ADCP SUSPENDED SEDIMENT TRANSPORT MONITORING USING ACOUSTIC PARTICLE RADIUS

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INTRODUCTION
Quantifying suspended sediment transport has been key in various coastal and river engineering projects, for example to study sediment budgets in estuaries or mitigating the impact of dredging activities.As numerical models become more important in understanding and predicting sediment transport phenomena, accurate direct measurements of hydrodynamics and suspended sediment concentration (SSC) will become increasingly crucial for calibration and validation.
Compared to hydrodynamic parameters such as currents and waves, which can be measured directly using a range of in situ instruments, quantifying SSC typically involves a more elaborate process due to limitations in available monitoring methods.Traditional methods such as water sampling are labour intensive and expensive, leading to low temporal and spatial resolutions.Indirect measurements can be based on optical backscatter (OBS), acoustic backscatter (ABS) or laser diffraction, of which OBS point measurement sensors are most widely used to determine SSC due to its well-documented procedure.
Using Acoustic Doppler Current Profilers (ADCPs)which record ABS as a by-product to the flow velocity signalto capture suspended sediment structures over depth has been investigated for over three decades (e.g.Reichel & Nachtnebel, 1994;Gartner, 2004;Nauw et al., 2014).If a proper relation between SSC and ADCP backscatter can be established, it is possible to monitor suspended sediment transport over the water column by combining the backscatter data with the flow velocity profiles measured by the instrument.This can then be done in vessel-mounted setups, to capture vast spatial resolutions (i.e.transects of tidal inlets) or in stationary buoy or bottom frame setups for long periods of time thanks to the limited vulnerability to biofouling.
Because sensors based on OBS or ABS including ADCPs do not measure SSC directly, but rather record a backscatter intensity ([V], [NTU], [counts], or [dB]) within a sampling volume, a modelreferred to as data calibrationmust be set up between the measured signal and reference measurements of SSC in [mg/L].Because SSC and the particle size of the sediment can vary significantly over time, for example with the tidal phase (Plancke et al. 2017), the process of the conversion between SSC and backscatter intensity can become labour intensive to execute and analyse.Therefore, if this dependency on reference measurements can be reduced, the potential of ADCPs as sediment transport monitoring tool can be significantly enhanced.
To this end, methods to derive information about particle size using multiple acoustic frequencies have been researched (e.g.Topping et al., 2007;Guerrero et al., 2012Guerrero et al., , 2013;;Jourdin et al., 2014).Not only does this potentially provide valuable water column information about sediment class, these estimates can also make the relation between backscatter and SSC more robust, therefore reducing the need for frequently obtaining (water sample) reference measurements.In these earlier studies, obtaining ADCP backscatter profiles at different frequencies required the use of multiple instruments, inevitably leading to alignment issues (Guerrero et al., 2013;Jourdin et al., 2014).To overcome these limitations, a Nortek Signature1000 ADCP was adapted to record near simultaneous and colocated backscatter profiles at multiple frequencies using its vertical beam echosounder transducer dedicated for high resolution backscatter measurements.Based on these measurements, particle radius estimates were derived and used to establish an adapted model between backscatter and reference SSC measurements, to assess whether certainty in monitoring suspended sediment concentration and subsequently sediment transport using ADCPs can be improved using this instrument.

Volume backscatter and signal losses
Traditionally, ADCPs record backscatter intensity (  ; [dB]) as a signal strength validation parameter for current measurements and is stored in cells over the depth profile.To use ABS as a source of information about suspended sediment particles and compare measurements over depth, the signal must be processed to account for signal losses that vary with distance from the transducer (), while considering instrument properties and settings, and removing data below the acoustic noise threshold ().This can be done using ADCP processing software (Nortek, 2023;Ocean Illumination, 2021)  ; where  is the speed of sound through water [m/s].If measurements are to be compared between instruments, the instrument gain parameter  must be determined following a lab calibration procedure where targets of known backscattering strength are lowered into the acoustic beam of the transducer (Demer et al., 2015;Nortek, 2022).Without instrument calibration, measurements of volume backscatter are relativeindicated with   ′ in this research.
In Equation 1,  is the attenuation coefficient [dB/m], which accounts for signal losses caused by 1) absorption by water (Ainslie & McColm, 1998), and 2) absorption by and scattering losses due to suspended particles.Determining the contribution of the latter requires information about the particles like concentration and size (Guerrero et al., 2016;Thorne & Meral, 2008;Urick, 1948).Methodologies have been developed for estimating attenuation losses due to suspended sediment (e.g.Guerrero & Di Federico, 2018;Sassi et al., 2012), however if concentrations are low enough, the contribution of sediment attenuation to  can be neglected (Gartner, 2004;Hay & Sheng, 1992).

