There have been many experimental studies on acoustic shadowing, but
once the effect is quantified, how is the compensation to be effected? This
work shows how, through postprocessing of stored time series, containing the
depth dependence of the volume backscattering strength for each ping, by a
simple formula. The a priori components of this are the mean backscattering
cross section and the mean extinction cross section

Foote, Kenneth G.

English

Brage IMR

{ International Council for the Exploration of the Sea C.M. 1990/B:24 -seBs. R Fish Capture Committee HOW TO CORRECT FISH DENSITY ESTIMATES FOR EXTINCTION by Kenneth G. Foote Institute of Marine Research 5024 Bergen, Norway ABSTRACT There have been many experimental studies on acoustic shadowing, but once the effect is quantified, how is the compensation to be effected? This work shows how, through postprocessing of stored time series, containing the depth dependence of the volume backscattering strength for each ping, by a simple formula. The ~ priori components of this are the mean backscattering cross section and the mean extinction cross section. RESUME: COMMENT CORRIGER UNE EVALUATION DE DENSITE DE POISSONS EN PRESENCE DU PHENOMENE D'EXTINCTION Plusieurs etudes experimentales sur l'ombre acoustique ont ete realisees mais, une fois le phenomene quantifie, comment doit-on effectuer la compensation? Ce travail montre comment le faire en utilisant une simple formule sur un traitement differe des donnees avec, pour chaque coup de sonde, la variation de la reverberation de volume en fonction de la profondeur. Pour cela, les donnees a connaitre a priori sont les surfaces equivalentes moyennes de reverberation et d'extinction. INTRODUCTION A favorite strategy used in the abundance estimation of fish stocks by acoustics (MacLennan 1990) is to survey the stock when it is gathered together, as on spawning grounds or when hibernating. The physical extent of the stock may then be quite limited. Recognized topographic peculiarities of the local sea area may mark the geographical extent. While the problem of knowing where the fish is is thus addressed, another intrinsic to the concentration itself is introduced. This is the effect of extinction. It has earlier been studied experimentally under quite controlled conditions, as by Davies (1973), R~ttingen (1976), Ishii et al. (1983), Furusawa et al. (1984), Armstrong et al. (1989), and MacLennan et al. (1990), - 2 -and in the field, as by Olsen (1986) and MacLennan et al. (1990). The effect has also been studied theoretically, for example, by Weston (1967), Foote (1978), and Lytle and Maxwell (1983). Interest in the subject of acoustic extinction by fish aggregations continues, with potentially important applications to the resurgent stock of Norwegian spring-spawning herring (Clupea harengus) (R~ttingen 1989). Curiously, few studies show how knowledge of the extinction effect is to be applied, and some of the ones that do are unclear in their methods. It is the aim here to show how to correct acoustic measurements of fish density for extinction. Reference is made to a recent publication on this topic (Foote 1990) to justify the present brevity. METHOD An aggregation of similar fish is assumed to be distributed over the depth range from 0 to z, relative to the transducer. The characteristic mean backscattering and extinction cross sections, ob and o , respectively, are each assumed at the outset