A Bayesian approach to estimating target strength

Numerical simulations and empirical measurements of swimming Atlantic salmon (Salmo salar) were used to describe the effects of fish behavior on side-aspect target strength (TS). Simulation results were based on the numerical solution of the Helmholtz equation with the finite element method (FEM). A three-dimensional geometric model approximated the shape of the swimbladder of an Atlantic salmon. Numerical simulations were used to study the dependence of TS on the fish length, orientation, and swimming behavior. The results showed strong variation in TS, both when the side-aspect angle was changed and when the swimbladder was bent to the direction of the sonar beam. A total of 11 swimming adult Atlantic salmon 62–107 cm long were measured with a horizontally aimed echosounder (200 kHz) and video camera, and the experimental results were compared with the corresponding simulation results. The linear regression between mean TS and the logarithm of fish length (L, cm) was TS = 24.4log10(L) – 72.9 dB. The strong variability of TS owing to the orientation and bending of the fish and large L/λ ratios reduces the usefulness of TS alone for fish size estimation or species discrimination.

Redlip mullet (Chelon haematocheilus) is distributed in coastal waters of the North-Western Pacific Ocean and is a cultured fish in Korea. A hydroacoustic technique constitutes a useful method to assess the biomass and spatial distribution of mullet in sea cages or in coastal waters, and acoustic target strength (TS) information of the target fish is an essential parameter in using this method. In this study, ex situ TS measurements of 16 live mullets were made in an aquaculture sea cage in Korea. The split-beam scientific echo-sounder used for measurements was comprised of 38, 120, 200, and 420 kHz frequencies. An underwater video camera was simultaneously used to observe the mullets’ behavior during the TS measurements. The mullet TS data was analyzed from a wide range of total fish length (FL: 14.3–40.3 cm). As results for all frequencies, the frequency dependence of the mean TS values were relatively low, and the difference in mean TS was within 2.5 dB. When the slope of the least-squares regression line was forced to 20 into the TS equation, the resulting value for the constant term (b20) at each frequency was −67.0 dB, −68.3 dB, −66.3 dB, and −68.5 dB, respectively. The data tended to be frequency dependent. Additionally, the maximum TS appeared between tilt angles of 0° and 10°. These results indicate that TS measurements can be applied to estimate the biomass of the mullet in sea cages or in coastal waters.

Knowledge of the acoustic target strength (TS) of capelin, Mallotus villosus (Müller), is important to scale integrator outputs for use in acoustic surveys, but experimental measurements of capelin TS are scarce. This paper reports a new ex situ experiment on capelin TS. Small groups of the fish were kept in a large sea cage that allowed them to swim freely between 4.5 and 10 m deep. TS measurements were made vertically with a scientific split-beam echosounder. Differences in behaviour could induce at least a 5 db change in TS owing to changes in tilt angle. The observed mean TS for capelin from the local Balsfjord stock was >1 db higher than expected from the TS–length relationship for Barents Sea capelin used during abundance estimation.

Data derived with a 38-kHz split-beam echo sounder have been analyzed to yield target strengths suitable for use with echo integrators. This has required compensation for both thresholding and saturation, since these operations can significantly bias data intended for use with systems, such as echo integrators, whose dynamic ranges are much larger. A nonparametric statistical method is introduced for this purpose. Pure-species acoustic data are extracted in several two-species cases by a method for separating superimposed frequency distributions. Mean in situ target strengths are presented for cod, saithe, Norway pout, herring, redfish, and greater silver smelt. For com- parison with other data, these are expressed through the standard equation ∼(TS) =20 log l +b, where ∼(TS) is the mean target strength in decibels, and l is the fish length in centimeters. For gadoids of lengths from 10 to over 105 cm, b=−67.5 dB. For herring of lengths from 24 to 34 cm, b=−72.1 dB. The often-ignored problem of obtaining unambiguous biological data by trawl sampling is discussed.

Vertical orientation (tilt angle) is known to affect the target strength (TS) of ensonified fish and is a large component of the variability inherent in acoustic-biomass estimates. To measure the effects of changes in tilt angle on TS during diel vertical migrations, a concentration of migrating Atlantic cod (Gadus morhua) was observed acoustically from a research vessel over several days. Single-target data were collected from a split-beam echosounder and were subsequently tracked, corrected for vessel orientation and movement, and analysed for 3-dimensional displacement (speed and direction). The results revealed a large variability in TS and several patterns of swimming behaviour from random to directed orientation and movement, with changes in both vertical and horizontal displacements and inferred orientation. These behavioural patterns and their affects on TS were analysed as a function of “time-since-sunset”. Regular diel orientation patterns were observed as cod rose from the ocean bottom in the evening, increasing their tilt angle, and descended at sunrise to regain the ocean floor. Standardized TS (B20) was found to be highly correlated with tilt angle. This relationship can be used to correct for the diel changes in the TS of these migrating cod as a function of the in situ-measured tilt angle and thus to improve the accuracy of acoustic-biomass estimation.

