ICES Journal of Marine Science, 59: 365–369. 2002doi:10.1006/jmsc.2001.1158, available online at http://www.idealibrary.com on

A consistent approach to definitions and symbols in fisheriesacoustics

David N. MacLennan, Paul G. Fernandes, andJohn Dalen

MacLennan, D. N., Fernandes, P. G., and Dalen, J. 2002. A consistent approach todefinitions and symbols in fisheries acoustics. – ICES Journal of Marine Science, 59:365–369.

Long-standing problems with acoustical terminology in fisheries applications such asecho-integration indicate the need for a more consistent approach. Based wherepossible on existing terms, a scheme of explicitly named quantities is proposed, backedby clearly stated definitions and preferred symbols. The emphasis is on scatteringphenomena because the terminology in this area presents the main source of difficulty.Starting with the scattering equations for a small target, the volume, area, and linecoefficients relevant to multiple, distributed targets are defined, leading to practicalformulas for the important application of remote biomass estimation from echo-integration. The aim is to incorporate, as far as possible, common practice infisheries-acoustics terminology and related fields. The developed scheme has beencommended by the ICES Fisheries Acoustics Science and Technology Working Groupas a constructive approach to better communication standards in fisheries-acousticspublications.

� 2002 International Council for the Exploration of the Sea. Published by Elsevier Science Ltd.All rights reserved.

Keywords: acoustics, definitions, fisheries, ICES, symbols, sonar, units, WGFAST.

Received 7 January 2001; accepted 10 November 2001.

D. M. MacLennan: Lake Victoria Fisheries Research Project, PO Box 2145, Jinja,Uganda; tel: +256/0 43 130013; fax: +256/0 43 121322; e-mail: unecia@source.co.ug.P. G. Fernandes: FRS Marine Laboratory Aberdeen, PO Box 101, Victoria Road,Aberdeen, AB11 9DB, Scotland, UK. J. Dalen: Havforskingsinstituttet, Postboks 1870Nordnes, 5817 Bergen, Norway; tel: +47 55 23 85 00; fax: +47 55 23 85 31; e-mail:John.Dalen@imr.no. Correspondence to P. G. Fernandes: tel: +44 1224 295403; fax:+44 1224 295511; e-mail: fernandespg@marlab.ac.uk

Introduction

In any scientific field it is essential to be clear about thedefinition of physical quantities and naming conven-tions. In the case of fisheries acoustics there has been along-standing problem mainly due to confusing descrip-tions of the various scattering measures that are centralto biological observations using sonars and echo-integrators. With the growing importance of acousticmethods in remote biomass estimation, many prac-titioners agree that a more consistent approach toacoustical terminology must be adopted in fisheriesapplications.

Existing guidance on these matters is limited andsomewhat contradictory. General texts on acousticalterminology (ANSI, 1994; Urick, 1983) do not defineadequately processes like area scattering which are

1054–3139/02/040365+05 $35.00/0 � 2002 International Council for the E

seldom mentioned outside fisheries’ applications. At themore specialised level, Hall (1995) considers that solidangle measures should be included in the definition oftarget strength and related parameters. However, thisidea is not supported by Medwin and Clay (1998) intheir more complete treatment of the ground rules thatapply to acoustical oceanography. For historical andother reasons different practices appear in the fisheriesliterature (Craig, 1981; MacLennan and Simmonds,1992; Foote and Knudsen, 1994). Our primary concernis to address the lack of consistency arising in the latterfield.

A common pitfall, for example, is the distinction be-tween the quantities sa and sA. Although these termshave been described (e.g. Foote and Knudsen, 1994),there is no common name for the quantity sA, notwith-

standing that this is the primary output from the most

xploration of the Sea. Published by Elsevier Science Ltd. All rights reserved.

