JULY 1982 

TESTING METHODS OF ESTIMATING 

RANGE AND BEARING TO CETACEANS 

ABOARD THE R/V D. S. JORDAN 

Tim D. Smith 

NOAA-TM-WMFS-SWFC-20 

U.S. DEPARTMENT OF COMMERCE 

National Oceanic and Atmospheric Administration 

National Marine Fisheries Service 

Southwest Fisheries Center 
NOAA Technical Memorandum NMFS 

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NOAA Technical Memorandum NMFS 

This TM series IS used for documentation and timely communication of preliminary results. imterim reports, or 

special purpose information and have not recetved complete formal revlew, editorial control. or detailed edltlng 

JULY 1982 

TESTING METHODS OF ESTIMATING 

RANGE AND BEARING TO CETACEANS 

ABOARD THE R/V D. S. JORDAN 

Tim D. Smith 

Southwest Fisheries Center 

National Marine Fisheries Service, NOAA 

La Jolla, California 92038 

NOAA-TM-NMFS-SWFC-20 

U.S. DEPARTMENT OF COMMERCE 

National Oceanic and Atmospheric Administration 

National Marine Fisheries Service 

Malcolm Baldrlge. Secretary 

John V. Byrne. Admintstrator 

Wllllam G. Gordon, Assistant Administrator for Fisheries 
PLACEMENT AND USE OF 25 POWER BINOCULARS 

BOARD THE R/V D. S. JORDAN DURING SIGHTING 

SURVEYS IN THE EASTERN TROPICAL PACIFIC. 
CONTENTS 

Page 

Introduction .................................................... 

Materials and Methods ........................................... 

Experiment 3. Angle to Sighted Cetaceans ................... 

Experiment 1. Range and Bearing to a Buoy .................. Experiment 2. Range and Bearing to Approaching Ships ....... 

Experiment 4. Reticle to Degree Conversion ................. 

Results 

Calibration of Methods of Estimating Range 

Shipboard measurements .................................. Reticle and range conversion ............................ 

Application of Methods .................................. Calibration of Methods of Estimating Bearing ............... 

Discussion ...................................................... 

Conclusions ..................................................... 

Acknowledgements ................................................ 

Literature Cited ................................................ 

4 

8 

12 

18 

25 

27 

29 

30 

i 
Table No. 

LIST OF TABLES 

Page 

1 Mean vi sua1 ly estimated distance, mean reticle 

measurement and radar range to buoy, with sample 

size (N), standard deviations (SD), and coefficient 

of variation (CV) of reticle measurements.. ............ 5 

2 Distance from top most reticle to each lower 

reticle in 25x binoculars, measured in the field 

of view at 53.1 m........................,.............. 11 

3 Wire angle, alidade angle, radar angle and radar 

distance to buoy recorded in Experiment l.............. 14-1 6 

4 Angular measurements (degrees) to bow of passing 

ships, with mu1 tiple replicates of the wire angles.. ... 21 

5 Reticle measurements (nunber bel ow horizon) to bow 

of approaching ships with radar measurements of 

distance. Means, standard deviations (SD) and 

predicted distances (D) with standard deviation 

(SD(D)) are given ...................................... 22 

6 Visually estimated and measured angles from bow 

to sighted cetacean schools............... ............. 23 

ii 
Fiaure No. 

LIST OF FIGURES 

Page " 

1 Mean visual estimates of distances to buoy versus 

distances measured by radar, with approximate 90% 

confidence i nterval s and 1 i ne denoting equal i ty shown.................................................. 6 

2 Mean estimated number of reticles at varying distance 

to buoy, with approximate 95% confidence intervals.. ... 7 

3 Diagram of re1 ationship among horizon, sighted 

object, observers' eye and ship height, labeling 

angles and distances needed in theoretical 

development (see text) ................................. 9 

6 

7 

8 

Angle (degrees) from top reticle to each lower 

reticle in 25x binoculars, with fitted regression 

line................................................... 10 

Predicted versus observed distances to buoy (Equation 7 

and Table l), with + 1 standard error (Equation 8) 

and the equality line indicated.. ...................... 

