An acoustic travel time method for continuous velocity monitoring in shallow tidal streams
Coastal Engineering Laboratory, Department of Civil and Environmental Engineering, Graduate School of Engineering, Hiroshima University, Higashi–Hiroshima, Japan
Corresponding author: M. Razaz, Coastal Engineering Laboratory, Department of Civil and Environmental Engineering, Graduate School of Engineering, Hiroshima University, 1–4–1 Kagamiyama, Higashi–Hiroshima 739–8527, Japan. (firstname.lastname@example.org)
 Long-term variations of streamflow in a tidal channel were measured using a Fluvial Acoustic Tomography (FAT) system through one transmission path. FAT is an innovative acoustic technology that utilizes the time-of-travel method to determine velocity between two points from multiple ray paths that traverse the entire cross-section of stream. Due to high spatial variability of flow distribution stationary ADCP measurements were not likely to yield true section-averaged flow velocity and moving-boat ADCP method was therefore used to provide reference data. As such, two short-term moving boat ADCP campaigns were carried out by the authors. In the first campaign, a couple of acoustic stations were added to the FAT system in order to resolve flow angularity in addition to the mean velocity. Comparing the FAT results with corresponding ADCP section-averaged flow direction and velocity indicated remarkable consistency. Second campaign was designed to capture the influence of salt wedge intrusion on the sound propagation pattern. It was found that FAT velocity measurements bias high if acoustic stations lay inside the cooler freshwater layer. Ray-tracing hindcasts suggest that installing acoustic stations inside the salt wedge may significantly improve function of output of the system. Comparing salinities evaluated from long-term FAT travel time records with nodal salinity measurements provided by conductivity-temperature sensors reveals the potential ability of FAT in measuring salt flux.
 Discharge measurement in tidal streams is a difficult and tedious task. Owing to the complex flow conditions generated by interaction of the marine and riverine influences, discharge measurement in tidal streams should be as quick as possible to yield an accurate and reliable estimation of the real-time discharge.
 While conventional acoustic methods such as acoustic velocity meters (AVMs), horizontal acoustic Doppler current profilers (H-ADCPs), and rating curves lack spatial or temporal resolution [e.g., Kawanisi et al., 2010; Ruhl and DeRose, 2004] and hence fail to meet requirements mentioned above, acoustic tomography approach seems to be a promising method for long-term river discharge gauging, particularly in tidal streams. Conventional time-of-travel sensors such as AVMs assume a straight line propagation to measure a representative index velocity [Sloat et al., 1995]. Calibration error is thus usually found to be a substantial source of error in discharge estimation. Also, straight-line propagation assumption makes AVM's susceptible to the multipath phenomenon that occurs in its extreme forms in shallow waters, and also to the ray bending phenomenon caused by temperature or salinity gradients [Laenen and Smith, 1983]. Doppler method lacks penetration capabilities of tomography equipment [e.g., Le Coz et al., 2008], because it has greater susceptibility to interference from boundary conditions and is subject to signal attenuation from same particles needed in backscattering the signal. On the other hand, conventional optical techniques such as Large-Scale Particle Image Velocimetry are not able to measure components along the vertical axis, z [e.g., Fujita and Kunita, 2011; Kantoush et al., 2011]. These components might not only be missed, but also introduce interference in the data for the horizontal components caused by parallax particularly in nonunidirectional flows such as estuaries with complex vertical distribution of current velocity.
 Ocean acoustic tomography (OAT) has been successfully demonstrated in deep ocean conditions for transmission via wholly refracted paths since 1970s, when Munk and Wunsch  proposed OAT. However, in other areas of the ocean, such as in bays and estuaries, characterized as acoustically shallow, very limited number of successful experiments were carried out to the best knowledge of the authors. In the present context, shallow describes water depth in which sound propagates over a certain distance by repeated reflections from both the water surface and bottom. Deep ocean tomographic methods may not be successful in shallow water applications due to the interference and scattering of the sound waves with the stochastic boundaries that render sound transmission difficult. Furthermore, predictions of the paths' stability, identification of ray paths, and estimating attenuation become difficult due to unknown effects of bottom scattering and reflection from stochastic surface, bottom, and subbottom.
