When organism densities are very high, multiple scattering (echoes that have scattered off multiple individuals before returning to the transducer) and shadowing have non-linear effects on the summation of echoes within a sampling volume (MacLennan 1990, Toresen 1991). The effect on Sv is difficult to predict. During nighttime surveys in the Great Lakes, this should not be a problem. It may however be a problem for daytime surveys when observing large and dense fish schools (Appenzeller and Leggett 1992).
Under high-density conditions, reliable in situ TS values cannot be obtained. Analysis bins that are unsuitable for in situ values should be identified and removed from σbs calculations.
Nv (in units of fish per acoustic sampling volume, Sawada et al. 1993) is a common diagnostic tool for identifying high-density cells. It may be calculated as:
c is the sound speed (m•s-1),
τ is the pulse duration (s),
ψ is the equivalent beam angle (steradians),
R is the range (m),
ρv is the density of targets (m-3), calculated from equation :
Calculation of Nv for an analysis cell with c = 1450 m•s-1, t = 0.0003 s (≡0.3 ms), ψ = 0.01 steradians (≡-20 dB re:1 steradian), R = 20 m, Sv = -60 dB, and TS = -50 dB.
Reliable in situ TS values could be obtained from this cell as Nv< 0.1.
Warner et al. (2002), Rudstam et al. (2003), and Parker Stetter et al. (2006) excluded cells with Nv> 0.10 from in situ calculations. Gauthier and Rose (2001) concluded that Nvshould not exceed 1.0.
Note that if you do not have info on beam angle in steradians, you can use equation 9 for equivalent beam angle to derive the steradian values for a given θ3dB.