Backscatter-SSC model
To understand the relation between volume backscatter and suspended sediment parameters such as concentration, size, shape, and density, a general backscatter- model is described here (Sassi et al., 2012).For spherical particles, the concentration of the particles in the water volume () can be modelled based on the mean particle radius 〈  〉, density   , and   , the number of scattering particles per unit volume: The terms written in 〈•〉 denote mean values of backscattering particle characteristics within the ensonified volume.The backscatter from the water volume is related to the mean particle radius within this volume via: (Medwin & Clay, 1998, Sassi et al., 2012).Here,  is the so-called form function, and describes the backscattering behaviour of the particles based on the product of the acoustic wavenumber and particle radius   (Thorne & Meral, 2008).For quartz sand particles this form function is expressed by Thorne & Meral (2008): Combining Equations 2 and 3 yields a relation between   and  (Sassi et al., 2012): In an ideal situation, where scattering particles are spherical with known homogeneous density   and mean particle radius 〈  〉, and the backscattering behaviour of the particles if well-described through ,  can be derived directly from   using Equation 5for each measurement volume.For ADCPs, this applies for every cell or bin in the profile over depth.In practice, information about particle properties is rarely known and usually a varying, heterogeneous mixture of suspended matter such as sand particles, flocculated silt and clay particles, and air bubbles is present in the water column.Therefore, the practical approach to derive SSC from ADCP backscatter in real world applications is to simplify the model to a log-linear relation between   and SSC, which must be tuned to site-specific SSC reference measurements using fitting parameters  and :   =  • 10 log 10 () +  (6)

Particle size-acoustic wavelength interactions
As with sensors using OBS, relation ( 6) should be redetermined whenever monitored particle properties change.Hence, continuous reference measurements must be carried out for recalibration of the backscatter-SSC relation.With the multi-frequency approach, it is proposed to capitalize on the sensitivity of the form function () to the emitted signal's frequency due to the interaction between particle size with emitted acoustic wavelength.Through simultaneously monitoring using three different frequencies, the differences between backscatter at those three frequencies can be utilized to infer sediment properties.The Nortek Signature1000 ADCP with three acoustic frequencies on the central beam echosounder of the ADCP ( = 1000,  = 500, and  = 250 kHz) can be used to exploit this sensitivity (Figure 1).

Acoustic particle radius
By assuming the sediment particle size to be unimodally and narrowly distributed (Jourdin et al., 2014), it is possible to derive an explicit relation between the difference in absolute volume backscatter recorded at two frequencies (Δ  ) and a theoretical or acoustic particle radius (  ) based on the backscatter form function derived by Thorne & Meral (2008): Following this approach, a specific range of particle radii can be estimated as a result of the particle size sensitivity on the frequencies used.For frequencies 1000, 500, and 250 kHz, the resolvable acoustic particle radius range varies for each frequency combination (Figure 2).Using the largest frequency interval available ( 1 = 1000 and  2 = 250 kHz), the widest resolvable range is obtained, with an unambiguous solution in the approximate range of 60 ≤   ≤ 2000 µm (Figure 2).