 Coastal acoustic tomography (CAT) was proposed as the application of Ocean Acoustic Tomography (OAT) to coastal seas, with the goal of continuously monitoring tidal currents in ports, bays, straits, and inland seas without disturbing shipping, fisheries, or marine aquaculture industries [Kaneko et al., 1994; Park and Kaneko, 2000]. Based on CAT, fluvial acoustic tomography (FAT) is designed for continuous measurement of the cross-sectional average velocities in shallow rivers using higher frequencies (10–30 kHz). Its ability to reconstruct a scalar function using tomographic techniques with only one acoustic path already resulted in a wealth of applications, e.g., measuring flow rate in freshwater rivers [e.g., Kawanisi et al., 2012] and measuring tidal bores with 4 kHz transducers [Zhu et al., 2012]. However, when only data from one acoustic transmission line is available, transformation of along-ray velocity data to streamwise velocity involves a major assumption, i.e., current is unidirectional and forms a constant angle with the sound ray. This assumption is not valid in flows with variable streamline orientation or in presence of large recirculating eddies. These issues have raised the need for developing a method that is capable to reconstruct vector fields. The contributions of the present study are significant and novel in both practical and technical sense. In a technical sense, this is the first time that 30 kHz frequency is successfully used in a water tomography system [Katsnelson, 2011] that further enabled streamflow monitoring in extremely shallow waters. From a practical point of view, what makes the present study significant is that acoustic measurements were conducted in intricate and complex flow conditions.
 Contained herein are the results of long-term reciprocal transmission experiments with only a couple of acoustic stations in the upper reach of a tidally dominated channel that are used to demonstrate that it is indeed possible to measure spatial averages of current and salinity using FAT. The surveyed zone is characterized by the frequent intrusion of saline water and by the irregular opening of sluice gates that control freshwater diversion. The results of the comparison between spatially averaged streamflow velocity and direction accuracy with those obtained using a standard method (moving-boat ADCP) is reported herein. In the paper, potential reasons of discrepancies observed between FAT and ADCP are also investigated using ray-tracing hindcasts, whereby sound propagation patterns in the river section are simulated.
 In its basic form, FAT consists of only two broadband monostatic transducers with omnidirectional horizontal and hemispherical vertical beam patterns. Transmitting elements are triggered by an accurate GPS clock and simultaneously (or sequentially) emit modulated pulse with an adjustable frequency bandwidth within the range of 1–35 kHz. Reciprocal sound transmission between each couple of monostatic transducers allows separating the influence of scalar factors, temperature or salinity, and flow on the effective sound speed. In contrast to other ultrasonic flowmeters such as AVM's, sound rays propagated from transducers traverse the entire cross section and the section-averaged velocity is therefore directly quantified. Although multiray path phenomenon turns to an advantage in FAT, rays may bounce several times and significantly attenuate under accumulative effects of bottom/surface reflection loss, dispersion, scattering spreading, and absorption. Hence, the longest effective ranges of FAT are always much less than those considered in deep ocean tomography, i.e., of the order of a few hundred meters to a few kilometers.
 The travel time along the reciprocal ray path Γ± between two acoustic stations in the flowing medium may be expressed by
where ± indicates the positive/negative direction from one transceiver to another. cm is the average sound speed along the considered path, δc the sound speed deviation from cm, ds the increment of arc length measured along the ray, u the mean current velocity, n the unit vector along the ray, and M the number of rays. Assuming that the geometries of two-way paths are identical and owing to shallowness of the propagation medium, the length along the curve is roughly equal to the horizontal distance between the two acoustic stations L (Γ± = L). Furthermore, if and , equation (1) is simplified to
in which um is the mean along-ray flow velocity. From equation (2), cm and um averaged along the sound path can be, respectively, given by
with and . Taking total derivation of equation (4) and neglecting terms containing time yields
that represents the relative error for the section-averaged velocity. Because transmitting and receiving of the signals are synchronized with a precise GPS clock, relative errors in time measurement are assumed to be trivial.
 When using only a couple of acoustic stations, it shall be postulated that streamflow makes an angle of θ with the transmission line so the section-averaged river velocity u can be computed from
 And the corresponding error in the FAT velocity due to a change δθ in the flow angle is given by
where δθ is expressed in radians.
 Among various equations that have been proposed to predict the underwater acoustic velocity, the authors adopted the formula proposed by Medwin  for the sound speed c, as a function of the temperature T (°C), salinity S, and depth D (m) at and .
 In an acoustically rough environment of extremely shallow waters, such as in rivers, a special technique for sound transmission and processing is required to prevent the sound pulse from fading away. Modulating the carrier signal with M-sequence and taking the cross correlation of the received signal with it has proved to be extremely efficient in shallow waters. M-sequence is a type of pseudorandom signals by which the phase shift of π in the carrier is generated with irregular time intervals [Simon et al., 1985]. Modulating transmitted signal with M-sequence of the order n escalates the SNR (sound-to-noise ratio) by 2n−1 times. By taking the correlation between the received signal and the M-sequence used for transmission, the precise arrival time is identified.