Re1 ati onshi p between radar angle and a1 i dade angle. .... 

13 

17 

Re1 ationshi p between angle measured from wire 

attached to 25x binoculars and bearing to buoy 

measured on radar...................................... 19 

Relationship between the estimated angle to the 

bow of approaching ships using a wire attached 

to the 25x binoculars and the angle as measured 

by radar. The equality line is shown .................. 20 

9 Angle to sighting measured by wire on binoculars 

versus visual estimated angle.. ........................ 24 

1 Oa Frequency of specific angles recorded without a 

measuring device as estimates of angle to sighted cetaceans.............................................. 26 

10b Frequency of specific angles recorded with a 

calibrated ring as estimates of angle to sighted cetaceans........................... ................... 26 

iii 
TESTING METHODS OF ESTIMATING RANGE AND 

BEARING TO CETACEANS ABOARD THE R/V D. S. JORDAN -- 

Tim D. Smith 

Southwest Fisheries Center 

National Marine Fisheries Service, NOAA 

La Jolla, California 92038 

I NTRODUCT ION 

There have been several attempts to apply 1 ine-transect density 

estimation theory to shipboard cetacean sighting data. The primary interest 

has been in obtaining absolute or relative estimates of the density of 

cetaceans. Line transect techniques use information on the distances at which 

cetaceans are sighted to account imp1 ici tly for vi sibil i ty 1 imitations. In 

general, a decreasing fraction of the cetaceans is detected with distance from 

the ship and its trackline. The rate of decrease of the probability of 

detecting cetaceans with distance varies with visibility conditions. 

Line transect theory was developed with the assumption that all of the 

objects or animals which are directly on the trackline being searched are 

detected. When sighting cetaceans from a ship, this assumption can be 

violated if some of the animals are missed because they are submerged, or if 

they simply are not seen as the ship approaches. An additional assumption 

made in line-transect theory is that the animals do not move away from the 

trackline prior to being detected. If either of these assumptions is 

violated, the nunber of animals sighted directly on the trackline will not be 

representative of the number which were actually on the trackline, and the 

distance to the animals will not be representative of the true distances from 

the track1 i ne. 

An important aspect of line transect theory is that the location of the 

sighted animals relative to the ship must be determined. Early developments 

of the theory assmed that the distance from the sighted object to the 

observer or to the trackline being traversed was determined without error. In 

practice aboard ships, the distance and the bearing to sighted cetaceans are 

determined at best inexactly, and with crude precision. 

If the assumptions of line transect theory are met, it is theoretically 

possible to obtain estimates of absolute abundance of cetaceans solely from 

shipboard sighting data. This has been attempted recently by Best and 

Butterworth (1980) and Horwood (1980) for southern hemisphere minke whales, 

using data from Japanese whale scouting vessels. These authors had 

difficulties in fitting line transect models to their sighting data and they 

specul ated on several possible viol ations of the theory's key assunptions. 
2 

Smith (1975l) used sighting data collected aboard tuna fishing vessels in 

1974, in conjunction with sighting data from an aerial survey, to obtain an 

absolute abundance estimate of spotted and spinner dolphins, concluding that 

absol te estimates from the ship data alone were not possible. Hammond 

(1981 1 used sighting data collected aboard tuna fishing vessels from 1974 

through 1979 to examine possi bl e trends in abundance of dol phins, concl udi ng 

that several questions must be answered before absolute abundance estimates 

are possible from these data. Both authors used the available data pooled for 

all cruises within years. A reassessment of this data set is currently 

underway, starting with a by-crui se examination of data consi stency , accuracy, 

area sampled, and sea state, and including data on other aspects of the 

fishing trip. 