Including acoustic particle radius in the backscatter-SSC model
In contrast to using single frequency ADCPs, where one resorts to Equation 6 in case no additional sediment parameters are measured, deriving acoustic particle radius estimates using a multi-frequency ADCP (Equation 7) allows the use of a backscatter-SSC model that considers particle radius variations.The is referred to as the multi-frequency model:

Methods
To assess whether certainty in deriving SSC estimates from ADCP backscatter is improved by considering acoustic particle radius estimates, performance of the single frequency model (Equation 6) and the multi-frequency model considering acoustic particle radii estimates (Equation 8) were compared based on a sample dataset.For this, a field campaign was carried out in Spring 2022 sampling several locations around the island of Texel, The Netherlands (Figure 3).This site was chosen as the type of sediment in suspension differs greatly between the tidal channel connecting the North Sea to the Marsdiep basin (more sandy) and the Marsdiep basin itself (more muddy), and the phase of the tide is expected to affect the sediment type in suspension.Backscatter measurements were taken at frequencies 1 = 1000 kHz, 2 = 500 kHz and 3 = 250 kHz using the central beam echosounder on a Nortek Signature1000 in a vessel mounted (VM) setup.Vertical cell size was set to 0.05 m, a transmit pulse length of 0.1 ms and the default power level () of 0.0 dB was used.Signal pulse compression was not applied.
Simultaneous reference measurements were taken using a Niskin bottle (NB) and a pumping system, where most of the samples were taken in the Molengat (MG) tidal channel using the NB during ebb ( = 15) and flood ( = 2) (see Figure 3 for sample positions).To exclude effects of inconsistencies in sampling method and to reduce impact of environmental variations between sites, only the NB samples taken at MG were further processed.Based on the assumption that different types of particles are transported in the tidal channel during different phases of the tide, the dataset was divided into two datasets, where Dataset 1 contained measurements with relatively consistent properties of the suspended particles comprising the ebb samples.Dataset 2 contained ebb and flood samples, representing measurements taken under conditions with varying suspended particle properties.The samples were analysed in the lab for SSC following the procedure mentioned in Jaarsma (2023), taking note of measurement uncertainty (Table 3).No additional particle properties such as particle size were determined.

Acoustic noise levels and signal intensity
As introduced in Section 2.1, the noise threshold () should be considered and removed before correlating backscatter measurements to SSC (Equation 1).It is good practice to regularly determine  for each frequency by using the ADCP in 'listening mode', which can be done by setting the power level to -100 dB.Alternatively, noise levels can be estimated by averaging the backscatter intensity recorded in the lowest cells in each profile.Because the ADCP profiling depth was configured to be at least twice the actual water column depth, the last cells in each profile correspond to the signal that has travelled the water column at least twicefirst reflecting off the bed and then the water surface (Figure 4).It can be assumed that at this point, the signal has attenuated to an extend where the recorded signal intensity in these cells primarily comprises acoustic noise. varied between 20 and 27 dB for the 1000 kHz measurements and between 15.5 and 26.5 dB for 500 kHz measurements, where  was observed to be largest for the flood measurements.
For the 250 kHz measurements, the signal was above the noise threshold only within a few meters from the instrument and at the sea floor (Figure 4c).Minimal backscatter intensity was recorded over most of the water column which can be attributed to reduced transducer efficiency at this frequency, little presence of particles large enough for sufficient sensitivity at 250 kHz, or a combination of both.Understanding to what extend using the ADCP's central beam echosounder at 250 kHz can be applied in the proposed multi-frequency method requires further assessment in consideration of these remarks.In this study, only the 1000 and 500 kHz measurements were further processed.

Averaging and calculating volume backscatter (𝑺 𝒗 )
The uncorrected backscatter measurements (  ) taken at 1000 and 500 kHz were aggregated to the water volume sampled using the Niskin bottle based on time and depth of sampling, by averaging over 0.50 m in the vertical domain and 30 seconds in time.The aggregated backscatter was then corrected for noise levels and echosounder loss terms (Equation 1), where the contribution on  attributed to water absorption was estimated following Ainslie & McColm (1998) and attenuation attributed to suspended sediment was neglected.