 There are two types of time scale involved in M-sequence: the period, Tp, and the width of one digit, Tr. The latter time scale is the time resolution of the system for multiple arrivals. That is to say, if two acoustic rays with same intensities arrive successively within an interval shorter than Tr, then the cross-correlation pattern for the rays is overlapped. However, if intensities are different, individual correlation peaks might be detected for overlapped arrival due to the difference in peak heights.
 The accuracy of travel time measurement, Ta, depends on Tr and SNR (sound-to-noise ratio) and can be expressed by Munk and Wunsch 
 Despite the fact that M-sequences are Doppler sensitive and the peak amplitude and shape can be improved by adjusting time dilation, because FAT uses forward scattering wave at fixed stations there is no need to account for Doppler shift in the arrivals.
3. Field Site and In Situ Measuring Technique
 The Ota River is a network of tidal-dominated river branches that flow through Hiroshima City, Japan. As shown in Figure 1a, the main stream bifurcates into two main branches nearly 9 km before discharging into the Hiroshima Bay; the westernmost branch is called Ota Diversion Channel. Arrays of sluice gates regulate amount of inflow to each branch. During normal operation, only 1/3 of the Gion sluice gates are open. In 2011, the riverbed upstream of the bifurcation zone was dredged and some of the loose bed materials have been gradually washed away downstream. Fine sand and mud settled afterward and formed sandbars near the northern end of the channel upstream of the observation site (Figure 1b).
 Geometry of the sluice gates and sandbar accumulated near the right bank along with asymmetric tidal currents results in very unsteady and complex flow regime. Flow pattern varies remarkably with the tidal phase and so does the amount of freshwater inflow passing through the sluice gates. Particularly when runoff is high, combination of asymmetric inflow and of saline wedge intrusion generates strong halocline and transverse density gradients in the observation site that adds to the overall site complexity. River depth variations in the deepest part of the river near the southern bank (as shown in Figure 1c) as well as the river discharge measured just upstream of the tidal compartment border are demonstrated in Figure 2. Note that the discharge shown in Figure 2 was measured at Yaguchi gauging station (Figure 1a) 5 km upstream of the survey zone. Also, approximately between 15% and 20% of the main branch discharge is diverted into the channel through normal gate operation.
 Channel discharge was monitored continuously from April to September 2012, using only OA-OB path. During this period, water level and vertical distribution of temperature and salinity were measured every 10 min by three conductivity-temperature (CT) sensors and a depth meter, attached to the pier of Gion Bridge located 40 m away from the southern river bank (Figure 1b).
 In addition to the ongoing long-term measurement, two short-term campaigns were carried out during two neap tides on 13–14 April and 10–11 August 2012, to assess the accuracy of measurement against a moving-boat ADCP. Each ADCP campaign was conducted for approximately 12 h, which is almost half of a complete semidiurnal tide cycle. In the first campaign, in addition to the OA-OB path, another pair of transducers (OC and OD) was added to create crossing paths in order to resolve the flow direction. In the second campaign, efforts were, however, focused on investigating sound propagation pattern and assessing the reliability of data collected by FAT during stable stratification. Thus, OC and OD transducers were not installed. Schematics of transducers location are shown in Figure 1b for the both field campaigns.
 Broadband monostatic transducers (Neptune T227) with central frequency of 30 kHz and source level of 197 dB re 1 µPa were employed throughout all campaigns. M-sequence of order 10 was applied to increase the processing gain by about 30 dB. Tr was taken as three times the period of the carrier (0.1 ms) and Tp was set to 102.3 ms. The transmitted signal frequency bandwidth was 20–35 kHz, considering frequency response of the transducers (data not shown here). Throughout both campaigns, sound transmission was performed at 60 s intervals.
 During the first campaign, in order to establish a set of reference velocity data for evaluating FAT, nominally every half an hour a round-trip across the river (Figure 1b, along the θ = 0° axis) was made by a broadband RDI 1200 kHz Workhorse Monitor ADCP mounted on a boat. Water velocities were acquired through the pulse-coherent mode (mode 11). The velocity bin size was set to 0.02 m and measured velocities were 7 ping-averaged. Blank distance was set to zero, although due to ringing issue, the upper six bins had to be removed later. Depth of the ADCP transducers was around 4 to 5 cm, although due to the presence of surface waves it is impossible to provide an exact number. All the data were referenced to the ADCP bottom tracking. Drift in the bottom tracking due to moving bed effects or compass error was not significant. Each transect began from or ended near the bank. During each transect, the boat speed was maintained approximately 0.25 m/s and, as a result, the boat travel time was less than 15 min. A wire across the river was used as a lead to make similar paths; however, tidally induced depth variations somewhat affected the transect length. Although settings of the ADCP for both the campaigns were identical, fulfilling transects along the OA-OB transmission line required more time rather cross river passes and round trips were performed nominally every hour during the second campaign. ADCP velocities were extracted from the WinRiver II software (Teledyne RD Instruments) and postprocessed as it is described in section 4.1. The unmeasured nearshore discharge was negligible; however, the missing data between the surface and the first ADCP cell were produced by extrapolation. Magnetic declination was accounted for using data from NOAA National Geophysical Data Center (http://www.ngdc.noaa.gov) that indicates −7.16○ declination for the observation site.
