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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

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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

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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

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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:

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Kirchhoff-ray mode Backscatter Model results

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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

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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]

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Method 1 - Inverse processing (2) 120kHz

[dB]

[m]

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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]

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Method 2 - Inverse processing (4)

[dB]

[m]

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Survey data (1) • NOAA/Alaska Fisheries Science Center - summer 2002 - Bering Sea• provided by Neal Williamson (PMEL - Seattle)

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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)

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Survey data analysis (4)

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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].

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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

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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

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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

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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).