THE PROBABLE DISTRIBUTION OF WHALES AS
SONAR TARGETS IN THE NORTH PACIFIC OCEAN
BY ANALYSIS OF WHALING DATA

Ronald Daniel Rinaldi

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESIS

The

Probable

Distribution

of WhaL

2S

as

Sonai

• Targets

in the

North

Pacific

Oc

ean

by Analy

sis of

Whaling Data

by

Ronald

Danie]

. Rinaldi

•

Thesis

Advisor:

Eugene

D.

Traganza

March 1972

Appn.ov2.cL faoh. puhtic n.oX<iaMi; dis&UbuutLon antimitzd.

The Probable Distribution of Whales as False Sonar Targets
in the North Pacific Ocean by Analysis of Whaling Data

by

Ronald Daniel Rinaldi

Lieutenant, United States Naval Reserve

B.S., Georgetown University, 1963

Submitted in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE IN OCEANOGRAPHY

from the

NAVAL POSTGRADUATE SCHOOL
March 1972

7~h*

ABSTRACT

False Sonar targets present a serious unpredicted problem to U.S.
Navy ASW units. It is believed that planning and operations could be
enhanced by a forecasting capability for whale distribution. As a
possible solution to this problem, a modified form of the "Transect
Method of population estimation" is applied to whaling data to calculate
probable numbers of false targets per 1000 nautical miles of steaming
with a 1000 yard sonar range. Japanese and Russian whale fishery data
are analyzed by the "q" and Expected Catch methods of population dynamics
to obtain two independent estimates of the populations of fin, sei and
sperm whales. The mean of the two estimates is applied to the equation
along with a term for assumed ideal sonar conditions. The data is
calculated by ten degree square of latitude and longitude, north of 30°N,
and presented on Fleet Numerical Weather Central polar stereographic
charts for the months April through December. The number of false targets
attributable to fin, sei and sperm whales alone range from 1 to 63 south
of the Aleutian Islands and 1 to 30 off Honshu, Japan.

TABLE OF CONTENTS

I. INTRODUCTION 8

II. METHODS 11

A. THE "q" METHOD 22

1. The Effects of Migration 28

B. AGE DETERMINATION 29

C. EXPECTED CATCH METHOD 46

III. RESULTS 51

IV. DISCUSSION 64

A. DATA 64

B. AGE DETERMINATION 65

C. AREAS OF DISTRIBUTION 67

D. SONAR PROBABILITY FACTOR 70

E. INCLUSION OF OTHER WHALE SPECIES 71

F. WHALE SIGHTING PROGRAM 72

V. CONCLUSIONS AND RECOMMENDATIONS 73

APPENDIX A, RAW WHALING DATA 74

COMPUTER PROGRAMS 149

LIST OF REFERENCES 171

INITIAL DISTRIBUTION LIST 179

FORM DD 1473 180

LIST OF TABLES

I.. Illustration of Quantities Used in "q" Method 26

II. Sample Calculation of Population by "q" Method Using

Computer Program WHLPOP 24

III. Calculated Populations of Fin, Sei and Sperm Whales in the
North Pacific by the "q" and Expected Catch Methods,

Areas II - V 62

IV. Calculated Populations of Fin, Sei and Sperm Whales in the

North Pacific by the "q" and Expected Catch Methods, Area VI 63

LIST OF DRAWINGS

1. Illustration of Terms Used in Modified Transect Equation 13

2. Statistical Areas 16

3. Distribution of Fin Whales from Japanese Historical Catch

Records 1945-1962 (after Nishiwaki 1967) 17

4. Distribution of Sei Whales from Japanese Historical Catch

Records 1945-1962 (after Nishiwaki 1967) 18

5. Distribution of Sperm Whales from Japanese Historical Catch
Records 1945-1962 (Nishiwaki 1967) and American Catch Records
1760-1920 (after Nishiwaki 1967) 19

6. Composite Distribution of Fin, Sei and Sperm Whales in the

North Pacific 20

7. Block Diagram Representation of the "q" Method 27

8. Male Fin Whale Body Length vs Count of Ear-plug Laminations,

Area II 30

9. Male Fin Whale Body Length vs Count of Ear-plug Laminations,

Area III 31

10. Male Fin Whale Body Length vs Count of Ear-plug Laminations,

Area IV 32

11. Male Fin Whale Body Length vs Count of Ear-plug Laminations,

Area V 33

12. Female Fin Whale Body Length vs Count of Ear-plug Laminations,

Area II 34

13. Female Fin Whale Body Length vs Count of Ear-plug Laminations,

Area III 35

14. Female Fin Whale Body Length vs Count of Ear-plug Laminations,

Area IV 36

15. Female Fin Whale Body Length vs Count of Ear-plug Laminations,

Area V 37

16. Male Sei Whale Body Length vs Count of Ear-plug Laminations,

Area II - III 38

17. Male Sei Whale Body Length vs Count of Ear-plug Laminations,

Area IV 39

18. Female Sei Whale Body Length vs Count of Ear-plug Laminations,

Area II - III 40

19. Female Sei Whale Body Length vs Count of Ear-plug Laminations,

Area IV 41

20. Male Fin Whale "Age-Length Curve" 42

21. Female Fin Whale "Age-Length Curve" 43

22. Male Sei Whale "Age-Length Curve" 44

23. Female Sei Whale "Age-Length Curve" 45

24. Expected False Target Distribution - April 53

25. Expected False Target Distribution - May 54

26. Expected False Target Distribution - June 55

27. Expected False Target Distribution - July 56

28. Expected False Target Distribution - August 57

29. Expected False Target Distribution - September 58

30. Expected False Target Distribution - October 59

31. Expected False Target Distribution - November 60

32. Expected False Target Distribution - December 61

33. Migratory Paths of Fin, Sei and American Gray Whales in the

North Pacific 66

34. Distribution of Zooplankton in the North Pacific 69

ACKNOWLEDGEMENT

The author would like to express his appreciation to Dr. Dale W. Rice
for making available the basic raw data, Dr. K. Radway Allen for his
advice and kindness in supplying data and a computer card deck for the
Expected Catch Method, and especially to Dr. Eugene D. Traganza whose
many hours of patient assistance made this work possible. Appreciation
must also be expressed to Dr. IV. Cummings , Dr. C. Fiscus, Dr. J. Fish,
Dr. W. Evans and Lcdr C. Roberts for their kind assistance. This work
was supported, in part, by Fleet Numerical Weather Central, Monterey,
California.

I. INTRODUCTION

To the ASW unit, one of the most serious problems encountered is the
vast amount of time wasted prosecuting spurious or false sonar contacts.
Detection of a contact requires the detachment of a ship or ships from
the task group to investigate the threat; thereby diminishing the overall
capability of the screen in protecting the main body. Of the many
sources of false sonar contacts, the most troublesome and most difficult
to distinguish from actual submarine contacts are whales. It is, there-
fore, imperative that methods be developed to reliably predict areas of
high whale density which will serve to alert sonar operators.

Since the resumption of the Japanese whale fishery following World
War II, a great deal of interest has been generated in determining the
areas of whale abundance and seasonal fluctuations in whaling grounds,
resulting in a research effort in the sub-arctic North Pacific Ocean.
To date, research has proceeded in three major areas of interest:
geographical distribution of the major whale species, investigation of
biological and behavioral characteristics, and examination of the
oceanographic conditions of the whaling grounds. Each of the three
is essential in attempting to determine the factors which control whale
migration and defining favorable whaling regions.

The first major work on whale migrations (Kellog 1929) described the
primary paths of migration for blue (Balaenoptera mus cuius) , sei
(B. borealis) and fin (B. physalus) whales in the Pacific and Atlantic
Oceans, in general terms, based on all sighting and catch information
available at that time. Whaling grounds developed over the years and

were illustrated by Townsend (1935) by plotting catches according to
logbook records of American whaling ships for a period of one hundred
fifty nine years (1761-1920) . Other researchers have concentrated on
more limited areas of the North Pacific in response to the whaling
interests of their own country's territorial waters (Omura and Nemoto
1955; Clarke 1957; Sleptsov 1961; Tarasevich 1965, 1970; Nishiwaki and
Kasuya 1970; Kasuya 1971). General distribution charts of cetaceans in
the North Pacific were developed by Nishiwaki (1967) . Experimental
investigations were also conducted (and continue) by means of whale
marking (Shevill and Watkins 1966; Ivashin and Rovnin 1966).

Feeding habits and food preferences were investigated by observation
and investigation of stomach contents (Nishimoto, Tozawa and Kawakami
1952; Nemoto 1957; Nemoto 1959; Nemoto 1962; Nemoto and Kasu 1965) which
were correlated with migration cycles of baleen whales (Nemoto 1959) .
Schooling behavior in the feeding areas was examined (Nemoto 1964) and
compared with patterns of sexual segregation (Ohsumi 1966) .

