ACOUSTICS UNPACKED A General Guide for Deriving Abundance Estimates from Hydroacoustic Data

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### Backscattering cross-section

When converting volume backscattering coefficients (sv) to numeric densities (•m-3), sv is scaled by σbs (backscattering cross-section, Equation 11).  This equation requires Sv and TS values in dB to be back-transformed before calculations.  Calculations of fish density must be done using sv in m2/m2 and σbs.in m2, not in the dB scale (Svand TS).

The reciprocal relationships between the two values are:

 [28]

and

 [29]

Three general methods are available for obtaining an estimate of sbs:

• in situ;
• ex situ, and;
• theoretical models.
•

#### In situ target strength

In general, a mean σbsis calculated for each analytical cell.  The mean TS given by most software except HTI’s trackman is calculated from σbs values and transformed to dB.  By calculating a σbs value for each analytical cell, horizontal and vertical variations in TS are accounted for.  However, if the analytical cells are too small, there is an increased risk of getting biased results.  If small analytical cells are needed (e.g., for geostatistics), it is better to apply an in situ σbs from a larger region.  The effect of using small number of targets to calculate average in situ σbsneeds to be investigated further.  As a rule of thumb, try to get at least 20 targets from the fish groups of interest to calculate in situ σbs.  For a discussion of the effect of single echo detection criteria, see the section on Single Echo Detection.

#### 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 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]):

 [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),
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.

#### Ex situ target strength

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.
• #### Theoretical model TS

A mean σbs may be calculated from theoretical TS modeling.  The same validation concerns and caveats listed for ex situ TS apply.