# Feasibility of Time-Dependent Amplitude in Pulse-Compressed Broadband Acoustic Signals for Determining the Dorsal Orientation of Fish

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experiment with Fish Observed in Dorsal Aspects

#### 2.1.1. Experimental Site

#### 2.1.2. Hydroacoustic Description and Settings

_{nom}at 120 kHz. The entire echosounder was operated with Simrad EK80 software (Simrad, Kongsberg Maritime AS, Horten, Norway) and calibrated with a 38.1-mm sphere of tungsten carbide (WC) containing 6% cobalt binder [21]. The system was set to transmit frequency-modulated upsweep pulses over a frequency band from 90 to 170 kHz with a pulse duration of 0.512 ms. The transmitted signals were either fast-tapered (fast ramping: the first two and last two wavelengths were smoothly tapered with a half cosine wave) or slow-tapered (slow ramping: half the pulse duration to reach maximum amplitude and the remaining half to decay [22]). The transducer was placed on the bottom below the working platform and supported by a float to balance the transducer sound beam to aim perpendicular to the water surface (Figure 1).

#### 2.1.3. Experimental Procedure

#### 2.2. Data Processing and Analysis

#### 2.2.1. Extraction of Amplitude Echo Envelopes

^{−1}). The matched-filter algorithm was run in Sonar5-Pro on the recorded matrix to generate a new similar matrix of complex numbers. The amplitude (A) for each range bin was obtained by averaging all the values in each range bin as shown below:

#### 2.2.2. Extraction of Amplitude Echo Descriptors

_{MAX}) and echo length (EL) at seven specified levels. To set length levels relative to all fish sizes and tilt angles, the length level was determined as a difference from A

_{MAX}. A

_{MAX}was considered the least influenced value, since the lowest amplitude values might be influenced by ambient noise. We empirically chose length levels at 3, 6, 9, 12, 15, 18 and 24 dB below A

_{MAX}, where EL

_{3dB}represents the highest level and EL

_{24dB}represents the lowest level. To calculate EL at a specified level, the maximum and minimum row values for all amplitude values higher than the specified level were subtracted (i.e., EL equals the number of amplitude range bins at the given level).

#### 2.2.3. Modeling of Amplitude Echo Envelopes and Descriptors

_{MAX}and ELs derived for the profile at each combination of the individual body angle × fish × replication separately). Each model was fitted separately for fast and slow ramping data; specifically, we effectively stratified the ramping type, allowing all effects to potentially interact with ramping type.

- ${Y}_{ita}$ is the response (such as the measured amplitude) for fish i, angle a, time t (within a pulse) and replicate r;
- $\mu $ is the (unknown) intercept parameter;
- ${b}_{i}~N\left(0,{\sigma}_{b}^{2}\right)$ is the individual-specific random effect (distribution of which depends on unknown variance parameter ${\sigma}_{b}^{2}$);
- ${s}_{size}$ is an (unknown) smooth component (function of one variable), implemented as a thin-plate spline [28];
- ${s}_{angleprofile}$ is an (unknown) smooth component (function of two variables), implemented as a factor smooth interactive term (called “factor smooth interactions”, [25]). This term formalizes the interaction between (within-pulse) time and angle. Specifically, it allows for time profile deformation in relation to the body angle. This is a key term with respect to the main purpose of the study;
- ${\epsilon}_{it}~N\left(0,{\sigma}^{2}\right)$ is a (theoretical) residual with unknown variance parameter ${\sigma}^{2}$.

- ${Y}_{ia}$ is the response (A
_{MAX}or EL) for fish i, angle a and replicate r; - $\mu $ is the (unknown) intercept parameter;
- ${b}_{i}~N\left(0,{\sigma}_{b}^{2}\right)$ is the individual-specific random effect (whose distribution depends on unknown variance parameter ${\sigma}_{b}^{2}$);
- $\beta $ is an (unknown) parameter (slope);
- ${s}_{angle}$ is an (unknown) smooth component (function of one variable), implemented as a thin-plate spline [28]. This is a key term with respect to the main purpose of the study (when focusing on characteristics derived from the profile).