Consideration of biological parameters has mainly been confined to
development of reliable methods of age determination by ear-plug lamina-
tion count (Nishiwaki 1952; Nishiwaki and Masaharu 1952; Nishiwaki et al
1957; Nishiwaki 1957; Nishiwaki 1958; Ichihara 1969, Ichihara 1963,
Ichihara 1964; Ichihara 1966) and dentine layer count in the case of
sperm whales (Nishiwaki 1958; Ohsumi 1963; Gambell and Grzegorzewska
1967) . Complimentary studies have focused attention on the determination
of average body proportions and growth rates (Mathews 1938; Omura 1950;
Nishiwaki and Ohe 1951; Nishiwaki and Hibiya 1951; Nishiwaki et al 1952;
Ohno 1952; Omura and Fujino 1954; Nishiwaki 1954; Fujino 1954; Omura and
Nemoto 1955; Fujino 1955; Nishiwaki 1956; Ohsumi 1958; Nasu and Masaki 1970)

Uda (1954), Uda and Dairokuno (1957), Uda and Suzuki (1958), Nasu
(1960), Uda (1962), Nasu (1963), Nasu (1966) have conducted oceanographic
studies with the objective of determining the exact physical parameters
which define favorable whaling grounds and correlating these with meter-
ological conditions (Uda 1956) e.g. fluctuations in sea surface temperature,
salinity and nutrients.

Leapley and Levenson (1969) have published the only study to date
evaluating the false target threat. This study plots contours of expected
numbers of false targets due to whales in the eastern North Atlantic ocean,
based on sighting records obtained over a five year period.

The objective of this thesis is to take advantage of these studies to
provide information on the number of whales which an ASW ship may expect
to encounter as false sonar contacts during operations in the North
Pacific Ocean. Instrumental to this objective is the application of a
modified form of the "transect method of population estimation" to whale
fishery data reported by Japanese and Russian whaling companies north of
30°N. This information may be applied by fleet units operating in the
North Pacific and by commanders planning operations in these areas.

10

II. METHODS

A recognized and frequently applied method of population estimation
for game, birds, and other animals, based on sighting observations, is
the Transect Method. This method uses the number of animals sighted in
a known distance, combined with the distance from the track of the
sightings to plot contours of relative abundance.

Mackintosh and Brown (1956) developed a modified version of this
method for use in determining the fin whale population of the Antarctic
whaling grounds. It is based on the number of sightings made while
steaming through a representative distance of an ocean area when no
estimates are made of the distance of the whales from the track of the
sighting vessel. This method may be expressed:

xt c u i -> Afnmi^j v n(whales)

N (whales) = , , . ,r / — nr x *■ i-

K J L(nmi)D(nni) P

where :

N = calculated total population of area A

2
A = area of ocean considered in square nautical miles, nmi

L = distance steamed through the area in nautical miles, nmi

D = lookout visibility in nautical miles, nmi

n = number of whales sighted in distance L

p = an empirically determined probability factor based upon
weather conditions, sea state and visibility.

Consideration of the behavioral characteristics of whales in feeding
and migration suggested the applicability of this method to evaluation
of false target threats. Nasu (1966) reports that feeding whales are

11

commonly found at depths less than fifty meters. The exception to this
would be sperm whales, which occasionally dive to great depths to feed on
giant squid (Heezen 1975; Okutani and Nemoto 1964). However, in the
North Pacific, they most frequently feed on schooling fish and therefore
can also be considered to be mainly distributed in the upper fifty meters.
Migration also takes place on or near the surface. Thus, although a sonar
ensonifies a volume of water, in the case of false targets attributable
to whales we may consider this ensonified region as an area. It is then
readily apparent that the searching sonar beam is analogous to the eye
of the lookout on a surface ship and this method may be applied to the
evaluation of false targets. In this concept, the sonar range is analogous
to the lookout's visibility.

Assuming ideal sonar conditions:

e , c r , . . -. n L(nm) x D(nm) x N (whales)
n (number of false targets) = P — — —

A (nm^)

where:

n = expected number of false targets

L = distance steamed in nautical miles

D = two times the sonar range in nautical miles

A = area of the oceanic region

N = calculated population of area A

P = probability factor determined by sonar conditions.
These quantities are illustrated in Fig. 1.

For the purposes of this study, ideal sonar conditions were assumed
and, therefore, P was taken to have a value of one; indicating that if
a whale is present it will be detected. Under actual operating condi-
tions this criterium is rarely met since the value will seldom be equal

12

Figure 1. Illustration of Terms Used in Modified Transect
Equation: A = ocean area, D = sonar range,

L = distance steamed through area A.

13

to one, but will be determined by the factors affecting the sonar range
in the particular area of operation.

In order to make clearer the techniques used and the sequence of
operations, the analysis scheme followed in this thesis is presented
diagramatically in the following flow diagram.

FLOW DIAGRAM

RAW DATA

q" METHOD

BODY LENGTH TO EAR-PLUG LAMINATIONS

LSQPL 2

BODY LENGTH TO AGE

AGE DETERMINATION

PROGRAM AGEPROP

PROGRAM

WHLPOP

POPULATION ESTIMATES

EXPECTED CATCH METHOD

ESTIMATES OF:

NATURAL MORTALITY
RECRUITMENT
FISHING MORTALITY

EXPECTED CATCH PROGRAM

POPULATION ESTIMATES

X

MEAN POPULATION ESTZiATE

MODIFIED TR1NSECT METHOD!

| FAI.SE TARGET PROGRAM]

EXPECTED FALSE TARGET DISTRIBUTION]

14

The raw data is taken from Russian and Japanese North Pacific fin
(Balaenoptera physalus) , sei (B. borealis) and sperm (Physeter catadon)
whale fishery catch results for the years 1966 to 1970. The total catch
was listed by ten degree square, effort (in catcher days) and length
frequency distribution. Two independent methods of population dynamics,
the "q" method and the expected catch method, ECM, were utilized to
estimate populations in selected geographical subdivisions shown in Fig.
2. For the purposes of this study, Brydes whales were included with sei
whales since they are distinct from sei whales only by the presence of
ventral grooves and otherwise have the same physical characteristics.

The age composition of the catch was determined and the data analyzed
by the "q" method (Allen 1966) , utilizing a computer program written to
apply this method. This program, designated WHLPOP (Appendix B) , yielded
the initial population estimate.

The second independent estimate of population size was calculated by
means of the "Expected Catch" method (Allen 1966) using values for natural
mortality and recruitment obtained from the reports of the International
Whaling Commission (IWC 1966-1970) . This method was applied using a
program provided by Dr. K. R. Allen, Fisheries Research Board of Canada,
Biology Station, Nanaimo, British Columbia. The program was modified to
conform to the IBM 360 located at the W.R. Church Computer Center, Naval
Postgraduate School, Monterey, California.

In accordance with procedures followed by the International Whaling
Commission (IWC 1968) the mean of the two population estimates was taken

The addition of whales to the hunted portion of the population by
growth from younger ages.

15

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and the average expected number of whales in each ten degree square, for
the period 1966-1970, was calculated by means of proportions as expressed
in equation (1) .

Number of whales in square (N ) = L_ x N. (1)

S CA

where :

N. = estimated mean whale population in the selected area by "q"
and ECM for the five year period 1966 to 1970.

C = average total catch in the ten degree square over the five
years.

C. = average total catch in the selected area 1966-1970.

Similarly, the average number of whales present per month in each
ten degree square was calculated by equation (2) :

Cm

Number of whales per month (N ) = _ x N (2)

F m c s

s

where :

C = average total catch in the month
m

C = average total catch in the ten degree square
N = population of the square calculated in equation (1) .
Historical records of Japanese whale fishing (Figures 3-5) for the
years 1945 to 1962 (Nishiwaki, 1966, 1967) were combined with studies of
migratory cycles and distribution by Nishiwaki and Kasuya (1970) and
historical catches (Townsend 1935) . This was done to determine areas of
distribution for fin, sei and sperm whales. From these, a composite area
chart was developed, Figure 6, showing where whales could be encountered
as false targets. In areas where no historical geographical data was
available, i.e. Russian fisheries in squares M28-30 and N27-30 (Figure 2),

21

a uniform distribution of the calculated average whale population per
month was assumed over the entire ten degree square. The number of
whales per one thousand miles steaming with a 1000 yard sonar range was
then calculated using the modified form of the Transect Method of popula-
tion estimation described earlier. This was then plotted on Fleet
Numerical Weather Central polar sterographic charts (Figures 24-32) .