366 D. N. MacLennan et al.

common scientific echosounder, the Simrad EK500.More disturbingly, although these terms differ by a fac-tor of 4�(1852)2 (Foote and Knudsen, 1994), such thatsa=sA/4�(1852)2, the Simrad EK500 instruction manualnotes that ‘‘. . . the Sa(mean) to be used for fish densitycalculations is Sa(mean)=SA/4�’’ (note also the incorrectuse of capitalisation: SA is used instead of sA). Thedefinitions depend critically on the relationships betweenfish density, sa, sA, and fish target strength but no singledocument exists which encompasses and defines all theseterms in a complete and consistent manner.

Here, we propose a complete scheme of definitionsand terminology which, hopefully, will encourage moreuniform use of terms to describe measurements infisheries-acoustics publications. The emphasis is on scat-tering phenomena because these are the main source ofdifficulty.

Primary measurements

Acoustical quantities such as the target strength are notmeasured directly. They are determined by numericalevaluation of a defining equation X=f(Qp) where Qp is aset of primary quantities which can be measureddirectly. The equations show inter alia the dimensionsand the units of the derived quantity in terms of primarymeasurements. Different Qp might be selected for thispurpose, however, to focus on scattering phenomena westart with the set listed below.

r Distance of the measurement positionfrom a small target. In this context,‘‘small’’ means a target whosecharacteristic size is less than the radius ofthe first Fresnel zone, namely √(r�/2)where � is the wavelength.

�,� Spherical polar angle coordinates of themeasurement position. The target is at theorigin and the transmitted wavepropagates in the direction (0,0).

x,y,z Cartesian coordinates. The transmittedwave propagates towards the target in the+z direction.

Iinc Intensity of the transmitted or incidentwave at the target.

Iscat(r,�,� ) Intensity of the scattered wave at themeasurement position.

Ibs(r) Intensity of the backscattered wave, equalto Iscat(r, �� 0).

I(z) Intensity of a plane wave as a function ofdistance along the propagation path.

V Volume occupied by a scattering mediumor multiple discrete targets.

A Area of a school echo-trace observed onan echogram.

Naming conventions

The first requirement is to adopt a set of names whichare unique for each quantity having a specific physicaldefinition. Furthermore, quantities which are scaled byfactors other than powers of 10 should have differentnames, like degrees and radians in the case of angles.Given a non-confusing and widely accepted set ofnames, the symbols are less of a problem, or at leastthose which have dimensions. In that case, SI units arethe norm, with 10n scaling factors as needed. On theother hand, it is not necessary to cover every quantitywhich might be expressed with non-decadal scaling. Theneed is to include those which are often used in fisheriesacoustics in order to eliminate any risk of confusion.

Table 1 shows a list of derived quantities relevant toscattering by one or more insonified targets. We startwith the intensity scattered by a small target which isnormally direction-dependent. This leads to variouscross-sections that describe the acoustical size in termsof the ratio of the scattered and incident intensities.Medwin and Clay (1998) prefer to start with the com-plex scattering length, L(�,�) which expresses phase aswell as amplitude information. It is usual to considercross-sections and scattering lengths as frequencydependent functions. Alternative models, based ontime dependent functions, may be simpler and morerobust. The latter could well become important as andwhen sonars have much wider bandwidths than currentinstruments.

We concur with Medwin and Clay (1998) that thename ‘‘differential scattering cross-section’’ be used todescribe the scattering over all directions, measuredbistatically. However, we believe the related symbolshould have a functional form such as �(�,�) or �(r), asopposed to ��(�,�). We prefer not to use the � qualifierin this context because it normally indicates a smallbut finite increment, whereas �(�,�) is a continuousfunction.

It follows that other cross-sections relating to specificdirections, or with no directional dependence, shouldhave different and less general names. Their symbolsshould be written as � followed by subscripts whichdescribe the context. In the case of the ‘‘backscatteringcross-section’’ (�bs), this is in line with current practice.In the case of the isotropic cross-section (4��bs, whichassumes no directional dependence), rather generalnames have been used in the past; it is often symbolisedby � with no subscripts. We feel something more specificis needed. The term ‘‘spherical scattering cross-section’’(symbol �sp) is suggested as being appropriate to theisotropic assumption in the definition of this quantity.

