## 5 Discussion  
To accurately estimate the amount of fish biomass, it is necessary to conduct continuous field investigation using acoustics. When using a scientific echo-sounder to investigate biomass estimation with the current technology, quantitative biomass estimation is possible only when many field surveys are performed. When estimating the quantitative biomass, sound attenuation is important. The attenuation by fish schools must be elucidated for variations in received acoustic signal and compensated in sound propagation in the water column [29]. Estimation of fish biomass is possible through the correction factor of the attenuation coefficient of fish schools [6], and will increase the efficiency of fishery surveys and monitoring. The amount of biomass can be calculated more accurately by compensating the \(\alpha\) from the scientific echo-sounder, which will be helpful in terms of quantitative calculation of maximum sustainable fisheries. If large fish schools appear, the attenuation will be generally high. However, the attenuation by the fish schools is related not only to the size but also to the volume density. The fish school density per volume is generally about 145 ind./m\({}^{3}\) when calculating the void fraction (\(\beta=(4/3)\pi r^{3}\)) [21; 30], and about 126 ind./m\({}^{3}\) based on the theoretical aggregative packing model of fish school density (\(V_{fish}=0.6 SL^{3}\)) [31] of the mean standard length (\(SL\)) of horse mackerel in this experiment. The previous study was compared intensively with the Exp3 results of about 100 ind./m\({}^{3}\) in this study (Figure 2b). However, attenuation as a function of size and volume density needs to be further investigated as future work. The scattering of sound mainly by swim bladders filled with air should be considered in addition to attenuation. According to scattering theory, scattering is dependent on the angles between the incident and scattered directions, the wavenumber (\(k\)), and the equivalent spherical radius (\(a\)) of a fish school [4]. The attenuation coefficient (\(\alpha\)) obtained from our experiments linearly increased with the number of individual fish at low frequencies but not at high frequencies. The reason for \(\alpha\) fluctuations is thought to be an interaction between the wavelengths (25 cm at 6 kHz and 21 cm at 7 kHz) and the fish \(L\). Given a high \(ka\) value in high frequency, forward scattering energy is high, resulting in low \(\alpha\)[2; 23; 32]. The effect of multiple scattering on the gas-filled swim bladder and the density within the fish schools should also be considered for accurate modeling and measurements of scattering [33]. The mean \(\alpha\) and maximum \(\alpha\) were measured to be 6.0-15.4 and 6.5-21.8 dB/m at all frequencies, respectively. \(\alpha\) is mainly generated by \(L\) of the fish body or swim bladder. The depth dependence of the target strength (\(TS\)) of a fish has long been recognized with the adjustable size of the swim bladder. A previous study showed that the depth dependence of \(TS\) of fish follows [PERSON]'s law [34; 35], and \(\alpha\) of fish schools is predicted to decrease as the depth increases. For the attenuation by the fish schools, the depth effects must be considered. There are some limitations to apply this result to the various fields, because the fish schools are artificially located in the net cage, and the attenuation effects may differ depending on the number of individual fish. Additionally, attenuation experiments were performed using the cage size of \(1\times 1\times 1\) m, and the fish schools appeared densely, which may be different from the actual marine environment in the case of high density. In order to represent the ocean environment more accurately, experiments with different densities in a larger net size are required. It was also not possible to reveal the resonance characteristics of the fish schools.