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THE ESTIMATION OF FISH LENGTH DISTRIBUTION FROM ITS ACOUSTIC
ESTIMATES USING DUAL FREQUENCY APPROACH
M. Moszynski and A.Stepnowski
Gdansk University of Technology Poland
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ON THE POSSIBILITY OF ESTIMATING FISH LENGTH
DISTRIBUTION FROM ITS TARGET STRENGTH STATISTICS
SummaryIn the paper the problem of estimating of fish length PDF from its target strength PDF obtained from acoustic surveys is considered. As it was shown, the target strength of a single fish can be treated in the first approximation as a function of two variables: one, which depends on fish size and the other, which depends on its angular orientation (aspect).
Outline• Fish backscatter models• Tilt angle dependance• Inverse processing • Simulations • Data survey analysis
3
Introduction (1)
Ei = SL+RS + TSi(li, i , zi ) + 2B(i ) - TVG ( Ri, α)
• Fish biomass estimation in fishery acoustics
for operating frequency f :
TS = 10log BS = 20log lBS
Q – biomass estimation
< BS >
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Introduction (2)
Backscattering modelTilt angle statistics
INVERSE PROCESSING
Sample catchRegression relation
MEAN VALUE PROCESSING
pTSBiomass
Q
< l >
pl
5
Simple backscatter 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
0.2L0.125L
6
Backscatter theory (1)T h e a m p l i t u d e o f a c o u s t i c b a c k s c a t t e r i n g l e n g t h o f a g a s - f i l l e d
c y l i n d e r i n w a t e r m a y b e e v a l u a t e d f r o m H e l m h o l t z - K i r c h h o f f i n t e g r a l( M e d w i n a n d C l a y ) :
)cos(
)sin(
)sin(sin)( 0
0
00
ecb
ecbBSBS kl
klll ( 1 )
l B S 0 = l e c b ( a e c b / 2λ ) 1 / 2 - m a x i m u m b a c k s c a t t e r i n g l e n g t h ,a e c b , l e c b - r a d i u s / l e n g t h o f t h e e q u i v a l e n t s w i m b l a d d e r a s a c y l i n d e r ,χ - f i s h a n g u l a r c o o r d i n a t eχ 0 - t i l t a n g l e o f t h e s w i m b l a d d e rk = 2π / λ - w a v e n u m b e r
+0
lecb
aecb
k
7
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:
8
Kirchhoff-ray mode Backscatter Model results
9
Backscatter theory (2)
I n t h e l o g a r i t h m i c f o r m :
),,,(),,( 00 flBfalTSTS ecbfecbecb
T S = 2 0 l o g | l B S |T S 0 m a x i m u m t a r g e t s t r e n g t h
2log200
ecbecb
alTS
B f ( . ) l o g a r i t h m i c f i s h a n g u l a r p a t t e r n i n d o r s a l a s p e c t
)cos()sin(
)sin(sinlog20),,,( 0
0
00
ecb
ecbecbf kl
klflB
10
Maximum Target Strength TS0
2log10
2
0ecbecb la
TS
c y l i n d e r m o d e l
l e c b = L / 4 a e c b = L / 4 0
33][log10log300 kHzfLTS
C o m m e n t s : T h e 3 0 l o g L r e l a t i o n i s e v i d e n t h e r e d u e t o d e p e n d e n c e o f
e q u i v a l e n t c y l i n d e r l e n g t h a n d e q u i v a l e n t c y l i n d e r r a d i u s . I t e v e n t u a l l y a l l o w s r e c o v e r i n g L d i s t r i b u t i o n f r o m T S 0
d i s t r i b u t i o n e s t i m a t e d p r e v i o u s l y b y i n v e r s i o n p r o c e d u r e .
