ICES Journal of Marine Science, 60: 419–428. 2003
doi:10.1016/S1054–3139(03)00004-3
A requiem for the use of 20 log10 Length for acoustic target
strength with special reference to deep-sea fishes
S. McClatchie, G. J. Macaulay, and R. F. Coombs
McClatchie, S., Macaulay, G. J., and Coombs, R. F. 2003. A requiem for the use
of 20 log10 Length for acoustic target strength with special reference to deep-sea
fishes. – ICES Journal of Marine Science, 60: 419–428.
Although it is well known that the slopes of target strength (TS) and length relationships vary
widely, it is common in fisheries acoustics to force the TS–length regression through a slope
of 20. Is it time to abandon this practice? The theoretical justification was that TS should be
proportional to cross-sectional area, and that area should scale as the square of the linear
dimension (fish length). There are now many species other than gadoids that are the subject
of acoustic surveys, and many of them do not have the same morphology as the gadoid fishes.
The slope of the TS–length regressions deviates significantly from 20. The empirical slope
should be used wherever it can be shown to be more appropriate than the 20 log10 L model.
Using the data from swimbladder models, it is shown that Macrourids, a merluccid hake
and Oreosomatidae have a different relationship between swimbladder size and fish size
compared with that of gadoids. It is demonstrated that the 20 log10 L model is not appropriate
for these deep-water fish and that deviations from the model arise, to a considerable degree,
from variation in fish morphotypes. The TS of deep-water Macrourids, a merluccid hake and
Oreosomatidae are lower than that of gadoids. This is related to the swimbladder size–fish
size relationship in different morphotypes, although not much evidence can be found to
support the concept that swimbladder sizes are generally smaller in deep-sea fishes.
Ó 2003 International Council for the Exploration of the Sea. Published by Elsevier Science Ltd. All rights
reserved.
Keywords: fish target strength, acoustic deepwater size morphology.
Received 26 June 2002; accepted 13 October 2002.
S. McClatchie, G. J. Macaulay, and R. F. Coombs: National Institute of Water and
Atmospheric Research Ltd, PO Box 14901, Kilbirnie, Wellington, New Zealand. Correspondence to S. McClatchie: tel.: þ64 4 386 0300; fax: þ64 4 386 0574; e-mail:
[email protected].
Introduction
It has become something of a paradigm to summarize the
relationship between tilt-averaged, acoustic target strength,
hTSi, and fish length (L) by hTSi ¼ m log10 L þ b, where
the value of m is assumed to be 20. This equation is
generally applied to TS of fish from the same species over
a range of sizes that were insonified at the same frequency.
A value of 20 for m is reasonable if backscattering is
proportional to cross-sectional area of the main scattering
structure, which in turn is directly proportional to L
(acoustic cross-section, rbs, scaling proportional to L2)
rather than to volume (rbs scaling proportional to L3), or
some other proportionality. In an early review, Love (1971)
combined all the available data on fish TS and obtained
a regression to predict the TS of an individual fish as
a function of length and wavelength. He concluded that
for an individual fish, the dorsal-aspect TS increases
in proportion to the square of fish length. Foote (1979)
proposed area-dependent scattering ðm ¼ 20Þ to describe
1054–3139/03/040419þ10 $30.00
the hTSi–length relationships for caged and free-swimming
clupeoids and for free-swimming gadoids. In their review,
MacLennan and Simmonds (1992) stated that, in the
absence of data to the contrary, the 20 log10 L dependence
of TS seemed a fair assumption and this relationship
continues to be in use (Benoit-Bird and Au, 2001; Iida et al.,
1998; Rose, 1998; Svellingen and Ona, 1999).
When the slope of the hTSi–L regression is estimated
from the data, m commonly has values between 18 and
30 (MacLennan and Simmonds, 1992), although Foote
(1987) reported an even wider range (5.1–29.7) for
gadoids, clupeioids, redfish and greater silver smelt.