A. THE "q" METHOD

Whaling in the North Pacific produces data which is highly variable,

2
particularly in the measure of catch per unit effort. This variation is

produced primarily as a result of the smaller effort employed, as compared

to the Antarctic fishery, and the exploratory nature of the fishing effort

to develop new whaling grounds. Methods utilized in population estimation

must therefore be designed to normalize the data in order to give reliable

estimates even in the presence of this high variability. One such method

is the "q" method.

The basic assumption of the "q" method is that the ratio between the

instantaneous fishing mortality rate, F, and the total fishing effort,

X, is constant, i.e.

q = instantaneous fishing mortality _ constant (3)

fishing effort

Using the pooled data for as many years as possible, an estimate of "q"
is obtained and the population computed by dividing the catch per unit
effort, C/E, by q. In this method a base year is selected in which it
is assumed that the population structure is determined by natural
mortality and that recruitment has been constant from year to year.

2
The total catch of whales, in numbers, divided by the effort

required to produce the catch (equation 4) .

22

The essential features of this method are:

(1) A single year group is followed throughout to avoid the effects
of recruitment.

(2) The relative abundance of the selected year or age group is
compared in each succeeding year with the base year^, where it is assumed
that the age structure is unaffected by exploitation. Thus, the population
structure by ages is determined by natural effects with no deaths due to
fishing.

(3) Estimates of the total fishing mortality5, for all age groups,
and the instantaneous fishing mortality of the specified age group are
obtained for increasing periods of years. Thus the effects of data
fluctuations due to seasonal variation are minimized. These estimates
are then divided by the total effort over the same periods to obtain a
mean estimate of "q," table II.

(4) The effort expended in the whale fishery by different size
catchers with varying endurance is standardized by multiplying catcher
days by vessel tonnage and dividing by one thousand, i.e.

Effort = Catcher days work X catcher tonnage ^

1000 L J

3
The portion of the population consisting of all whales of a

specified age and older.

4An arbitrarily selected year in which the population is assumed
to be affected by natural effects only with no deaths attributable to
the effects of man. This year is used as a reference.

The ratio of the number of deaths to the total number of whales in
the population, summed over the year.

23

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rH

O

\D

u

u

vD

r-.

OO

CTi

o

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vO

vO

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r^

a

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14H
O

U

3

rt

.— 1

0)

03

>H

>

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g

•P

s

^

o

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MH

Xi

m

LU

■M

+->

^

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03

G

<L>

=)

X

^

c

0)

•H

Oh

■P

X

*H

o

O

+->

<+H

o3

m

C_3

w

O

u

+->

i-H

X

^

o

rt

+->

<L>

o3

>-

u

C

b0

•H

•H

+->

13

V<

•H

O

>

<-H

■H

LM

Q

w

X

+->

X

•

•H

4->

c

t3

*H

3

o>

r-

o

4->

CTi

<+4

Jh

•

03

LO

<+4

0)

X

i-H

o

W

Cu

4->

3

o

•H

o

o

+->

X

•-H

.-H

•

•H

o

•

03

03

o

c

+->

+-)

4->

U

o

rt

h

M

II

u

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c

fH

m

2

o

Q>

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tL,

Q-

II

II

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II

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II

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or

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+->

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Ph

^la-

s'

24

The basic equation is:

F = In
t

'l,r

Qo,r+t-l v <h

Qt,r+1-1

Qo,:

i

(5)

where :

F = total instantaneous fishing mortality from year 1 to year t.
Q, = proportion of the catch in year 1 of whales of age r

(the first fully recruited age group) and older.
Q , = proportion of the catch in year t of this same year
group (i.e. if in the base year six year old whales are
examined then two years later the proportion of whales
eight years and older must be considered.
Qq r+t-i = proportion from the catch of the previously unexploited

stock of the same age groups.
Qq = proportion in the catch from the previously unexploited

stock of whales of age r and older.
(J)-. = catch per unit effort in year 1.
(J>£ = catch per unit effort in year t.
These quantities are illustrated in table I.

Since the estimate of F obtained in this method refers to the
decrease from the average population in one season to the average level
in a later year, the effort X may be written by means of integrating by
the Trapazoid Rule:

X. =1

Xl + 2X2 +

+ 2Xt-l + Xt

(6)

The total of the effort, E, expended from mid-season in one year
to mid-season in the next.

25

TABLE I

ILLUSTRATION*OF QUANTITIES USED IN "q" METHOD

Cumulative Proportions in Catch of Whales
Age (r) and Older (Russian Area V)

Age
Group

Base Year
1966 5

0

1.0000

1

.9984

2

.9892

3

.8768

4

.8227

5

.7438

6

7
8

.6208Q r

•4672Qo,r
.3776

9

.2880

10

.2105

11

.1337

Year 1

1967 5

1.0000

1.0000

.9991

.9808

.8926

.8043

.6810Q

.5024

.4125

.3230

.2734

.2242

l,r

Year 2
1968 5
1.0000 '
1.0000

.9987

.8876

.8309

.7238

.5712

•3985Qt +t>1

.3003

.2021

.1414

.0812

Year 3

Year 4

1969 5

1970 5

1.0000

1.0000

1.0000

.9960

.9969

.9799

.8220

.8336

.7604

.7568

.6581

.6468

.5260

.5228

.3591

.3527

.2737

.2692

.1888

.1862

.1287

.1359

.0686

.0861

*Total set of data are in appendix.

*0utput from Computer Program AGEPROP in Proportion of Each Age
Group in the Total Catch Converted to Cumulative Distribution

for Purposes of Illustration.

26

The error due to random effects on the fishery may be minimized by

extending the estimate of "q" from the base year to successive years and

taking the mean as the value for the area, Table II.

Thus:

T

T
v

q =

t sx,.

(7)

where T is the total number of years in the series.

An estimate of the mid-season recruited population is then given

by:

&t

NtSq

The "q" method may be explained more simply by the block diagram in
Figure 7.

FIGURE 7
Block Diagram Representation of the "q" Method
BASE YEAR YEAR 1 YEAR 2

i M

6+ 7+

H ii

M

T

6+

M

7+
J_

M = natural mortality

F = fishing mortality
The large rectangles represent the total catches in years 1 and 2.
Considering first the catch in year 2, the small rectangle, 7+, represents
the proportion of the catch in year 2 which is seven years old and older.

27

It can easily be seen that if there were no fishing or natural mortality
then the level for the seven year age group would include rectangles F
and M. Going back one year, the whales which were seven years old and
older in year two are represented by the six year old and older whales in
year one. Again we can see the represented effects of natural and fishing
mortalities. There are two unknowns, F and M, affecting the age structure
of the population. Thus, if an estimate can be made of one, then both in
combination, the other can be determined. To accomplish this end, the
ratio of the six year olds and older in year one, to the seven year olds
and older in year two (term 1 of the basic equation (5)), is compared to
the ratio of the seven year olds and older to the six year olds and older,
in the base year where only natural mortality has been affecting the age
structure of the population (term 2 of the basic equation (5)).

Finally, an adjustment must be made to compensate for the variation
in abundance from year to year. It is obvious that if the same amount of
effort is expended, the catch per unit effort in a year of greater
abundance will be greater than the catch per unit effort in a year of
lesser abundance. Therefore, the ratio of the C/E in year one to the
C/E in year two, provides a measure of the relative abundance in the two
years (term three of the basic equation (5)). Thus by comparing the
ratios between successive years with the ratio existing in the base year,
an estimate of the natural mortality is obtained and, since this is
assumed to be constant, the total fishing mortality may be obtained.

1. The Effects of Migration

As a result of the seasonal migration, in the case of baleen
whales, and the more general spreading in the case of sperm whales, there
exists a north-south age segregation of the population for a major

28

portion of the year (Ohsumi 1966, Nishiwaki, 1967, Nishiwaki 1966). Older
males penetrate further into the waters of the North Pacific followed by-
younger males who usually preceed the population front of the migrating
main body of whales. There then exists a high probability that an
examination of the age structure in any one ten degree square will not be
representative of the age structure, but will yield a disproportionately
high number of one particular age group. To eliminate the effects of
migratory segregation of the population, the age structure and effort are
considered for ten degree squares in geographic areas. These areas are
composed of twenty degrees of longitude extending from the equator to the
pole, Figure 2, thus considering the age structure at all latitudes.
Then, for example, for area III between 140°W - 160°W:

XIII = XM27 + XM28 + '•• + Xp28

and

C =C +C +...+C
III M27 M28 P28

Since the yearly totals of X, C, C/E, etc. are used in the estimation

of q and these yearly totals are the sum of the individual squares, "q"

may be applied to the individual squares to yield monthly estimates of

population. This approach, however, requires extensive hand calculations.

