### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental Setup
- 3. Postprocessing of Reference ADCP Data
- 4. Configuration of H-ADCP Discharge Computation Strategies
- 5. Evaluation of Discharge Computation Methods
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[1] Fixed side-looking Doppler current profilers (H-ADCP) recently emerged as an innovating technique for the continuous monitoring of river discharges. The discharge can be computed from the flow velocities measured by the H-ADCP along a horizontal profile across the section. This paper reports a field assessment of the quality of velocities and discharges provided by a 3-narrow-beam Teledyne RD Instruments, Inc. (RDI) 300 kHz H-ADCP installed at the Saint-Georges gauging station (Saône river in Lyon, France). Reference velocity and discharge values were established from 18 conventional ADCP river gauging campaigns over an extended discharge range (100–1800 m^{3}/s). The comparison with ADCP data revealed that H-ADCP velocity measurements were reliable (deviations <5%) in a near-field range only (60 m out of a 95 m total section width). In the far field (beyond 60 m), H-ADCP velocity measurements showed negative bias of up to −50% 90 m from the instrument. For section-averaged velocities lower than 0.4 m/s approximately, H-ADCP velocity measurements were found to be significantly underestimated over the whole cross section. The performances of several strategies (index velocity method and velocity profile method) for computing discharge were tested, compared, and discussed. For the velocity profile method, several profile laws and far-field extrapolation methods were implemented. Both methods gave acceptable discharge values (deviations <5% typically) excepted at low-flow conditions. The reasons why H-ADCP velocities were unacceptably biased low in the far field and for low flow conditions require further investigation in order to define correcting measures.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental Setup
- 3. Postprocessing of Reference ADCP Data
- 4. Configuration of H-ADCP Discharge Computation Strategies
- 5. Evaluation of Discharge Computation Methods
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[2] The real-time monitoring of discharge in natural streams and man-made canals is difficult. It requires both the continuous survey of some hydraulic parameters and the knowledge of their relationships with the stream discharge. The most common method consists of measuring the water level and establishing a stage-discharge relationship (so-called rating curve [e.g., *Schmidt*, 2002]) fitted from a set of discharge measurements. In some cases, the accuracy and stability of the stage-discharge relationship may be improved if the hydraulic control is exerted by a designed hydraulic work (sill, weir, flume, etc.).

[3] Rating curves are subject to a number of limitations. The stage-discharge relationship can vary with time, according to changes in the channel geometry or roughness (vegetation for instance). When the river reach is hydraulically influenced by backwater effects (dams, lake, sea, etc.), a single-parameter rating (stage for example) is impossible to establish. Extra information is therefore necessary, for instance a second water level measurement for water slope gauging stations [*Rantz*, 1982], or flow velocity measurements.

[4] In recent years, several innovative velocity monitoring systems were applied to streamflow monitoring where the total discharge is computed from the cross-sectional bathymetry profile, the water height and velocity measurements in a more or less extended part of the cross section. For streams with stable geometry over time, the bathymetry profile can be measured by conventional means or extracted from gauging data sets and considered as constant. For unstable sections, the difficult assessment of the wetted area may increase the uncertainty associated with discharge outputs, especially during morphogenic events. Among these flow monitoring techniques, the continuous Doppler flowmeters (so-called sewer meters) measure the bulk velocity in the acoustic beam; however, they can be used for small streams or urban networks only because of their very limited range. Emerging noncontact techniques such as large-scale particle image velocimetry (LSPIV) [*Hauet et al.*, 2008] and radar wave scattering [*Costa et al.*, 2006] allow the measurement of the surface flow velocities. The acoustic transit time flowmeters measure the average velocity along one or several horizontal paths across the section. Fixed side-looking Doppler current profilers (H-ADCP) follow the same principle of operation as acoustic Doppler current profilers (ADCP) increasingly used to gauge rivers; they measure the horizontal water velocity profile along a horizontal line across the section.

