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 fromsbs 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 (see also [Equation 10]):
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 [Equation11]:
Example: (See also Density Effects-Nv Example) Calculation of Nv for an analysis cell with c = 1450 m•s-1, t = 0.0003 s (≡0.3 msec), 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 Nv should not exceed 1.0.
Many marine surveys apply a σbs derived from ex situ TS estimates. This approach rely on target species have being observed in contained cages, but cage measurements on Great Lakes fish are rare (but see Brooking and Rudstam submitted).
Ex situ TS-L relationships may be applied to trawl catches for use in scaling density. Before applying σbs based on trawl proportions, the following must be considered:
species- or age-based trawl bias;
how to deal with trawl contamination during set and haul-back, and;
appropriateness of fishing depth(s) and whether to use discrete depths or stepped oblique trawls.
A mean σbs may be calculated from theoretical TS modeling. The same validation concerns and caveats listed for ex situ TS apply.