* B. AGE DETERMINATION

Application of the "q" method requires that the age groups of the
catch be analyzed with respect to the length-frequency distribution. The
relationship of length to age was determined indirectly from frequency
diagrams, Figures 8-19, relating body length to the count of ear-plug
laminations.

29

Figure 8. Male Fin Whale Body Length vs Count of Ear-Plug Laminations
(Compiled by Biologists at the Japanese Whaling Institute)

Numbers Indicate Totals of Observations
Area II

Body length (ft)
Laminations

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

1

2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
4.4
45

2

1

2

2

2

1

2

4

1

1

1

1

1

1

1

1

1

2

1

2

2

1

2

1

1

1

1

1

3

1

1

1
1

1

1

1

2

2

1

1

1

3

1

1

1

1

L 1

1

I 1

1
1

1
1

1

1

1

1

1

1

1
2

1
1

1

1

1

1

1
2

1

1
1

2

1

1
2

1
1

30

Figure 9. Male Fin Whale Body Length vs Count of Ear-Plug Laminations
(Compiled by Biologists at the Japanese Whaling Institute)

Numbers Indicate Totals of Observations
Area III

Body length (ft)53 54 55 56 5? 5g 5g 6Q 61 62 63 64 65 66 6? 6g 6g ?Q
Laminations

1

2

3

4

5

6

7

8

9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45

31

1

1

1

3

2
3

1
2

1
2

2

1

4

1

5

6

3

1

1

3

3

3

1

2

1

7

3

5

5

5

1

1

1

3

1

2

1

1

4

1

3

2

4

1

1

2

1

3

1

5

1

3

1

1

1

2

2

5

2

2

2

1

4

4

1

1

5

4

1

2

1

1

1

1

2

4

1

2

1

2

2

3

4

4

3

1

1

2

1

3

1
1

2

4
2

2
1

2
1

1

4

3

3

2

1

•

1

1

1

3
2
1

2
1
1

1
3

1
1

3
2
1

1

2

1

1
1

2

3

4
2

1

1
1

1

1

1

1

2

2

1

1

1

1

1

1

1

2

3

1

1

2

3

2

1

1

2

2

2
3
1

2
1
1

4
3

1
1
2

1

1

1

1

1

2

2

1

2

1

3
1

2
1

1

1

1

1

1

1

1
1

1
1

1
1

1
1

1
1

1
1
1

1

3
1

2

1
2
1

1

1

1

1

1

2

1

Figure 10. Male Fin Whale Body Length vs Count of Ear-Plug Laminations
(Compiled by Biologists at the Japanese Whaling Institute)

Numbers Indicate .Totals of Observations

Area IV

Body length (ft) M 55 $6 5? 5g 5g 6Q 61 62 63 ^ 65 66 6y 6g 6g
Laminations

1

2

3

4

5

6

7

8

9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45 4 111

32

2

2

1

1 10

5

3

3

1

1

4

3

3

3

4

5

1

10

6

7

4

9

4

3

1

1

4

5

15

8

8

3

4

1

1 3

7

9

11

8

4

1

1

2

3

7

2

6

4

1

2

1

3

3

7

3

2

2

2

2

3

8

6

5

4

3

2

1

1

2

2

5

5

6

1

1

1

1

1

4

2

4

2

3

2

1

1

4

6

2

3

1

2

1

1

3

1

1

2

5
1

1
4

1
1

1

1

2

2

3

2

2

1

1

3

1

5

3

1

1

3

2

1

1

1

2

5

4

1

1

1

3
1

2

2
2

1
1
1

3
3
3
2

1
3
1
3

2

2

1

1

3

4

1

1

1

1

1

1

3

1

1

3

2

1

3

1

1

1

1

1

1

4

2

1

2
1

1

1

1

4

2

1

1

2

2

1
1

1
3

1
3

3

1
1

1
1
1
1

1
1
1
1

1
1

3

1

2

2

1

1

1

1
2
1

1

1
1

1
2

4

1
1

2

2
5

1
1

4

2
1

1

3
2

1
1

1
2

3

1

1

1

1

1

1

1

1

1

1

2

1

2

1

1

1

1

1

1

Figure 11. Male Fin Whale Body Length vs Count of Ear-Plug Laminations
(Compiled by Biologists at the Japanese Whaling Institute)

Numbers Indicate Totals of Observations

Area V

Body length (ft)53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 7Q
Laminations

1

2

3

4

5

6

7

8

9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45

2

1

4 :

L 1

2

2

l :

L 3

6

4

2 ;

> 1

1

1

4

2

2 :

L 2

1

4

1

3 :

L 4

2

1

2

1

2 :

5 1

1

1

2 :

L 3

1

1

2

3

1

1

l :

L 1

3

1

3

1

1

1

5 4

1

1

1

1

L 2

1

2

2

1

1

1

1

l :
l :

L 2

1

2

2

1

1

1
1

L 1

3

3

1

1

1

l ;

2 2

L 2

L 2
1

L 2

1

1

2

1

2

1
3

2
2
2
1
2
4
4
1

3

6

2
3
1
1
3

1

1

3

3
1

2

3
2

2

1
3

2

1
1
1

2

1

1

l .

L 1

1

2
1

1
2

3
2

1

L 1

1

4

1

1

1

2

1

3

4

2

l

1
L 1

1

1

1

1

2
1

3
2

2

2

1

1

1
1

1

1

1

l

L
1

L

2
1

1
2

1
1

1
1

1

1

33

Figure 12. Female Fin Whale Body Length vs Count of Ear-Plug Laminations
(Compiled by Biologists at the Japanese Whaling Institute)

Numbers Indicate Totals of Observations

Area II

Body length (ft)54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 6g 7Q 71
Laminations

1

2

3

4

5

6

7

8

9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

31 !

32 1111

33
34
35
36

39
40
41
42
43
44
45

1

1

3

2

1

1

1

1

2

1

2

1 1

1

2

1
1
1

2
1
1

1

i

1
1

1

1

1

1

1

2
1

1

2
1
1
1

1

1

2

2

1
1

2

1
1

1
1

1
1

2
1
2
1

1
1

1

1
1

1
3
2

1

1

1
1

1
1

2
1

1
1
1
2
1

2
2
1

3

1

1
1
1

1

2
1

1

1
1

1

1
1

1

1
1

1

2

1

1 1

1

1

37 1111

38 i

1

1

34

Figure 13. Female Fin Whale Body Length vs Count of Ear-Plug Laminations
(Compiled by Biologists at the Japanese Whaling Institute)

Numbers Indicate Totals of Observations

Area III

Body length (ft)
Laminations

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45

2

3

1

1

2

1

1

2

5

2

4

2

1

1

3

1

1

1

1

2

2

3

1

2

1

2

5

2

2

4

4

1

1

1

5

5

2

2

1

1

2

2

5
1

1

1

5

1
2

1
1

1

3
2
4
4

2
1
5
3
2

1
1

1

1

1

2
3

1
1
1

1

1

1

2

2

6

4

2

2

1

1

1

1

1
2

4
1

3
2

3

2
2

1

1
1

1

2
2

2
3

2
3

2
2

4
3

1

2

1

1

1

1

2

2

2

1

3

1

2
1

1

2

2
1

1

1
2
2

3
2

1
5

2
1
1

1

1

1

1
1

1

1
1

1
2
1

3

2
1

1

4
2

2
1
5

2

1
2
2
1
2

1

2
1
1

3

1

3
2

1
1

1

2

1

1

1

3

3

3

1

1

1

1

1

1
1
1

1
1

2

1

1
2

2

1

1

2

1
2

3
1

1

1

1

2
1

1
2

1

1

2
1

1

1

2

1

2
1

1

2

1

1

1

1

35

Figure 14. Female Fin Whale Body Length vs Count of Ear-Plug Laminations
(Compiled by Biologists at the Japanese Whaling Institute)

Numbers Indicate Totals of Observations
Area IV

Body length (ft) 5g
Laminations

1

2

3

4

5

6

7

8

9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44>
45

36

4

1

1

1

3

1

2

3

7

6

4

8

9

6

4

1

7

8

5

8

8

7

3

1

1

1

3

9

13

12

7

9

7

3

3

4

2

2

10

4

9

5

8

2

2

1

1

3

5

8

6

5

3

2

2

1

1

1

2

4

4

9

5

5

3

4

6

1

2

1

1

2

2

5

5

4

1

2

3

2

2

1

1

1
1

1

5
5

2
3

3
4

3
4

3
3

1
1

1

2

1

1

1

2

3

6

3

5

3

1

1

2

1

1

1

2

1

2

1
4

2
3

2

2
1

2
3

2

3

3
1

1
1

2
1
2
1

2
2
4
1

6

2

4
1

1

1

2
4

1
1
1

2

1

1
1

1

1

2

1

5

2

3

3

1

1

1

1

1
1

1

1

1

1

1

1

2
1
1
1

1

1
2

1

1
2

2
1
2

1

1

1

2
1
2
2
3
3
1
1
1
1
3
1

2

1

1

1
1

2
4
5
1

3

1
1

2

2
1

2

2
1

1
3
5
1
2
2
1
3

2
3

3

1
1

2

3
2
3

1
2
4
1
1

1

2
1

2

1

5
3

1

1
1
1
1

2

1

1
3

2
3
1
1
1

2
2

1
1

2
1

2
2

2

1

1

1
1

1
1

1
1

Figure 15. Female Fin Whale Body Length vs Count of Ear-Plug Laminations
(Compiled by Biologists at the Japanese Whaling Institute)