McClatchie et al. (1996a) found m to be ranging between
11 and 25 for the TSmax–L regression, where TSmax is
the maximal TS. Since the book by MacLennan and
Simmonds has been published, many new measurements
of fish TS have been made, so that data are now available
on the hTSi–length relationships for many species other
than gadoids.
Ó 2003 International Council for the Exploration of the Sea. Published by Elsevier Science Ltd. All rights reserved.
420
S. McClatchie et al.
The objective of this article was to use some of these
data, derived from swimbladder modelling of the TS of
deep-water fishes (800–1500 m), to test whether the
20 log10 L relationship is valid for these species, and to
test whether the TS–length relationships of deep-water fish
with air-filled swimbladders are different from more
shallow-living species. In the process of determining as to
why this might be so, the generalization that deep-water
fish have smaller swimbladders is examined critically. The
question, whether reframing the TS–length relationship in
terms that account for a greater extent of the diversity of
fish morphology and provide a clearer summary of the size
dependence of TS, is discussed. Many studies addressing
the relationship between fish size and TS begin from a
physics or engineering perspective, i.e. assume a model fish
of x, y, z dimensions. This study takes a more biological
approach, combining experimental measurements with
empirical model results in a meta-analysis to test the
validity of a statistical relationship. As pointed out by a
reviewer, the 20 log10 L relationship is no better or worse
than another, but if another relationship can be shown to be
more appropriate, then the best one should be used. One of
our points is simply that the 20 log10 L relationship should
not be used without first determining whether it is the most
suitable one.
could be matched to their sizes (McClatchie et al., 1996a)
(Table 1). The published data included fish that were either
alive, stunned or killed. There were no species in this dataset in which TS was measured on both live and dead fish.
In this analysis, we include both live and dead fish, but not
the fish that had been frozen. It is now known that when
fish have been frozen, the TS of dead and live fish can differ
owing to air inclusions (McClatchie et al., 1999) and the
differences in the tissue characteristics after death (Gytre,
1987), though these are less important for swimbladder fish
as 95% of the backscattering comes from the swimbladder
(Foote, 1980). To minimize these biases, we excluded nonswimbladder fish from the analyses.
Swimbladder modelling
Swimbladder-model data were produced using methods
detailed in Macaulay et al. (2002). The methods for estimating TS were the same as in McClatchie et al. (1996b),
except that a resin was used to produce better swimbladder casts, the volume of the cast was adjusted to that
required for neutral buoyancy and the shape was estimated using a hand-held laser scanner rather than by crosssectioning, digitization and triangulation (Macaulay et al.,
2002).
Analyses
Methods
Dataset
The data used in this article were from swimbladder
modelling and from a dataset of published experimental measurements of TS, where the TS of individual fish
All the statistical analyses were performed using the
R programming language and environment (Ihaka and
Gentlemen, 1996). All the regressions in this article were
orthogonal least-squares rather than geometric regressions,
despite the x, y, data being bivariate and assumed normal.
Table 1. Species plotted in Figure 1, including those used for swimbladder modelling, listed with their species codes.
Common name
Black oreo
Smooth oreo
Lookdown dory
Javelinfish
Hoki
Ridge scaled rattail
Bollon’s rattail
Serrulate rattail
White rattail
Notable rattail
Four-rayed rattail
Black javelinfish
Red cod
Ling
Barracouta
Frostfish
Hake
Southern blue whiting
Atlantic cod
Pollack
Saithe
Silverside
Species
Species code
Morpho-type
Allocyttus niger
Pseudocyttus maculatus
Cyttus traversi
Lepidorhynchus denticulatus
Macruronus novaezelandiae
Macrorurus carinatus
Caelorinchus bollonsi
Corypaenoides serrulatus
Trachyrinchus aphyodes
Caelorinchus innotabilis
Coryphaenoides subserrulatus
Mesobius antipodum
Pseudophycis bachus
Genypterus blacodes
Thyrsites atun
Lepidopus caudatus
Merluccius australis
Micromesistius australis
Gadus morhua
Pollachius pollachius
Pollachius virens
Menidia menidia
BOE
SSO
LDO
JAV
HOK
MCA
CBO
CSE
WHX
CIN
CSU
BJA
RCO
LIN
BAR
FRO
HAK
SBW
–
–
–
–
Oreo
Oreo
Oreo
Whiptail
Whiptail
Whiptail
Whiptail
Whiptail
Whiptail
Whiptail
Whiptail
Whiptail
Other
Other
Other
Other
Gadoid
Gadoid
Gadoid
Gadoid
Gadoid
Gadoid
A requiem for the use of 20 log10 Length
421
Table 2. The linear regression equations and measures of goodness-of-fit for the hTSi–L (units, dB, cm) relationship at 38 kHz for each of
species for which we have sufficient data points ðn [ 30Þ. s.e., standard error. The t-value here is for a test that the slope is 20. Significance
indicates a difference from the slope value of 20 (two-tailed test); ***significance level of p \ 0:001; *p \ 0:05; NS indicates p [ 0:05.
