Volume_integration

Let A be the set of samples s in the analysis domain for which Volume_integration is being calculated.

Then the volume of any one sample in A is defined as follows (see also About integration algorithms):

	for Single beam algorithm
	for Multibeam cruise scanning algorithm
	for V and S mode cruise scanning algorithms
	for H mode cruise scanning algorithm
	for Target-locked scanning algorithm and V and H mode instrument scanning algorithms

Where:

Vs = Volume of sample s (m3)

= Unit distance along the cruise track = 1 (m)

= Unit cross-sectional area across the cruise track = 1 (m2)

Dxp = Distance along the cruise track for ping p (m) = Vgp·Dtp where Vgp is available, and otherwise

Where:

Vgp = Vessel speed over ground at ping p (m/s)
Dtp = Pulse repetition interval for ping p (s)

fp = Bearing angle of the ping p (radians).
Note: This bearing angle is measured clockwise when viewed from above with 0 bearing in the direction of travel (direction of Vgp). The measure of bearing is however instrument (and mode) specific and translations are performed where required.

Dqb = Angular width of beam b (radians) = q / (Nb)
Dqbv = Angular width of beam b in the V-mode ping of a target-locked pair (radians) = q / (Nb)
Dqbh = Angular width of beam b in the H-mode ping of a target-locked pair (radians) = q / (Nb)

Where:

q = Full sector angle of the respective ping (radians)
Nb = Number of beams in full sector of the respective ping (-)

rs = Range of sample s (m) = rminp + (ns+0.5)·Drs

Where:

rminp = Minimum range for ping p (m)
ns     = zero based sample number measured from transducer (-)
Drs   = Thickness of sample s in the range dimension (m) = (rmaxp– rminp)/ (Nsp)

Where:

rmaxp = Maximum range for ping p (m)
rminp = Minimum range for ping p (m)
Nsp   = Number of samples in ping p

Tp = Tilt angle of the ping p (radians), read from the data file for H- and S- mode and 0 in V-mode.

Ts = The effective Tilt angle of a sample s (radians), defined as follows:

if s is on an H-mode ping then Ts = Tp
if s is on a V-mode ping then Ts is calculated as (b + 0.5) x Dqbv

Where:

b = the number of the V-mode ping on which sample s lies (-)
Dqbv = as defined above (radians)

Note: The Single beam algorithm is used for integration of single beam data, and the remaining algorithms for integrating multibeam data. See About integration algorithms for more information on the various algorithms.

Then the integration volume is determined as:

	for Target-locked scanning algorithm
	for all other algorithms

Where:

V
= the integration volume, Volume_integration (m3)

= 0 if sample s is not in the analysis domain

1 otherwise, including below threshold data.

Vs
= Volume of sample s (m3) - as defined above

d
= the set of samples in the analysis domain.

B
= the set of beams in the analysis domain and on the H-mode ping of a target-locked pair.

b
= the set of samples in the analysis domain and on the beam b of the H-mode ping of a target- locked pair.

r
= the set of samples in the analysis domain and on the beam i of the H-mode ping of a target- locked pair,
where i is the number of the reference beam,
which is that beam which the V-mode ping of the target-locked pair intersects.

n
= the set of samples in the analysis domain and on the V-mode ping of a target-locked pair.

nb
= the number of samples in the set b

nr
= the number of samples in the set r

Notes

Volume_integration is NOT calculated whenever is used. The sample volume, Vs may still be calculated for use in the calculation of Sv_mean but any calculation of Vs by using is not considered useful for the purposes of volume or biomass estimation. If Volume_integration is not calculated for this reason, a special value will be provided instead. The following variables depend upon Volume_integration and cannot be calculated if Volume_integration is not calculated:
- Fish_weight
- Fish_number
- N_sigma_bs

Vs	=	Volume of sample s (m3)
	=	Unit distance along the cruise track = 1 (m)
	=	Unit cross-sectional area across the cruise track = 1 (m2)
Dxp	=	Distance along the cruise track for ping p (m) = Vgp·Dtp where Vgp is available, and otherwise

V	=	the integration volume, Volume_integration (m3)
	=		0 if sample s is not in the analysis domain
			1 otherwise, including below threshold data.
Vs	=	Volume of sample s (m3) - as defined above
d	=	the set of samples in the analysis domain.
B	=	the set of beams in the analysis domain and on the H-mode ping of a target-locked pair.
b	=	the set of samples in the analysis domain and on the beam b of the H-mode ping of a target- locked pair.
r	=	the set of samples in the analysis domain and on the beam i of the H-mode ping of a target- locked pair, where i is the number of the reference beam, which is that beam which the V-mode ping of the target-locked pair intersects.
n	=	the set of samples in the analysis domain and on the V-mode ping of a target-locked pair.
nb	=	the number of samples in the set b
nr	=	the number of samples in the set r

Volume_integration

See also