 It was assumed that spatially averaged salinity and temperature in the area confined by the four acoustic stations does not change significantly. During the first field campaign, salinity and temperature variations induced by tidal currents were observed by casting a JFE Advantech Compact-CTD (conductivity-temperature-depth) at five points across the river (Figure 1b). In the second campaign, the number of casts was increased to six points along OA-OB path. All the CTD readings were made after fulfilling ADCP round trips within 10 min. Throughout the observations, water surface was calm and only negligible wind-driven waves were detected by visual inspection.
4. Long-Term Measurement Results
 Temporal variations of the water level at the river mouth, hM, at the Gion sluice gates, just upstream of the survey site, hG, and in the main branch outside the tidal compartment, hY, are shown in Figures 3a–3c, respectively. Figure 3d indicates that the general trend of average temperature variations derived from the three CT sensors correlates well with the sea level rise. Equation (8) points out that the mean sound velocity computed from the FAT readings along path OA-OB, (Figure 3e), is approximately twice as sensitive to the temperature as to salinity. Thus, the general trend of sound speed variations follows that of the temperature, meanwhile salinity changes induced by tidal currents are more likely to influence sound velocity fluctuations in shorter periods such as of the order of a tidal cycle period. Subscript AB refers to the path OA-OB. Results shown in Figure 3f are computed from equation (6) assuming a constant flow direction of θAB = 90° and averaging over 12 h after removing spurious data points [Razaz and Kawanisi, 2011]. The most probable source of error involved in the FAT mean velocity estimation while a constant flow direction is used would be the intermittent mean flow direction fluctuations. A large portion of error involved in mean flow estimation is contributed by intermittent flow direction changes when the flow direction is not resolved. A possible range of such error is discussed in section 'Comparison of the Direction and Mean Flow Velocity With Crossing-Paths FAT and ADCP'. Owing to the complexity of the flow, stationary vertical profile measurement in limited number of points across the channel would not represent the virtual mean flow velocity and also it is impossible to maintain continuous moving-boat ADCP measurement for such a long period. Therefore, there is no reference velocity data available for benchmarking the FAT results with during this 6 month period. However, FAT velocity variations, plotted in Figure 3f, comply remarkably well with high runoff events displayed in Figure 3c, e.g., on 7 July when the sluice gates were completely open, FAT results indicate a relatively strong seaward flow. The effect of sea level rise on estuarine circulation (Figure 3a), particularly after August 2012, can be traced in the FAT velocities. That is to say, stronger landward currents and weaker seaward flows are apparent in the FAT reports after August 2012. Moreover, FAT velocity temporal variations indicate larger fluctuations during spring tides (Figure 3b) as expected.
5. Short-Term Comparison Between FAT and ADCP
5.1. ADCP Field Campaigns
 In order to evaluate the velocities provided by FAT, ADCP data had to be postprocessed to establish reference mean velocity data and mean flow direction for each measurement campaign. For each series, the crossing yielded similar boat tracks. However, track length was somehow affected by tidal river depth variation. The averaged bed elevations from the four beam measurement during high water were considered as the reference bathymetry. Approximately, the average difference between the reference bathymetry and other crossings for the first campaign was estimated to be ±7% and ±12% for the second campaign. Bed elevations from successive ADCP crossings during the first campaign are plotted in Figure 4.
 In none of the transects did the bad bins portion exceed 2% of the total measurement. The ADCP computes sound speed, cADCP, and depth based on salinity and temperature readings at its transducer. It is, therefore, necessary to account for sound speed vertical gradients in stratified flows. CTD measurement was used to calculate the sound speed spatial distribution along the ADCP path from equation (8) noted as creal. Multiplying the measured values by creal/cADCP provides the correct depth and velocity. After implementing sound speed corrections, in order to reduce dispersion induced by turbulence, density stratification, as well as Doppler noise linked to the ADCP technology, the inverse distance weighting (IDW) method was applied to the velocity data. This method averages the closest Ni velocity data relative to the ith grid node using a code developed by the authors (Figure 4). IDW was used because of its simplicity and low computational cost. The sensitivity of the ADCP-averaged vertical profiles to Ni was tested by computing maximal median absolute deviation of the velocity profiles of each transect. As a result, the fixed number of Ni = 21 was determined such as to compromise between distorting the shape of the profile and smoothing out the deep irregularities in the vertical velocity profiles. Herein, the search surface was a 3 point wide 7 point high rectangle as shown in Figure 4. Consequently, search surfaces overlapped both horizontally and vertically. If less than 21 points were found due to irregular bottom shape, the averaging was performed over the available data points. As there are no other vertical velocity profile data measured by a stationary ADCP, the profiles averaged with Ni = 21 were taken as the reference true profiles.
