Transcript ON THE POSSIBILITY OF ESTIMATING FISH LENGTH …

A METHOD FOR ESTIMATING FISH
SIZE DISTRIBUTION
FROM ACOUSTIC DATA
M.Moszynski
Gdansk University of Technology
Poland
1
Outline
1.
2.
3.
4.
Introduction
Fish directivity pattern and tilt angle dependance
Inverse techniques in fish length estimation
Survey data analysis
2
Introduction
Fish echo processing chain:
acoustical measures
Echo
Level E
physical measures
Target
Strength
Fish
length
Fish
Biomass
TS
L
Q
regression models
measurements:
• ex situ
• in situ
Catch
data
3
Introduction
• Fish biomass estimation in fishery acoustics
propagation
Ei = SL+RS + TSi(li, i , zi,, fo ) + 2B(i ) - 2TL( Ri, α)
transducer beam pattern
hydroacoustic system
TS = 10log BS = 20log lBS
< BS >
sounding volume V
Q – biomass estimation
4
Introduction
MEAN VALUE PROCESSING
Sample catch
Regression relation
<l>
Fish
length
pTS
L
INVERSE PROCESSING
Backscattering model
Tilt angle statistics
pl
5
Why statistical inverse processing ?
if
z=x+y
then
pz ( z )   px , y ( x, z  x)dx
 if x y independent random variables then
pz ( z )   px ( x) p y ( z  x)dx
 if x y dependent random variables then
p z ( z )   p x ( x) p y| x ( z  x, x)dx
6
Fish length estimation
problems:
• unknown titl angle during ensonification
• unknown fish directivity pattern
pTS
pTS0
pl
backscattering model
-tilt angle statistics
-backscattering model
7
Fish backscatter models
for swimbladdered fish
• tilted cylinder
- Haslett (1962)
• finite bent cylinder model
- Stanton (1989)
• low resolution acoustic model
- Clay (1991)
• Kirchhoff ray mode model (KRM)
- Clay, Horn (1994)
• boundary element model
- Foote, Francis (2002)
simple
precise
8
Haslet model
for swimbladdered fish
Haslett, 1962
• swimbladder is approximated by a combination of:
a hemisphere,
a short cylinder,
a cone of fixed dimensions relative to the fish fork length.
• then this shape is modified to:
a cylinder maintaining their geometrical cross section.
lecb=0.24L
2aecb=
0.049L
0.125L
0.2L
9
Kirchhoff-ray mode
Backscatter Model (KRM)
Clay and Horne, 1994
• fish body as a contiguous set of fluid-filled cylinders that surround
a set of gas-filled cylinders representing the swimbladder
Sockeye salmon
(Oncorhynchus nerka)
Lateral radiograph:
Dorsal radiograph:
10
Kirchhoff-ray mode
Backscatter Model results
11
Boundary element model
Foote, Francis 2002
• swimbladder mesh required
• obtained by X-rays, PCX, CT
12
Backscatter theory (1)
The amplitude of acoustic backscattering length of a gas-filled
cylinder in water may be evaluated from Helmholtz-Kirchhoff integral
(Medwin and Clay):
l BS (  )  l BS 0
sin klecb sin(    0 ) 
cos(   0 )
klecb sin(    0 )
(1)
lBS0 = lecb (aecb/2λ)1/2 - maximum backscattering length,
aecb , lecb - radius/length of the equivalent swimbladder as a cylinder,
χ - fish angular coordinate
 +0
χ0 - tilt angle of the swimbladder
k
k=2π/λ - wave number
aecb
lecb
13
Backscatter theory (2)
In the logarithmic form:
TS  TS 0 (lecb , aecb , f )  D f (  ,  0 , lecb , f )
TS=20log|lBS|
TS0 maximum target strength

aecb 

TS 0  20 log  lecb

2



Bf (.) logarithmic fish angular pattern in dorsal aspect
 sin klecb sin(    0 ) 


D f (  ,  0 , lecb , f )  20 log 
cos(    0 ) 
 klecb sin(    0 )

