# The Acoustic Properties of Suspended Sediment in Large Rivers: Consequences on ADCP Methods Applicability

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Areas and Sampling Campaigns of Water-Sediment Mixture

^{6}km

^{2}crossing the borders of Brazil, Bolivia, Paraguay and Argentina. Downstream of the confluence of the Parana River and the Paraguay River (Figure 1a), the mean annual discharge is 19,500 m

^{3}·s

^{−1}, and the water surface slope is in the order of 10

^{−5}. The channel bed is composed mostly of fine- and medium-sized sand [27]. The channel planform pattern is classified as an anabranch with a meandering thalweg [26]. A succession of wider and narrower sections is typical, with mean channel widths and thalweg depths ranging from 600 to 2500 m and from 5 to 16 m, respectively. In the middle and lower reaches, the bed material is composed almost completely of sand (>90%), with small amounts of silt and clay (<4%) according to Drago and Amsler [27].

^{3}·s

^{−1}and 1983 m

^{3}·s

^{−1}, respectively, and in the main channel on 16–17 November 2010 when the Parana total discharge was 14,320 m

^{3}·s

^{−1}. Those discharge values in the Colastiné River may correspond to about one tenth of the total discharge in the main channel.

**Figure 1.**(

**a**) The Parana-Paraguay watershed and (

**b**) sampling sections in the Parana River and the Colastiné River (a Parana River secondary reach) close to Santa Fe and Rosario (Argentina); (

**c**) The Danube River watershed and (

**d**) its section in Hungary at Esztergom investigated by using the LISST-SL device by Sequoia Inc (Bellevue, WA, USA).

**Figure 2.**(

**a**) US P-61 point sampler; (

**b**) depth integrated sampler and (

**c**) the LISST-SL used in the Parana secondary channel Colastiné, Parana main channel (Argentina) and the Danube (Hungary), respectively.

^{3}·s

^{−1}and a mean slope of about 10

^{−4}[32]. The average width and depth of this section is in the range of about 500 m and 6 m, respectively. Gravel and sand-gravel material forms the riverbed [33]. A single field campaign was conducted at a flow discharge of about 3290 m

^{3}·s

^{−1}, in the falling limb of an approximately 1-year flood event. Two 500 m wide cross-sections were chosen for the investigation, with water depths in the range of 3–9 m, upstream and downstream of the inflowing section of a tributary called River Hron (Figure 1d). Twelve verticals were investigated by using the LISST-SL device by Sequoia Inc (Bellevue, WA, USA) (Figure 2c), which combines a stream lined (SL) isokinetic sampler with an on-board laser diffraction particle size analyzer [34,35,36]. These measurements were conducted in each vertical for levels regularly spaced from 0.5 to 1.0 m, depending on the actual water depth (i.e., a finer resolution for lower depths was chosen), starting from 0.5 m beneath the water surface until about 0.5 m above the riverbed. A total number of 102 points were sampled in the two cross-sections. For each point, a two-minute long measurement was carried out, resulting in 60 acquisitions (considering the sampling frequency of 0.5 Hz), providing the same number of PSDs spanning 32 classes (diameter size from 2.07 to 350 μm). The two-minute long sampling time was determined based on a preliminary sensitivity analysis, where subsequently time averaged characteristics of the suspended sediment were used [37].

#### 2.2. Acoustic Theory

_{t}, for a given system setting; (ii) the ability of suspended particles to scatter sound back to a mono-static transducer (i.e., backscattering strength) at a distance R; (iii) the two-way round-trip attenuation; (iv) the geometrical spreading. This may be written as reported in Equation (1), which is derived under Thorne and Hanes [24] and is usually referred as the sonar equation:

_{s}

^{2}times the mass concentration M

_{s}is the backscattering strength; (ii) ${\alpha}_{w}$ and ${\alpha}_{s}$ are the water viscosity and suspended sediment attenuation coefficients, respectively; (iii) R

^{2}ψ

^{2}is the geometrical spreading that includes the near field correction coefficient ψ [41]. It is worth noting that much of the existing literature, regarding the use of ADCPs to assess the concentration of suspended sediment, reports a logarithmic form of the sonar equation, including the target strength or an equivalent decibel expression of the backscattering strength that is ten times the common logarithm of K

_{s}

^{2}M

_{s}. This is because the echo levels recorded by an ADCP are proportional to the received sound intensity in a dB scale [37,42].