Holt and Powers (MS3) analyzed similar dolphin sighting data collected 

aboard research vessels, concluding that it was not possible to use those data 

in line transect models. They noted an unexpected shape of the frequency 

distribution of right angle distances, possibly due to schools avoiding the 

ship as noted above. In lieu of using line transect methods in a relative 

context, Holt and Powers used nunbers of sightings per trackmile searched, 

stratified by sea state, as a measure of relative density of schools. 

c1 

The right angle distances (D) from the trackline to the cetaceans have 

generally been estimated from estimates of range (R) and bearing (B) at the 

time of sighting, as D = R Sin (B). The estimates of R and B have usually 

been visual, made without an actual measuring device. In the Antarctic minke 

whale studies, ranges to sighted whales were estimated from the time needed to 

approach the sighted whale and the vessel speed. These estimates do not 

appear to be very precise, generally with angles recorded to 5 or 10 degrees 

and distances to half mile intervals, and are properly treated as grouped 

data. The statistical properties of the derived right angle distances D are 

unknown. Additional ly , vi sual estimates of distances at sea are generally 

difficult, with large differences between observers, low precision and 

possi bl e bias. 

The purpose of this DaDer is to report results of a series of brief 

experiments i made aboard 'the R/V David Starr Jordan in October 1979, SWFC 

cruise 564, aimed at expl oring theproblems mvi sual estimation, and 

eval uatiny two methods .for actual ly . measuring angles and di stances to 

'Smith. T. D. 1975. Estimates of Two Powlations of Porpoise (Stenella) in 

the eastern tropical Pacific Ocean. Southwest Fisheries kenter' -- Admin. Rep. 

L J- 7 5-67. 

'Hammond, P. 

eastern tropical Pacific using data collected aboard tuna purse seiners. 

Draft internal report of the Inter-American Tropical Tuna Commission, La 

Joll a, Cal i fornia. 

3Holt, R. and J. Powers. Abundance estimation of dolphin stocks 

involved in the eastern tropical Pacific yellowfin tuna fishery determined 

from aerial and ship surveys (Manuscript). 

1981. Estimating the density of dolphin populations in the 

1981. 
3 

cetaceans. 

MATERIALS AND METHODS 

The ship used for the experiments was the R/V D. S. Jordan. It is 171 

feet long, 900 tons displacement, and cruises at-approxmy 10 knots. 

Searching is conducted from the flying bridge, through two 25x sling mounted 

binoculars (Fuji Meibo 25 x 150) and with smaller hand held binoculars. The 

large binoculars have a 2.7' field of view. The flying bridge is 

approximately 30 feet above the water, and the binoculars are mounted 

approximately 5 feet above the deck. The sighting team members alternate 

between searching with the 25x binocul ars and hand-he1 d binocul ars, and search 

for dolphins in a sweep from slightly across the bow to directly behind the 

ship. Search patterns within this field are determined by the individual 

scientists. 

The five-person sighting team on SWFC cruise 564 carried out three 

separate experiments under my direction. After the cruise a fourth experiment 

was conducted on land to check the calibration of the reticles. 

To obtain more accurate measurements of bearing to the sighted cetaceans, 

a device consisting of a stiff wire that rotated with the binoculars was 

attached to the right-hand 25x binoculars stand. Paper was attached to the 

deck around the binoculars stand, and pencil marks were made to record the 

position of the wire. Angular measurements were made from the paper later, 

using a protractor. 

To obtain more accurate measurements of the distance to sighted 

cetaceans, the 25x binoculars were equipped with eyepieces containing a series 

of equally spaced horizontal marks (reticles), arranged vertically. Counts of 

the number or fraction of marks from the horizon down to the object of 

interest were recorded. These counts can be related to angle from the horizon 

to the object, and thence via trigonometric relationships to the distance to 

the object. 

In addition to these devices, the ship's radar was used to measure the 

range and bearing to some objects, and an alidade on the repeating gyro 

compass on the flying bridge was used to measure the angle to some objects. 

The alidade is a sighting device without optics, and could only be used for 

objects which were large or at close range. 