14
Inverse processing
if
then
z=x+y
(TS = TS0 + Bf)
pz ( z )   px , y ( x, z  x)dx
 if x y dependent random variables then
p z ( z )   p x ( x) p y| x ( z  x, x)dx
 for TS0 and Bf
pTS (TS )   pTS 0 (TS 0 ) p B f |TS 0 (TS  TS 0 , TS 0 ) dTS 0
15
Maximum Target Strength TS0
2
 aecblecb


TS0  10 log 
 2 
cylinder model
lecb=L/4 aecb=L/40
TS 0  30 log L  10 log f [ kHz]  33
Comments:
 The 30logL relation is evident here due to dependence of
equivalent cylinder length and equivalent cylinder radius.
 It eventually allows recovering L distribution from TS0
distribution estimated previously by inversion procedure.
16
Mean Target Strength <TS>
• Reduced scattering length – RSL
TS = 20 log L + 20 log (RSL)
• regression relationship for average target strength
( according to the National Marine Fisheries Service):
 TS   20 log L  26  20 log L / 20
• use lecb = L/4 as in Haslett model for estimate of <lecb>
• example - fish fork length: L = 31.5 cm
- from theoretical equation:
TS0( f = 38kHz) = -32dB TS0( f =120kHz) = -27dB
- from regression:
<TS>= -36dB
17
Tilt angle dependance (1)
 sin klecb sin(    0 ) 


D f (  ,  0 , lecb , f )  20 log 
cos(    0 ) 
 klecb sin(    0 )

f = 38kHz
0=8°
lecb=L/4
18
Tilt angle dependance (2)
 sin klecb sin(    0 ) 


D f (  ,  0 , lecb , f )  20 log 
cos(    0 ) 
 klecb sin(    0 )

f = 120kHz
0=8°
lecb=L/4
19
Tilt angle dependance (3)
Target strengths as a function of tilt angle for a 31.5cm pollock
at dorsal aspect at 38kHz and 120kHz Foote (1985)
Walleye pollock
Theragra chalcogramma
(Horne - Radiograph Gallery)
20
Tilt angle dependance (4)
TS/length relationship on tilt angle for atlantic cod
TS = 20log L + B20 , McQuinn, Winger (2002)
EK500 38kHz SB 7
Atlantic cod
Gadus morhua
B
(Horne - Radiograph Gallery) 20

21
echo trace
900
0
Tilt angle statistics (5)
950
1000
500
1000
fno=151(12) 902..913
fno=152(3) 908..910
fno=153(10) 909..918
5
5
5
0
0
0
-5
-5
-5
fno=154(5) 919..923
fno=155(4) 919..922
fno=156(5) 921..925
fno=157(7) 928..934
5
5
5
5
0
0
0
0
-5
-5
-5
-5
fno=158(12) 931..942
fno=159(12) 931..942
fno=160(1) 969..969
fno=161(2) 971..972
5
5
5
5
0
0
0
0
-5
-5
-5
-5
fno=162(4) 971..974
fno=163(1) 974..974
fno=164(2) 977..978
fno=165(11) 985..995
5
5
5
5
0
0
0
0
-5
-5
-5
-5
-5
0
5
-5
0
5
-5
0
5
22
-5
0
5
Simulation
Random generation
Statistical processing