_{s}

^{2}, depends on mass concentration and PSD through the backscattering coefficient that is written in Equation (2):

_{s}is the sediment density (i.e., 2650 kg·m

^{−3}), a and f are the particles mean radius and the form factor [20], respectively. It is worth noting that for the Rayleigh scattering region (i.e., for the wave number, k, particles radius, a, product x much less than unit; x = ka << 1), f scales as the square of x, while in the geometric region (x >> 1), f asymptotes to be 1.1, with a transition for x close to unity. Equation (3) is the expression given by Thorne and Meral [20] that was applied in this work to assess the form factor for each class forming the analyzed PSDs:

_{s}= α

_{ss}+ α

_{sv}) and may produce a relevant dissipation, depending on mass concentration, the actual PSD and the ensonified range R. For fine particles such as clay-silt, the viscous attenuation coefficient, α

_{sv}, is dominant, while, for sand, it becomes negligible and the attenuation is a result of the scattering attenuation coefficient, α

_{ss}, which is related to the total scattering cross-section, χ, of the ensonified particles.

_{ss}for actual PSDs from samples in the Parana and the Danube, which included the Equation (6) evaluation for each class. ζ between brackets denotes the mean expected value of the attenuation coefficient, normalized over mass concentration. This normalized coefficient only depends on the actual PSD. Equation (7) reduces to Equation (8) for a mono-size suspension:

^{−6}m

^{2}·s

^{−1}for water at about 15 degree Celsius), d is the particle size diameter, and σ the sediment to fluid density ratio. For a mono-size suspension, Equation (13) simply reduces to the normalized viscous attenuation coefficient (ζ

_{sv}given by Equation (12)) times the mass concentration.

**Figure 3.**Sketch summarizing the use of most important parameters in Equations (2)–(13) to be applied while solving Equation (1) with a direct and an inverse approach.

## 3. Results

#### 3.1. Results from Samples

**Figure 4.**Subset of four PSDs (two minutes averaged) from LISST-SL point measurements in two verticals with different water depths in the Danube River at Esztergom.

**Figure 5.**Subset of four PSDs from analysis of wash-load contents: point samples in two verticals with different depths in the secondary reach Colastiné of the Parana system.

**Table 1.**Particle size distributions (PSDs) first and second order moments averaged among entire datasets.

Dataset | Particle Size Number Distribution, p(a) | Particle Size Volume Distribution | |||
---|---|---|---|---|---|

Mean Size, D (μm) | Standard dev., std (μm) | std/D (-) | Geometric Mean (μm) | Geometric std (-) | |

Danube | 3.7 | 4.0 | 1.1 | 28.0 | 2.2 |

Colastiné (Parana): wash-load | 1.0 | 0.8 | 0.8 | 6.7 | 2.8 |

Colastiné (Parana): suspended-load | 92.1 | 31.5 | 0.3 | 117.4 | 1.3 |

Parana main channel: suspended-load | 82.5 | 26.3 | 0.3 | 105.7 | 1.4 |

Dataset | Minimum | Mean | Maximum |
---|---|---|---|

Danube | 256 | 326 | 401 |

Colastiné (Parana): wash-load | 389 | 426 | 449 |

Colastiné (Parana): suspended-load | 6.5 | 34.8 | 92.4 |

Parana main channel: suspended-load | 10.3 | 19.3 | 32.2 |

**Figure 6.**Subset of four PSDs from analysis of sediment suspended from the riverbed: samples in two verticals with different depths in the secondary reach Colastiné of the Parana system.

**Figure 7.**Subset of two PSDs from analysis of sediment suspended from the riverbed: depth-averaged samples of two verticals with different water depths in the main channel of the Parana River at Rosario bifurcation.

#### 3.2. Backscattering Coefficient and Viscous-Scattering Attenuation Normalized Coefficients

_{s}

^{2}, ζ

_{sv}and ζ

_{ss}, respectively) vary with the number PSD, which is in agreement with equations reported in the subtopic 2.2. As already mentioned, these variations deteriorate the backscattering strength to concentration correlation.

**Figure 8.**(

**a**) Backscattering coefficient; (

**b**) scattering attenuation normalized coefficient and (

**c**) viscous attenuation normalized coefficient: values at 1200 kHz among measured number PSDs, functions at three frequencies (600, 1200 and 8000 kHz) for mono-size suspension and values at 1200 kHz for synthetic number PSDs (Figure 9) characterized with fixed values of the std (2, 4, 18 and 28 μm).