Accounting for use of an uncalibrated instrument and narrow frequency interval
Because an uncalibrated instrument was used, no formulation of  (Equation 1) was available leading to an unresolved calibration offset Δ between the frequencies: indicate relative volume backscatter obtained from the 1000 and 500 kHz measurements respectively.To mitigate implications of using an uncalibrated instrument in the multi-frequency approach to infer SSC from ADCP backscatter, the following iteration scheme was applied to estimate the calibration offset between the frequencies (Δ).By ranging Δ, Equation 7 was solved for acoustic particle radius based on the varying sets of Δ  datapoints that were obtained from Equation 9.These obtained acoustic particle radii were then substituted in the multi-frequency model (Equation 8) and assessed for best fit with the reference SSC measurements, which was found to consolidate to Δ = −31.4dB.
Using 1 = 1000 kHz and 2 = 500 kHz results in unambiguous solutions for   when 6.0 < Δ  < 12.0 dB (blue line in Figure 2).For values of 3.7 < Δ < 6.0 dB, multiple solutions for   exist, which is a result of the frequency interval being relatively small.Using a larger frequency interval, e.g., 1 = 1000 kHz and 2 = 250 kHz would result in an unambiguous solution for 0 < Δ  < 24.0 dB (red line in Figure 2), which was however not possible due to the low backscatter intensities obtained at 250 kHz (Figure 4).For the data points within the ambiguity range, the lowest possible solution for   (Table 1) was substituted in the multi-frequency backscatter model (Equation 8).For one of the flood samples it was not possible to derive   because Δ  was outside the resolvable range (sample 2 in Table 1).Therefore, this sample was removed from the dataset and only one remaining flood sample could be considered in further analysis.

Performance of the single vs. multi-frequency approach
The capabilities of using ADCP backscatter to predict SSC is determined by how well the applied backscatter model fits the backscatter measurements based on the reference SSC data.Both the single and multi-frequency backscatter models were applied to Dataset 1 (ebb measurements) and Dataset 2 (ebb and flood measurements), and performance of each fitted relation was assessed based on Pearson correlation coefficients ( 2 ).Based on the good correlations observed for the single frequency backscatter model (Table 2), this traditional approach is considered suitable for predicting SSC for the ebb only dataset, where the 500 kHz signal ( 2 = 0.80) outperformed the default 1 1000 kHz signal ( 2 = 0.69).For the combined ebb and flood dataset, the significantly deviating backscatter intensity recorded for the flood measurement led to a poor fit of the single 1 By default, the Nortek Signature1000 records backscatter intensity at 1000 kHz using its vertical beam echosounder.frequency backscatter model (Figure 5a and 5b).Therefore, the single frequency approach is not considered fit to predict SSC under these varying measurement conditions.The established multi-frequency relations (Equation 8 fitted to  ,1000 ′ and  ,500

′
) are expected to predict SSC well for both datasets based on favorable correlations of the fitted model (Table 2), which is represented in the well aligned backscatter measurements for the combined ebb and flood dataset (Figure 5c and 5d).
The difference in skill to predict SSC between the single and multi-frequency approach is demonstrated by comparing estimates with the SSC reference measurements (  ) (Table 3).The multi-frequency relation with the best fit -Equation 8 fitted to  ,1000 ′ predicts SSC within the uncertainty range of the reference measurements for 10 of the 16 datapoints, whereas the predictions following the best fitted single frequency relation -Equation 6 fitted to  ,500 ′ were within the uncertainty range for only 2 of the datapoints (Table 3).

DISCUSSION
After establishing a reliable relation with SSC reference measurements, profiles of concentration predictions inferred from ADCP backscatter (Figure 6c) can be combined with flow velocity and direction measurements over the water column (Figure 6a).Based on the findings in Section 4.5, using the multi-frequency approach can make SSC inversions more robust, reducing the need for frequent water sampling to redetermine the backscatter-SSC relation.Because acoustic particle radius can be derived for each measurement cell corresponding to the multi-frequency backscatter signal, it can be plotted over depth together with the flow measurements and SSC predictions (Figure 6b)leading to potentially valuable information about sediment class.Combining the three measured quantities offers great potential for direct monitoring of sediment transport using a single instrument.
Variations in particle properties have however not been confirmed using a lab analysis, and the size of the sample set leaves room for further investigation on performance of the method.Also, the applied value of  in the fitted multi-frequency backscatter models (Table 2) significantly deviated from the theoretical value of  = 2 in the general backscatter model (Equation 5), indicating a potentially limited applicability of the applied form function for quartz sand particles (Equation 4) for this sample set.