Numbers Indicate Totals of Observations

Area V

Body length (ft)
Lamination

1

2

3

4

5

6

7

8

9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

1 1

4 4

1 1

37

Figure 16. Male Sei Whales Body Length vs Count of Ear-Plug Laminations
(Compiled by Biologists at the Japanese Whaling Institute)

Numbers Indicate Totals of Observations
Areas II-III

Body length (ft) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Laminations

1
2
3
4
5
6

7 1

8 1

9 1
10

11

12

13

14

15

16

17

18

19

20

21 1

22

23

24

25

26

27 1

28

29

30

31

32

33

34

35

36

37

38

39 1

40

41

42 1

43

44

45

38

1

1

1

1

1

1

1

2

1

1

1
1

1

1

1

1

1

2

2

1

2

2

1

1

1

1
1

1
2
1

1
2

1

3

1

2

1

1

1

1

1

1

1

2

1

1

1

2

1
1

2

1

2
2

1

1

1

1
1

1

2

3

1

1

1

1

3

1

1

2

1

1
1

1
2
3

1

1

1

2

1
1

Figure 17. Male Sei Whale Body Length vs Count of Ear-Plug Laminations
(Compiled by Biologists at the Japanese Whaling Institute)

Numbers Indicate Totals of Observations
Area IV

Body length (ft) 41 42 43 44 45 46 47 48 49 50
Laminations

1

2

3 1

4

5

6

7

8

9
10

11 1

12
13

14 1

15 . 1
16

17

18 1

19 1

20 1

21 1
22

23 12 1

24 1

25 1

26 11

27 112

28 11

29 11
30

31 1 1

32 11
33

34 1

35 1

36 1

37 12 1

38 11

39 1
40

41 11

42

43 1 1

44 1
45

39

Figure 18. Female Sei Whale Body Length vs Count of Ear-Plug Laminations
(Compiled by Biologists at the Japanese Whaling Institute)

Numbers Indicate Totals of Observations
Areas II-III

Body Length (ft)
Laminations 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

1

2

3

4

5

6

7

8 111

9

10 1

11 1 1

12 1 1
13

14 1

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29 1

30 1 2

31 1

32 1 1

33 13
34

35 12

36 1 1

37 1
38
39
40

41 1

42

43 1 1

44
45

40

1

1

1

1

1

1

1
1

2

2

1

1

1

1

1

1

1
1

1
1

1

2

1

1

1

1
1

1

1

2

1
1
2

1
1
1
1
1
1

1
1

1

1

Figure 19. Female Sei Whale Body Length vs Count of Ear-Plug Laminations
(Compiled by Biologists at the Japanese Whaling Institute)

Numbers Indicate Totals Of Observations

Area IV

Body length (ft) 3g 3g 4Q ^ ^ 44 45 ^ 4? 4g 4g 5Q $2 53 $4
Laminations

1
2
3
4
5

6 1

7 1 1

8 1
9

10 1

11 1

12 1

13 1
14

15

16

»

17

18 1

19 1
20

21

22 1

23 111
24

25 1

26 12 1

27 11

28 1
29

30

31 1

32

33 1

34

35 1

36

37

38 2

39

40 1 •

41

42 1

43 1
44

45

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A best fit curve was determined for each length lamination frequency-
diagram by the least squares method using the LSQPL 2 subroutine in the
W.R. Church Computer Center library. This subroutine has a maximum
capacity of one hundred points. For length- frequency diagrams having
more than this number of observations, the mean value of body length was
calculated for each number of laminations and the least squares curve
fitted to these points.

The individual curves obtained were then plotted, Figures 20-23,
and a mean curve determined by applying the known lengths and ages of
physical and sexual maturity to these curves. The final curve is
approximately exponential in form and agrees reasonably well with von
Bertalanffy 's theoretical growth equation (Mackintosh 1965, Laws 1959):

1 = L (l-e"k(t_to))

where :

1. = length at any age

L = mean length at physical maturity

k = a constant determined by the physiological characteristics
of the animal

A computer program designated AGEPROP (see Appendix B) was written
to calculate the proportion of each age group in the catch, based on
the age- length curves.

C. EXPECTED CATCH METHOD

The basic concept of this method is to obtain an estimate which mini-
mizes the sum of the squares of the differences between actual and
expected catches. The unknown parameters are the initial population
size, N, and the ratio, q, between the instantaneous fishing mortality,

46

F, and the fishing effort, X. Natural mortality is assumed constant,
and recruitment is obtained by examination of the age structure in
successive years. The method constructs the population in successive
years by taking the initial population, subtracting the actual catch,
subtracting mortality, and adding recruitment. This process is
repeated in successive years using each estimate obtained as the initial
population for the following year. The expected catches are then
obtained for each year by dividing the estimated average population
during the season by the estimated fishing mortality rate. The mortality
rate is obtained by multiplying q times the known effort. The method
assumes that catching, natural mortality and recruitment proceed
successively thereby simplifying the calculations. The essence of the
method is paraphrased here; for further detail the reader is referred
to the original paper (Allen, 1966).

Mathematically, letting C and X be catch and effort respectively,

then

N-, = initial population

-M

(N-j-C-j^e = survival to the next year

r

(N, - —1) qX = expected catch

Then the following year (No) :

N2 =

(N1 - Cpe'M
(1 - W)

where W is the number of recruits in the next year,

M is the natural mortality and

C is the catch in year 1.
1 '

47

survival to the beginning of the next season

(N1-C1)e-

-m

" C2

(1-W )

L_

and expected catch

(Ni-C^e"

-m

C2

(1-W2)

2

>-m

qX2

Continuing in this manner we can show that at the beginning of year t
the population equals:

N

-(t-l)M

t

% (1-W.)
i=2

Nl-Cl "

c2 (i-w

-m

-(i-l)m

t-1

C S(l-W) c^sd-w.)
/ . JJ=2 • 2zl

(t-2)m

A N -f(C)t 1
t 1 t ■

-(t-l)m

where: A = —
t +

S (1-W.)

• o 1

1=2

and

t-1 C.

fCCVl = ci + S "ST

r 1 l i-2 Ai

In year t the difference between the actual and expected catch is given
by:

qX1

Ct " (Nt " f} qXt = Ct 1+-^~ qXtNt

The sum of the squares of the differences, d, for the period year 1 to
year T equals :

48

T

2

t=l

qX
CJl.—) _qXtNt

= d'

Expanding and regrouping terms yields :

d2 = K + L + PN q2 + SN2 q2 + U 2
q ln 1 n Q

where the coefficient:

K = 2C.

L- «<X ♦ 2scVtfcot.i

P =

R =

S =

2 K X A
t t t

-.[ SCA2At + 2 , Xt2At fCC)tlj

SX2A2
b t

J ICt Xt + SCtXt Atf(C)t_1+ S Xt At f CC)t.!

where all terms are summed from t = 1 to t = T.

The normal equations for which the sum of squares is a minimum are
obtained by differentiating with respect to N. and q and setting equal
to zero . Thus :

ad 2

■Sg— = P + Rn + 2SN,q = 0

?N q q ln

?a2 2

££_ =L + 2q + PN, + 2RN+2SN,q = 0

Solving for N. and q gives

N =

LR - 2P

1 RP - 2SL

49

RP - 2SL
q =

4SU - R^
Once N has been estimated, the populations for subsequent years can be

estimated by:

N = A [ N - f(C) 1

t t L i t-ij

50

III. RESULTS

Figures 24-32 are average monthly estimates of the number of whales
which will be encountered as false sonar targets in 1000 nautical miles
of steaming with a 1000 yard sonar range, assuming ideal sonar conditions.
The values for expected false targets with other sonar ranges may be
obtained by multiplying these estimates by the sonar range in kiloyards.

