A common question from Nortek users is whether backscatter data from Nortek instruments can be related to turbidity to study Suspended Sediment Concentration (SSC). In this FAQ we address this issue, by splitting the study into four categories with increasing levels of complexity according to the user’s needs. Traditionally, optical backscatter sensors and water sampling have been used to estimate SSC, however, these methods are restricted to a fixed coordinate (single point measurement). The advancement of SSC studies using Acoustic signal has enabled a higher spatial resolution, resulting in cheaper and integrated studies.

Nortek instruments send acoustic pulses (a ping) into the water which will be reflected back by suspended sediment, organic matter, fish, bubbles, and other materials in the water column. The return signal from the acoustic pulses (basckatter) is mainly used to measure the velocity of the particles, but multiple studies have used backscatter signals as a proxy to estimate SSC profiles via distinct models. For a thorough review examining the use of acoustic signals for SSC estimation using the sonar equation, please refer to Thorne & Hurther (2014) and Venditti et al. (2016). Extra references can be found here.

1. Single point correlation between Amplitude and SSC

This first case can be applied when the user doesn’t want a complex investigation, so that a simple correlation is valid. This correlation can be achieved when the acoustic signal is at the same level as the water sampling, and one single reference height is used, as opposed to a profile.

The acoustic signal from ADCPs is proportional to the logarithm of the echo strength below a certain SSC threshold. To evaluate whether the recorded SSC values are within the linear range, the user should first plot the calibration samples or reference instrument (such as an Optical Backscatter) against the Echo Intensity of the Nortek instrument. To do so, the amplitude must be firstly converted from the internal unit of counts to a linear or log scale, also referred to as Echo Intensity [dB]. General experience indicates that for sediment concentrations of about 1-10000 mg/L this relationship is linear (multiply Amplitude by 0.43 to achieve echo intensity), but this should be verified by the user.

Figure 1 shows a linear correlation between the variables below ~82 dB in the acoustic instrument. This is due to a cap in the Echo intensity received by the instrument, so that above this threshold, the effect is nonlinear. That effect can also be observed when plotting a time series, however, it is easily observed when compared against a reference instrument. In this study, the HR mode in the Signature 1000 enabled a vertical resolution of 0.02 m. Due to the pulse coherence characteristics of the instrument, low-noise and highly accurate data were retrieved.

Figure 1: Correlation between Optical instrument data and a Signature with HR Amplitude (dB). This figure was generously provided by William Edge. Source: Edge et al, 2021.

Since the acoustic technique is an indirect method, the measured Echo Intensity has to be related to sediment samples by applying a simple linear correlation:

2. Profile correlation between Amplitude and SSC

This second case is recommended when the user is applying extending the Amplitude and sediment correlation to an amplitude profile. In this case, the Echo Intensity has to be corrected to account for two-way transmission loss by beam spreading and attenuation by water, transmit power, an instrument constant, a near field correction, and if necessary also sediment attenuation (Deines, 1999;  Gartner, 2004;  Gostiaux and van Haren, 2010 for a correction to the method) as shown in this FAQ . As this information is not easily available in a single-frequency, non-echosounder instrument, these terms are often ignored, and an empirical relationship is stablished between backscatter and SSC. Our experience dictates that in well-sorted beaches where the sensor is near the sampling area this is a good assumption (e.g., Fugate & Friedrichs, 2002; Gartner, 2004; Ha et al., 2009; Kim & Voulgaris, 2003).

From the sonar equation (Eq. 1) simplified by Deines (1999):

PL, G, c and \(\tau\) can be fixed during sample calibration, so that target reflectivity and equivalent beam angle can be replaced by a single constant. With that, Eq. 2 becomes similar to Eq. 1 if multiple in-situ samples are available along the profile. If they’re not available, a laboratory mixing chamber can be used to calibrate the instrument to SSC.

We recommend the study conducted by Ha et al. (2011) to study the importance of sediment attenuation \(\alpha_s\) in total sound attenuation. This is a function of SSD, distance from the instrument (R), scattering loss and viscous absorption. The authors published a sediment attenuation as a function of grain diameter and instrument frequency, which should be considered in the user’s deployment.

3. Absolute calibration

As explained in this FAQ, instrument calibration is necessary to determine the absolute strength of the backscatter signal, accounting for gain and Power lever. Without instrument calibration, backscatter strength indicates relative volume backscatter rather than absolute volume backscatter. This implies that comparisons of backscatter intensities between instruments and sites are not feasible due to unknown offsets in backscatter strength. With relative backscatter, an empirical relation has to be derived for every field campaign and in every different location and time.

