Suggestions for a list of procedures in the calculation of abundance and
biomass from the Acoustic Survey for Herring
Working Paper to be presented at the meeting of the ICES Planning Group for Herring Surveys
(PGHERS), IJmuiden, 11-15 Dec. 2000
Soenke Jansen, Federal Research Centre for Fisheries, Hamburg, FRG
Introduction:
In a review of the methods that had been applied within the German part of the Acoustic Survey for
Herring it became apparent that in the past some errors had been made with regard to the way the
total number of fish was allocated to the age-classes and in the calculation of mean weight-at-age. In
order to avoid these errors in future and to secure the reproducibility of results, a computer program is
at the time being constructed that will perform the calculations. For the lay-out of this software a
detailed list of procedures is necessary and the following text is part of this list.
While a good deal of the chapters 1 and 2 are covered by the existing survey manuals
(C.M.1994/H:3 and C.M.2000/G:7), I have not found any written information as to the calculations in
chapters 3 and 4.
The procedures described here are catered to the needs of the German part of the Acoustic
Survey for Herring with a species mix of herring and sprat in the schools and a survey-design that uses
ICES statistical rectangles as geographical strata. But with a few changes it might be of use in other
survey designs or with other species mixtures as well. Anyway, the text thought as food for a
discussion about a possible standardisation of procedures within the survey in general. Corrections,
comments and opinions are welcome.
List of procedures:
1
Identification of the ‘echo-response’ of a rectangle:
1.1
Echograms are recorded on parallel east-westerly tracks with a maximum latitudinal distance of
15NM, which should secure at least 2 tracks per statistical rectangle. A higher spatial resolution
should be aimed for when the density of fish is high.
1.2
The echograms are evaluated ‚by eye’. Echo traces of schools are marked and each is allotted
to one four classes of which only class a) and class b) are used for further calculations:
a) = certainly clupeids
b) = quite certainly clupeids
c) = could be clupeids
d) = certainly not clupeids
1.3
The echo-integration software gives the SA-values [m²/NM²] of these schools and these are then
summed up for each nautical mile (NM) of the survey track.
1.4
The 1NM-sums are entered into a database and the mean SA-value per rectangle is calculated.
This is mean then multiplied with the number of nautical square miles of the relevant rectangle to
give

the reflective area [m²] of the rectangle.
2
Calculation of the total number of clupeids per rectangle
2.1
The input values from hauls in the rectangle are:
the numerical relation between herring and sprat (see chapter 3.3)
the representative relative length/frequency-distribution (LFD) for herring and for sprat in
the rectangle (see 3.4)
2.2
A = SA / <> ; the requested mean area density of the fishes [N/NM²] equals the reflective are
of the rectangle [m²/NM²] divided by the mean acoustic cross-section of a single fish [m²]
2.3
<> = const. * <L²> ; the mean acoustic cross-section of a single fish equals the mean
squared length of the fishes multiplied with a species-specific constant.
1
2.4
The <L²i> for herring and the <L²i> for sprat are calculated using the species’ representative
relative LFD for the rectangle in question.
Example:
length-class
rel.freq.
7,25
7,75
8,25
8,75
9,25
sum
0,02
0,50
0,20
0,20
0,08
1,00
7,25² * 0,02 =
7,75² * 0,50 =
8,25² * 0,20 =
8,75² * 0,20 =
9,25² * 0,08 =
<L²i> =
1,05
30,03
13,61
15,31
6,85
66,85
2.5
For both species the mean acoustic cross-section of a single fish, <i>, is calculated using the
species-specific <L²i>.
2.6
The <i> of both species are then multiplied with the numerical proportion of the species in the
catches of that rectangle (see 3.3) and the product of these multiplications is added. The
resulting <> is the mean acoustic cross-section of a single clupeid in the rectangle.
2.7
According to A = SA / <> the mean area density of clupeids is calculated for the rectangle and
multiplied with the number of nautical square miles of the rectangle to get the absolute number
of clupeids of the rectangle. This number is divided between the species according to their
numerical proportion in the catches.