It can be seen that the false target threat exists in three major areas:
a northern area extending across the North Pacific encompassing the Aleutian
Islands and the Bering Sea; a central area adjacent to the coast of Japan;
and a southern area in the Central North Pacific from 30°N-40°N which
broadens to 50°N in the area east of 160° W.

. The concentrations of whales as false targets in the northern region
gradually increases and spreads from west to east beginning in April with
the northern migration of fin and sei whales along the coast of Japan into
the Aleutian waters and Bering Sea. The maximum of sixty-three false
targets per 1000 nmi is reached in the southern portion of this northern
area in August. At this time, the feeding fin and sei whales are accompa-
nied by the maximum of male sperm whales which have migrated from the
equatorial regions. In subsequent months, the number of whales in the
northern region decreases and shifts westward as the whales migrate south-
ward to their winter grounds in warmer waters. This area is virtually
empty of whales from December to late March.

In the central region adjacent to Japan, the minimum concentration
also occurs during the period January through March. The population
begins to increase in early April due to the northward migration of fin

51

and sei whales and later with the more general spreading of male sperm
whales .

The central region exhibits a bimodal distribution; the first peak in June
is due to the northern migration of fin and sei whales and the second
maximum is in October and corresponds to the peak southern migration.
This second maximum of thirty whales per 1000 nmi is greater than the
first of 9 per 1000 nmi. This is because the southward migration of both
fin and sei whales closely coincides while the northern migration is
distributed over a longer period of time (Kellog 1929) .

The southern area shows its initial increase in May in the eastern
region due to the arrival of sperm whales along with the appearance of
some fin whales off the west coast of the United States. The population
of this region reaches a maximum in July, coincident with the passage of
fin whales into the northern region. Concurrently, young male, female
and calve sperm whales arrive in the Central North Pacific and spread
along 30°N. The sperm whale maximum occurs in Spetember and then de-
creases until, in November, this area is also virtually empty of whales.

The total estimated populations of fin, sei and sperm whales in the
North Pacific north of 30°N, for the years 1966-1970, are listed in
Table II. Results are provided for both the "q" and Expected Catch
methods of population dynamics. Areas III through VI contain estimates
based on combined Japanese and Russian data, while Area II contains
Russian data only. The blank squares represent areas for which the
particular method produced anomalous negative results and do not appear
in the table. Direct comparison, from the table, of the results gener-
ated by the two methods is difficult since the Expected Catch method
yields the population at the start of the season and the "q" method
yields the population at mid-season.

52

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61

TABLE III

CALCULATED POPULATIONS OF FIN, SEI AND SPERM WHALES IN THE
NORTH PACIFIC BY THE "q" AND EXPECTED CATCH METHODS

1966-1970
AREA II - V

Calculated

Populations

Fin

S

ei

Sperm

"q"

Expected

"qM

Expected

nqii

Expected

Method

Catch

Method

Catch

Method

Catch

AREA II

8423

1124

2183

21455

39913

8813

1120

4441

25404

40399

7188

1079

1890

22176

40461

4113

710

1303

16335

38939

5265

613

2934

25637

37191

Average population N.

6761

929

2550

22201

39381

AREA III

12402

1299

11017

5943

20383

4890

449

4268

5382

31568

5038

360

18778

5968

38222

.1948

264

28746

6219

20760

17500

4026

211

8551

6158

21316

Average population N.

5661

517

14268

5934

26450

17500

AREA IV

3589

2719

3517

9657

15734

3526

1966

9442

9872

21573

9836

1677

4637

9484

19297

22100

3662

1525

5251

10694

21267

27300

1991

1181

3319

11062

23208

Average population N.

4521

9068

5233

10153

20216

24700

AREA V

2757

4853

4579

17124

20177

5185

4554

8620

9601

14362

20724

4302

4034

8237

8437

11501

21416

4075

3614

4667

6071

9853

21970

2252

3460

4090

4856

15161

22679

Average p

opulation N^

3714

4103

6039

7241

13194

21392

62

TABLE IV

CALCULATED POPULATIONS OF FIN, SEI AND SPERM WHALES IN THE
NORTH PACIFIC BY THE "q" AND EXPECTED CATCH METHODS

1966-1970

AREA VI

Calculated Populations

Fin

Sei

Sperm

"q"

Expected

Mq"

Expected

itqii

Expected

Method

Catch

Method

Catch

Method

Catch

AREA VI

5221

1530

2875

19104

6340

1506

3986

5063

20807

3856

1053

7849

4906

17397

10382

863

3298

4399

13917

4448

835

5165

4368

20654

Average

population N.

6049

1151

4635

4684

■

18376

— ■ ■— ■■ ■ — .»- -

63

IV. DISCUSSION

A. DATA

The data used in this thesis were extracted from the basic raw data
reports prepared by Japanese and Russian whaling institutes for inclusion
in the International Whaling Statistics. In their basic form, these
reports contain, for each ten degree square, monthly listings of catch
by species, sex and catcher effort expended. An annual length- frequency
distribution by statistical area is also included. By using these
reports, information may be derived for monthly population estimates.
Whaling data presented in the International Whaling Statistics are or-
ganized by geographic area and seasonal totals and can only be used for
estimates of total annual population of the North Pacific.

A serious limitation exists in using whaling data for monthly popula-
tion estimates in that not all areas are fished in every month. The
whaling season is limited by regulation of the International Whaling
Commission to six months annually for baleen, and eight months for sperm
whales. This limitation is compensated for in part in that the whaling
fleet follows the migration of the whale herds and seeks out areas of
significant concentration.

A second problem which exists lies in the minimum size limitations of
the Commission which are 57 feet for fin (Balaenoptera physalus) , sei
(Balaenoptera borealis) , and sperm (Physeter catadon) whales. Thus the
length frequency distribution may not truly reflect the age composition
of the catch since certain ages, determined by length, are excluded from
the catchable population. This may bias the estimates of recruitment used
in the dynamical methods.

64

Third, due to the seasonal nature of the fishery, data relating to
the abundance of whales outside the normal season is virtually non-existent,
This results in a period of a year for which no population estimates may be
calculated. In this study, this period comprises the months of January,
February and March. However, examination of the migratory cycles of the
major whale types (Fig 33, Kellog 1929) indicates that very few whales
are found in these northern waters in the winter months. The few that
persist consist of old sperm and fin bulls which can withstand large
temperature extremes. As these whales are usually loners, they should
present no significant false target threat.

Finally, the data represents only the catch statistics for the
commercially exploited species, fin, sei, bryde's, sperm and, for earlier
years, humpback whales. The ramifications of this problem are discussed
further below.

B. AGE DETERMINATION

Age determination is important for development of accurate methods in
the fisheries biology of whales, and has been the subject of intensive
investigation. Of all the age characteristics studied, the accumulated
laminae in the ear plug of the external auditory meatus is believed to be
most valuable criteria for age determination of the catch (Ichihara 1966) .
The conical shaped plug consists of alternating layers of dark keratinized
cells and bright degenerated fatty cells which form at a rate of one to
two per year. It is believed that the formation of alternating layers is
in response to the biannual hormonal cycle and periodic changes of food
supply. It is assumed that vitamin A, plentiful food supply, and growth
hormones result in the formation of a bright layer. Vitamin A deficiency,
fasting and estrogen result in formation of a dark keratinized layer.

65

o

"* *■* - — - *■* ~

g^

•H

o

0,

J-' '

W

<

+J

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o

+->

c

•H

to

0)

I '

1 1
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I— 1
o3

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o

•H

1

1

1 *

1

03

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L

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0)

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66

The bright layer in the sexually mature whale is formed during the period
of feeding migration and the dark layer during a breeding migration.

The annual rate of formation of ear-plug laminations has been a source
of disagreement among biologists. Several of the possibilities offered
are:

1) one lamina formed per year

2) two lamina formed per year

3) two lamina formed per year until sexual maturity is reached and
one lamina per year thereafter

4) 1.5 lamina formed per year.

For the calculations carried out in this paper, age structure was based
upon an assumed rate of lamina formation of 1 . 5 per year for the sexually
immature whales. This figure was selected as the most probable estimate
in view of work done by Ichihara (1966) who verified it by three methods
and Oshumi (1964) who reached the same conclusion by investigation of
natural mortality rates. As the same standard is used for age determina-
tion of catches in successive years for comparison of year groups, any
error introduced is constant in the determined age structure, and is
insignificant in the final calculations. Allen (1967) calculated the
fin whale population of the North Pacific using three conversions from
ear-plug laminations to years (one per year, one per year to five years
and then two per year and two per year) . His results showed an average
difference of only two percent between the calculated populations.

C. AREAS OF DISTRIBUTION

A significant point in the consideration of whale distributions is
the identification of the specific areas of distribution. These areas

67

must be arrived at by examination of the catch statistics in conjunction
with the migratory cycles of the animals of interest. Whales migrate in
response to two factors :

1) location of areas containing specific foods in sufficient
concentration

2) the requirement for a suitable environment for the production and
rearing of young.