The overall regressions are significant at p \ 0:001.
Species
Black oreo
Ribaldo
Bollon’s rattail
Ling
Hake
Hoki
Smooth oreo
Ridge scaled rattail
Frostfish
Lookdown dory
Intercept (s.e.)
68.4
63.4
76.2
64.6
67.4
75.4
104.7
81.4
91.1
75.9
(2.7)
(1.8)
(6.9)
(2.2)
(3.6)
(2.2)
(3.6)
(1.8)
(1.9)
(2.0)
Slope (s.e.)
21.5
19.8
26.4
18.5
20.6
22.5
41.6
28.2
29.6
29.1
(1.8)
(1.1)
(4.2)
(1.2)
(2.0)
(1.2)
(2.4)
(1.1)
(0.9)
(1.4)
t-Value
Adj r2
0.9 NS
0.2 NS
1.5 NS
1.3 NS
0.3 NS
2.1*
9.2***
7.8***
10.4***
6.5***
0.60
0.91
0.31
0.84
0.79
0.58
0.88
0.93
0.92
0.94
DF
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
98
30
83
45
28
263
42
51
85
28
Figure 1. Morphotypes (oreo, whiptail and cod morphs) illustrated by fishes from the New Zealand fauna. Species representing each
morphotype are given in Table 1. Fish sizes are not to scale.
422
S. McClatchie et al.
It should be noted that the slopes obtained can be quite
different from those produced by geometric regressions
(Saenger, 1989).
The first step was to test the hypothesis that the slopes of
the hTSi–L regression of each deep-water species was
different from a value of 20. The analysis was limited to
species for which there were sufficient data (see degrees of
freedom in Table 2). A linear regression was fitted relating
hTSi to log10 L for each species in turn and a t-value was
calculated as (fitted slope-20)/standard error of fitted slope.
Significance was estimated from the t-distribution for the
two-tailed case, and deviation of the slope from a value of
20 was considered true if the p-value for t was significant.
Next, we examined whether the TS of deep-water fish
might be lower than shallow-living species because of their
smaller swimbladders. It has been suggested that deepwater fish using low-density oils, watery tissues and
reduced ossification to maintain buoyancy would need
smaller swimbladders (Marshall, 1979). Following this
idea, we investigated as to how the concentration of oil in
whole fish (Vlieg, 1988) varies with their weighted-mean
z) and with their swimbladder
depth of occurrence (X
surface area (Asb). For these analyses, we used swimbladder-modelling data for the New Zealand species on which
z was obtained
there were published data for oil content. X
from Anderson et al. (1998). To compensate for differences
in fish sizes, swimbladder surface areas were normalized to
fish length ðAsb =L2 Þ: Fish length was measured as fork
length, for species with forked tails, or total length in the
cases of whiptails and oreos. We plotted Asb =L2 as a
z and fitted a LOWESS smooth to the data to
function of X
detect any trend towards smaller swimbladder size with
increasing depth.
Results
Which fish deviate from the 20 log10 Length
relationship?