The result is the total number of herring and the total number of sprat per rectangle.
3
Calculation of the number of fish and biomass per age/maturity-class per rectangle:
(The example used here is herring. Sprat is calculated accordingly)
3.1
For the collection of biological data, 1-3 hauls are made per rectangle. Per haul, a (sub-)sample
of 200-300 herring are measured to the lower ½cm (if there are enough for that). The resulting
absolute LFD is scaled up to the haul and standardised to a haul duration of 60min.
3.2
In each rectangle, 12 individuals per length-class (LC) of both species are taken for further
analysis. These may come from different hauls. The aim is to sample the whole length spectrum
as completely as possible. These fish are weighed on board (±0,5g) the maturity is determined
on a scale of four and the otoliths are taken for age-determination. Alternatively the sampled fish
are frozen and the entire weight/length/age/maturity(WLAM)-determination is done in the
laboratory.
3.3
For the determination of the numerical proportion of the species, the number of all herring in all
60min-standardised hauls of the rectangle are added and the same is done for sprat. From
these two sums the relative proportions of the total of clupeids are calculated as proportions of
1,0.
3.4
For the determination of the representative relative LFD of the rectangle, all standardised
absolute LFDs of an rectangle are added up and the number in each LC expressed as fractions
of 1,0.
3.5
From the WLAM-determinations of each rectangle, a length/(age&maturity)-key is calculated: for
each LC the relative proportions of all age&maturity-combinations is determined.
Example: of the 12 WLAM-determinations for LC 17,25 in rectangle NNFN 3 fell into the
age&maturity-class 2i, 6 fell into A&M-class 2m and 3 in 3m.
LC \ A&M
16,75
17,25
17,75
3.6
n
...
12
...
1
...
0,0
...
2i
...
0,25
...
2m
...
0,5
...
3i
...
0,0
...
3m
...
0,25
...
4m
...
0,0
...
...
...
...
...
The total number of herring in each rectangle (see 2.7) is distributed into the LCs using the
representative relative LFD of the rectangle. With the help of the key in 3.5 the total numbers in
each LC are then distributed into the age&maturity-classes. Thus, the total number per rectangle
per length per age&maturity is known (and on more disaggregated levels the total number of
herrings per age&maturity-class and the total number per LC for each rectangle).
2
3.7
From the WLAM-determinations of all herrings pooled from all rectangles, a
weight/(length&age&maturity)-key is calculated which is taken to be representative for the whole
area of investigation.
Example: 120 herrings were sampled for WLAM-determinations in the LC 17,25 in the whole
area of investigation. Of these 23 were determined to be 2i and these had a mean weight of
34,2g. 70 were 2m (mean weight 38,2g) and 27 were 3m (39,8g).
LC \ A&M
16,75
17,25
17,75
1
...
n/a
...
n
0
2i
...
34,2
...
n
20
2m
...
38,2
...
n
70
3i
...
n/a
...
n
0
3m
...
39,8
...
n
30
4m
...
n/a
...
...
...
...
...
3.8
The total numbers per length&age&maturity-class per rectangle (from 3.6) are now summed up
over the rectangles of the whole area of investigation and these sums are then multiplied with
the appropriate mean weight for each length&age&maturity-class. The resulting total weights per
length&age&maturity-class are the summed up for each age&maturity-class and divided by the
total number of herrings in this age&maturity-class. The result is the mean weight of a single
herring in each age&maturity-class that takes account of the (often skewed) length distribution of
this class.
3.9
With these mean weights the total numbers of each age&maturity-class of each rectangle (3.6)
is multiplied to gain the biomass per age&maturity-class per rectangle.
4
The treatment of rectangles without hauls:
4.1
Rectangles for which sufficient echo-acoustic information exists but that have not been sampled
with the net are interpolated using the biological data from the neighbouring rectangles.
4.2
The interpolation of the biological data is done in two steps: (a) the estimation of the total number
of herring and sprat in the rectangle (4.3 below) and (b) the distribution of these numbers on the
age&maturity-classes (4.4) followed by the multiplication with the mean weight to determine the
biomass. In both steps, the data of all neighbouring net-sampled rectangles is used. This
excludes those neighbours where the biological data is the result of an interpolation itself.
4.3
For (a) the numerical relation of herring and sprat (4.3.1 below) and a relative LFD for each
species is (4.3.2) needed. The further steps are then identical to the net-sampled rectangles
(chapter 2).
4.3.1
The numerical relation of herring and sprat calculated as the weighted arithmetic mean of
the numerical relations of the net-sampled neighbour rectangles. According to their relative
position, two classes of neighbours are differentiated: those that have a common boundary
with the rectangle to be interpolated („full neighbour“), and those neighbours that only have
a common corner („corner neighbour“). The values of the full neighbours are weighted
twice, those of the corner neighbours are weighted single for the calculation of the mean.
4.3.2
The required relative LFD is calculated separately for herring and for sprat from the
absolute numbers per LC (3.6) in the net-sampled neighbouring rectangles with the same
idea of weighing as above:
 n

 n
j , RFN
f j ,RC
RFN
RFN
with: fj,RC
Nj, RFN
Nj, RCN
NRFN
NRCN
* 2 
n
* 2   n
j , RCN
RCN
RFN
(1)
RCN
RCN
= relative frequency of lenght-class j in the rectangle to be interpolated
= total number of fish in lenght-class j in a full neighbour rectangle
= total number of fish in lenght-class j in a corner neighbour rectangle
= total number of fish in a full neighbour rectangle
= total number of fish in a corner neighbour rectangle
Using the interpolated relative LFDs and the interpolated numerical relation of herring and sprat
together with the echo-acoustic information from the rectangle the total number of herring and
sprat are calculated as described in chapter 2.
3
4.4
The number of fish in each age&maturity-class is calculated for each species separately as
follows:
N AM ,RC  N RC
 N
*
 N
AM , RFN
RFN
RFN
with: NAM, RC
NRC
NAM, RFN
NAM, RCN
NRFN
NRCN
4.5
* 2 
N
* 2   N
AM , RCN
RCN
RFN
(2)
RCN
RCN
= total number of fish in one age&maturity-class (e.g. 1i, 2m) in the rectangle
to be interpolated
= total number of fish in the rectangle to be interpolated
= total number of fish in that age&maturity-class in a full neighbour rectangle
= total number of fish in that age&maturity-class in a corner neighbour
rectangle
= total number of fish in a full neighbour rectangle
= total number of fish in a corner neighbour rectangle
The total numbers in each age&maturity-class are the multiplied with the mean weight of one fish
of that class (3.8) to estimate the biomass-values of the rectangle in question.
4