were measured by a remotely control boat with an ADCP and RTK GPS.The advantages of this technique include high productivity, fast measurements, operator safety, and high accuracy.However, there are concerns about controlling and operating a remote boat to achieve measurement goals, especially during extreme events such as floods.The raw estimates of discharge show more than a 10% difference compared with well-established rating tables.When performing river discharge measurements, the main error source has been identified as the boat path.Due to the rapid flow in a flood condition, the boat path is not regular and this can cause a measurement error of discharge.To resolve the differences, DMG heading modifications were established.The DMG heading modification uses a line that produces the largest discharge under the cross section where the flow vectors should remain perpendicular to the DMG line.As a result, the modified discharges are very close to the observed discharge in the flood flow conditions.With these modifications, a comprehensive discharge measurement with high accuracy is achieved.
Rhumb line on Mercator projection map

Figure 2 :
Figure 2: Rhumb line and distance made good.

Figure 4 :
Figure 4: Discharge data from Chungju regulation dam and water levels at the Mokgye site.

Table 1 :
Specification of remote-controlled boat.

Table 3 :
Time series of hydrologic events used in this study.

Table 4 :
Discharge measurements in this study.

Table 5 :
Comparison of maximum measured and observed discharge.

Table 6 :
Discharge estimation results according to DMG heading modification.

Table 7 :
Comparison of modified and observed discharges.