to be constants independenteof depth. The mean volume backscattering coefficient sv over the depth interval [z 1 ,z2] within [O,z] is, in the neglect of beam spreading, where the depth dependence of the density p is explicitly shown. Given measurements of sv through the water column, it is desired to determine the form of p(z). This can be done in the following way. The depth range of interest or influence is divided up into N horizontal layers, with bounding depths of z 1 ,z2 , ... ,zN+ 1 , within each of which the density is constant. The j-th layer thus lies between zj and zj+ 1 =z.+~zj, and its density is denoted by Pj· The first integral factor in equation 11) 1s rewritten thus: n-1 exp(-2 ~ p,o ~z.) . 1 J e J J= assuming interest in the interval [zn,zn+ 1]. For the case n=1, the summation in the integral is assumed to vanish, hence the factor is unity. The second integral term is also rewritten: z ob n+1 ab P -4 f exp[-2p o (l;;-z )]ds 8'1Trr [1- exp(-2p o ~z )] n 'TT n e n 11v n e n z e n Combining the several parts, while expressing the volume backscattering coefficient in the same abbreviated terms, s v,n n-1 ob exp (- 2 ~ p . o ~z . ) -8-..,.--,.- [ 1 - exp (- 2 p o ~z ) ] . 1 J e J 'TT DZ 0 n e n J= n e Solution for p is immediate. Defining n (1) ( 2) ~ s  v , n  1  - 3  -n - 1  s  e x p  (  2  L :  p  .  o  6 . z  .  )  v , n  .  1  J  e  J  J =  p n  = - 2 0  6 . z  e  n  l n  ( 1  - S T i s  6 . z  o  / o b )  v , n  n  e  T o  e v a l u a t e  t h i s ,  ~v,n a n d  P n  a r e  c o m p u t e d  i n  o r d e r  f r o m  n = 1  t o  n = N .  A t  t h e  b e g i n n i n g  o f  t h i s  p r o c e s s ,  i n  a c c o r d a n c e  w i t h  t h e  a b o v e  i n t e r p r e t a t i o n  o f  t h e  s u m m a t i o n  i n  t h e  e x p o n e n t i a l  a r g u m e n t  o f ' .  e q u a t i o n  ( 3 a ) ,  s  = s  .  v , 1  v , a . . . .  C O M P U T A T I O N A L  E X A M P L E  T h i s  i s  t a k e n  f r o m  a  r e p e a t e d  s u r v e y  o f  p a r t  o f  t h e  1 9 8 3 - y e a r  c l a s s  o f  h e r r i n g  i n  G r a t a n g e n ,  a  f j o r d  i n  n o r t h e r n  N o r w a y .  T h e  p a r t i c u l a r  s u r v e y  w a s  p e r f o r m e d  b y  R / V  M I C H A E L  S A R S  o n  1 0  D e c e m b e r  1 9 8 9 ,  u s i n g  t h e  S I M R A D  E K 5 0 0  ( 3 a )  (  3 b )  e c h o  s o u n d i n g  s y s t e m  ( B o d h o l t  e t  a l .  1 9 8 8 ,  1 9 8 9 )  w i t h  t h e  3 8 - k H z  E S 3 8 B  t r a n s d u c e r .  T h e  h e r r i n g  w e r e  d i s t r i b u t e d  i n  a  r a t h e r  d e n s e  l a y e r  i n  t h e  f j o r d .  T h i s  w a s  m o s t l y  s t a t i o n a r y  i n  a b o u t  t h e  u p p e r  5 0  m  o f  t h e  w a t e r  c o l u m n ,  b u t  d e s c e n d e d  t o w a r d s  t h e  b o t t o m  d u r i n g  t h e  s e v e r a l  h o u r s  o f  m i d d a y  t w i l i g h t .  T h e  a t m o s p h e r i c  w e a t h e r  w a s  v e r y  f i n e ,  h e n c e  t h e  o b j e c t  r e g i s t r a t i o n ,  m a d e  a t  1 4 0 0  h o u r s  G M T  a n d  r e p r e s e n t e d  b y  t h e  e c h o g r a m  i n  F i g .  1 ,  s h o w s  t h e  h e r r i n g  a t  t h e  b e g i n n i n g  o f  t h e i r  r e t u r n  t o  t h e  n e a r - s u r f a c e  l a y e r .  C o r r e s p o n d i n g  t o  t h e  e c h o g r a m  a r e  v a l u e s  o f  t h e  v o l u m e  b a c k s c a t t e r i n g  s t r e n g t h  S  ,  s t o r e d  b y  m e a n s  o f  t h e  B e r g e n  E c h o  I n t e g r a t o r  ( K n u d s e n  1 9 8 9 ) .  