fish
size and
orientation
generator
backscatter
model
pˆ BF
backscatter
model
inversion
L
TS0
TS
pL
pTS0
pˆ TS 0
pTS
pˆ L
backscatter
model
23
Simulation
Fish size and orientation - assumptions:
• backscattering length of fish school between 30cm and 60cm
normally distributed
• random distribution of fish orientation in consecutive fish echoes
• trace of the fish
- straight line,
• fish tilt angle
- normal distribution
• 8° as mean value
for swimbladder tilt angle
24
Conditional fish beam pattern PDF
TS0 [dB]
Bf [dB]
25
Conditional fish beam pattern PDF
TS0 [dB]
Bf [dB]
26
Inverse processing
[dB]
[m]
27
Experiment
• R/V “G. O. Sars”
• March 17 to April 5, 2004
• Lofoten 2004 survey
• Lofoten islands, from 67oN to 70oN,
• spawning grounds of North East Arctic Cod
• shelf between 500 m to about 50 meters
• sea temperature 6.8 – 7.1oC from 40–300m
• 5 Simrad EK60 split beam echosounders
28
Experiment
• standard sphere calibration methods
CU64 (18 kHz), CU60 (38 kHz) , WC38.1 (70, 120 and 200 kHz)
• transducers mounted in one of the instrument keels of the vessel
• full half-power beam widths 7o, except for the 18 kHz (11o)
• the transmitted pulse duration was identical on all frequencies - 1.024 ms
• the Bergen Echo Integrator, BEI.
• heave, roll, pitch and yaw Seatex MRU 5 -Simrad EM 1002 at 10 Hz
• CTD observations (Sea-Bird SBE9).
• trawling partly on fixed locations,
mostly on registrations for identification of the targets and for
biological sampling.
• Campelen 1800 bottom survey trawl
• Åkratrawl, a medium sized midwater trawl
• Standard biological parameters were measured on all catch samples,
• individual total length, weight, gonad and liver index, age and stomach content.
29
Trawl data
30
Survey data
• provided by Egil Ona (Institute of Marine Research - Bergen)
Norwegian cod echoes at depth range 100-160m acquired with
18kHz system
31
Survey data
• provided by Egil Ona (Institute of Marine Research - Bergen)
Norwegian cod echoes at depth range 100-160m acquired with
38kHz system
32
Survey data
• provided by Egil Ona (Institute of Marine Research - Bergen)
Norwegian cod echoes at depth range 100-160m acquired with
70kHz system
33
Survey data
• provided by Egil Ona (Institute of Marine Research - Bergen)
Norwegian cod echoes at depth range 100-160m acquired with
120kHz system
34
Survey data
• provided by Egil Ona (Institute of Marine Research - Bergen)
Norwegian cod echoes at depth range 100-160m acquired with
200kHz system
35
Target strength data
pTS 18kHz (20-03-2004)
pTS 38kHz (20-03-2004)
pTS 70kHz (20-03-2004)
150
100
50
0
-60
-40
-20
500
250
400
200
300
150
200
100
100
50
0
-60
-40
-20
0
-60
-40
-20
pTS 120kHz (20-03-2004) pTS 200kHz (20-03-2004)
400
500
300
400
300
200
200
100
0
100
-60
-40
-20
0
-60
-40
-20
36
Processing example
a)
b)
c)
d)
a) acoustically measured target strength TS at 200kHz
b) conditional PDF of the fish directivity pattern
assuming swim bladder tilt angle 5
c) estimated maximum target strength PDF
d) reconstructed fish length distribution along with the
catch histogram (in cm)
37
Results
38kHz
1
1
1
0.5
0.5
0.5
0
40
1
60
80
100 120
0
40
1
60
80
100 120
0
40
1
60
80
100 120
60
80
100 120
60
80
100 120
60
80
100 120
70kHz
0.5
0
40
1
120kHz
60
80
100 120
0.5
0
40
1
200kHz
0.5
60
80
100 120
0.5
60
80
100 120
0.5
0
40
0
40
1
0.5
0
40
1
0.5
60
80
100 120
0.5
60
80
2°
100 120
0
40
0
40
1
0
40
1
0.5
60
80
5°
100 120
0
40
8°
38
Conclusions
 The modeling of scattering properties of the fish based on the
theory of scattering from tilted cylinder is used for statistical
estimation of fish target strength PDF.
 The estimated PDF of acoustic backscattering length of the fish
differs from actual fish length PDF.
 The transformation of physical fish length distributions is a result
of combined effect of random fish length and its random
scattering pattern.
 The process of removing fish beam pattern effect requires
application of inverse technique as fish length information is
included in maximum fish target strength TS0.
 The knowledge on distribution of fish tilt angle is required (may
be obtained from tracking analysis in successive echoes) and the
knowledge of mean fish swimbladder tilt angle (can be estimated
by dual frequency approach).
39
Thank you very much ...
Thank you very much

40