The problem of representing the length dependence of acoustic target strengths of fish is addressed by studying the legitimacy of merging target strengths that are inhomogeneous in species or frequency. The target strengths are of two kinds: maximum and averaged dorsal aspect target strengths, which are derived from measurements of gadoid target strength functions of three species at two ultrasonic frequencies. The target strengths are expressed variously according to unnormalized, wavelength-normalized and length-normalized schemes. Overall coincidences and coincidences of slopes among simple linear regressions of target strength on fish length, when segregated by target strength type and manner of representation, are investigated through analysis of covariance. Examination of computed significance levels demonstrates that merging of target strengths in species or frequency is generally unjustified and that no one representation method is superior to another in facilitating the merging of such data. The unnormalized representation is to be preferred when merging is justified because of its simplicity and avoidance of the frequency bias inherent in the normalized representations. The hypothesis of scaling of target strengths is refuted. Key words: target strength, regression, covariance analysis, fish abundance estimation

The squids, one of the cephalopods, is important species in fisheries and ecology. If acoustic properties of squid can be well examined, especially target strength (TS), acoustic method can be provided a good tool for squid survey. The purpose of the study is to investigate the TS property of the Japanese common squid, Todarodes pacificus, and parameters influencing TS: swimming angle and material properties, density (g) and sound speed contrast (h). In the swimming angle measurement, the mostly head part of the squid stands below the horizontal axis, and averaged swimming angle was -17.7deg (s.d.:plusmn12.7deg). Based on the tethered TS measurements, the mean standardized TS values (b20) were found to be highly correlated with the tilt angle, and the resultant fitted equations for b 20 were expressed as: b20=-73.3+0.48middotthetas+0.0122middotthetas2 +0.00016middotthetas3 for 38 kHz and b20=-72.6+0.53middotthetas+0.0134middotthetas2 +0.00014middotthetas3 for 120 kHz, where thetas is the negative tilt angle in degrees. The material properties, g ranged between 1.0209 and 1.0396 (mean 1.0288), and mean h for individual, multiple and tilted squid were 1.041, 1.042, and 1.039, respectively. In the model estimation, the estimated TS data from the measured h (1.04) were higher than those of previous studied h (1.007) and were close to maximum TS data that were obtained from live squid. The results suggest that further work is needed to conduct the TS measurement for various sized squid, and to decide suitable acoustical parameter for model estimation. These data can help in making acoustics a quantitative survey tool for biomass estimation of the squids

We found mean target strength to be a reliable in situ predictor of fish weight, which allows direct estimation of the pelagic planktivore fish biomass from target strength measurements. Fish were collected by midwater trawling concurrent with target strength measurements (120-kHz frequency) in Lake Michigan. The mean weight of fish caught ranged from 2 to 71 g and mean target strength ranged from –54.9 to –38.0 decibels. Changes in mean target strength explained 73% of the variability in mean weight for combinations of various planktivore species, principally rainbow smelt Osrnerus mordax, bloaters Coregonus hovi, and alewives Alosa pseudoharengus. Bloaters were found to be less acoustically reflective than the other pelagic species, and a linear regression model with a classification variable was used to predict weight from target strength for bloaters and for the other species. We demonstrated that variations in the backscattering properties of different fish species must be considered to obtain accurate acoustic-based estimates of fish biomass.

Objective The Bayesian model plays an important role in diagnostic test evaluation in the absence of the gold standard, which used the external prior distribution of a parameter combined with sample data to yield the posterior distribution of the test characteristics. However, the correlation between diagnostic tests has always been a problem that cannot be ignored in the Bayesian model evaluation. This study will discuss how different Bayesian model, correlation scenarios, and prior distribution affect the outcome. MethodsThe data analyzed in this study was gathered during studies of patients presenting to the Nanjing Chest Hospital with suspected tuberculosis. The diagnostic character of T-SPOT.Tb and KD38 tuberculosis antibody test were evaluated in different Bayesian model, and discharge diagnosis as a gold standard was used to verify the model results in the end. Result The comparison of four models under the conditional independence situation found that Bayesian probabilistic constraint model was consistent with the Conditional Covariance Bayesian model. The results were mainly affected by prior information. The sensitivity and specificity of the two tests in Conditional Covariance Bayesian model in prior constraint situation were considerably higher than the Bayesian probabilistic constraint model in prior constraint situation. The results of the four models under the conditional dependence situation were similar to the conditional independence situation; pD was also negative with no prior constraint situation in both model Bayesian probabilistic constraint model and Conditional Covariance Bayesian model. The Deviance Information Criterion of Bayesian probabilistic constraint model was close to model Conditional Covariance Bayesian model, but pD of Conditional Covariance Bayesian model in Prior constraint situation (pD=2.40) was higher than the Bayesian probabilistic constraint model in Prior constraint situation (pD=1.66). Conclusion The result of Conditional Covariance Bayesian model in prior constraint with conditional independence situation was closest to the result of gold standard evaluation in our data. Both of the two Bayesian methods are the feasible way for the evaluation of diagnostic test in the absence of the gold standard diagnostic. Prior source, priority number, and conditional dependencies should be considered in the method selection, the accuracy of posterior estimation mainly depending on the prior distribution.