I n  t h e  a n a l y z ¥ d  d a t a  f i l e  t h e  S  - v a l u e s  a r e  r e c o r d e d  f o r  e a c h  p i n g  a t  0 . 5 - m  i n c r e m e n t s  f r o m  t h e  t r a n s d u c ¥ r  d e p t h  t o  2 5 0 - m  r a n g e .  T h e  d a t a  w e r e  g a t h e r e d  a t  a  n o m i n a l  p u l s e  r e p e t i t i o n  f r e q u e n c y  ( P R F )  o f  5 0 / m i n u t e  a t  a  v e s s e l  s p e e d  o f  6  k n o t s .  S i n c e  t h e  l o g - b a s e d  r e p r e s e n t a t i o n  m o d e  i s  u s e d  h e r e ,  w i t h  e v e n l y  i n t e r p o l a t e d  s u b d i v i s i o n  o f  e a c h  n a u t i c a l  m i l e  i n t o  2 0 0  i n t e r v a l s ,  t h e  d i s t a n c e  b e t w e e n  e a c h  s o u n d i n g  i s  n o m i n a l l y  9 . 2 6  m .  I n  t h e  p r e s e n t  e x a m p l e  t h e  h e r r i n g  w e r e  s u r v e y e d  a l o n g  a  z i g z a g  g r i d ,  t h u s  a  c r o s s  s e c t i o n  o f  t h e  f j o r d  i s  r e p r e s e n t e d  i n  F i g .  1 .  T h e  b o t t o m  e c h o  s i g n a l  i n  t h e  e c h o  s o u n d e r  w a s  t r i g g e r e d  b y  t h e  u p p e r  s u r f a c e  o f  t h e  l a y e r  o v e r  m u c h  o f  t h e  s a i l e d  i n t e r v a l ,  h o w e v e r ,  i t  i s  e a s y  t o  i g n o r e  t h i s  w h e n  p r o c e s s i n g  t h e  d a t a .  T h e  m e a n  a r e a  b a c k s c a t t e r i n g  c o e f f i c i e n t  s A  w a s  c o m p u t e d  i n  e a c h  o f  t w o  w a y s  f o r  t h e  l o g  i n t e r v a l  5 5 1 1 . 3 5 5 - 5 5 1 2 . 1 6 0  f o r  t h e  c o n s t a n t  d e p t h  r a n g e  0 - 1 3 5  m  r e l a t i v e  t o  t h e  t r a n s d u c e r .  T h e  c o e f f i c i e n t  w a s  c o m p u t e d  b o t h  i n  t h e  n e g l e c t  o f  e x t i n c t i o n  a n d  a s s u m i n g  i t s  p r e s e n c e .  A  s a m p l e  o f  h e r r i n g  a c q u i r e d  f r o m  a  l o c a l  s e i n e r  i n d i c a t e d  t h a t  t h e  m e a n  l e n g t h  w a s  3 3 . 1  c m .  T h e  b a c k s c a t t e r i n g  c r o s s  s e c t i o n  O b  w a s  d e t e r m i n e d  b y  M a c L e n n a n  e t  a l .  ( 1 9 9 0 )  t o  b e  8 . 7 0  c m2,  w h i c h  i s  c o n s i s t e n t  w i t h  t h e  t a r g e t  s t r e n g t h  r e l a t i o n  T S = 2 0  l o g  9 . ,  - 7 2 . 0 ,  w h e r e  9 . ,  i s  t h e  m e a n  l e n g t h  i n  c e n t i m e t e r s ,  a n d  T S  i s  t h e  t a r g e t  s t r e n g t h  i n  d e c i b e l s .  T h i s  r e l a t i o n  r e s e m b l e s  t h a t  r e c o m m e n d e d  b y  I C E S  ( A n o n .  1 9 8 3 )  ,  T S = 2 0  l o g  9 . , - 7 1 . 2 ,  a s  l a t e r  r e f i n e d  t o  T S = 2 0  l o g  9 . , - 7 1 . 9  ( F o o t e  1 9 8 7 ) .  T h e  m e a n  e x t i n c t i o n  c r o s s  s e c t i o n  o f  t h e  s a m e  f i s h  w a s  m e a s u r e d  b y  D .  N .  M a c L e n n a n ,  w i t h  t h e  r e s u l t  2  0  = ( 1 . 4 ± 0 . 3 ) o b  ( M a c L e n n a n  e t  a l .  1 9 9 0 ) .  H e r e  t h e  c e n t r a l  v a l u e  0  = 1 2 . 2  c m  i s  u~ed. e  en ....... " 1,1 .~ ·~ ,, -~ ·l ------~~~-~---~·--~~~~~-------~~~~7---~~--~~~------~~~------~ ....... ,..__ ~ ·-SS" . . :; riiWJ'.J'jll'~[.. kl,..;~"55lllllllllll !IIIIC!lL. '-4W:i wmm-£i'C"'WTTP!'¥iA£1.& ,...,. r;~, :I' ~--. '·' :t~ '.;·, "·' j .