It can be seen that the composite areas of distribution, Figure 6, closely
agree with the zooplankton distribution, Figure 34. This is expected
since it is known that the abundance of food controls the limit of migra-
tion (Nemoto 1959) .

The oceanic structure is intimately associated with the production of
zooplankton and, therefore, determines the location of whaling grounds.
Vertical and horizontal temperature gradients and vertical stability of
sea water masses play an important role in the replenishment of micro-
nutrients, mainly phosporic and nitrogen salts. These salts are the
limiting factors in the production of phytoplankton, the food supply of
zooplankton. Therefore, the highest concentration of whales, and thus
the most troublesome false target areas, are those where cold and warm
water masses meet and the three basic conditions of light, nutrients and
oxygen are present (Ruud 1938, Nasu 1963). It should be noted that whale
schools do not concentrate in the rapid, easterly rapidly flowing zones
of warm water. Therefore, few whales are found in the west wind drift.

The accuracy of the areas of whale distribution (Figure 6) is
substantiated by the fact that in the 1969 season, only 183 whales out of
a total catch of approximately ten thousand were taken outside these areas
in spite of the efforts of scouting boats to locate new whaling grounds
(International Whaling Commission 1969).

68

>>

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69

D. SONAR PROBABILITY FACTOR

Ideal sonar conditions were assumed in this study; therefore, a value
of 1 was used for the sonar probability factor in the application of the
modified "Transect Method." Since the effective sonar range is a function
of the thermal structure, density and salinity characteristics of the
oceanic region, the sonar probability factor will vary seasonally with
the meteorological and oceanographic conditions.

ASW units operating in the North Pacific provide the best immediate
source of data to evaluate the sonar probability factor and accurately
determine the values associated with specific oceanic regions. A feed-
back system from operational units would expedite the resolution of this
problem.

It is known that the migration and feeding grounds of fin and sei
whales are a function of the sea surface temperature and the locations
of water mass fronts (Uda 1954, Omura 1955, Uda 1956, Nasu 1957, Uda
1957, Uda 1958, Nemoto 1959, Nasu 1960, Uda 1962, Nasu 1966). It may,
therefore, be possible to determine the sonar probability factor through
Fleet Numerical Weather Central's thermal structure analysis program.
Use of this program may provide prediction of the location of the main
body front of the migrating herds of whales, and determination of favorable
feeding grounds .

The prototype atlas produced by Leapley and Leavenson (1969) bases
prediction of false targets on sighting reports by aircraft and shipping.
This approach is limited by several factors. First, whale sighting,
especially from aircraft, is seriously hampered by adverse meteorlogical
conditions which reduce visibility. Second, the characteristic diving
behavior of whales may result in their being unobserved from a rapidly
moving platform, i.e. a survey aircraft. These factors could result in

70

a lesser number of whales being observed in an area than are actually
present. On the other hand, when whales are sounding and surfacing the
same whale may be counted more than once. This would result in an
erroneously high count for the area under observation. Finally, this
approach is limited in that no provision is incorporated for variations
in sonar conditions. It is felt that the approach taken in this thesis,
the analysis of whaling data, can provide more accurate estimates of the
false target threat if it is combined with oceanographic research to
determine the value of the sonar probability factor. Both can be sent
out to the fleet as a part of the Fleet Numerical Weather Central
forecast.

E. INCLUSION OF OTHER WHALE SPECIES

This thesis considers only the species of whales hunted and reported
on by the commercial fisheries, i.e. fin, sei, brydes (included under
sei) and sperm whales. Other whales of importance to the false target
problem in the North Pacific include: the Northern Right (Eubalaena
sieboldii) , Gray (Eschrichtius gibbosus) , Pigmy Sperm (Kogia breviceps)
and Humpback (Megaptera novae-angliae) . Further study and analysis of
the distribution and migratory patterns of these whales would provide
further refinement of the analysis method presented in this paper.

For example, a census is being conducted this year of the gray whale.
At Point Yankee, California, the southern migration reached a peak with
the passage of two hundred whales per day (Dr. Dale W. Rice, private
communication) . The daily count of the passage of the whales past a
specific point such as Point Yankee, would yield the distribution of the
whale population in migration. This distribution may be combined with
the known migratory swimming speed of four knots and the known migratory

71

paths along the coast of North America into the Bering Sea (Pike 1962,
Rice 1971) . Thus an estimate of the arrival times of the main body in
specific areas can be derived.

F. WHALE SIGHTING PROGRAM

In the Fall of 1971, Dr. Paul Sund of the National Marine Fisheries,
initiated a whale sighting program for the Pacific Ocean (Dr. C. Fiscus,
Marine Mammal Laboratory, Seattle, Washington, personal communication).
Under this program, officers of United States merchant ships are being
taught to recognize species of whales swimming through the water and
report whales sighted during transits of the Pacific Ocean. These sighting
reports will be card punched for computer processing and will provide a
valuable source of data on whale distribution patterns when a sufficient
quantity of data has been accumulated to give meaningful results.

72

V. CONCLUSIONS AND RECOMMENDATIONS

The analysis of commercial whaling data for the North Pacific provides
a useful method for estimating the false target threat in this area.

Studies should be undertaken to determine the values of the sonar
probability factor for those areas identified with significant whale
density. This may be accomplished by means of feedback reports from
operational units combined with Fleet Numerical Weather Central's thermal
structure forecast. These studies should also incorporate the results of
the new whale sighting program initiated by Dr. Paul Sund of the National
Marine Fisheries, in 1971.

73

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108

CATCKEP. DAYS x VESSEL TONNAGE 1070
JAPANESE EFFORT EXPRESSED AS — ~ xyfU

BALEEN

SQUARE

JAN

FEB

MAR

APR

MAY

J UN

JUL

AUG

SEP

OCT

N0\

DEC

M21

155

lUT

127

120

118

60

11

18

M22

M23

M24

M25

M26

M27

M28

M29

M30

N21NP

7

h6

51

U3

hU

3U

u

N210S

11

12

10

5

uu

N22NP

N220S

N23

97

59

101

3k

N24

-

85

150

28

28

N25

53

57

6

19

12

N26

98

lUU

26

92

59

N27

6

18

12

38

6

N28

70

50

63

N29

19

118

38

N30

P23NP

6

11

P23BS

22

P24NP

6

6

17

P24BS

28

33

P25NP

13

P25BS

37

P26NP

7

13

P26BS

U9

P27

25

P28

88

P29

51

32

109

— — ——————————— — — — 1 1

CATC'Zr BAYS x VESSEL TONNAGE 1970
JAPANESE EFFORT EXPRESSED AS r^—r ±y ' u

SPERM

SQUARE

JAN

FEB

>L\R

APR

MAY

J EN

JEL

AUG

SEP

OCT

NOV

DEC

M21

M22

M23

M24

M25

M26

M27

M28

M29

M30

N21NP

N210S

N22NP

N220S

N23

11

11

10

3k

N24

6

25

6

22

N25

18

6

19

13

N26

18

63

6

81

56

N27

12

38

6

N28

19

57

N29

12

38

N30

P23NP

6

11

P23BS

5

P24NP

P24BS

28

17

P25NP

6

P25BS

P26NP

6

P26BS

P27

13

P28

19

P29

32

32

110

T \ Ti A N"T" C T7 L"1 T7T7 /~>D T E

CATCHEF DAYS x VESSEL TONNAGE ic

)69

,EEN

JAPANLbL LrrUrCl LArivLoonj t\a

1000

BAI

SQUARE

JAN

FEB

MAR

APR

MAY

J UN

JUL

AUG

SEP

OCT

NOV

DEC

M21

177

188

1U9

12

12

102

59

38

M22

M23

M24

M25

M26

M27

M28

M29

M30

N21NP

1

3

5

65

65

56

10

11

N210S

N22NP

N220S

12

12

N23

157

188

108

N24

1U8

161

30

N25

19

75

106

N26

31

106

30

N27

6

58

23

N28

100

2li

N29

N30

P23NP

P23BS

P24NP

6

P24RS

6

P25NP

12

36

P25BS

P26NP

>*3

P26BS

P27

19

P28

13

P29

111

JAPANESE EFFORT E

v Dr v c

''Prn

l

:ATCKEr DAYS x VESSEL TONNAGE ]