Of the species for which we have sufficiently large datasets
to fit hTSi–L regressions, five out of 10 had slopes that were
significantly different from a value of 20 (Table 2). Slope
values varied between 18.5 and 41.6, with the highest slope
estimated for smooth oreo. The species that deviated
Figure 2. Maximal acoustic cross-section rmax in relationship to fish length L expressed in wavelength-normalized form ðrmax =k2 and
L=k) for species grouped into three morphological types (gadoids, oreos and whiptails). The species representing each morphotype are
given in Table 1. rmax is the maximal acoustic cross-section (m), where TSmax ¼ 10 log10 ðrmax Þ, L is fish length (m), and k is the acoustic
wavelength (m). The whiptails and oreo-like fishes were from deep-water.
A requiem for the use of 20 log10 Length
strongly from the 20 log10 L relationship (i.e. p \ 0:001)
included smooth oreo, lookdown dory, ridge-scaled rattail
and frostfish (Table 2; species in Table 1). Black oreo did
not deviate from the 20 log10 L relationship. This is odd
because black oreo are almost identical in shape to smooth
oreo. The slope for hoki was only marginally significantly
different from 20. The slopes for Bollon’s rattail, ribaldo,
ling and hake did not deviate significantly from a value of
20 at p \ 0:05 level. The unusually high slope obtained for
smooth oreo appears to arise from the differences in the
423
shape of swimbladders in small and large fish that warrant
further investigation.
Do deep-water fish have lower TS?
The wavelength-normalized universal graph (Love, 1971)
provides a convenient way of comparing the TS of deepwater fish with those of more shallow-living gadoids.
Normalizing by k shows length-dependent scattering at a
single frequency (Love, 1971). Twelve species of fish with
Figure 3. The relationship between swimbladder length and fish length for species from several families (Gadidae, Gempylidae,
Macrouridae, Merluccidae, Oreosomatidae). Species and morphotypes are listed in Table 1. Deep-water fish are denoted by open symbols
to differentiate them from shallower-living species, marked by filled symbols.
424
S. McClatchie et al.
oreo-like or whiptail morphologies (Figure 1), occurring
in deep-water off New Zealand, had significantly lower
rmax =k2 (and hence TSmax) than that of gadoids of the same
length at the same frequency (Figure 2).
Why do these deep-water fish have lower TS?
Relatively smaller swimbladder size is an important factor
explaining as to why the TSmax of the deep-water species,
we examined, was lower than that of gadoids. For fish
longer than 30 cm, swimbladder length is shorter in hoki,
macrourids and oreos compared with that in gadoids and
barracouta (Figure 3). Macrourids and merluccid hake
(hoki) with swimbladders that are relatively short compared
with that of their long whiptailed bodies, group together
with the oreos (Oreosomatidae) that are short-bodied with
egg-shaped swimbladders. The trend for ‘‘whiptails’’ and
oreos differs from that for gadoids (pollack, cod and
southern blue whiting) and barracouta. Among the species
examined, whiptails and oreos are common morphotypes in
deep-water. Despite differences in swimbladder morphology, the data show a consistent relationship between
swimbladder length and hTSi (Figure 4). However, it is
the surface area of the swimbladder, which has a rather
complicated relationship with fish shape, rather than its
length that determines the backscattering from it. The
Figure 4. The tilt-averaged TS in relationship to swimbladder length for species from several families. Species and morphotypes are listed
in Table 1.
A requiem for the use of 20 log10 Length
relationship between swimbladder area and hTSi was more
variable than the relationship between swimbladder length
and hTSi, suggesting that it would be incorrect to say that
deep-water fish have a lower hTSi because their swimbladders are smaller. In fact, as is discussed subsequently,
there is no strong evidence that deep-water fish in general
have smaller swimbladders. Also, the observed differences
in relative swimbladder size do not segregate cleanly into
deep- and shallow-living species, because some species like
hoki (Macruronus novaezelandiae) span depths from 50 to
1250 m, although their preferred depth is 650 m (Table 3).
The allometric slopes relating the log of swimbladder
cross-section to the log of fish length are steeper for hoki,
smooth oreo, frostfish and white rattail than for the
isometric case (Figure 5). In contrast, pollack and hake
did not deviate from the isometric case, i.e. the 20 log10 L
relationship holds. This indicates that the swimbladder
cross-section grows more rapidly, in relation to fish size, in
these deep-water fish than in pollack and hake, and suggests
a reason as to why deep-water fish do not follow the
20 log10 L relationship.
