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TS and biological attenuation, which are much greater at f0 than at other frequencies, are controlled by the mag- nitudes of r, f0, and the number of fish per cubic meter, known as the number density. Consequently, measure- ment of f0 and the magnitude of the attenuation coefficient at f0 permits calculation of the number density versus fish length. This is possible using the well-established theory for when fish are far apart (Medwin and Clay, 1997). A more sophisticated theory, however, is required to infer the number densities when fish are in close proximity in schools (Raveneau and Feuillade, 2015).
A Brief Historical Review of
Fisheries Sonar
Sonar as Fish Finder
The development of transducers, which was driven by the need to detect and track submarines near the end of World War I, paved the way for the development of fisher- ies sonar. The feasibility of the sonar detection of fish was first reported by Sund (1935), who detected the presence of Atlantic cod (Gadus morhua) in the wild. Develop- ments in sonar technology during and after World War II also led to an increased sophistication of fisheries sonar. By the 1970s, echo sounders were widely employed by fishers and fisheries scientists to find fish (MacLennan and Simmonds, 1991). It was, no doubt, apparent that large fish produce strong echoes and small fish produce weak echoes when both are at the same range. However, the lack of quantitative knowledge of the TS of fish pre- cluded an estimation of abundance.
Target Strength of Individual Fish: The Basis for Estimation of Abundance
Subsequently, new instruments, called split beam echo sounders, which were developed in the late 1970s, per- mitted measurement of the TS of individual fish in the wild (Ehrenberg, 1979). Split beam sonars have four crystals that permit measurement of the TS of fish as function of their orientation. At frequencies of echo sounders, the TS of swim bladders is extremely sensi- tive to fish orientation. Because they are horizontally elongated, swim bladders act almost like small mirrors, which cause reflected echoes to be very strong only when the swim bladders are nearly perpendicular to the direc- tion of the sonar beam. This technological development transformed echo sounders from being merely fish find- ers to a tool for abundance estimation.
Knowledge of TS is a prerequisite for the estimation of fish abundance. As a result, the swim bladder and how it affects the TS have received much attention by the fisheries sci- ence community (Stanton, 2012). Extensive measurements have revealed that TS is species dependent. In particular, the TS of species that cannot control the amount of gas in their swim bladders (known as physostomes), such as sardines and anchovies, decreases with the depth of the animal. Because this change is understood, it is possible to predict how the resonance frequency changes with depth. In contrast, the TS of species that can control the amount of gas in their swim bladders (known as physoclists), such as cod and hake, is independent of depth. These species are able to adjust the amount of gas in their swim bladders through special secretory mechanisms, but the process is slow. Thus, when a physoclist changes depth, its swim blad- der requires hours to adjust to the new depth. As a result of the long timescale of this process, the TS of physoclists may not be readily predictable, especially after changes in depth (see Helfman et al., 2009, for a discussion of swim bladder filling mechanisms).
Effect of Biological Attenuation on Echo Level
Because measured echo levels are controlled not only by the TS of fish at a specified depth but also by the attenua- tion due to all the fish between the sonar and the specified depth, initial estimates of fish abundance were biased by disregarding this effect. Biological attenuation due to fish was measured and theoretical corrections for the effect of sound attenuation on echo level were developed by Foote (1990). The magnitude of this effect is species dependent and increases with the size and number density of the fish at each depth that are generally not known because concurrent trawls generally provide information on spe- cies composition usually at only one depth.
Estimation of fish abundance assumes that echo sound- ers are capable of detecting the species of interest, independent of their depth. Fisheries echo sounders, being hull mounted, cannot detect fish near the sur- face. Commercially important species, such as sardines and anchovies, that are generally assumed to reside at depths far from the surface have in fact been observed in large numbers near the surface (Scalabrin et al., 2007). Hull-mounted echo sounders are also ineffective at discriminating between echoes from fish that are near the bottom and those at the bottom. As a result, they
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