969

ArKtbDcij i\o

i nnn

SPERM

SQUARE

JAN

FEB

MAR

APR

MAY

J UN

JUL

AUG

SEP

OCT

NOV

Dl C

M21

M22

M23

M24

M25

M26

M27

M28

M29

M30

N21NP

N210S

N22NP

N220S

N23

67

12

72

N24

*

80

72

30

N25

12

19

36

6

N26

19

25

18

6

N27

6

12

1+1

N28

2k

51

N29

102

N30

P23NP

38

P23BS

6

P2ANP

6

6

P24BS

13

25

P25NP

6

25

25

P25BS

6

P26NP

31

50

P26BS

P27

6

2U

P28

12

kl

7

P29

19

112

JAPANESE EFFORT t

>

V TV !* T C

■• r» i~" t^

catcher days x vessel tonnage i

.968

,EEN

Xrhhb^r.u no

1000

BAI

SQUARE

JAN

FEB

MAR

APR

MAY

J UN

JUL

AUG

SEP

OCT

N'0'\

L' : L

M21

„

182

180

151

156

106

77

U5

U9

M22

M23

M24

M25

M26

M27

M28

M29

M30

N21NP

8

30

36

70

76

53

13

N210S

6

N22NP

N220S

N23

96

210

138

N24

107

170

51

N25

9

N26

9

N27

51

N28

U3

N29

N30

P23NP

38

6

P23BS

P24NP

6

3U

P24BS

12

P25NP

17

P25BS

17

60

P26NP

9

26

P26BS

P27

3U

P2S

26

P29

113

JAPANESE EFFORT E

V'T) »r

CATC?

:ep DAYS x VSS

5EL T'-::>:ach 1968

lAruboLU rv.T

1000

SPERM

SQUARE

JAN

FEB

MAR

APR

MAY

J UN

JUL

AUG

SEP

OCT

N'0'\

u C

M21

M22

M23

M24

M25

me

M27

M28

M29

M30

N21NP

N210S

N22NP

N220S

N23

29

53

12

N24

23

5T

12

11

N25

51

35

N26

6

115

IT

N27

6k

12

N28

12

2k

N29

6

18

N30

P23NP

6

P23BS

P24NP

29

6

P24BS

23

35

6

P25NP

6

11

11

P25BS

6

6

P26NP

6

P26BS

P27

IT

k6

P28

P29

114

————————————

JAPANESE EFFORT E

V TDI*1 IT

CATCH"? DAYS x \'ESSEL TEENAGE

L967
1EEN

ArKtbm.D r\C5

1000

BAJ

SQUARE

JAN

FEB

MAR

APE

EAY

J UN

JUL

AEG

SEP

OCT

NO v

Di >..

M21

75

92

70

119

85

86

126

68

M22

M23

M24

M25

M26

M27

M28

>I29

M30

N21NP

1

7

31

32

73

79

21

N210S

N22NP

12

N220S

N23

26

60

N24

113

8U

77

N25

UU

8U

3U

N26

32

N27

N28

N29

N30

P23NP

208

P23BS

101

P24NP

58

38

P24BS

61

P25NP

6

6

12

P25BS

6

P26NP

93

P26BS

P27

hi

P28

29

P29

115

JAPANESE EFFORT E

V D E T C

CATCHER DAYS x "FSSEL TONNAGE

1967

Ari\Lb.^ i.u t\s

1000

SPERM

SQUARE

JAN

FEB

MAR

APR

MAY

J UN

J VI.

AUG

SUP

OCT

N 0\

.

M21

M22

M23

M24

M25'

M26

M27

M28

M29

M30

N21NP

N210S

N22NP

6

N220S

N23

11

N24

30

6

ll

N25

12

23

38

38

N26

2k

22

108

N27

hi

N28

N29

N30

P23NP

29

P23BS

33

P24NP

22

23

6

P24BS

16

22

50

P25NP

IT

16

11

P25BS

22

33

27

P26NP

3i+

P26BS

P27

^5

P28

kh

P29

116

■

JAPANESE EFFORT E

v v>'y y c

SATCKEF DAYS x VESSEL TANNAGE 1966

.ArhLb^uiJ r\3

moo

No separate effort data for sperm whaling in 1966.

SQUARE

JAN

FEB

MAR

A PR

MAY

J UN

JUL

AUG

SEP

OCT

NO'\

Dl C

M21

101

106

102

111

112

98

96

1*0

M22

M23

:i24

M25

M26

M27

M28

M29

K30

N21NP

9

12

30

U3

61

65

31

N210S

7

38

N22NP

t

N220S

N23

26

18

N24

15

15

N25

T

11

U2

26

N26

25

7

20

N27

N28

N29

N30

P23NP

HI

19

15

P23BS

11

29

P24NP

25

20

26

18

P24BS

11

37

133

102

13

P25NP

IT

20

133

uo

7

P25BS

11

63

63

126

P26NP

37

7U

33

37

P26BS

16

11

P27

15

U3

35

22

P28

292

95

105

P29

7

117

w

Q

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o

o

tO

LO

o

to

Eh
O
O

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CM

LO

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LO

o

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tO

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LO

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CO

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Oh
W

co

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BIBLIOGRAPHY

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178

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation Center 2
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Alexandria, Virginia 22314

2. Library, Code 0212 2
Naval Postgraduate School

Monterey, California 93940

3. Department of Oceanography 3
Naval Postgraduate School

Monterey, California 93940

4. Asst Professor E.D. Traganza 1
Department of Oceanography

Naval Postgraduate School
Monterey, California 93940

5. Oceanographer of the Navy 1
The Madison Building

732 N. Washington Street
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6. Dr. Ned A. Ostenso 1
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Office of Naval Research
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7. Lt. Ronald D. Rinaldi 2
U.S. Naval Destroyer School

Newport, Rhode Island

8. Mr. N. Rinaldi 1
281 Hughes Avenue

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9. Lcdr E. Sipe 1
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179

.

Security Classification

DOCUMENT CONTROL DATA -R&D

• Security c las silication o( title, body of abstract and indexing annotation must be entered when the overall report is classified)

originating ACTIVITY (Corporate author)

Naval Postgraduate School
Monterey, California 93940

2a. REPORT SECURITY CLASSIFICATION

Unclassified

2b. GROUP

3 REPOR T TITLE

The Probable Distribution of Whales as False Sonar Targets
in the North Pacific Ocean by Analysis of Whaling Data

4. DESCRIPTIVE NOTES (Type ol report and, inclusive dates)

Master's Thesis; March 1972

5. au THOR(S) (First name, middle initial, last name)

Ronald Daniel Rinaldi

6. REPORT DATE

March 1972

Bfl. CONTRACT OR GRANT NO.

6. PROJ EC T NO.

7«. TOTAL NO. OF PAGES

181

76. NO. OF REFS

115

9a. ORIGINATOR'S REPORT NUMBER(S)

9b. OTHER REPORT NO(S) (Any other numbers that may be assigned
this report)

10. DISTRIBUTION STATEMENT

This document has been approved for public release and sale;
its distribution is unlimited.

II. SUPPLEMENTARY NOTES

12. SPONSORING MILITARY ACTIVITY

Naval Postgraduate School
Monterey, California 93940

13. ABSTRACT

False Sonar targets present a serious unpredicted problem to U.S. Navy ASW units.
It is believed that planning and operations could be enhanced by a forecasting
capability for whale distribution. As a possible solution to this problem, a
modified form of the "Transect Method of population estimation" is applied to whaling
data to calculate probable numbers of false targets per 1000 nautical miles of
steaming with a 1000 yard sonar range. Japanese and Russian whale fishery data are
analyzed by the "q" and Expected Catch methods of population dynamics to obtain two
independent estimates of the populations of fin, sei and sperm whales. The mean of
the two estimates is applied to the equation along with a term for assumed ideal
sonar conditions. The data is calculated by ten degree square of latitude and
longitude, north of 30°N, and presented on Fleet Numerical Weather Central polar
stereographic charts for the months April through December. The number of false
targets attributable to fin, sei and sperm whales alone range from 1 to 65 south
of the Aleutian Islands and 1 to 30 off Honshu, Japan.

DD

FORM

t NOV 85

S/N 01 01 -807-681 1

1473 (PAGE1)

Security Classification

A-31408

ISO

Security Classification

k e v wo R OS

fhale Distributions

■alse Target Prediction

'opulation Estimation

•q" Method

Expected Catch Method

Transect Method

Sonar Probability Factor

>b,F,r„i473 "BACK.

lOIOI -807-6821

ROLE XT

181

Security Classification

» - 3 I

"Q JUN74

2275U

Thesis

R557
c.l

28JVH?4

c c'on of , 'e d!st.^.

RInaldi

The probable distri-
bution of whales as
false sonar targets in
the North Pacific Ocean
by analysis of whaling
data.

««?5«

134079

thesR557

The probable distribution of whales as f

3 2768 001 91342 9

DUDLEY KNOX LIBRARY