EXPERIMENT 1, Range and Bearing to a Buoy 

An anchored buoy approximately 15 feet high was located near Santa 

Barbara Island. At varying distances and angles of approach to the buoy, the 

angle as indicated by the alidade, the radar and the wire device was 

recorded. Similarly, distance to the buoy was measured using radar and the 

reticles, and was estimated visually. Measurements were made with the vessel 

at complete stop, but allowed to drift. The sea was completely calm with no 

wind, and drift was negligible during the course of a set of observations. 

Rep1 icate measurements of angles by individual observers were made by swinging 

the binoculars away from the target each time, thus minimizing serial 

correlation of consecutive measurements. 
4 

EXPERIMENT 2, Range and Bearing to Approaching Ships 

The bearing and range to the bow of ships transiting at angles to the R/V 

D. S. Jordan were measured, using the radar and the wire device, and the radar 

anhrem, respectively, while the R/V D. S. Jordan was underway. There 

were some difficulties in making the retfile measurements while underway, 

especially at the closer ranges where the relative motion of the two vessels 

caused relatively rapid changes. The angle measurements using the wire device 

required 10 to 30 seconds time to complete. Replicates of the measurements 

were attempted, but vessel movement precluded true rep1 ication. 

EXPERIMENT 3, Angle to Sighted Cetaceans 

Angles to sighted cetaceans were estimated vi sua1 ly , and measured using 

the wire device. Replicate measurements were made as rapidly as possible by 

having the scientist looking through the binoculars indicate verbally when he 

was lined up on the cetaceans, and having someone else mark the position of 

the wire on the paper on the deck. A series of replicate measurements was 

made within 30 to 90 seconds following the first measurement. 

EXPERIMENT 4, Reticle to Degree Conversion 

The relationship between the reticle counts and the actual angle below 

the horizon was determined in an experiment conducted on shore. The 

binoculars were set up in an empty parking lot and focused on a large piece of 

paper at a distance of 53.1 m. The top and bottom of the image seen through 

the binoculars was marked on the paper, along with the position of each 

reticle mark. Subsequently the diameter of the field of view and the distance 

between the top reticle and each successive reticle was measured with a meter 

stick. 

RESULTS 

Calibration of Methods of Estimating Range 

Shipboard Measurements 

During experiment 1 radar measurements of the distance to the buoy, 

visual estimates of the distance to the buoy, and reticle counts were made 

(Table 1). Each observer made estimates independently, and none had any 

quantitative knowledge of how to interpret the reticle measurements in terms 

of distance. 

The relationship between the mean visual estimates and the radar ranges 

is shown in Figure 1. The mean distance estimates follow the radar 

measurements fairly consistently , but the range of individual estimates is 

wide as indicated by the 90% confidence intervals. The mean visual estimates 

exceed the radar measurements slightly 10 of the 12 times. This is most 

consistent at distances less than 3 nm, with 8 of 10 overestimates occurring 

in this region. Between 3 and 5 nm equal numbers of observations are over and 

under the radar measurement. 

The re1 ationshi p between the reticle measurements and the radar 

measurements of distance is shown in Figure 2. Over the range of 0.3 nm to 
5 

Table 1. Mean visually estimated distance, mean reticle measurement 

and radar range to buoy, with sample size (N), standard 

deviations (SD), and coefficients of variation (CV) of 

reticle measurements. 

Radar Visual Estimate Reticle Measurement 

Di stance N mean SD N mean SD cv 

(nm) (nm) (nm) 

-- 

0.29 5 0.35 0.31 5 13.86 0.89 0.06 

0.49 5 0.57 0.26 5 7.76 0.96 0.12 

0.67 5 0.81 0.23 5 5.76 0.70 0.12 

1.00 4 1.01 0.45 4 4.35 0.47 0.11 

1.06 5 1.26 0.36 5 2.54 1.59 0.63 

1.40 5 1.67 0.38 5 1.80 1.34 0.74 

1.92 3 2.07 0.40 3 1.08 0.16 0.15 

2.36 5 2.64 0.28 5 0.75 0.05 0.07 

3.16 5 3.55 0.27 5 0.40 0.08 0.20 

3.39 5 3.11 0.56 5 0.39 0.08 0.21 

4.90 5 4.50 0.47 5 0.18 0.12 0.67 

5.50 4 5.80 0.36 - - - - 
6 

7 

n 

E 

W ‘6 

W 

2 

z5 Irn 

W 

W 

04 

z 

tv) 