(b) (a) (d) (c) 6 CONCLUSIONS AND RECOMMENDATIONS
For the ebb only dataset, where particle properties were deemed relatively consistent, fitting the traditional single frequency backscatter model (Equation 6) yielded good performance, where a better performance was observed for the 500 kHz signal compared to the default 1000 kHz measurements.For the ebb and flood dataset, very poor correlations were obtained for both frequencies.The observed backscatter corresponding to the sample taken during flood did not align with those taken during ebb, which may have been attributed to the presence of different types of scattering particles in the water column.Following this, the importance of redetermining the relation between backscatter and SSC when scattering properties of particles change, induced by changes in particle size, shape, and nature has been confirmed.
To counteract the sensitivity of established backscatter-SSC relations to changing particle properties, a methodology is proposed where acoustic particle radius (  ) is derived from multi-frequency backscatter measurements using a Nortek Signature1000 ADCP.By considering these estimates in an adapted form of the backscatter-SSC model (Equation 8), significantly higher correlations between manually sampled and ADCP predicted SSC were obtained for the ebb and flood dataset, aligning the samples taken during each tidal phase.
Applying the multi-frequency method that incorporates acoustic particle radii in the relation between backscatter and SSC on this proof-of-concept dataset shows promising improvement of predicted SSC.Follow-up work should include an analysis of sample's particle diameter to confidently attribute the improved performance of the multi-frequency method to predict SSC under changing sediment properties and should assess a larger sample size.Also, increasing the interval between the two frequencies can overcome solution ambiguity in determining   , which could be achieved by investigating methods to increase strength of the 250 kHz signal.Further development of the method can include researching performance in environments with high silt and clay concentrations, considering alternative backscatter form functions and accounting for sediment signal attenuation.
After further validation and development, application of the multi-frequency approach using the vertical beam echosounder on the Nortek Signature1000 ADCP can significantly enhance the capability of predicting SSC andsince backscatter is recorded over depth in conjunction with profiles of current velocity and directionthe ability to monitor suspended sediment transport using a single instrument.
represents volume backscatter, which is the contribution of the ensonified cloud of particles normalized over a theoretical measurement volume of 1 m 3 (Acoustics Unpacked, n.d.).Relevant instrument parameters include transducer radius  [m], the applied power level  [dB], transmit pulse length  [s], and the acoustic wavenumber  [-]. depends on the acoustic frequency  [Hz] through  = 2(1000 •)

Figure 1 .
Figure 1.Backscatter form function () of quartz sand particles, corresponding to  = ,  =  and  =  kHz.The gray dash-dotted lines indicate the Rayleigh scattering regime, where  is a log-linear relation of the acoustic wavenumberparticle radius product (  ).The gray dotted line indicates the geometric regime, where  = . (Thorne & Meral, 2008).
• 10 log 10 () + 10 log 10 (  and , an additional fitting parameter  is introduced to account for potentially limited applicability of the applied form function () on the scattering particles present in the measurement volume.For example, Equation 4(Thorne & Meral, 2008) was empirically derived for quartz sand particles while in practise clay, silt and organic matter can be present.

Figure 3 .
Figure 3. Various locations were sampled around the Dutch barrier island Texel: Molengat (MG) tidal channel, Marsdiep (MD) tidal inlet, near the Prins Hendrikzanddijk (PHZD) coastal nourishment and Waddenzee (WZ).The North Sea is on the left side of the image, the Waddenzee back barrier basin on the right side.

Figure 4 .
Figure 4. Example profiles of uncorrected backscatter intensity (  ) at (a) 1000, (b) 500, and (c) 250 kHz recorded simultaneously using the vertical beam echosounder on a Nortek Signature1000 ADCP in the seaward tidal channel MG during flood.The profile depth was configured to be larger than twice the water depth (, indicated by the red dashed lines).The noise threshold () was estimated based on the uncorrected backscatter intensity recorded in the lowest measurement cells in each profile for all three frequencies.

Figure 5 .
Figure 5. Quality of the single frequency (Equation 6) (a and b) and multi frequency backscatter model (Equation 8) (c and d).Data and linear regression are shown for the 1000 and 500 kHz data based on the combined ebb and flood dataset.