· :~ ·~ •\ ·11 ? ~I 'l -~'I ,:L .. Fig. 1. Echogram of a herring aggregation in Gratangen, a northern Norwegian fjord at 68°44'N 17°20'E, on 10 December 1989 at 1400 hours GMT, as recorded by '1e SIMRAD EKS00/38-kHz echo sounder. The horizontal lines and that following the bottom or upper side of the aggreg~_Lon indicate integration channels. ~-- the case of the bottom-tracking line, this is placed 10 m above the detected bottom, from whatever target, whether fjord bottom or dense fish aggregation. ,j:::. - 5 -5 5 2 ~e results are simply stated. The sA-values are 3. 92 10 and 3. 95 10 m /NM , without and with assumption of extinction. That is, in the present example there is little difference apropos of sA. Values of density in the layer do show significant differences as extinction is neglected or heeded. The maximum measured density, according to the extinction-corrected value of the volume backscattering strength, occurred at log 5511.710 at a range of 89 m. The values of density wihout and with allowance for extinction are 103.5 and 116.7 fish/m3 , respectively. The corresponding value of sv are 0.00686 and 0.00723 m-1. DISCUSSION The formula given in equation (3) is mathematically well-behaved and easy to execute by means of a digital computer. The assumption of constant density in each analyzed layer need not limit the use of this for ordinary computer processing, for the layer thickness can - with foresight - be chosen sufficiently small, e.g., 1 m, to avoid the possibility of significant variation. In the computational example the: layer thiakness i 1s 0. 5 m. The solution does apply to the mean field, or echo intensity in the mean of a large number of observations or in the presence of a large number of scatterers. Since extinction is only significant in the presence of many scatterers, the implicit mean-field assumption is believed to be good. This may be examined by simulation, however, although involving considerable computations, at least according to one scheme (Foote 1989). Another assumption underlying equation (3) is that effects of beam spreading are negligible. This is reasonable because of the high degree of directionality of typical transducers used in echo surveying. For the SIMRAD ES38B transducer, for example, the beamwidth between -3-dB levels is about 8 deg, while that for the ESS transducer in its narrow-beam mode is about 5 deg. The assumption of one-dimensional propagation indicated in equation (1) is thus reasonable. This, like the mean-field assumption, can be investigated by simulation, thus touching on so-called second-order or multiple-scattering effects too (Stanton 1983). In developing the present method for correcting measurements of scatterer density for extinction the mean backscattering and extinction cross sections are assumed to be constant, independent of depth. This assumption is unnecessary, and both cross sections may vary arbitrarily and independently with depth. In fact, this more general case can be incorporated into equation (3) by replacing all instances of ob and oe by the respective subscripted quantity, e.g., ob n and oe n in equation (3b), where the additional assumption is now made that the new quantities, like Pn' are constant within the applicable layer. If the present scheme seems at all complicated - it is not - then it should be remembered that the requirements on interpretation are no different from those implicit in every quantitative analysis of echo