Density

Density calculations may be the survey goal or may be needed for abundance calculations.  Either way, the calculation of density assumes that:

target species or groups have been separated from non-target backscatter, and;

an appropriate σ_bs has been identified for each species, group, or depth layer.

Two calculations are common:

average density within a vertical bin, and;

areal or total density within a vertical bin.

 

Density per unit volume (ρ_v)

If density is expressed as #•m^-3, s_v and σ_bs are used to calculate average density (ρ_v, m^-3) by Equation 11:

where:
s_v is volume backscattering coefficient (dB re: 1 m^-1), and;
σ_bs is backscattering cross-section (m²).

This method is sometimes referred to as sv/ts scaling.  Note that this density estimates is based on echo integration (s_v or s_a) values and an estimate of σ_bs.  If fish populations are sufficiently sparse, echo counting or trace counting are possible.  This may be the case in Lake Superior.  We have not dealt with this issue in this SOP as echo counting cannot be used in all the Great Lakes.

Areal or total density (ρ_a)

For the calculation of stock size, a density estimate based on area is more useful.  ABC (s_a) or NASC (s_A) may be used to calculate total density ((ρ_a, m^-2 or nmi^-2):

[31]

[32]

where:
ABC (s_a) is area backscattering coefficient (m^-2);
NASC (s_A) is nautical area scattering coefficient (nmi^-2), and;
σ_bs is backscattering cross-section (m²).