-J 

z) 

v) 

a 

03 

a 

52 

a 

ZI 

7 

W 

0 I 2 3 4 5 6 7 

RADAR DISTANCE TO BUOY (nm) 

Figure 1. Mean visual estimates of distances to buoy versus distances 

measured by radar, with approximate 90% confidence intervals 

and 1 ine denoting equal i ty shown. 
7 

v) 

W 

J 

Iw 

U 

LL 

0 

2 

a 

W 

m 

z 

3 

z 

n 

W 

Ia 

2 

r 

v) 

W 

z 

a 

W 

2 

0 I 2 3 4 5 6 7 

DISTANCE TO BUOY FROM RADAR (nm) 

Figure 2. Mean estimated number of reticles at varying distance to 

buoy, with approximate 95% confidence intervals. 
8 

5 nm it is possible to make reticle measurements in a reasonably consistent 

manner, as indicated by the confidence intervals for the observations. Beyond 

5 nm the change in reticle with distance is so small as to preclude using this 

device. The distance to the horizon at the 35 feet elevation of the 

binoculars on the R/V D. S. Jordan is approximately 6.2 nm, suggesting that 

this device is not likFly-tobeeful beyond 5 nm. The reticles marked in 

the 25x binoculars cover approximately one half of the field of view. By 

covering more of the field of view it may be possible to measure distances 

smaller than 0.3 nm. The principal difficulty is that the observer must be 

able to count the large nwnber of marks at a glance. A solution might be to 

include numbers near the reticles to assist in counting. 

Reticle and Range Conversion 

The relationship between the reticle counts and the range to sighted 

objects can be derived from the sighting geometry shown in Figure 3 and the 

results of experiment 4. 

The relationship between the range a and the angle below the horizon c 

can be derived from Figure 3 following Heinemann (1981). Note that 

a = b tan (d), 

and that d can be obtained from 

tan (c+d) = (a+e)/b, 

a+e 

b 

d = arctan (-1 - c. 

Substituting this expression into equation 1 yields 

a+e a = b tan (arctan (-1 - c). 

b 

The distance to the horizon is given by Bowditch (1966) as proportional to the 

square root of the height of the eye, converting to nm, 

(5 1 /2 a+e = 89.173 b . 

The relationship between the angle below the horizon to the sighted 

object, c, and the reticle marks was explored in Experiment 4. The measured 

distances from the topmost reticle to each successive reticle (d) (Table 2) 

were transformed to angles as arctan (d/53100) (Figure 4). These angles were 

fitted to the reticle number minus one (r) as 

c = fr, 
9 

Perceived Height of eye 

Horizon above horizon 

Figure 3. Diagram of relationship among horizon, sighted object, observers' 

eye and ship height, labeling angles and distances needed in 

theoretical development (see text). 
10 

1.2 

1 .o 

0.8 

n 

v) 

Q) 

0 

L 

0.6 v 

w 

A 

(3 

z 

a 

0.4 

0.2 

0 .c 5 10 15 

RETICLE NUMBER 

Figure 4. Angle ("1 from top reticle to each lower reticle in 25x 

binoculars with fitted regression line. 
11 

Table 2. Distance from top most reticle to each lower reticle in 

25x binoculars, measured in the field of view at 53.1 m. 

Reticle Distance 

(mm) 

- 

1 0 

2 78.8 

3 156.0 

4 

5 

239.9 

319.0 

6 400.5 

7 470.5 

8 540.5 

9 615.8 

10 

11 

12 

13 

14 

15 

687.8 

764.4 

845.1 

915.1 

982.6 

1051.1 
12 

using linear regression through the origin. The slope was estimated as 

0.0823, with a standard deviation of the estimate of 0.00035. 