 Departures of the measured velocity profiles from the logarithmic distribution were probably due to acceleration/deceleration of tidal flow, stratification, bottom form, and to the proximity to the sluice gates. Profiles also did not correlate well neither with the log linear form of logarithmic profile [Kawanisi, 2004; Razaz and Kawanisi, 2012], deduced from the Monin-Obukov similarity, nor with the conventional two-layered flow equations [Mccutcheon, 1981]. Hence, the top flow velocity was estimated by extrapolating the value of the first five good bins to the surface. This method extrapolates data in a straight line to the surface. For the missing layer caused by the side-lobe effect, the bins present in the lower 20% of the depth were used to determine a power fit, while in the absence of any good bins in the lower 20%, the last single good bin was used. This fit was forced to pass through zero at the bed.
 Figure 5 shows typical sections of current velocity collected with the ADCP during both campaigns. Velocity data used in this figure were averaged using the IDW method and missing measurement near the top and bottom were replaced as described in the previous paragraph. Positive values denote currents oriented toward downstream while the negative ones are directed upstream.
 As shown in Figure 5a, when the river discharge was high (Figure 2a), downstream velocities peaked up to 0.5 m/s and, most of the time, flow was vertically well mixed but its direction varied significantly across the channel. However, while the strain-induced stratification was relatively weak, the influence of straining is still apparent in the development of stability, particularly at the first half of the ebb (6:00 A.M. on 14 April). Apparently, during low tide flow, discharging from sluice gates was diverted toward the southern bank by the sandbar formed near the northern end of the channel. When river discharge was lower (Figure 2b), ADCP data indicate that tidal straining was dominant most of the time, leading to stable stratification throughout the second campaign. Due to the low river discharge rate, speed of currents oriented downstream did not exceed 0.3 m/s. Meanwhile, the maximal speed of flooding tidal was as large as 0.1 m/s, which is comparable with that measured during the first campaign.
 Typical vector plots of the depth-averaged current velocities across the river and along the OA-OB sound transmission line that were obtained from the ADCP data are shown in Figure 6. During the second campaign, the stable stratification prohibited sound rays emitted from the FAT transducers to propagate into the lower layers. Hence, the ADCP velocity data are not integrated over the full depth but over a portion of water column that sound rays could propagate in. Influence of stratification on sound transmission is discussed in section 'Stratification Effect on FAT Velocity Measurements'.
 Horizontal views of the depth-integrated velocities exhibit nonuniform current between the two acoustic stations, with occasionally opposite flow directions. In the first campaign, the mean angle between the stream direction and the OA-OB transmission path was estimated as 37.5° ± 11.9°, with the path OC-OD as 40.5° ± 11.9°. If the mean flow direction was not resolved, the corresponding relative error for ±11.9° change could vary between 16% and 18% for the OA-OB and OC-OD transmission paths, respectively. This may lead to very large discharge estimation error, i.e., O(57%) [Kawanisi et al., 2012].
5.2. Comparison of the Direction and Mean Flow Velocity With Crossing-Paths FAT and ADCP
 In this section, the ADCP mean flow speed is computed as the weighted average of the postprocessed velocity data, plus the velocity estimates for near-surface and near-bed unmeasured zones. Weights considered are the distance traveled by the boat during each ensemble. ADCP section-averaged flow direction θADCP with respect to north was also quantified using postprocessed ADCP data, excluding the replaced missing top/bottom bins and accounting for the magnetic declination from
where νN and νE are horizontal velocity components measured by ADCP in the local East, North, Up (ENU) coordinate system, N is number of ensembles for each transect, and n is the number of valid bins in each ensemble.
 According to Teledyne RD Instruments Inc., the velocity accuracy for the 1200 kHz Workhorse Monitor ADCP is ±0.25% of the water velocity relative to the ADCP's ±2.5 mm/s with velocity resolution of 1 mm/s. The accuracy of compass (tilt) sensor is ±2° (±0.5°). A wide range of potential error sources such as the missing near-surface/bottom data due to ringing and side-lobe effects, Doppler noise, signal aliasing, velocity fluctuations, vibrations during measurement, and other disturbances [Blanckaert and Lemmin, 2006] are, however, associated with ADCP measurement. The ADCP signal is also likely to be adversely affected further by velocity shear across the sampling volume, particularly in estuarine zones, by complex boundary geometry or by limitations in the sensor's nominal velocity range.