[5] The installation of a transit time flowmeter station usually requires more extensive infrastructure than the installation of a H-ADCP station. Typically, four sensors have to be installed in the river channel below the free surface, instead of one H-ADCP head. Though alleviated thanks to new communication technologies [*Lengricht et al.*, 2007], cabling operations remain more difficult than for a H-ADCP system. The measuring range of transit time flowmeters is much longer (up to 2000 m) than the range of available H-ADCP systems. However, in case of too high concentration in suspended particles, the measurement may be disrupted because of the attenuation of the acoustic signal throughout the whole cross section. Recently, French hydropower producers Compagnie Nationale du Rhône (CNR) (French hydropower company) and Electricité de France (EDF) [*Carré et al.*, 2008] estimated the installation costs to be on average 10–30 k for a classical gauging station (based on water level measurements only), and 100–300 k for an ultrasonic station (either H-ADCP or transit time). Whereas the installation costs may be 10 times higher for an ultrasonic station, the operating costs are usually quite similar whatever the type of station (in the range of 10–12 k per year).

[6] Several strategies are possible for estimating the discharge from a given bathymetry profile, the externally gauged water height, and H-ADCP velocity measurements. Methods requiring numerical flow modeling are not considered in the present study. The index velocity method (IVM) consists of regressing the section-averaged velocity *U* given by direct discharge measurements against an index velocity [*Rantz*, 1982] built from the simultaneous H-ADCP velocity measurements. This method is very simple but relies on empirical fits. If the distribution of the dimensionless depth-averaged velocity across the section remains constant over the range of hydraulic conditions, a linear correlation may be found. Alternatively, the total discharge can be computed from theoretical vertical velocity profiles made dimensional with the H-ADCP velocity measurements across the section and integrated over the flow depth (velocity profile method, VPM). Discharge estimates are necessary in unmeasured areas in the vicinity of the transducer and beyond the measuring range. The most commonly used theoretical profiles are the power law (equation (1)), the logarithmic law of the wall (equation (2)), or the van Rijn profile (equation (3)) [*Aqua Vision BV*, 2003; *van Rijn*, 1986], i.e., a linear combination of a logarithmic law and a perturbation law derived from the wake law of the wall [*Coles*, 1956]:

with *u*_{z} the velocity at elevation *z* above the bed, the velocity at the reference elevation *z*_{a}, and *m* an empirical coefficient linked to the bottom roughness.

with κ the von Kármán constant (0.41), *u*_{*} the shear velocity, and *z*_{0} the roughness length, i.e., the elevation above the bed where the velocity is zero.

with *h* the water depth, *u*_{z=h} the surface velocity, *ξ* = (*z* − *z*_{0})/(*h* − *z*_{0}), *A*_{1} an empirical coefficient, and *t* computed so that *u*_{z=0.5h} is the same for all *A*_{1} values.

[7] Since 2005, several H-ADCP have been installed in French rivers by the hydrometry services of hydropower producers: Rhône river at Lyon-Perrache and Montélimar, Saône river at Lyon–Saint-Georges, Isère river at Romans on behalf of Compagnie Nationale du Rhône (CNR); Rhône river near the Saint-Alban and Tricastin nuclear power plants on behalf of Electricité de France (EDF). Early verification tests consisted of the comparison of discharges provided by the H-ADCP systems (with VPM) with reference discharge measurements. The Saint-Alban H-ADCP yielded unstable discharge series, with deviations from the reference discharge data being often greater than 20% [*Legras*, 2006]. These bad results were mainly attributed to an inappropriate reach: the H-ADCP was installed in a river bend, with very irregular bed. The resulting complex structure of the flow was assumed to deteriorate the velocity measurement and/or the discharge computation. On the opposite, the Saint-Georges H-ADCP yielded good results (deviations in discharge lower than 5%) obtained in the Saône river during floods [*Pierrefeu*, 2006]. At this time, the few underestimated discharges observed for low-flow conditions were not interpreted as a systematic bias, but as isolated problems probably due to inaccurate stream gauging or influence of the operation of the downstream hydraulic structures, at Pierre-Bénite dams.