In the case of multiple distributed targets volume-scattering measures are straightforward. The ‘‘volume-backscattering coefficient’’ is well understood ass =�� /V where the sum is taken over all the discrete

v bs

367A consistent approach to definitions and symbols in fisheries acoustics

Table 1. Preferred names, definitions and symbols for scattering quantities in fisheries acoustics.

Symbol Name Defining equation Dimensions Units

� Acoustic absorption coefficient �=10 log10 [I(z)/I(z+�z)]/�z L�1 dB m�1

(I measured in the absence of biological scatterers)

� (�,�) Differential scattering cross-section � (�,�)=[r2 Iscat(r,�,�) 10�r/10/Iinc] L2 m2

�bs Backscattering cross-section �bs=[r2 Ibs(r) 10�r/10/Iinc] L2 m2

�sp Spherical scattering cross-section �sp=[4� r2 Ibs(r) 10�r/10/Iinc] L2 m2

2� ��s Total scattering cross-section �s=# [# �(�,�) sin � d�] d� L2 m2

0 0

�e Extinction cross-section �e=[�I(z)/�z��ln(10)/10]/[n I(z)] L2 m2

(I measured in the presence of biological scatterers)

�a Absorption cross-section �a=�e��s L2 m2

TS Target strength TS=10 log10 (�bs) — dB re 1 m2

sv Volume backscattering coefficient sv=��bs/V L�1 m�1

z2

sa Area backscattering coefficient sa=# sv dz — (m2 m�2)z1

sA Nautical area scattering coefficient(NASC)

sA=4� (1852)2 sa — (m2 nmi�2)

sL Line backscattering coefficient sL=# # sv dx dz L mA

Sv (Mean) Volume backscattering strength Sv=10 log10 (sv) — dB re 1 m�1

(MVBS when sv is averaged over a finite volume)

Sa Area backscattering strength Sa=10 log10 (sa) — dB re 1(m2 m�2)

SA Nautical area scattering strength SA=10 log10 (sA) — dB re 1(m2 nmi�2)

SL Line backscattering strength SL=10 log10 (sL) — dB re 1 m

targets in the volume V, or sv=��bs/�V in the case ofa continuous scattering medium. The SI unit (m�1) isthe norm for sv and 4� scaling is seldom if ever used. Inthis case, � is used in its correct mathematical context(cf. above).

Area scattering is more of a problem. Being dimen-sionless, the units of area-scattering coefficients are moredifficult to express clearly when different scaling factorsare applied. A naming convention is essential to distin-guish the various scaled versions. By analogy with thevolume case the unscaled quantity is the ‘‘area-backscattering coefficient’’ (sa) which is defined as theintegral of sv over a range interval. The most commonlyused scaled coefficient is denoted by the symbol sA asimplemented in the Simrad EK500 echosounder. Therelevant scaling factor is 4�(1852)2; for historicalreasons, the nautical mile enters the calculation(1 nmi=1852 m). In the absence of a better idea, we havecalled this scaled quantity the ‘‘nautical area-scatteringcoefficient’’. That is a rather long expression,but in practice it could be contracted to the acronymNASC.

There has been much work recently on the echostatistics of fish schools (Reid, 2000). Various measuresare needed for echo-trace classification purposes, inparticular, a measure of the total-echo strength. Con-sider an echosounder on a ship running a line transect.The echogram shows a 2D section of a school as acomposite over several pings. The required measure isthe integral of sv over A, the area of the section. Thisquantity has the dimensions of length. By analogy withthe volume and area cases, we call it the ‘‘line-backscattering coefficient’’ for which sL is an appropri-ate symbol. A is the mean echo-trace height multipliedby the length determined from the ship speed and thetransit time.