Substituting equations 5 and 6 into equation 4 yields the relationship 

between the range and the reticles as 

a = b tan (arctan (89.173/ rb) - fr). 

The variance of predicted ranges depends on the variability of the estimates 

of f and r approximately as 

where v( ) denotes the variance of the quantity within the parentheses, r 

denotes the nwnber of reticles below the topmost reticle, and k = arctan 

(89.173/ A), 

The predicted distances to the buoy (equation 7) are plotted against the 

distances measured by radar (Table 1) in Figure 5. There is some consistent 

lack of fit at the intermediate ranges, the cause of which is not known. For 

illustration, the standard errors of the predicted distances (equation 8) are 

a1 so shown, calcul ated asswni ng the observed variances of the reticles 

(Table 1). The range of sizes of these standard errors reflects the 

variability of the repl icate reticle readings. 

Calibration of Methods of Estimating Bearing 

Measurements of the angles to a buoy were made during Experiment 1, in 

addition to the range measurements analyzed above. Angles were measured using 

the wire device attached to the binoculars stand, the alidade, and radar 

(Table 3). At each of 14 locations replicate measurements of the wire angle 

were attempted in order to determine sampling variability. Unfortunately, in 

most of the locations the vessel itself drifted and/or rotated slightly during 

the repl icate, as indicated by changing radar angles within r e p l i c a t e s (Tab1 e 

3). Replicate variability was examined by computing variances for the data 

grouped to the nearest 5 degrees, and does not appear to vary consistently 

with either the size of the angle being measured, or the distance to the buoy. 

The radar measurement of the angle to the buoy appears to be consistently 

greater than the alidade measurement (Figure 6). The ship's officers 

indicated that the radar angle is known to be in error due to the installation 

of the mechanism itself. Fitting a linear relationship to predict radar angle 

from alidade angle results in a intercept of 2.92 and a slope of 1.00. The 

standard deviations of these estimates are 0.192 and 0.0008 respectively. The 

fit is good and the residuals show no pattern with the alidade angle. The 

slope is clearly not different from unity, implying that a sufficient 

correction to the radar is to subtract the constant 2.92. The wire angles 

have been scaled against the radar in the field measurements, and so have 
13 

PREDICTED DISTANCE (nm) 

0 N P CJl 0) 0 

Figure 5. Predicted versus observed distances to buoy (Equation 7 

and Table 1), with + 1 standard error (Equation 8) 

and the equal i ty 1 ine indicated. 
14 

Table 3. Wire angle, alidade angle, radar angle and radar 

distance to buoy recorded in Experiment 1. 

Radar A1 idade Wire Ani1 e An81 e An81 e 

Rep. Di stance ( nm) 0 0 0 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

4 

4 

23 .9 

23.0 

23 .c) 

24.5 

27.5 

29.0 

29.5 

29.5 

30 .O 

32.0 

32.5 

33.5 

34.5 

35.0 

35.5 

86.0 

87.5 

88.0 

89 .O 

90.0 

100 .o 

102.0 

105 .O 

67.0 

67 .O 

67.0 

67.5 

69.0 

74.9 

79.0 

89.9 

97.0 

98.5 

3.0 

3 .c) 

3.0 

3 .O 

3.0 

5 .c) 

4.0 

3 .o 

21.8 

21.4 

20.7 

22.5 

24.8 

26.0 

27.7 

28.8 

29.7 

31.9 

29.2 

32.5 

30.7 

32.0 

34.5 

85.5 

86.5 

88.2 

83.2 

84.0 

87.5 

98.0 

102.0 

57.6 

64.3 

64.5 

65.3 

59.5 

71 .O 

74.0 

84 .O 

96.3 

96.3 

3.5 

3 .O 

3.0 

2 .o 

1.5 

5 .O 

4.8 

2.7 
15 

Table 3. Continued 

Radar A1 i dade Wi re 

Angl e Angle Angl e 

Rep. Distance (nm) 0 (O) 0 

4 

4 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

11 

11 

11. 