 The FAT mean flow velocity is computed from the two crossing paths following
where CD index denotes the OC–OD path. θAB (θCD) is the angle that the path OA–OB (OC–OD) makes with the mean flow direction. Using FAT along-ray velocity data and the geometry of the transducers' location, mean flow direction can be expressed in the form of
φ in Figure 1b is shown to be the angle that path OA-OB makes with North direction and γ is the angle between the two transmission lines.
 Mean flow velocity and direction estimated from FAT are compared with the ADCP data averaged over each round trip in Figure 7. The relation between discrete ADCP directions and the corresponding FAT data can be expressed by (Figure 8a). Note that FAT gives the flow direction averaged over a bulk of flow (about 160 m long, 120 m wide, and variable river depth), and ADCP reports the flow direction averaged over a section. The relative error of the FAT mean flow directions shown in Figure 8b rarely exceeded 10%, but revealed that in higher values θFAT was 10% larger than θADCP. Considering the substantial difference between the sampling volumes of the two methods, the average deviation of ±5.4° that leads to less than 10% error in flow direction measurement (Figure 8b) seems reasonable. Note that between 10:00 and 11:00 JST on 14 April, OA and OB stations were dried out.
 As shown in Figure 8c, the ADCP velocity data comply quite well with the FAT results ensemble averaged over 30 samples (=30 min). Figure 8d is the plot of difference between the ADCP and FATs velocities normalized against the absolute velocity values reported by FAT, . Angle brackets stand for taking average over the entire campaign interval. Evidence presented in this figure reveal that the relative difference between the two techniques lies within 20%. Root-mean-square of residuals (RMSR) was evaluated to be 0.03 m/s. From equation (7), it is likely that 6 to 10% of the relative velocity error is due to the angularity difference between the two techniques.
 Figure 9 illustrates the role of angularity errors in the mean flow speed measurement by FAT. Values shown in this figure are computed from equation (6) using only data obtained from path OA-OB assuming that flow direction was perpendicular to North direction throughout the campaign. From results shown in Figure 7a, flow direction had RMSR of δθ = ±8.7° relative to θ = 90°, which causes a corresponding velocity error of 11%. The full range of δθ is determined from crossing path's results. The velocity error variations associated with δθ fluctuations are shown in Figure 10, which reveal that the angularity error may produce up to 30% error in velocity estimation from FAT in this particular case. Dotted lines in Figure 10 denote the corresponding angularity error to θAB = 36° and mean misalignment of δθ = 8.7°.
 As for the errors associated with the estimation of velocity with FAT, apart from sources discussed already, the velocity resolution of FAT ur might also be thought of as one of the principal sources of errors, particularly in slow flows.
 In equation (13), f is the central frequency of transmitted sound. The mean sound speed averaged over the entire observation period (∼12 h) was 1451.2 m/s that yields ur = 8.86 cm/s. This relatively low velocity resolution signals the necessity of averaging the results over a certain interval. Statistical reliability of the FATs increases with the square root of the number of the samples per ensemble. In other words, by applying ensemble average over 30 samples, the accuracy increases to . A nominal time of 30 min is required to complete a round trip ADCP survey.
 Considering that only one digit length of M-sequence was used in the experiments, multiarrival peak resolution can be estimated as 53.17 cm/s from equation (4). Similar to the velocity resolution, by taking the ensemble average of 30 samples, multiarrival peak resolution reduces to 9.71 cm/s.
 The uncertainties discussed above become of particular importance when the mean flow velocity is close to zero. That is to say, it is possible that uncertainty due to low velocity resolution is the most influential factor in deviation of FAT measured velocity from the expected value in very low velocities.
 Due to the extremely shallow nature of the flows that FAT is designed to operate in, this device does not treat each ray path separately and arrival time of a group of rays is used to determine time of travel. Thus, the nonreciprocal effects are not likely to induce a serious problem. The final note concerns the accuracy of the travel time measurement Ta that its mean value computed 12.61 µs for the both campaigns.
 Considering complexity of the flow and the substantial differences in sampling geometries, FAT is a promising technique/sensor for measuring mean velocity, particularly in tidally induced estuaries. It is worth mentioning that work previously conducted by Kawanisi et al.  showed that the relative error may reduce to ±10% in freshwater zone characterized with no density gradients or remarkable changes in flow direction.
6. Stratification Effect on FAT Velocity Measurements
 Current velocity distributions shown in Figure 5b suggest that during the second campaign vertical mixing weakened due to very low freshwater discharge. Stable stratification formed in the survey zone allowed authors to investigate reliability of travel time measurement by FAT in the presence of sharp sound speed vertical gradients. During the second campaign, only OA-OB path was installed; therefore, to cancel the flow angularity error as much as possible, the along-ray ADCP flow direction averaged over each round trip is used for rotating the along-ray velocity data.