#### 2.2.4. Software

## 3. Results

#### 3.1. Interaction between Fish Tilt Angle and Amplitude Echo Envelope

#### 3.2. Interaction between Fish Tilt Angle and Amplitude Echo Descriptors

_{i}was similar between both fast- and slow-tapered acoustic pulses, allowing possible comparison of s

_{angle}between two ramping sets. Most importantly, the effect of fish tilt angle s

_{angle}showed that the greatest influence was found on A

_{MAX}for fast-tapered pulses, while it was not pronounced in slow-tapered pulses. In the general view of EL, there was an increase in the effect of the fish tilt angle on EL from the highest level (EL

_{3dB}) to EL

_{18dB}and EL

_{15dB}for fast- and slow-tapered acoustic signals, respectively. Thereafter, the effect of the fish tilt angle on EL decreased.

_{MAX}was relatively low. The maximum of A

_{MAX}was shifted to the head-down positions, 5 and 10 degrees off the true dorsal aspect at fast- and slow-tapered signals, respectively. This indicates that the strongest reflection (largest incident area of swim bladder) did not come from the true dorsal position but from the position in which the fish was slightly tilted with its tail closer to the transducer (head-down dorsal orientation). Moreover, the effect of the fish tilt angle on A

_{MAX}generally decreased faster for the head-down than for the head-up dorsal orientations.

_{MAX}for both fast- and slow-tapered acoustic signals, suggesting that the highest levels would not be appropriate for determining fish tilt angles. In most cases, the effect minimum was slightly shifted to the head-down dorsal orientation and was most noticeable at slow-tapered acoustic signals. The effect measure was dissimilar and changed at different rates toward the oblique tilt angles between the head-up and head-down dorsal orientations. The head-down dorsal orientation showed higher rates for the effect measure. The most stable and symmetrical shapes of the effect of the fish tilt angle on EL between the head-up and head-down dorsal orientations were observed at EL

_{15dB}and EL

_{18dB}, especially for fast-tapered acoustic signals, indicating that these two levels could be the most appropriate candidates for determining fish tilt angle.