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20/log2026log20 LLTS
• regression relationship for average target strength ( according to the National Marine Fisheries Service):
Mean Target Strength <TS>
• 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
• Reduced scattering length – RSL
TS = 20 log L + 20 log (RSL)
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Tilt angle dependance (1)
)cos()sin(
)sin(sinlog20),,,( 0
0
00
ecb
ecbecbf kl
klflB
f = 38kHz0=8°lecb=L/4
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Tilt angle dependance (2)
)cos()sin(
)sin(sinlog20),,,( 0
0
00
ecb
ecbecbf kl
klflB
f = 120kHz0=8°lecb=L/4
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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)
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Tilt angle dependance (4) TS/length relationship on tilt angle for atlantic cod
TS = 20log L + B20 , McQuinn, Winger (2002)EK500 38kHz SB 7
B20
Atlantic codGadus morhua(Horne - Radiograph Gallery)
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900 950 10000
500
1000
echo trace
-5
0
5
fno=151(12) 902..913
-5
0
5
fno=152(3) 908..910
-5
0
5
fno=153(10) 909..918
-5
0
5
fno=154(5) 919..923
-5
0
5
fno=155(4) 919..922
-5
0
5
fno=156(5) 921..925
-5
0
5
fno=157(7) 928..934
-5
0
5
fno=158(12) 931..942
-5
0
5
fno=159(12) 931..942
-5
0
5
fno=160(1) 969..969
-5
0
5
fno=161(2) 971..972
-5 0 5
-5
0
5
fno=162(4) 971..974
-5 0 5
-5
0
5
fno=163(1) 974..974
-5 0 5
-5
0
5
fno=164(2) 977..978
-5 0 5
-5
0
5
fno=165(11) 985..995
Tilt angle statistics (5)
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Inverse processing (1)
i f z = x + y t h e n dxxzxpzp yxz ),()( , ( T S = T S 0 + B f )
i f x y i n d e p e n d e n t r a n d o m v a r i a b l e s t h e n
dxxzpxpzp yxz )()()( f o r T S 0 a n d B f
000 )()()(0
dTSTSTSpTSpTSpfBTSTS
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Inverse processing (2)
i f z = x + y t h e n dxxzxpzp yxz ),()( , ( T S = T S 0 + B f )
i f x y d e p e n d e n t r a n d o m v a r i a b l e s t h e n
dxxxzpxpzp xyxz ),()()( | f o r T S 0 a n d B f
000|0 ),()()(00
dTSTSTSTSpTSpTSp TSBTSTS f
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R e c o n s t r u c t i o n o f T S 0 P D F ( p T S 0 ) f r o m T S P D F ( p T S )
M e t h o d 1 – u s i n g f i s h b e a m p a t t e r n P D F f o r m e a n f i s h l e n g t h
000 )()()(0
dTSTSTSpTSpTSpfBTSTS
M e t h o d 2 – u s i n g c o n d i t i o n a l f i s h b e a m p a t t e r n P D F
000|0 ),()()(00
dTSTSTSTSpTSpTSp TSBTSTS f
Inverse processing (3)
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fishsize and
orientationgenerator
pTS
L TS0TS
pL pTS0
Simulation
BFp̂
0ˆTSp
Lp̂
Random generation Statistical processing
inversionbackscatter model
backscatter model
backscatter model
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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
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Method 1 - Inverse processing (1) 38kHz
[dB]
[m]
23
Method 1 - Inverse processing (2) 120kHz
[dB]
[m]
24
Method 1 - Inverse processing (3)
30 35 40 45 50 55 60100
200
300
400
500
600
700
800
900
assumed mean fish length [cm]
rms estimation error
f=38kHz f=120kHz
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Method 2 - Conditional fish beam pattern PDF
Bf [dB]
TS0 [dB]
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Method 2 - Conditional fish beam pattern PDF
Bf [dB]
TS0 [dB]
27
Method 2 - Inverse processing (4)
[dB]
[m]
28
Survey data (1) • NOAA/Alaska Fisheries Science Center - summer 2002 - Bering Sea• provided by Neal Williamson (PMEL - Seattle)
29
Survey data (2)
•Simrad EK500 v.5.30 echosounder• 38kHz split beam transducer• logged w/ Sonardata's Echolog 500• 14-07-2002 8:57 – 11:22 am• 6776 pings (540MB) • 2002 tracks of walleye pollock (Theragra chalcogramma)
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Survey data analysis (1)
30 40 50 600
10
20
30
40
pL1
14-07
30 40 50 600
10
20
30
40
50
pL2
14-07
-80 -60 -40 -200
100
200
300
400
pTS
14-07
30 40 50 600
0.2
0.4
0.6
0.8
1
pL,p'
L
f=38kHz
[dB]
[cm]
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Survey data analysis (2)
-80 -60 -40 -200
100
200
300
400
pTS
(f=38kHz) 14-07
-80 -60 -40 -200
500
1000
1500
pTS
(f=120kHz) 14-07
30 40 50 600
10
20
30
40
pL1
14-07
30 40 50 600
10
20
30
40
50
pL2
14-07[dB]
[cm]
32
Survey data analysis (3)
33
Survey data analysis (4)
34
Survey data analysis (5)
30 40 50 600
0.5
1f=38kHz
0=5
30 40 50 60
0=6
30 40 50 60
0=7
30 40 50 60
0=8
30 40 50 60
0=9
30 40 50 60
0=10
30 40 50 600
0.5
1f=120kHz
0=5
30 40 50 60
0=6
30 40 50 60
0=7
30 40 50 60
0=8
30 40 50 60
0=9
30 40 50 60
0=10
Reconstruction of fish length PDF for different mean swimbladder tilt angle 0 along with estimate from catch data.
Upper sequence for 38kHz and lower for 120kHz. X-axis represents fish length in [cm].
35
Survey data analysis (5)
5 6 7 8 9 100.1
0.2
0.3
0.4
0.5
Root mean square error function obtained from 38kHz and 120 kHz estimates
36
Survey data analysis (6)
Estimates of length PDF for mean swimbladder tilt angle 0=7 along with catch data
30 35 40 45 50 55 600
0.2
0.4
0.6
0.8
1
37
Acknowledgements
The authors would like to thank:
• Neil Williamson and • John Horne
for providing sample data files collected by Alaska Fisheries Science Center (NOAA) during summer 2002 survey
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).