[8] The investigation of not only discharges but also velocity measurements provided by H-ADCP systems appears necessary to assess their performance, according to environmental conditions and to the chosen discharge computation strategy. This paper reports the methodology and results of the study of the H-ADCP at Saint-Georges gauging station (Saône river in Lyon, France). In section 2, the characteristics of the flow monitoring system by H-ADCP and the reference measurements by ADCP are described. In section 3, the methodology for postprocessing the reference ADCP data is defined and validated. In section 4, both H-ADCP and postprocessed ADCP velocity data are analyzed in order to define discharge computation strategies, according to the observed H-ADCP performance and flow structure. Last, the quality of the discharges yielded by the IVM, the VPM and the edge extrapolation methods are presented and discussed.

[9] In this paper, the results of the comparison of a quantity *X* with a reference quantity *X*_{ref} are expressed by the residuals *R*(*X*, *X*_{ref}):

As a general convention, *u* stands for point velocity; 〈*u*〉 for depth-averaged (2Dh) velocity; *U* for section- or subsection-averaged (1-D) velocity; *A* for wetted area; *Q* for discharge.

### 5. Evaluation of Discharge Computation Methods

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental Setup
- 3. Postprocessing of Reference ADCP Data
- 4. Configuration of H-ADCP Discharge Computation Strategies
- 5. Evaluation of Discharge Computation Methods
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[44] The quality of discharge estimates provided by the index velocity method (IVM) and velocity profile method (VPM) was assessed by comparison with the reference ADCP data. In the IVM approach, a rated cross section is used to determine the wetted area for computing the discharge. This bathymetry profile may correspond to a separate location than the measurement section. In the VPM approach, the bathymetry profile of the H-ADCP cross section is required in order to compute vertical velocity profiles and the corresponding discharge.

[45] In this study, both methods were applied using the same user-defined H-ADCP bathymetry profile, which was established as the mean of the postprocessed ADCP bathymetry profiles. Thus, the comparison of mean velocities *U* = *Q*/*A*_{H}, with *A*_{H} the wetted area calculated from the H-ADCP bathymetry profile and the measured water level, is equivalent to the comparison of discharges *Q*. For each gauging campaign, the reference mean velocity in the H-ADCP section writes: *U*_{H} = *Q*_{0}/*A*_{H}, with *Q*_{0} the reference discharge, gauged by ADCP.

#### 5.1. Index Velocity Method

[46] Following the index velocity method (IVM), a linear fit of the gauged section-averaged velocity *U*_{H} function of an index velocity *U*_{IV} was performed by a least squares regression technique. *U*_{IV} was defined as the average of all H-ADCP velocity measurements validated against the corresponding ADCP data, i.e., from 4 m to 60 m from the H-ADCP sensor. From the velocity analysis reported above, a linear correlation *U*_{H} = *f*(*U*_{IV}) was expected to be accurate excepted for low-flow conditions were H-ADCP velocities were found to be biased low. The corresponding IVM discharge was computed as

[47] The linear regression over all 18 ADCP campaigns (Figure 11) yielded *f*_{1}(*U*_{IV}) = 0.8770 *U*_{IV} + 0.0303 with goodness of fit *R*^{2} = 0.9980. As the campaign SG1 (corresponding to the lowest discharge 115 m^{3}/s) was observed to be an outlier, the regression was also performed excluding SG1, leading to *f*_{2}(*U*_{IV}) = 0.8876 *U*_{IV} + 0.0100 with goodness of fit *R*^{2} = 0.9984.

[48] Residuals *R*(*f*_{1}(*U*_{IV}), *U*_{H}) and *R*(*f*_{2}(*U*_{IV}), *U*_{H}) for both empirical relationships *f*_{1} and *f*_{2} are presented Figure 12a. As expected from the evaluation of H-ADCP velocity measurements, *f*_{1}(*U*_{IV}) was biased low at low-flow conditions (*U*_{a} < 0.4 m/s), with unacceptable deviation (−34.1%) for *U*_{a} = 0.17 m/s (SG1). For *U*_{a} > 0.4 m/s, residuals were acceptable (mean deviation: +0.6%): they were lower than 5%, excepted for the two campaigns with *U*_{a} ≈ 0.8 m/s (+6.5% for SG10 and +5.3% for SG18). Results for *f*_{2}(*U*_{IV}) were quite similar, but residuals were lower than 5% for all campaigns, excepted for SG1, which showed decreased though still unacceptable underestimation (−15.8%).