## 4. Discussion

_{MAX}, the results confirm that the maximum TS of backscatter from the dorsal aspect is at a slight head-down tilt for most fish (e.g., [36,38]). This corresponds to the position of the swim bladder, which predominantly contributes to the backscatter [39,40]. In common bream, the swim bladder contains two chambers; the second chamber is larger and typically cone-shaped, with a downward-curved end in older fish (e.g., [41]). The deviation of the maximum value from the true dorsal aspect was five and almost ten degrees off the true dorsal aspect for fast- and slow-tapered signals, respectively. This needs to be considered for the future development of algorithms to avoid underestimation of fish size.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Simmonds, J.; MacLennan, D.N. Fisheries Acoustics: Theory and Practice, 2nd ed.; Simmonds, J., MacLennan, D., Eds.; Blackwell Publishing: New York, NY, USA, 2005; ISBN 978-0-470-99529-7. [Google Scholar]
- Demer, D.A.; Andersen, L.N.; Bassett, C.; Berger, L.; Chu, D.; Condiotty, J.; Cutter, G.R., Jr.; Hutton, B.; Korneliussen, R.; Bouffant, N.L.; et al. 2016 USA–Norway EK80 Workshop Report: Evaluation of a Wideband Echosounder for Fisheries and Marine Ecosystem Science. ICES Coop. Res. Rep. (CRR)
**2017**, 336, 79. [Google Scholar] [CrossRef] - Turin, G. An Introduction to Matched Filters. IEEE Trans. Inf. Theory
**1960**, 6, 311–329. [Google Scholar] [CrossRef] - Ehrenberg, J.E.; Torkelson, T.C. FM Slide (Chirp) Signals: A Technique for Significantly Improving the Signal-to-Noise Performance in Hydroacoustic Assessment Systems. Fish. Res.
**2000**, 47, 193–199. [Google Scholar] [CrossRef] - Stanton, T.K.; Reeder, D.B.; Jech, J.M. Inferring Fish Orientation from Broadband-Acoustic Echoes. ICES J. Mar. Sci.
**2003**, 60, 524–531. [Google Scholar] [CrossRef] - Zakharia, M.E.; Magand, F.; Hetroit, F.; Diner, N. Wideband Sounder for Fish Species Identification at Sea. ICES J. Mar. Sci.
**1996**, 53, 203–208. [Google Scholar] [CrossRef] - Bassett, C.; De Robertis, A.; Wilson, C.D. Broadband Echosounder Measurements of the Frequency Response of Fishes and Euphausiids in the Gulf of Alaska. ICES J. Mar. Sci.
**2018**, 75, 1131–1142. [Google Scholar] [CrossRef] - Blanluet, A.; Doray, M.; Berger, L.; Romagnan, J.-B.; Bouffant, N.L.; Lehuta, S.; Petitgas, P. Characterization of Sound Scattering Layers in the Bay of Biscay Using Broadband Acoustics, Nets and Video. PLoS ONE
**2019**, 14, e0223618. [Google Scholar] [CrossRef] - Gugele, S.M.; Widmer, M.; Baer, J.; DeWeber, J.T.; Balk, H.; Brinker, A. Differentiation of Two Swim Bladdered Fish Species Using next Generation Wideband Hydroacoustics. Sci. Rep.
**2021**, 11, 10520. [Google Scholar] [CrossRef] - Horne, J.; Jech, J.M. Multi-Frequency Estimates of Fish Abundance: Constraints of Rather High Frequencies. ICES J. Mar. Sci.
**1999**, 56, 184–199. [Google Scholar] [CrossRef] - Fässler, S.M.M.; Santos, R.; García-Núñez, N.; Fernandes, P.G. Multifrequency Backscattering Properties of Atlantic Herring (Clupea harengus) and Norway Pout (Trisopterus esmarkii). Can. J. Fish. Aquat. Sci.
**2007**, 64, 362–374. [Google Scholar] [CrossRef] - Jaffe, J.S.; Roberts, P.L.D. Estimating Fish Orientation from Broadband, Limited-Angle, Multiview, Acoustic Reflections. J. Acoust. Soc. Am.
**2011**, 129, 670–680. [Google Scholar] [CrossRef] [PubMed] - Kubilius, R.; Macaulay, G.J.; Ona, E. Remote Sizing of Fish-like Targets Using Broadband Acoustics. Fish. Res.
**2020**, 228, 105568. [Google Scholar] [CrossRef] - Kubilius, R.; Bergès, B.; Macaulay, G.J. Remote Acoustic Sizing of Tethered Fish Using Broadband Acoustics. Fish. Res.
**2023**, 260, 106585. [Google Scholar] [CrossRef] - Frouzova, J.; Kubecka, J.; Balk, H.; Frouz, J. Target Strength of Some European Fish Species and Its Dependence on Fish Body Parameters. Fish. Res.
**2005**, 75, 86–96. [Google Scholar] [CrossRef] - Miyanohana, Y.; Ishii, K.; Furusawa, M. Dorsal Aspect Target Strength Functions of Eight Species of Fish at Four Frequencies. Tech. Rep. Natl. Res. Inst. Fish. Eng. Fish. Boat Instrum.
**1990**, 189, 317–324. [Google Scholar] - De Robertis, A.; Schell, C.; Jaffe, J.S. Acoustic Observations of the Swimming Behavior of the Euphausiid Euphausia Pacifica Hansen. ICES J. Mar. Sci.