 Ensemble-averaged FAT velocity measurements are compared with the ADCP postprocessed readings averaged over each round trip as shown in Figure 11. This signifies that before 22:00 JST on the first day, FAT mean velocities are notably biased high. It seems that the halocline/thermocline generated by the salt wedge intrusion during flood tide prohibited transmitted sound from traversing the entire section, i.e., sound rays were reflected by the boundary between the freshwater and saltwater without touching the bottom.
 According to the data shown in Figures 11 and 12a, removing the salt wedge from ADCP section-averaged velocity measurement significantly enhances the agreement between the two techniques, and RMSR decreases from 0.07 m/s to 0.03 m/s in ADCP. Using the ADCP data in the upper layer (Figure 11a) implies that the mean streamflow deviated 35° ± 19° from OA-OB path. Depth of the layer over which ADCP data are integrated is approximated from ray tracing hindcasts that is discussed in section 'Stratification Effect on Sound Transmission'. As shown in Figure 12b, if the ADCP data are averaged over the entire section, relative error gradually grows with stream velocity to as much as 300%. Mainly, this inconsistency can be attributed to the partial propagation of sound rays through the river section.
6.1. Stratification Effect on Sound Transmission
 To confirm sound channel formation in the upper layer, further investigation was conducted by hindcasting sound propagation pattern with standard ray-tracing techniques and by inspecting the arrival time variation through the second campaign.
 The standard ray tracing model that assumes smooth bottom/surface was used to hindcast the pulse response of the channel. Computation of the channel pulse response proceeds as follows. First, the spatial distribution of underwater sound speed is calculated from replacing Compact-CTD readings in equation (8). Considering the presence of very weak tidal currents, it is argued that physical properties of the flow do not change significantly during the 30 min of data collection using ADCP and Compact-CTD. The equations of motion for a ray traveling through a body of water are then solved in Cartesian coordinates [Bowlin et al., 1992; Dushaw and Colosi, 1998]. Finally, considering a nominal 1.5–2 dB loss per surface/bottom bounce, rays with more than 30 interactions with surface and bottom are excluded. Ray tracing results for two cases of extreme (20:30 JST on the first day) and moderate deviation (2:30 JST on the second day) between the FAT and ADCP are plotted in Figure 13. Although due to shallowness of the survey zone one is almost assured of interaction between sound and bottom/surface, considering the wavelength range (4.20–7.25 cm) attributed to the frequency bandwidth used in the experiments emphasizes that the bed size may not create 3D effects.
 As indicated in Figure 13, the typical result of ray tracing for 20:30 JST shows a pattern in which rays are entirely trapped in the upper 80 cm layer containing fresher and colder water that leads to slower sound speed. To observe such phenomena, both transducers should be essentially placed inside the upper colder layer. By contrast, ray tracing result for 2:30 JST reveals that sound rays traversed the entire section due to relative homogeneity of water column properties.
 The time that an acoustic wave requires to propagate from source to receiver is representative of the average sound speed along the considered path. Scalar influences such as temperature or salinity affect the speed of sound independent of the direction of sound propagation, while the influence of flow depends on the direction. Figure 14 shows stack plots of arrival time for the signals transmitted from station OB and received at OA. Arrival time is determined by taking the cross correlation between the M-sequence used in the transmission and the received signal. Despite abundance of ambient noise, the irregular bottom shape, and the noticeable signal attenuation, the cross-correlation function presents sharp peaks.
 Figures 14 and 15b support the argument that sound rays were channeled efficiently by the upper layer. As it took more time for the scattered sound to travel the distance between the two acoustic stations, one may suggest that the scattered sound was travelling through cold freshwater characterized with lower sound speed than warmer saltwater. The sudden jump in the peak position of correlation might be attributed to the moment when transducers were submerged completely into the salt wedge. However, most often, peak position shifts slightly due to the changes in water temperature and salinity driven by tidal currents and freshwater inflow from the sluice gates.
 The effect of velocity of the medium on sound propagation can be found in arrival time differences ΔtAB (Figure 15a), while effect of variations of salinity and temperature on sound speed is more likely to be observed in tmAB plot (Figure 15b).
 To investigate the role of dynamic stability induced by vertical salinity gradient and weak tidal currents on sound propagation, the Richardson number, Ri, is evaluated from equation (14) for the deepest parts of the section shown in Figure 1c
is the buoyancy frequency, g gravitational acceleration, ρ fluid density, z vertical coordinate, and the shear frequency term S2 can be obtained from . Quantified Ri values from ADCP and Compact-CTD readings are then averaged over the water column to provide a relative index of dynamic density stratification shown as in Figure 16a. Static stability measured through the buoyancy frequency is also averaged over the depth and is plotted in Figure 16b.