[49] Of course, polynomial fits with higher orders can be used to reduce these low-flow residuals. However, using such a high-order relationship to compute discharges may be very dangerous because it not only reflects a hydraulic relationship but also compensates a measuring bias that is not fully understood at present. At least, many repeated low-flow ADCP campaigns for varying suspended sediment concentration should be used to test the validity of the index relationship over the whole range of low-flow measuring conditions.

#### 5.2. Velocity Profile Method in the Near Field

[50] The velocity analysis showed that because of low-biased H-ADCP velocities beyond 60 m, discharges needed to be extrapolated in a large part of the section. Before evaluating the total discharges derived by the VPM, implying the selection of an appropriate far-field extrapolation technique, mean velocities averaged over the near-field subsection were compared to *U*_{a}^{nf} the mean velocity gauged by ADCP in the corresponding subsection. This comparison intended to test the performance of the VPM depending on the selected profile law (and not on the extrapolation method).

[51] The log, power, log constant and van Rijn profile laws and their configurations are reported above (section 4.3). The residuals *R*(*U*_{VPM}^{nf}, *U*_{a}^{nf}) of the corresponding near-field mean velocities against the reference near-field velocities are plotted in Figure 12b.

[52] VPM near-field velocity estimates appeared to be underestimated for the three campaigns with *U*_{a} < 0.4 m/s, as expected from the H-ADCP velocity analysis. But they were acceptable for *U*_{a} > 0.4 m/s, though a systematic overestimation was observed for all the four profile laws. The average deviation over the 15 campaigns with *U*_{a} > 0.4 m/s were +2.4% (log constant), +4.2% (power), +3.3% (log), and +5.6% (van Rijn). Consequently, the log constant theoretical profile appeared as the most recommended law to use for the application of the VPM at the Saint-Georges gauging station. This was to be expected from the ADCP velocity analysis, since the log constant profile was the closest to the mean experimental profile. However, all fitted laws led to velocity estimates affected by a positive bias, likely due to the limitations of the theoretical profiles to represent accurately the mean profile established experimentally from ADCP data.

#### 5.3. Velocity Profile Method With Far-Field Extrapolation

[53] As the log constant configuration yielded the best velocities in the near-field subsection, this profile law was selected for further evaluation of the performance of far-field discharge extrapolation methods. As for the evaluation of IVM results, comparisons of section-averaged velocities *U*_{VPM} = *Q*_{VPM}/*A*_{H} with the total reference mean velocity *U*_{H} are presented hereafter. The M extrapolation (mean ADCP 2Dh profile), F extrapolation (constant Froude), U extrapolation (mean velocity), and C extrapolation (last velocity) methods are defined and discussed in section 4.2.

[54] The residuals of *U*_{VPM}^{M}, *U*_{VPM}^{F}, *U*_{VPM}^{U}, and *U*_{VPM}^{C} against *U*_{H} for all 18 gauging campaigns are plotted Figure 12c. *U*_{VPM} remained biased low or very low for *U*_{a} < 0.4 m/s. For *U*_{a} < 0.4 m/s, the systematic deviation observed for *U*_{VPM}^{nf} with the log constant law (mean deviation +2.4%) was enhanced or attenuated. The trends were coherent with the a priori assessment of biases expected for the four extrapolation methods (section 4.2). For the M and F extrapolation methods, assumed to be unbiased, the residuals for *U*_{VPM} (mean deviations +5.6% and +3.6%, respectively) were slightly higher than the residuals previously observed for *U*_{VPM}^{nf}. The C extrapolation method (expected bias +5%) increased the *U*_{VPM} velocity overestimation to unacceptable levels (mean deviation +9.3%). On the opposite, the U extrapolation method (expected bias −4%) compensated the *U*_{VPM} velocity overestimation (mean deviation +1.7%).