Information on fish orientation has lagged behind the development of models to estimate target strength from fish swimbladders, despite fish tilt angle being an important variable influencing target strength. Few studies compare models, because authors generally compare their own model results with experimental data. We contrast three models for estimating target strength from fish swimbladders, and compare the magnitude of the differences between models to the effects of fish tilt angle on target strength. The swimbladder models compared were the mapping method, a deformed cylinder model, and the equicylinder model. The deformed cylinder model should give average target strengths with accuracy between the “exact” mapping method solution and the “approximate” equicylinder solution. The effect on average target strength of having a 5° or a 15° standard deviation of tilt angles is far more significant than the choice of model used to estimate target strength. We estimate the first averaged target strengths for three New Zealand commercial fish species: southern blue whiting (Micromesistius australis Norman, 1937), red cod (Pseudophycis bachus Bloch and Schneider, 1801), and barracouta (Thyrsites atun Eupharasen, 1791). We suggest that the greatest gains in target strength accuracy may be made from acquiring better information on fish orientation, rather than from the development of more elaborate modelling methods.

The swimming angle of larval Japanese anchovy (Engraulis japonicus) was measured in a tank, and target strength (TS) was calculated using a theoretical scattering model. The mean swimming angle was 12.8° (SD ±22.1). Increased speeds of flow led to increased mean swimming angles. The mean swimming angle at flow of 5 cm s−1 was higher than at other speeds. TS values were estimated using a distorted-wave Born approximation model for two cases. Average values were 1–3 cm s−1 (11.5° ± 22.1) and 5 cm s−1 (16.6° ± 21.7) for cases 1 and 2, respectively. For case 1, TS ranged from −92.0 to −74.7 dB with a mean of −79.4 dB at 120 kHz. For case 2, TS ranged from −92.2 to −75.2 dB with a mean of −79.9 dB. The mean TS in case 2 was lower than that in case 1, with the maximum difference being 1.0 dB at 120 kHz (standard length 22.0 mm). However, there were no significant differences between the regression lines of cases 1 and 2. Thus, changes in flow speed altered the swimming angle of larval Japanese anchovy, but had little influence on TS.

The target strength of walleye pollock (Theragra chalcogramma) at 38 kHz has been determined in each of two ways: (1) in situ measurement with dual-beam and split-beam echo sounders, and (2) theoretical calculation based on the swimbladder form. Respective probability density functions of target strength are compared. The several estimates of mean target strength (T̄S̄) determine the relation T̄S̄=20 log l−66.0, where l is the fish fork length in centimeters.

The acoustic characteristics of bladderless fishes were examined by measuring the target strength (TS) of three species, pointhead flounder (flat-shaped), Arabesque greenling (spindle-shaped) and sandeel (cylinder-shaped). TS measurements were collected in a seawater tank (10 × 6 × 5 m) using the EK80 echo sounder (Simrad, Norway) and ES70-7C transducer (Simrad) over a frequency range of 45–90 kHz with a tether method. After TS measurement of the whole fish, we separated the flesh from the body (for pointhead flounder and arabesque greenling) and measured the TS of the head and bones. Pitch angle characteristics were measured from a head-down orientation (−30 deg) to a head-up orientation (30 deg), and TS was processed using Echoview 9 software (Echoview, Australia). TS patterns were examined with respect to orientation using the distorted-wave Born approximation model. The standard length, width, and height of fish were inputted into the model. The three bladderless fishes tested have different body shapes, meaning different areas are exposed to sound waves at the same body length. Therefore, the relationship between TS and the cross-section of the dorsal aspect of bladderless fish is discussed. [Work supported by the Sasakawa Scientific Research Grant from The Japan Science Society.]

Target strength of some European fish species and its dependence on fish body parameters

Measuring fish target strength (TS) in the wild is challenging because: (i) TS varies versus physical (orientation relative to the incident sound wave, size, and depth) and physiological fish attributes (maturity and condition), (ii) the target species and its aforementioned attributes are difficult to assess in near real time, and (iii) in the case of packed fish schools, accepted echoes may originate from multiple unresolved targets. We propose a method for controlled TS measurements of densely packed small pelagic fish during daytime, based on the joint use of a Remotely Operated Towed Vehicle, “EROC”, with a pelagic trawl fitted with a codend opening system, “ENROL”. EROC, equipped with a 70-kHz split-beam echosounder (Simrad EK60) and a low-light black and white camera, can be moved inside the fishing trawl. Pelagic fish are funnelled into the open trawl and their TS is measured in the middle of the net, where small groups actively swim towards the trawl mouth. The swimming behaviour allows for near-dorsal TS to be measured, minimizing the large effect of incidence angle on TS variability. The EROC camera, located near the open codend, provides optical identification of the species. This method was used to measure the TS of European Anchovy, Engraulis encrasicolus in the Bay of Biscay during 2014. The mean, near dorsal TS was −43.3 dB, for a mean fork length of 12.5 cm. This value is compared to published values of clupeiforms mean TS obtained for a range of natural incidence angles and discussed in the light of TS modelling results obtained for E. encrasicolus.