All the above mentioned quantities have equivalentlogarithmic versions. Many are in regular use,especially the target strength TS=10 log10 (�bs) whichremains unaltered in our consistent scheme. In the caseof volume, area and line scattering, the log name issimply the linear name with ‘‘strength’’ substituted for‘‘coefficient’’. Note that expressions like ‘‘mean targetstrength’’ imply the logarithm of the averaged linear

368 D. N. MacLennan et al.

quantity, not the average of the logarithms. Animportant example is the ‘‘mean volume-backscatteringstrength’’ or MVBS, which is well known as 10 log10

[mean (sv)].

Symbols

We suggest that the following conventions should beadopted. To a large extent they correspond to currentpractice.

(1) Linear measures have symbols beginning with (a)brush script ‘‘L’’ for scattering lengths; (b) Greek‘‘�’’ for cross-sections; and (c) lower case Roman‘‘s’’ for volume, area, and line coefficients.

(2) Logarithmic measures have symbols beginningwith a capital Roman letter.

(3) The final subscript letters, the case is immaterial,indicate the context, e.g. bs for backscattering.They are not normally relevant to the particularquantity or the units of measurement.

(4) In the case of area scattering only the subscript caseis significant. sa and sA refer to the area-backscattering coefficient and the NASC, respect-ively. This convention has been adopted toconform to current practice and to be consistentwith the vast amount of archived historical data.

Biomass estimation

Perhaps the most important application of acoustics infisheries research is the estimation of the density orabundance of biological targets. It is essential to be clearabout the formulas used to convert the acousticalmeasurements to biological quantities. Consider thesimple example of a layer between depths z1 and z2

below the transducer. a is the density of targetsexpressed as the number per unit surface area of thelayer. a is proportional to sa and inversely proportionalto K�bsL, the expected backscattering cross-section of onetarget. K�bsL is so written to denote an expected valuerather than a mean, since it is determined indirectly fromthe size distribution of fished samples and empiricalequations relating the target strength to fish length.Equivalent formulations may be written in terms of sa orsA, K�bsL or K�spL with the appropriate scaling factor.Some examples are, with the units of a in squarebrackets:

a=sa/K�bsL [m�2]

a=106 sa/K�bsL [km�2]

a=sA/{4� K�bsL}=sA/K�spL [nmi�2]

In practice, it is the last of these equations which is themost important as it includes the quantity (sA) that isoutput from the principal instrument used in fisheriesacoustics (the Simrad EK500), and the backscattering

cross-section (�bs) which is derived from the well knowntarget strength (TS).

Discussion and conclusionsThe names proposed for key quantities relevant tofisheries acoustics, together with their definitions andsuggested symbols are summarised in Table 1. The list inTable 1 is not intended to be exhaustive. The need is toinclude those which frequently appear in the literaturepertaining to fisheries acoustics. We have incorporatedcommon formulations from related fields as far as ispracticable. Thus the absorption coefficient, � (dBm�1), has been used in preference to (nepers m�1) sothat our definitions correspond to those recognised byacoustical oceanographers (Medwin and Clay, 1998).

As is the normal practice in physical descriptionsnames should be chosen to avoid confusion betweendifferent quantities and, in each case, the quantity isdefined by an equation which shows how it is deter-mined from primary measurements. The units anddimensions follow from those of the quantities in thedefining equation. SI units are normally adopted as isgenerally required in formal publications. It is necessaryto allow for non-SI units in a few cases; in particularwhen a non-SI unit is needed to conform to currentpractice in the field.

While the scheme presented here is not the only onethat might be considered, it has been commended by theWorking Group on Fisheries Acoustics Science andTechnology (WGFAST) of the International Councilfor the Exploration of the Sea (ICES), as a consistentapproach to better communication standards in fisheriesacoustics. As such it should help to prevent some ofthe common pitfalls which beleaguer fisheries scientistswhen negotiating the tricky waters of the largely‘‘engineering science’’ of fisheries acoustics.

AcknowledgementsMuch of the discussion leading to this article wasmotivated by the ICES WGFAST. We thank our manycolleagues in WGFAST and others consulted bycorrespondence for their valuable contributions to theideas expressed here, particularly Noel Diner, JohnSimmonds, and Clarence Clay, and to Andrew Brierleyfor suggestions on the text.

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