Consequence of swimbladder model choice and fish orientation to target strength of three New Zealand fish species

Sam McClatchie 0 Jon Alsop 0 Zhen Ye 0 Roger F. Coombs 0 0 S. McClatchie and R. F. Coombs: National Institute of Water and Atmosphere (NIWA) , PO Box 14-901, Kilbirnie, Wellington , New Zealand. J. Alsop : Department of Mathematics and Statistics, University of Otago , PO Box 56, Dunedin , New Zealand. Z. Ye: Ocean Acoustics, Institute of Ocean Sciences , Sidney, British Columbia , Canada V8L 4B2 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 diVerences between models to the eVects 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 eVect 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. Introduction The feasibility of estimating target strengths from calculations based on morphological measurements and acoustic scattering theory has led to a proliferation of models. Few studies compare model results, because authors generally compare their models with experimental data (Clay and Horne, 1994; Foote, 1985; Foote and Traynor, 1988; Miyanohana et al., 1990). At the frequencies of 38 Hz and 120 kHz commonly used in fisheries surveys, about 9095% of the backscattering from swimbladdered fish comes from the swimbladder (Foote, 1980b). In this paper, we neglect the contribution of fish flesh and bones to backscattering. Calculation of the target strength of fish swimbladders is not trivial, because this organ often has an irregular geometric form for which the boundary conditions are not analytically tractable. Several approximation methods have been developed to overcome this diYculty. The T-matrix method (Waterman, 1969) and the boundary integral method (Schenck, 1968) are the two most notable solutions for scattering from an arbitrary shape. Both these methods involve ponderous numerical computation. Recently, analytical approximations were used to compute the target strength of slender bodies with revolution (Junger, 1982; Stanton, 1988). For an elongated target, they approximate the scattering amplitude by summing the scattering from diVerential elements along the longitudinal axis, assuming the elements are within an infinitely long cylinder. Application to exactly solvable targets such as spheres and prolate spheroids yielded encouraging results. Fish orientation, particularly the tilt angle or pitch, is an important variable aVecting target strength. We compared the importance of fish orientation to the diVerence between model estimates of target strength to determine whether model development or studies of fish behaviour should be emphasized. Despite Footes (1980) plea for more information on fish behaviour, the development of scattering models proceeded apace of information on fish orientation. The swimbladder models we compared were the mapping method (Foote, 1985), the equicylinder method (Do and Surti, 1990), and a deformed cylinder model (Junger, 1982). Foote (1985) measured the surface area of pollack (Pollachius pollachius) and saithe (Pollachius virens) swimbladders by triangularization, and then used the mapping method to estimate target strength averaged over a distribution of fish tilt angles, <TS>. He obtained excellent agreement between theoretical and experimentally measured target strengths. Estimating target strength with the mapping method is complicated enough that Do and Surti (1990) devised a simpler method that they argued was suYciently accurate to estimate averaged target strength for use in fisheries echo integration surveys. They estimated the surface area of hoki (Macruronus novaezelandiae) swimbladders by summation of right-angled cylinders with an area equivalent to the actual swimbladder, and then estimated target strength with Uricks (1983) equation for a cylinder, modified to account for the angular oVset of the swimbladder from the nose to tail axis of the fish. In this paper, we compare <TS> estimated with three swimbladder models for southern blue whiting (Micromesistius australis), barracouta (Thyrsites atun) and red cod (Pseudophycis bachus). There are no previous estimates of <TS> for these sepcies. Red cod and barracouta both form schools that are suited to acoustic assessment, but target identification is more diYcult for red cod because they are often associated with other species. There are no plans for acoustic surveys of red cod or barracouta stocks. Southern blue whiting now support a 27 000 t fishery in New Zealand (Annala, 1994). Relative biomass estimates derived from echo integration surveys of southern blue whiting in single species aggregations are used for stock assessment. Although a target strengthlength relationship for small Atlantic cod was applied to southern blue whiting in the past, accurate <TS> measurements are needed to estimate absolute biomass from acoustics. We provide some of these estimates in this paper. Methods Plaster casts of swimbladders Southern blue whiting have simple cylindrical swimbladders with tapering ends, similar in shape to pollack and saithe swimbladders (Foote and Ona, 1985). Barracouta swimbladders also resemble straight cylinders with tapering ends, but have irregular constricted margins along the anterior quarter of their length (Fig. 1a). In contrast, red cod swimbladders are divided at the anterior end into two lobes (Fig. 1b,c) attached behind the cranium (Paulin, 1988). There are no published descriptions of barracouta or southern blue whiting swimbladders (C. Paulin, pers. comm.). The surface area of swimbladders was estimated from plaster of paris casts. Flesh was removed from the swimbladder by dissection. Small holes were made in the anterior and posterior ends of the swimbladder, and liquid plaster of paris injected through the posterior hole to fill the bladder as it lay in the body. Care was taken to exclude air through the anterior hole. (...truncated)