Density Effects

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 S_v 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 σ_bs calculations.

N_v (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:

[30]

where:
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),
ρ_v is the density of targets (m^-3), calculated from equation [11]:

Calculation of N_v 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, S_v = -60 dB, and TS = -50 dB.


Reliable in situ TS values could be obtained from this cell as N_v< 0.1.

Warner et al. (2002), Rudstam et al. (2003), and Parker Stetter et al. (2006) excluded cells with N_v> 0.10 from in situ calculations.  Gauthier and Rose (2001) concluded that N_vshould 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.