### 6. Conclusions

- Top of page
- Abstract
- 1. Introduction
- 2. Experimental Setup
- 3. Postprocessing of Reference ADCP Data
- 4. Configuration of H-ADCP Discharge Computation Strategies
- 5. Evaluation of Discharge Computation Methods
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[55] Horizontal velocity cross profiles measured by the H-ADCP at Saint-Georges gauging station (Saône river in Lyon, France) were compared to concurrent ADCP measurements for 18 discharge values distributed over the 100–1800 m^{3}/s range. H-ADCP discharges were computed by the index velocity method (IVM) and the velocity profile method (VPM, with several far-field extrapolation techniques). Once properly postprocessed, the ADCP data were useful for analyzing the mean flow structure, assessing the quality of H-ADCP velocity measurements, and defining reasonable discharge computation methods. Similar analyses can also be conducted with data from velocity-area gauging data sets measured with current meters, for instance.

[56] The comparison with ADCP data revealed that H-ADCP velocity measurements were reliable (deviations <5%) in a near-field range only (60 m out of a 95 m total section width). In the far field (beyond 60 m), H-ADCP velocity measurements showed negative bias of up to −50% 90 m from the instrument. For section-averaged velocities lower than 0.4 m/s approximately, H-ADCP velocity measurements were found to be significantly underestimated over the whole cross section. The main practical conclusions are that (1) avoiding free-surface and bed reflections by considering the main lobe geometry is not a sufficient condition to extend the H-ADCP profiling range; (2) H-ADCP limitations must be taken into account for defining robust discharge computation procedures; and (3) whatever the computation method, discharge estimates are unacceptably biased low under a critical discharge value.

[57] At Saint-Georges gauging station, for *U*_{a} > 0.4 m/s, both the IVM and VPM gave acceptable discharge values (typically deviations <5%). However, over the 18 available gauging campaigns by ADCP, the H-ADCP section-averaged velocities provided by the IVM were more accurate than those provided by the VPM for any tested configuration, which are overestimated by a few percent (Figure 12). For the application of the VPM, the log constant law and the Froude constant extrapolation method were found to be the most accurate options separately. However, the uniform velocity extrapolation method, with slight underestimating bias, somehow compensated the slightly overestimated near-field velocity computed with the log constant law.

[58] A physically robust method is required for the computation of discharges from H-ADCP velocity measurements, while a limited number of direct discharge measurements over a limited discharge range are available. As an empirical optimization, the IVM is designed to yield the best agreement between H-ADCP outputs and the available control data. Of course, if the VPM theoretical profile was calibrated empirically, the resulting H-ADCP discharges would reach a similar degree of accuracy. The configuration of the VPM parameters on a physical basis requires more sophisticated assumptions on the flow structure than the application of the IVM. However, this study shows how this can be achieved with previously acquired gauging measurements, or with reasonable a priori hydrodynamical assumptions. Both methods require extensive verification tests after installation by stream gauging campaigns over the widest range of hydraulic conditions.

[59] Anyway, in the VPM approach, the physical relevance of the chosen vertical velocity distribution could be checked, whereas the physical relevance of the IVM relationship may be more difficult to assess for a given site. Problems such as instrumental bias or temporary changes in the flow field structure may affect the IVM relationship, even if it remains linear. Therefore the IVM empirical relationship may hide some basic errors that would require a large number of control discharge data to be evidenced and corrected. Following these considerations, the physically based VPM is expected to be more robust, especially for ungauged conditions. The VPM can be seen as a compromise choice between an IVM empirical correlation and hydraulic modeling strategies, which require much more expertise.

[60] The reasons why H-ADCP velocities are unacceptably biased low in the far field and for low velocity and low suspended sediment concentration conditions are still under investigation. Further research work on the H-ADCP backscatter intensity is planned in order to look for methods for discarding/correcting low-biased velocity measurements, and also for converting the backscatter intensity into suspended sediment concentrations, in order to monitor solid fluxes continuously.