Are swimbladders smaller with depth?
The relationship between swimbladder size and depth was
investigated and the rationale as to why swimbladders might
be smaller at depth was looked into. No relationship was
found between the %oil content of the whole fish and their
z (Table 3). Also, no
weighted-mean depth of occurrence, X
relationship was found between the %oil content of the whole
fish and the mean surface area of the swimbladder corrected
for fish length ðAsb =L2 Þ, although a negative correlation was
expected based on the buoyancy considerations. Although a
z (Table 3), it
relationship was found between Asb =L2 and X
was weak and thus should not be over-interpreted. The
variability in Asb =L2 was also considerable owing to the
425
differences in swimbladder sizes between the individuals of
approximately the same length. The depth ranges over which
individual species are found is also wide (Table 3).
Does a shape correction help?
The TS data are now available for marine organisms with a
wide variety of shapes. Among fish, the diversity of forms
is very wide. Length measurements are dependent upon
shape as, for example, in the length of the body and tail.
This introduces a problem when comparing the length
dependence of TS for organisms of different shapes. One
way to adjust for different shapes is to calculate a shape
coefficient, rM, as a ‘‘volumetric length’’, defined as
Volume1=3 Length1 . Length is multiplied by rM to
compensate for the shape (Kooijman, 2000). Where the
volume is unknown, the shape coefficient may be estimated
from the wet weight, Ww, and the density, q, such that
rM ¼ ðWw =qÞ1=3 L1 : Comparing the length dependence
of frequency-independent echo amplitudes using rbs =k2
versus L=k for fishes of different shapes without correcting
rM, introduces a shape-related error of unknown magnitude. The same problem would arise if length-normalized
TS ¼ TS=L were calculated for fish of different shapes. To
test whether shape correction merges the distinct regressions for different morphotypes, the lengths of pollack,
oreos and hoki were corrected using shape coefficients
calculated with respect to fish length and the data were
plotted on a modified universal graph (rbs =k2 versus L=k).
Weights were obtained from length–weight regressions,
and densities were assumed to be close to seawater. It was
found that the shape coefficient as calculated in this study
did not provide sufficient correction to narrow the gap in
the hTSi–L relationship between gadoid and deep-water
whiptails and oreos. Shape correction appears to be a more
complicated matter than was presumed.
Table 3. A comparison of the swimbladder surface area and the whole-fish oil content (Vlieg, 1988) for fish species inhabiting different
z is the weighted-mean depth of occurrence for adults and the depth ranges are the approximate 5%
depth ranges off New Zealand. X
quartiles of the depth distributions for adult fish (Anderson et al., 1998). Asb =L2 is the swimbladder surface area normalized to the square
of fish length. The species were listed only if oil-content data were available and so were a subset of species used in swimbladder
modelling (Table 1). NA indicates data not available.
Common name
Orange roughy
Black oreo
Smooth oreo
Javelinfish
Frostfish
Lookdown dory
Barracouta
Hake
Southern blue Whiting
Hoki
Ridge-scaled rattail
Red cod
Ling
Species
Hoplostethus atlanticus
Allocyttus niger
Pseudocyttus maculates
Lepidorhynchus denticulatus
Lepidopus caudatus
Cyttus traversi
Thyrsites atun
Merluccius australis
Micromesistius australis
Macruronus novaezelandiae
Macrourus carinatus
Pseudophyycis bachus
Genypterus blacodes
z (range) m
X
1112
924
1101
629
237
511
182
665
503
651
1164
250
481
(650–1500þ)
(550–1250)
(600–1500þ)
(200–1200)
(50–550)
(250–850)
(0–450)
(250–1100)
(250–700)
(50–1250)
(600–1500þ)
(50–500)
(50–850)
Asb/L2
Oil (range) %
X
NA
0.0291
0.0146
0.0132
0.0119
0.0758
0.0260
0.0322
0.0210
0.0134
0.0192
0.0341
0.0341
17.6
7.5
5.7
5.4
5.4
4.9
4.5
4.1
4.1
2.5
2
1.8
1.5
(16.2–18.1)
(1.4–20.7)
(2.7–9.1)
(3.4–7.9)
(3.4–9.7)
(2.4–7.0)
(1.8–10.1)
(2.4–5.7)
(2.2–5.1)
(2.4–2.8)
(1.5–2.2)
(1.3–2.6)
(1.1–2.5)
Figure 5. The allometric relationship between a measure of swimbladder cross-section and fish size (total fish length for hoki and smooth oreos, or fork length for hake, Merluccius australis,
and pollack, Pollachius pollachius). The heavy solid line in the lower panel is the isometric relationship (y ¼ aWb , where b ¼ 1). Curves are plotted in the lower panel only for species with
slopes significantly different from b ¼ 1 ðp \ 0:05Þ. Species codes in the legend are given in Table 1.