**2003**, 60, 885–898. [Google Scholar] [CrossRef] - Genin, A.; Jaffe, J.S.; Reef, R.; Richter, C.; Franks, P.J.S. Swimming against the Flow: A Mechanism of Zooplankton Aggregation. Science
**2005**, 308, 860–862. [Google Scholar] [CrossRef] - Tušer, M.; Kubečka, J.; Frouzová, J.; Jarolím, O. Fish Orientation along the Longitudinal Profile of the Římov Reservoir during Daytime: Consequences for Horizontal Acoustic Surveys. Fish. Res.
**2009**, 96, 23–29. [Google Scholar] [CrossRef] - Burwen, D.L.; Nealson, P.A.; Fleischman, S.J.; Mulligan, T.J.; Horne, J.K. The Complexity of Narrowband Echo Envelopes as a Function of Fish Side-Aspect Angle. ICES J. Mar. Sci.
**2007**, 64, 1066–1074. [Google Scholar] [CrossRef] - Demer, D.A.; Berger, L.; Bernasconi, M.; Bethke, E.; Boswell, K.; Chu, D.; Domokos, R.; Dunford, A.; Fässler, S.; Gauthier, S.; et al. Calibration of Acoustic Instruments. ICES Coop. Res. Rep. (CRR)
**2015**, 326, 136. [Google Scholar] [CrossRef] - Oppenheim, A.V.; Schafer, R.W. Discrete-Time Signal Processing, 2nd ed.; Prentice Hall: Upper Saddle River, NJ, USA, 1989; ISBN 978-0-13-216292-0. [Google Scholar]
- Tušer, M.; Frouzová, J.; Balk, H.; Muška, M.; Mrkvička, T.; Kubečka, J. Evaluation of Potential Bias in Observing Fish with a DIDSON Acoustic Camera. Fish. Res.
**2014**, 155, 114–121. [Google Scholar] [CrossRef] - Hastie, T.J.; Tibshirani, R.J. Generalized Additive Models; CRC Press: Boca Raton, FL, USA, 1990; ISBN 978-0-412-34390-2. [Google Scholar]
- Wood, S.N. Generalized Additive Models: An Introduction with R, 2nd ed.; Chapman and Hall/CRC: New York, NY, USA, 2017; ISBN 978-1-315-37027-9. [Google Scholar]
- De Boor, C. A Practical Guide to Splines; Springer: New York, NY, USA, 2001; Volume 27, ISBN 978-0-387-95366-3. [Google Scholar]
- Tukey, J.W. Exploratory Data Analysis; Addison-Wesley Publishing Company: Boston, MA, USA, 1977; ISBN 978-0-201-07616-5. [Google Scholar]
- Wood, S.N. Thin Plate Regression Splines. J. R. Stat. Soc. Ser. B (Stat. Methodol.)
**2003**, 65, 95–114. [Google Scholar] [CrossRef] - Wood, S.N. Fast Stable Restricted Maximum Likelihood and Marginal Likelihood Estimation of Semiparametric Generalized Linear Models. J. R. Stat. Soc. Ser. B (Stat. Methodol.)
**2011**, 73, 3–36. [Google Scholar] [CrossRef] - Wood, S.N.; Pya, N.; Säfken, B. Smoothing Parameter and Model Selection for General Smooth Models. J. Am. Stat. Assoc.
**2016**, 111, 1548–1563. [Google Scholar] [CrossRef] - R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2022. [Google Scholar]
- Wickham, H.; François, R.; Henry, L.; Müller, K.; Vaughan, D. Dplyr: A Grammar of Data Manipulation; 2022. Available online: https://CRAN.R-project.org/package=dplyr (accessed on 12 March 2023).
- Wickham, H. Ggplot2: Elegant Graphics for Data Analysis; Springer: New York, NY, USA, 2016; ISBN 978-3-319-24277-4. [Google Scholar]
- Wood, S.N.; Goude, Y.; Shaw, S. Generalized Additive Models for Large Data Sets. J. R. Stat. Society. Ser. C (Appl. Stat.)
**2015**, 64, 139–155. [Google Scholar] [CrossRef] - Ho, T.K. Random Decision Forests. In Proceedings of the 3rd International Conference on Document Analysis and Recognition, Montreal, QC, Canada, 14–16 August 1995; Volume 1, pp. 278–282. [Google Scholar]
- Au, W.W.L.; Benoit-Bird, K.J. Acoustic Backscattering by Hawaiian Lutjanid Snappers. II. Broadband Temporal and Spectral Structure. J. Acoust. Soc. Am.
**2003**, 114, 2767–2774. [Google Scholar] [CrossRef] - Lavery, A.C.; Bassett, C.; Lawson, G.L.; Jech, J.M. Exploiting Signal Processing Approaches for Broadband Echosounders. ICES J. Mar. Sci.
**2017**, 74, 2262–2275. [Google Scholar] [CrossRef] - Henderson, M.J.; Horne, J.K.; Towler, R.H. The Influence of Beam Position and Swimming Direction on Fish Target Strength. ICES J. Mar. Sci.
**2008**, 65, 226–237. [Google Scholar] [CrossRef] - Foote, K.G. Importance of the Swimbladder in Acoustic Scattering by Fish: A Comparison of Gadoid and Mackerel Target Strengths. J. Acoust. Soc. Am.
**1980**, 67, 2084–2089. [Google Scholar] [CrossRef] - Macaulay, G.J. Anatomically Detailed Acoustic Scattering Models of Fish. Bioacoustics
**2002**, 12, 275–277. [Google Scholar] [CrossRef] - Beregi, A.; Székely, C.; Békési, L.; Szabó, J.; Molnár, V.; Molnár, K. Radiodiagnostic Examination of the Swimbladder of Some Fish Species. Acta. Vet. Hung.
**2001**, 49, 87–98. [Google Scholar] [CrossRef]

