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Full text of "The probable distribution of whales as false sonar targets in the North Pacific Ocean by analysis of whaling data."

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 C A 

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) : 

C m 

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 mortality 5 , 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. 

4 An 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 



cH.°1 



Pk 



vO 


vO 


to 


vO 


o 


o 


cti 


00 


CO 


to 


o 


1—1 


\o 


to 


CM 


•* 


I— 1 


1— i 


I— 1 


I— 1 



a 
o 
as 

H 



CQ 
< 



o3 
0) 



C 
•H 



4-» 
O 



o 


CM 


to 


CTi 


■«* 


00 


o 


o 


r^ 


i-H 


LO 


Tf 


o 


CM 


o 


t— 


CM 


CM 


o 


<tf 


LO 


cn 


rH 


o 


o 


1—1 


i— 1 


r-H 


r-H 


\D 



to 
I-H 

00 



r-- 


oo 


o 


00 


to 


to 


i-H 


CTi 


CTl 


r-H 


CM 


o 


i—t 


to 


<tf 


o 



o 
o 
o 
o 



to 

o 

LO 

to 



CM 

o 
oo 
to 



CTl 
00 



lo 

CM 



to 



CM 



CM 



to 



«*■ 


LO 


to 


r-. 


00 


o 


to 


^r 


\D 


to 


CT) 


i— 1 


o 


CM 


to 


to 


l»- 


o 


00 


r^ 



O 

W 



o 
■p 

u 



to 

LO 



CM 

00 

o 






LO 

to 

CM 



CTl 
O 
CTi 



00 


CM 


CM 


r— 1 


r~- 


CTi 


r~- 


r^ 


CM 


\D 


CM 


r^ 


rH 


O 


\D 



u 



u 


vD 


r-. 


OO 


CTi 


o 


vO 


vO 


vO 


vO 


r^ 


a 


CTi 


CTi 


CTi 


CTi 


CTi 


>H 


i-H 


i-H 


i-H 


i-H 


i-H 



14H 
O 









U 






3 






rt 






.— 1 






0) 






03 






>H 






> 






•H 






g 






•P 






s 






^ 












o 






X 






MH 






Xi 






m 












LU 






■M 






+-> 






^ 






•H 






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 


O 


O 


c 






fH 




m 


2 


o 






Q> 


<4H 


m 




•H 


00 




CU 


O 


w 


M 


■M 


*fr 


00 








C 


03 


CM 


CTl 


X 


o 


i-H 


•H 


i-H 


o 


O 


o 


•H 


03 


X 


3 


• 


o 


■M 


■P 


+-> 


V) 


PL, 


\D 


i-H 


rt 


oj 


O 


•H 


o 






U 


OS 


E-i 


tL, 


Q- 


II 


II 


II 


II 


II 


II 


1 


or 


UJ 


+-> 


X 


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 



X l + 2X 2 + 



+ 2X t-l + X t 



(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 





1.0000 


1 


.9984 


2 


.9892 


3 


.8768 


4 


.8227 


5 


.7438 


6 

7 
8 


.6208Q r 

• 4672 Qo,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 

•3985Q t +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 

N t S q 

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: 

X III = X M27 + X M28 + '•• + X p 28 

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 


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1 




2 
1 


1 

2 


2 
1 


1 


1 
2 
2 


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2 


1 
5 


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1 
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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 


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1 

3 
2 


1 
1 

1 

2 


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1 


1 


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3 


3 


1 


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1 


1 


1 
1 
1 


1 
1 


2 


1 

1 
2 


2 


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1 


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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 


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1 


1 
1 


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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_t o)) 

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) : 



N 2 = 



(N 1 - 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 





(N 1 -C 1 )e- 


-m 


" C 2 




(1-W ) 

L_ 




and expected catch 








(Ni-C^e" 


-m 


C 2 




(1-W 2 ) 




2 



>-m 



qX 2 

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 



N l- C l " 



c 2 (i-w 



-m 



-(i-l)m 



t-1 



C S(l-W) c^sd-w.) 
/ . J J= 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. 

f C C Vl = c i + S "ST 

r 1 l i-2 A i 



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

qX 1 



C t " (N t " f } qX t = C t 1+ -^~ qX t N t 



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.—) _ q X t N t 



= d' 



Expanding and regrouping terms yields : 

d 2 = K + L + PN q 2 + SN 2 q 2 + U 2 
q l n 1 n Q 



where the coefficient: 



K = 2C. 



L- «<X ♦ 2sc Vt fco t . i 



P = 



R = 



S = 



2 K X A 
t t t 



-.[ SC A 2 A t + 2 , X t 2 A t f C C) tl j 

SX 2 A 2 
b t 

J IC t X t + SC t X t A t f(C) t _ 1+ S X t A t 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 + R n + 2SN,q = 

?N q q l n 



?a2 2 

££_ =L + 2q + PN, + 2RN+2SN,q = 



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 


"q M 


Expected 


n q ii 


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 


M q" 


Expected 


it q ii 


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 

U 

o 

+-> 

c 

•H 

to 

0) 


I ' 

1 1 
I' 
















I— 1 
o3 

X 


1 \ * I 








O 

c 

o 

•H 




1 


1 










1 * 


1 






03 

•H 


1 1 


L 






•H 
O 






UJ 




to 
•p 

o- 


V P* 






\ 


J-i 

o 
+-> 

03 

•H 








1 

\ 
\ 


2 






0) 

u 

•H 











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 




>> 

H 

<D 

-p 

•H 

o 

P 
•H 



H 
O 
> ^ 

o VD 

On 

On H 

O 

H ^ 
•H 

^ o> 
<U K 

P4 

to <D 
-P P 

cd <ti 



CD CO 

e a) 

3 cj 

H O 

o 

t> o 

•H 

C Cm 

O -H 

P> O 

M cd 

H CD 

P 43 

O -P 
O 

CNl <H 



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o 
o 

•H 

p 
,a 

•H 

p 
to 

•H 



e 
o 



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P< 
P 

CD 

-P 



J- 

•H 



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




BALEEN 




SQUARE 


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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 


:ATCKE r 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 













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BIBLIOGRAPHY 



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174 



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175 



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178 



INITIAL DISTRIBUTION LIST 

No. Copies 

1. Defense Documentation Center 2 
Cameron Station 

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 
Alexandria, Virginia 22314 

6. Dr. Ned A. Ostenso 1 
Code 480D 

Office of Naval Research 
Arlington, Virginia 22217 

7. Lt. Ronald D. Rinaldi 2 
U.S. Naval Destroyer School 

Newport, Rhode Island 

8. Mr. N. Rinaldi 1 
281 Hughes Avenue 

Pawtucket, Rhode Island 02861 

9. Lcdr E. Sipe 1 
USS TIRANTE (SS420) 

FPO New York 



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 



28 JVH ?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 

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