data. The single new ingredient is the mean extinction cross section. This is known for some fish species under some circumstances (Fcote 1978, Ishii et al. 1983, Furusawa et al. 1984, MacLennan et al. 1990), and will undoubtedly be .specified - 6 -better for these and other species in the future. The purely computational part of the analysis is not especially encumbered by the algorithm given in equation (3), or its mentioned generalization, for postprocessing by a workstation-level computer is entirely feasible (Knudsen 1989). ACKNOWLEDGEMENT N. Diner is thanked for rendering the abstract into French. REFERENCES Anon. 1983. Report of the 1983 planning group on ICES-coordinated herring and sprat acoustic surveys. ICES C.M. 1983/H:12. 11 pp. [mimeo] Armstrong, F., Simmonds, E. J., and MacLennan, D. N. 1989. Sound losses through aggregations of fish. Proc. IOA, 11(3): 35-43. Bodholt, H., Nes, H., and Solli, H. 1988. A new echo sounder system for fish abundance estimation and fishery research. ICES C.M. 1988/B:11. 6 pp. [mimeo] Bodholt, H., Nes, H., and Solli, H. 1989. A new echo-sounder system. Proc. IOA, 11(3): 123-130. Davies, I. E. Soc. Am., 1973. Attenuation of sound by schooled anchovies. 54: 213-217. J. acoust. Foote, K. G. 1978. Analysis of empirical observations on the scattering of sound by encaged aggregations of fish. FiskDir. Skr. Ser. HavUnders., 16: 423-456. Foote, K. G. 1987. Fish target strengths for use in echo integrator surveys. J. acoust. Soc. Am., 82: 981-987. Foote, K. G. 1989. Simulating echograms. ICES C.M. 1989/B:6. 11 pp. [mimeo] Foote, K. G. 1990. Correcting acoustic measurements of scatterer density for extinction. J. acoust. Soc. Am., 88(3). Furusawa, M., Ishii, K., Miyanohana, Y., and Maniwa, Y. 1984. Experimental investigation of an acoustic method to estimate fish abundance using culture nets. Jpn. J. Appl. Phys., 23(S23-1): 101-103. Ishii, K., Furusawa, M., and Miyanohana, Y. 1983. Measurement of attenuation of sounds by schooling fish. Tech. Rep. Natl. Res. Inst. Fish. Engr., Fishing Boat, and Instrument (4): 73-94. Knudsen, H. P. 1989. 1989/B:9. 8 pp. Bergen Echo Integrator: An introduction. [mimeo] [J. CIEM (in press)] ICES C.M. Lytle, D. W., and Maxwell, D. R. 1983. Hydroacoustic assessment in high density fish schools. FAO Fish. Rep., 300: 157-171. - 7 -MacLennan, D. N. 1990. Acoustical measurement of fish abundance. J. acoust. Soc. Am. , 8 7: 1-15. MacLennan, D. N., Armstrong, F., and Simmonds, E. J. 1990. Further observations on the attenuation of sound by aggregations of fish. Proc. IOA, 12(1): 99-106. Olsen, K. 1986. 1986/B:44. Sound attenuation within schools of herring. 15 pp. [mimeo] ICES C.M. Rt;t>ttingen, I. density. 1976. On the relation between echo intensity and fish FiskDir. Skr. Ser. HavUnders., 16: 301-314. Rt;t>ttingen, I. 1989. Reappearance of Norwegian spring spawning herring on spawning grounds south of 60°N. ICES C.M. 1989/8:22. 4 pp. [mimeo] Stanton, T. K. 1983. Multiple scattering with applications to fish-echo processing. J. acoust. Soc. Am., 73: 1164-1169. Weston, D. E. 1967. Sound propagation in the presence of bladder fish. In Underwater Acoustics, Vol. 2, pp. 55-88. Ed. by V. M. Albers, Plenum Press, New York. 416 pp. 

How to correct fish density estimates for extinction

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How to correct fish density estimates for extinction

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