**Figure 1.**Illustration of experimental design for collecting hydroacoustic data of anesthetized fish of known size with controllably adjustable dorsal body orientation. (

**A**) Fish positioned in true dorsal body orientation. (

**B**) Fish positioned at tilt angle with head closer to the transducer, i.e., in head-up dorsal orientation.

**Figure 2.**An example of raw amplitude data for a 295-mm-long bream observed in given dorsal orientations (0° correlates to the true dorsal aspect; negative angles correlate to the head tilted toward the transducer; positive angles correlate to the tail tilted toward the transducer) using fast- and slow-tapered acoustic pulses.

**Figure 3.**Amplitude echo envelopes modeled using the generalized additive mixed model M1 for given individual tilt angles (0° correlates to the true dorsal aspect; negative angles correlate to the head tilted toward the transducer; positive angles correlate to the tail tilted toward the transducer) in fast- or slow-tapered acoustic pulses. Individual curves correspond to the plot of s

_{angle profile}(a, t) for given angle a.

**Figure 4.**Effect of the fish tilt angle (0° correlates to the true dorsal aspect; negative angles correlate to the head tilted toward the transducer; positive angles correlate to the tail tilted toward the transducer) on the amplitude echo descriptors in the fitted generalized additive mixed models (GAMM) for fast- and slow-tapered broadband acoustic pulses. A black line represents a smooth component (function of one variable) implemented as a thin-plate spline, with a gray area representing a 95% confidence interval. A

_{MAX}stands for the amplitude maximum. EL stands for the echo length at several levels, expressed as the number of decibels below A

_{MAX}(dB; labeled as a subscript). Note the different y-axis scales.

**Table 1.**Body measurements of the common bream Abramis brama (L.) observed in dorsal aspect using pulse-compressed broadband acoustic pulses. The data is sorted in ascending order of fish size.

ID | Standard Length [mm] | Total Length [mm] | Weight [g] |
---|---|---|---|

bream5 | 165 | 205 | 94 |

bream1 | 170 | 225 | 120 |

bream3 | 205 | 255 | 186 |

bream6 | 240 | 295 | 304 |

bream2 | 290 | 355 | 518 |

bream4 | 310 | 375 | 628 |

bream7 | 325 | 400 | 622 |

**Table 2.**Results of the generalized additive mixed model M1 assessing variation in individual model components for fast ramping (n = 1,202,670; deviance explained = 82.3%; restricted maximum likelihood score (REML) = 3.9 × 10

^{6}; Akaike information criterion (AIC) = 7,887,672) and for slow ramping (n = 1,058,036; deviance explained = 76.7%; REML = 3.9 × 10

^{6}; AIC = 7,769,839). The effective degrees of freedom (edf), F statistic (F) and the probability value of the statistic (p) are represented.