**Figure 9.**Generated lognormal number distributions (i.e., synthetic PSDs) for (

**a**) clay-silt fraction and (

**b**) sand fraction; (

**c**) Particle mean sizes and corresponding standard deviation over mean size ratios for the synthetic PSDs.

#### 3.3. Backscattering Strength and Viscous-Scattering Attenuation Coefficients

**Table 3.**Correlations among acoustic variables (reported in the first line) and corresponding sediment features (i.e., concentration, D and std/D) for different datasets (from Danube and Parana rivers); note that the statistically significant correlations are reported with a bold font and underlined font is used for correlations corresponding to most relevant acoustic features, which are the assessed backscattering strength with appreciable variation (5–20 dB) and viscous attenuation with moderate-high magnitude (0.1–0.4 dB/m) as reported in Figure 10 and Figure 11.

Dataset | Backscattering Strength | Scattering Attenuation Coefficient | Viscous Attenuation Coefficient | |
---|---|---|---|---|

Danube | 0.69 | 0.63 | 0.49 | Concentration |

−0.20 | −0.21 | −0.11 | D | |

0.17 | 0.16 | −0.64 | std/D | |

Colastiné (Parana): wash-load | 0.10 | 0.19 | 0.80 | Concentration |

−0.73 | −0.67 | 0.30 | D | |

0.10 | 0.17 | 0.08 | std/D | |

Colastiné (Parana): suspended-load | 0.86 | 0.91 | 0.96 | Concentration |

0.36 | 0.27 | −0.11 | D | |

0.46 | 0.44 | 0.14 | std/D | |

Parana main channel: suspended-load | 0.87 | 0.86 | 0.97 | Concentration |

0.64 | 0.70 | 0.48 | D | |

0.36 | 0.34 | −0.17 | std/D |

**Figure 10.**Assessed backscattering strength among samples (

**a**) for changing concentration and standard deviation over corresponding mean size ratio, std/D, and (

**b**) for changing concentration and mean size, D.

**Figure 11.**Assessed scattering attenuation coefficient among samples (

**a**) for changing concentration and standard deviation over corresponding mean size ratio, std/D, and (

**b**) for changing concentration and mean size, D; Assessed viscous attenuation coefficient among samples (

**c**) for changing concentration and standard deviation over corresponding mean size ratio, std/D, and (

**d**) for changing concentration and mean size, D.

## 4. Discussion

#### 4.1. Implications of the Acoustic Features Assessed from the Observed PSDs

_{s}

^{2}, of mono-size distributions entailing small changes in the representative mean size. On the contrary, the deviation for mono-size values of the acoustic coefficients (K

_{s}

^{2}, ζ

_{sv}and ζ

_{ss}) appeared relevant for the case of clay-silt content.

_{s}

^{2}. In fact, in this case, the backscattering coefficient of a mono-size distribution characterized with the particles mean size of the measured PSD was three to four orders of magnitude lower. This occurrence would produce a not reliable correlation between concentrations and backscattering strengths. In this case, therefore, there is a need of a priori information about the actual PSD. In addition, the viscous attenuation coefficient appeared inverse correlated to std/a ratio characterizing the measured PSD (Table 3). In spite of that, the same arguments regarding beam range as the Parana case may be exhibited for viscous attenuation relevance with respect to corresponding backscattering strength variation in the Danube case. In this case, the beams projected by a down-looking ADCP would be limited even more, resulting into lower water depths (6 m on average) that would keep the two-way round-trip attenuation moderate.

#### 4.2. Recommendations

_{t}in Equation (1). Although this should be retrieved by means of laboratory tests, in the instrument setting and from the manufacturing, where it is a common practice to calibrate K

_{t}by solving the direct problem by measuring the actual PSDs and echo intensity levels at the same time in the field. Besides that, another common practice is to include unpredicted and not directly investigated contributes to Equation (1) in that calibration. This may be the case of a moderate contribution of clay-silt concentration when tracking sand by investigating the corresponding backscattering strength.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Guerrero, M.; Rüther, N.; Szupiany, R.; Haun, S.; Baranya, S.; Latosinski, F.
The Acoustic Properties of Suspended Sediment in Large Rivers: Consequences on ADCP Methods Applicability. *Water* **2016**, *8*, 13.
https://doi.org/10.3390/w8010013

**AMA Style**

Guerrero M, Rüther N, Szupiany R, Haun S, Baranya S, Latosinski F.
The Acoustic Properties of Suspended Sediment in Large Rivers: Consequences on ADCP Methods Applicability. *Water*. 2016; 8(1):13.
https://doi.org/10.3390/w8010013

**Chicago/Turabian Style**

Guerrero, Massimo, Nils Rüther, Ricardo Szupiany, Stefan Haun, Sandor Baranya, and Francisco Latosinski.
2016. "The Acoustic Properties of Suspended Sediment in Large Rivers: Consequences on ADCP Methods Applicability" *Water* 8, no. 1: 13.
https://doi.org/10.3390/w8010013