 Comparing the results given in Figure 11b with those presented in Figure 16a, it can be concluded that velocity shear effect measured through depth-averaged Richardson number is not the dominant factor for stratifying flows regarding sound speed gradients, or at least sound entrapment cannot be predicted reliably through . In contrast, a strong correlation was found between static stability associated with vertical change of density (N) and inconsistency of FAT with ADCP. Figure 17 demonstrates that the discrepancy between the FAT and the ADCP measurements gradually decreased with buoyancy frequency, as flooding currents weakened toward high water slack. Least values of relative error occurred, corresponding to N ≈ 0.26. This dip was followed by a raise in the difference between ADCP and FAT results caused by straining encouraged as ebbing tide started.
 In Figure 18, vertical distributions of physical flow properties along with buoyancy frequency and sound velocity are plotted for the deepest part of the river in the right bank (Figure 1c), typically for different stages of tide. According to this figure, sharp peaks of N(z) mark the local depth of thermocline formed by the intrusion of warmer seawater. Considering the ray patterns shown in Figure 13, it may be inferred that this sharp peak indicates the interface between the two layers with different sound velocities at which sound rays are reflected without having interaction with bed. As seen, sharp vertical gradients in N(z) occurred particularly during the turning of tide when freshwater flow rate is comparable with seawater intrusion rate and transducers lay inside the layer with slower sound velocity.
 Installing transducers inside the salt wedge may be considered a solution to prevent the reflection of sound by the boundary of the two layers with distinct sound speed. To verify this solution, spatial sound velocity distribution shown in Figure 13a was used while transducers were relocated inside the salt wedge. The result of running ray-tracing model for the new source and receiver location shown in Figure 19 reveals that this solution would effectively enable sound rays to traverse the entire section. This solution, however, comes with the price of much higher attenuation and smaller section through which sound rays are propagated. The former shortcoming may result in larger section-averaged velocity errors. The latter drawback is that most of the sound rays propagated with obtuse launch angles are blocked by the bottom due to the particular shape of the section. Only rays with acute launch angle successfully reach the receiver after numerous interactions with bottom/surface that leads to significant sound attenuation. Installing the transducers near the bottom, therefore, may not be the ideal solution for this particular site. However, it should be considered as a potential way to encounter salt wedge intrusion.
 Continuous measurement of flow velocity using the Fluvial Acoustic Tomography (FAT) system were conducted in a tidal channel with complex flow pattern generated under influence of salt wedge intrusion and freshwater discharge from a sluice gate. For long-term monitoring purposes, FAT equipped with only a pair of 30 kHz transducers was deployed to estimate section-averaged stream velocities. It was concluded that FAT represents a promising method/sensor for the continuous monitoring of tidal rivers discharge. Unfortunately, it was neither possible to compare the FAT result with stationary ADCP measurement due to horizontal nonuniform current distribution nor with a moving-boat ADCP due to the 6 month long period of observation.
 For implementing delicate comparisons between FAT and a moving-boat ADCP in measuring flow direction and magnitude, a short-term observation campaign was further carried out. Adding a couple of transducers to the FAT to make crossing acoustic paths enabled the system to accurately resolve the flow direction. In spite of complexity of the flow pattern and the time required for fulfilling a transect with ADCP in such unsteady flow, the difference in sampling geometry between the two sensors and the relatively low resolution of FAT when measuring velocity in short distances between acoustic stations, the agreement between the two sensors in measuring mean flow direction and velocity was remarkable.
 While the river discharge was very low, strong salt wedge intrusion occurred in the survey zone. In this extreme case of salt wedge intrusion, FAT velocity measurements were compared with a moving-boat ADCP. It was found that a duct was formed when freshwater flow rate was comparable with seawater intrusion rate. This duct is able to channel the sound from the sources inside quite effectively, especially during the flood tide that tidal straining is strong. Consequently, when both the source and receiver lay inside this duct, FAT reports extremely overestimated flow velocities. Ray-tracing hindcasts suggested that an effective solution for removing the shadow zone generated by seawater intrusion is to install transducers in the bottom of section, inside the salt wedge.
 The authors wish to express their gratitude to Noriaki Gohda of Hiroshima University/Aqua Environmental Monitoring Limited Liability Partnership (AEM-LLP) for his unwavering technical support. This study is supported by the fund “Grant-in-Aid for Young Scientists (B) (24760395)” offered by “Japan Society for the Promotion of Science (JSPS).”