Ramping | Model M1 Component | edf | F | p |
---|---|---|---|---|

fast | b_{i} | 5 | 2441 | <2 × 10^{−16} |

s_{size} | 1 | 87 | <2 × 10^{−16} | |

s_{50} | 14 | 33,001 | <2 × 10^{−16} | |

s_{60} | 14 | 40,008 | <2 × 10^{−16} | |

s_{70} | 14 | 49,688 | <2 × 10^{−16} | |

s_{80} | 14 | 44,410 | <2 × 10^{−16} | |

s_{90} | 14 | 40,766 | <2 × 10^{−16} | |

s_{100} | 14 | 47,679 | <2 × 10^{−16} | |

s_{110} | 14 | 41,846 | <2 × 10^{−16} | |

s_{120} | 14 | 40,478 | <2 × 10^{−16} | |

s_{130} | 14 | 44,044 | <2 × 10^{−16} | |

slow | b_{i} | 4 | 4662 | <2 × 10^{−16} |

s_{size} | 1 | 18 | <2 × 10^{−16} | |

s_{50} | 14 | 25,782 | <2 × 10^{−16} | |

s_{60} | 14 | 26,706 | <2 × 10^{−16} | |

s_{70} | 14 | 24,904 | <2 × 10^{−16} | |

s_{80} | 14 | 28,241 | <2 × 10^{−16} | |

s_{90} | 14 | 29,702 | <2 × 10^{−16} | |

s_{100} | 14 | 25,088 | <2 × 10^{−16} | |

s_{110} | 14 | 27,635 | <2 × 10^{−16} | |

s_{120} | 14 | 29,312 | <2 × 10^{−16} | |

s_{130} | 14 | 24,902 | <2 × 10^{−16} |

**Table 3.**Results of the generalized additive mixed model M2 for the amplitude maximum (A

_{MAX}) and echo lengths (EL) at several levels assessing their explained deviance, generalized cross-validation criterion (GCV), and variation (F = F statistic) in their components of b

_{i}(effective degrees of freedom = 5, p-value = <2 × 10

^{−16}) and s

_{angle}(effective degrees of freedom = 7, p-value = <2 × 10

^{−16}) for fast (n = 5928) and slow ramping (n = 5212).

Deviance Explained [%] | F | ||||
---|---|---|---|---|---|

Ramping | Explanatory | GCV | b_{i} | s_{angle} | |

fast | A_{MAX} | 61 | 6 | 91 | 7580 |

EL_{3dB} | 17 | 28 | 51 | 128 | |

EL_{6dB} | 20 | 71 | 39 | 170 | |

EL_{9dB} | 35 | 93 | 108 | 311 | |

EL_{12dB} | 52 | 87 | 124 | 556 | |

EL_{15dB} | 71 | 61 | 164 | 1308 | |

EL_{18dB} | 81 | 40 | 127 | 2342 | |

EL_{24dB} | 61 | 104 | 127 | 875 | |

slow | A_{MAX} | 46 | 9 | 92 | 193 |

EL_{3dB} | 24 | 39 | 76 | 66 | |

EL_{6dB} | 31 | 46 | 44 | 178 | |

EL_{9dB} | 62 | 38 | 103 | 738 | |

EL_{12dB} | 68 | 52 | 186 | 1003 | |

EL_{15dB} | 71 | 63 | 175 | 1031 | |

EL_{18dB} | 69 | 77 | 124 | 852 | |

EL_{24dB} | 51 | 187 | 57 | 464 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tušer, M.; Brabec, M.; Balk, H.; Draštík, V.; Kubečka, J.; Frouzová, J.
Feasibility of Time-Dependent Amplitude in Pulse-Compressed Broadband Acoustic Signals for Determining the Dorsal Orientation of Fish. *Water* **2023**, *15*, 1596.
https://doi.org/10.3390/w15081596

**AMA Style**

Tušer M, Brabec M, Balk H, Draštík V, Kubečka J, Frouzová J.
Feasibility of Time-Dependent Amplitude in Pulse-Compressed Broadband Acoustic Signals for Determining the Dorsal Orientation of Fish. *Water*. 2023; 15(8):1596.
https://doi.org/10.3390/w15081596

**Chicago/Turabian Style**

Tušer, Michal, Marek Brabec, Helge Balk, Vladislav Draštík, Jan Kubečka, and Jaroslava Frouzová.
2023. "Feasibility of Time-Dependent Amplitude in Pulse-Compressed Broadband Acoustic Signals for Determining the Dorsal Orientation of Fish" *Water* 15, no. 8: 1596.
https://doi.org/10.3390/w15081596