426
S. McClatchie et al.
A requiem for the use of 20 log10 Length
427
Discussion
Acknowledgements
The results from the swimbladder-modelling data showed
that five of the 10 species did not conform to the 20 log10 L
relationship. How general is this result? McClatchie et al.
(1996a) reported the slopes and the 95% confidence intervals on the slopes of the TSmax–L regressions for 26 species.
Of these 26 slopes, 19 had confidence intervals indicating that the slope did not fit the 20 log10 L relationship.
This suggests that many deviations from the 20 log10 L
relationship will be found as more data are collected on
hTSi–L relationships for a wider variety of species.
The idea that swimbladders of mesopelagic fish are,
in general, smaller than those of more shallow-living species was advanced by Marshall (1979). He did not provide empirical data to support the claim, but relied on
calculations of the volume of air in the swimbladder that
would be required to provide neutral buoyancy (HardenJones and Marshall, 1953). Koslow et al. (1997) repeated
the claim for small swimbladders when trying to explain
observations of lower-than-expected TS of mesopelagic fish
calculated from the regressions of Foote (1987, Table 2, pp.
983).
However, the generalization that deep-water fish have
smaller swimbladders, and hence smaller TS, is not well
supported by the evidence presented in this study. Nevertheless, it appears to be true that the TS of some deep-water
fish is smaller or, more accurately, that the TSmax of deepwater fish of the same size at the same frequency is lower
than that of shallow-living fish. The explanation for this
phenomenon can reasonably be attributed to the peculiar
morphology of the deep-water fish, mainly whiptails and
oreo-type forms, which were examined. These morphotypes
are among the commonest in our deep-water (600–1500 m)
fish fauna. It is not claimed, however, that all the deep-water
fish have lower TS. Another consequence of this un-cod-like
morphology is that the scaling of the TS–length regression
is different and deviates from the rule of scaling by L2. It
would seem that the differences in relative swimbladder size
are more clearly related to morphology than to the depth.
A challenge remains to explain fully as to why the hTSi
of deep-water fish are lower. It has been shown that the
difference is partly due to morphology. How the allometry
of growth in swimbladder length, swimbladder crosssection and fish length combine to affect the TS of deepwater fish compared with other species is a subject that
could be explored in the future work. The differences
observed in this article show that gadoid-like hTSi–L
relationships cannot be extrapolated to these deep-sea fish.
It would seem that whenever new TS data are collected, the
empirical TS–length relationship should be established
rather than a priori fitting the 20 log10 L relationship to the
data. Authors of hTSi–L regressions should also state as to
what kind of regression they used, as the slopes can be quite
different depending on the least-squares minimization
applied.
Preparation of swimbladder casts was performed with
impressive dedication at sea and in the laboratory by Paul
Grimes and Alan Hart. We thank Brian Bull for guidance
with the statistical analyses and Richard Barr for a helpful
review of an early draft. We thank Lars Rudstam and Ian H.
McQuinn for their constructive reviews on behalf of the
journal. This work was funded in part by NZ Ministry of
Fisheries project code OEO200001.
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