Eq. 1 should be primarily used where one can assume a constant Particle Size Distribution (PSD) in time and space. This method has a few limitations:

• Changes in the Particle Size Distribution can be common in dynamic environments;
• flocculation processes can influence an acoustic instrument’s response;
• a high number of samples is necessary to correlate these variables, which could be expensive and time-consuming

The development of the Echosounder feature in the Signature presents a big advancement in the applicability of these types of studies. Before diving into the Echosounder, let’s take a look at estimating SSC with instruments that don’t have it (including Signature and midlife instruments). This process is made easier with the Echosounder, which outputs the target strength (\(TS\), [dB re \(1 \, \text{m}^2\)]) or volume-backscattering strength (\(S_v\), [dB re \(1 \, \text{m}^2 \, \text{m}^{-3}\)]), based on the backscattering cross-section (σbs [m²]) and other characteristics of the backscattering source. In practical applications, this limitation can be mitigated by correlating backscatter data with reference SSC measurements from water samples or other sources. By establishing a model between relative volume backscatter and SSC specific to a dataset, instrument-specific variables can be accounted for.

An important limitation for all single-frequency acoustic instruments is that they cannot differentiate between changes in concentration level and changes in particle size distribution. For that, multi-frequency ABS systems have been developed, as different frequencies respond differently to particle size variations, enabling the derivation of mean particle size and concentration from the multi-frequency signal. The second limitation is that the signal attenuation (from water and suspended material) is highly correlated with frequency. This is related to the Rayleigh scattering model, being restricted to \(k\alpha_p < 1\), where \(k\) is the instrument’s frequency wavenumber.

The quality of echo intensity from ADCPs is usually limited by a low dynamic range and temperature-sensitive gain (the temperature is only measured at the instrument’s height. In applications involving a single-frequency Echousounder (Signature 1000 and Signature 500), SSC values can be derived by correlating with reference SSC measurements (water sampling), provided the same instrument is used. Gain can be determined by conducting instrument calibration in the lab for each instrument and frequency, as applicable. It's important to note that due to potential transducer drift over time, gain must be recalculated at regular intervals.

4. SSC profile estimation from single-point Amplitude data

This last step requires a higher knowledge of the area and the physics behind it. We recommend the inversion calculations published by Thorne and Hurther (2014).

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References:

Deines, K. (1999). Backscatter estimation using Broadband acoustic Doppler current profilers. Paper presented at the Proceedings of the IEEE Sixth Working Conference on Current Measurement (Cat. No.99CH36331). https://doi.org/10.1109/CCM.1999.755249

Edge, W. C., N. L. Jones, M. D. Rayson, and G. N. Ivey. “Calibrated suspended sediment observations beneath large amplitude non‐linear internal waves.” Journal of Geophysical Research: Oceans 126, no. 12 (2021): e2021JC017538

Gartner, J. W. (2004). Estimating suspended solids concentrations from backscatter intensity measured by acoustic Doppler current profiler in San Francisco Bay, California. Marine Geology, 211(3–4), 169–187. https://doi.org/10.1016/j.margeo.2004.07.001

Gostiaux, L., & van Haren, H. (2010). Extracting meaningful information from uncalibrated backscattered echo intensity data. Journal of Atmos-pheric and Oceanic Technology, 27(5), 943–949. https://doi.org/10.1175/2009JTECHO704.1

Ha, H. K., Hsu, W.-Y., Maa, J.-Y., Shao, Y., & Holland, C. (2009). Using ADV backscatter strength for measuring suspended cohesive sediment concentration. Continental Shelf Research, 29(10), 1310–1316. https://doi.org/10.1016/J.CSR.2009.03.001

Kim, Y. H., & Voulgaris, G. (2003). Estimation of suspended sediment concentration in estuarine environments using acoustic backscatter from an ADCP. Proceedings of Coastal Sediments,

Lohrmann, Atle. "Monitoring sediment concentration with acoustic backscattering instruments." Nortek Technical Note 3 (2001): 1-5.

Thorne, P. D., & Hurther, D. (2014). An overview on the use of backscattered sound for measuring suspended particle size and concentration pro-files in non-cohesive inorganic sediment transport studies. Continental Shelf Research, 73, 97–118. https://doi.org/10.1016/j.csr.2013.10.017