Organism
or Structure

Geometric
Form or Measurement

Zooplankton 
Fluidfilled
sphere; Fluidfilled cylinder; Bent fluidfilled cylinder 
Fish
Body 
Gasfilled
sphere; Array of point scatterers 
Fish
Swimbladder 
Gasfilled
spherical bubble; Gasfilled spheroid bubble; Gasfilled cylinder

Whole
Fish 
Gasfilled
swimbladder; Gas and fluidfilled cylinders 
Empirical
Models 
Literature
review; Caged; Tethered; In situ; Statistical 
Simple geometric
shapes (e.g. sphere) regularly used in acoustic modeling efforts
do not realistically represent fish body and swimbladder anatomy.
To illustrate by example, here is a line drawing and corresponding
lateral radiograph of an Atlantic cod (Gadus morhua).
The Kirchhoffray
mode model represents the culmination of several backscatter modeling
efforts. Foote (1985) and Foote and Traynor (1988) used the HelmholtzKirchhoff
integral to develop an accurate and elaborate method to estimate
backscattered sound from fish. This approach was simplified by Clay
(1991; 1992) who incorporated Stanton's (1989) finite bent cylinder
equation and fluid or gasfilled cylinders to model fish backscatter.
Clay and Horne (1994) combined these approaches to model backscatter
by representing the fish body as a contiguous set of fluidfilled
cylinders that surround a set of gasfilled cylinders representing
the swimbladder.

Using
radiographs like the cod image above, lateral (i.e. side) and
dorsal (i.e. back) silhouettes of the fish body and swimbladder
are traced, scanned, and digitized. c
is the angle of the swimbladder relative to the longitudinal
(i.e. sagittal) axis of the fish. Normal resolution of the cylinders
is 1 mm. 
Backscatter
from each cylinder is estimated using a low mode cylinder solution
and a Kirchhoffray approximation (ka>0.2). Backscattering crosssections
from each finite cylinder are summed over the whole swimbladder
or body and then added coherently. The model calculates backscatter
as reduced scattering lengths, a nondimensional linear unit. Reduced
scattering length (RSL) is converted to the more familiar target
strength (TS) by:
TS = 20 log
(RSL) + 20 log (L)
For
any digitized fish, we use the KRM model to estimate backscatter
as a function of fish length, wavelength (i.e. speed of sound in
water/acoustic frequency), and fish tilt. Results from the model
can be reported for the swimbladder, body, or the whole fish to
show the contribution of the body parts to the total backscatter.
Model results
can be combined to summarize backscatter characteristics of a single
fish. A backscatter response surface plots reduced scattering length
as a function of fish aspect (q) and
a ratio of fish length (L) to acoustic wavelength (l).
Below is a backscatter response surface for an Atlantic cod.
The dependence
of echo amplitude on aspect angle is low at low L/l
values. As fish length or acoustic frequency increases, the influence
of fish aspect on echo amplitude increases. Since maximum backscatter
occurs when the top surface of the swimbladder is parallel to the
transducer and corresponding incident wave front, maximum backscatter
occurs at 85 degrees with the fish tilted slightly head down. The
influence of fish aspect increases as L/l
increases. The response surface becomes quasisymmetrical as q
deviates positive or negative from 85^{o}. Along the fish
length to acoustic wavelength axis, if fish length is kept constant
then higher L/l values correspond to
higher acoustic frequencies. Keeping frequency constant illustrates
the effect of changes in fish length. The periodic peaks and valleys
along the maximum backscatter ridge correspond to constructive and
destructive interference between the swimbladder and body.
Component backscatter
plots and backscatter response surfaces can be modeled for any species.
Tilt angles, lengths, and frequencies are chosen to reflect the
species and behavior of interest. You can model your own backscatter
component plots and response surface using our web based interactive
program KRMCompare.
We have expanded
the model to include backscatter calculations as a function of fish
roll. This is important as fisheries sonars are insonifying fish
aggregations at angles other than 90 degrees incidence (i.e. looking
downward). Be sure to see our model
visualizations of threedimensional fish backscatter and model
your own.
Cited
References 
Clay,
C. S. 1991. Lowresolution acoustic scattering models:
fluidfilled 

cylinders and fish with swimbladders. The Journal of the
Acoustical Society of America 89: 21682179. 
Clay,
C. S. 1992. Composite raymode approximations for backscattered


sound
from gasfilled cylinders and swimbladders. The Journal
of the Acoustical Society of America 92: 21732180. 
Clay,
C. S. and J. K. Horne. 1994. Acoustic models of fish:
The Atlantic 

cod
(Gadus Morhua). The Journal of the Acoustical Society
of America 96: 16611668. 
Foote,
K. G. 1985. Ratherhighfrequency sound scattering by
swimbladdered 

fish.
The Journal of the Acoustical Society of America 78: 688700. 
Foote,
K. G. and J. J. Traynor. 1988. Comparisons of walleye
pollock 

target
strength estimates determined from in situ measurements
and calculations based on swimbladder form. The Journal
of the Acoustical Society of America 83: 917. 
Stanton,
T.K. 1989. Sound scattering by cylinders of finite length.
III. 

Deformed
cylinders. The Journal of the Acoustical Society of America
86: 691705. 

Relevant
Publications 
Clay,
C.S. and J.K. Horne. 1994. Acoustic models of fish: the
Atlantic 

cod
(Gadus morhua). The Journal of the Acoustical Society
of America 96: 16611668. 
Horne,
J.K. and C.S. Clay. 1998. Sonar systems and aquatic organisms:


matching
equipment and model parameters. Canadian Journal of Fisheries
and Aquatic Sciences 55: 12961306. 
Horne,
J.K. and J.M. Jech. 1999. Multifrequency estimates of
fish 

abundance:
constraints of rather high frequencies. ICES Journal of
marine Science 56: 184199. 
Jech,
J.M. and J.K. Horne. Three dimensional visualization
of fish 

morphometry
and acosutic backscatter. ICES FAST working group
manuscript. 

