1 THE ESTIMATION OF FISH LENGTH DISTRIBUTION FROM ITS ACOUSTIC ESTIMATES USING DUAL FREQUENCY APPROACH M. Moszynski and A.Stepnowski Gdansk University of Technology Poland

2 ON THE POSSIBILITY OF ESTIMATING FISH LENGTH DISTRIBUTION FROM ITS TARGET STRENGTH STATISTICS Summary In 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) E i = SL+RS + TS i (l i,  i, z i ) + 2B(  i ) - TVG ( R i, α) Fish biomass estimation in fishery acoustics for operating frequency f : TS = 10log  BS = 20log l BS Q – biomass estimation

4 Introduction (2)  Backscattering model  Tilt angle statistics INVERSE PROCESSING  Sample catch  Regression relation MEAN VALUE PROCESSING p TS Biomass Q plpl

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.

6 Backscatter theory (1)  +  0 l ecb a ecb 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)

10 Maximum Target Strength TS 0

11 regression relationship for average target strength ( according to the National Marine Fisheries Service): Mean Target Strength use l ecb = L/4 as in Haslett model for estimate of example - fish fork length: L = 31.5 cm - from theoretical equation: TS 0 ( f = 38kHz) = -32dB TS 0 ( f =120kHz) = -27dB - from regression: = -36dB Reduced scattering length – RSL TS = 20 log L + 20 log (RSL)

12 Tilt angle dependance (1) f = 38kHz  0 =8° l ecb =L/4

13 Tilt angle dependance (2) f = 120kHz  0 =8° l ecb =L/4

14 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)

15 Tilt angle dependance (4) TS/length relationship on tilt angle for atlantic cod TS = 20log L + B 20, McQuinn, Winger (2002) EK500 38kHz SB 7  B 20  Atlantic cod Gadus morhua (Horne - Radiograph Gallery)

16 Tilt angle statistics (5)

17 Inverse processing (1)

18 Inverse processing (2)

19 Inverse processing (3)

20 fish size and orientation generator p TS  LTS 0 TS pLpL p TS 0 Simulation Random generationStatistical processing inversion backscatter model backscatter model backscatter model

21 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

22 Method 1 - Inverse processing (1) 38kHz [dB] [m]

23 Method 1 - Inverse processing (2) 120kHz [dB] [m]

24 Method 1 - Inverse processing (3)

25 Method 2 - Conditional fish beam pattern PDF B f [dB] TS 0 [dB]

26 Method 2 - Conditional fish beam pattern PDF B f [dB] TS 0 [dB]

27 Method 2 - Inverse processing (4) [dB] [m]

28 Survey data (1) NOAA/Alaska Fisheries Science Center - summer 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 :57 – 11:22 am 6776 pings (540MB) 2002 tracks of walleye pollock (Theragra chalcogramma)

30 Survey data analysis (1) [dB] [cm]

31 Survey data analysis (2) [dB] [cm]

32 Survey data analysis (3)

33 Survey data analysis (4)

34 Survey data analysis (5) 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) 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

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