11 

11 

12 

12 

12 

12 

12 

4.5 

4.5 

4.1 

4 .O 

4.0 

3.9 

3.8 

3.8 

3.7 

3.5 

3.4 

3.3 

2.9 

2.8 

2.8 

2.7 

2.6 

2.5 

2.2 

2.1 

2.1 

2 .o 

1.9 

3.3 

3.3 

3.2 

3.1 

3.1 

2.9 

2.8 

2.8 

2.8 

2.7 

2.5 

2.5 

2.5 

2.5 

2.4 

1.9 

1.7 

1.7 

1.7 

1.6 

1.3 

1.3 

1.2 

1.2 

1.2 

5.0 

3 .O 

11.0 

10.0 

10.0 

10.0 

12.0 

11.0 

12.0 

10.0 

10.0 

11.0 

21.5 

21.5 

19.0 

22 .o 

22.0 

22.0 

33.0 

33 .O 

32.0 

31 .O 

31.0 

17 .O 

19.0 

20 .o 

23.0 

21 .o 

44.0 

45 .O 

43.0 

44 .O 

41.0 

65 .!I 

60.0 

63 .O 

64.0 

60 .O 

13.0 

13.5 

13.5 

13.0 

7.5 

8.0 

8 .O 

7.0 

7 .O 

--- 

--- 

--- 

8 

9 

6 

6 

11 

10 

10 

7 

8 

9 

19 

19 

16 

20 

19 

19 

31 

29 

28 

28 

27 

14 

17 

16 

20 

19 

41 

42 

40 

42 

38 

57 

60 

51 

57 

9 

10 

11 

10 

10 

5 

5 

4 

3 

3 

--- 

4.0 

3.7 

11.5 

12.4 

9.0 

12.3 

13.6 

13.5 

13.5 

10 .o 

10.9 

12.5 

22.2 

21.5 

20.0 

22.6 

22.6 

22.6 

33.4 

31.5 

32.1 

30 .O 

30.5 

16.5 

19.0 

19 .o 

24.0 

22.3 

44.5 

45.5 

44.0 

45 .O 

42.1 

62.2 

60.0 

63 .O 

62.0 

62.0 

11.6 

12.3 

12.6 

12.6 

12.0 

6.4 

7.1 

7.1 

4.7 

4.6 
16 

Table 3. Continued 

Radar AI i dade Wire 

An31 e Angl e An31 e 

Rep. Di stance (nm) 0 (O) 0 

13 

13 

13 

13 

13 

14 

14 

14 

14 

14 

1.1 

1 .o 

1.0 

1 .o 

0.9 

0.8 

0.8 

0.8 

0.8 

0.8 

18.0 

18.5 

18.5 

18.7 

19.5 

92.5 

96.0 

98 .O 

98.0 

98.5 

16 

15 

15 

15 

16 

18.7 

18.6 

17.6 

17.1 

18.5 

89.4 

94.3 

96.8 

97.6 

97.1 
17 

W 

z 

a 

a 

a 

a 

0" 20" 30" 40" 50" 60" 

ALIDADE ANGLE 

Figure 6. Relationship between radar angle and alidade angle. 
18 

effectively been corrected for this error. 

The wire angles agree very closely with the radar angles, as shown in 

Figure 7. Fitting a linear relationship yields an intercept of 0.247 and a 

slope of 0.968, with standard deviations of 0.292 and 0.006 respectively. The 

fit is reasonable, with one apparent outlier at 100 degrees. The intercept is 

not significantly different from zero, (~051, suggesting a regression though 

the origin may be appropriate. The slope estimate then is 0.972 with a 

standard error of 0.004, and is significantly different from unity (P<.Ol). 

Appl icati on of Methods 

During Experiment 2 the radar angle, wire angle and alidade angle were 

measured as a ship approached (Table 4). The wire angles were rep1 icated in 

order to explore the precision of this method of measuring angles. During the 

time needed to complete the replicate wire angle measurements there was 

detectable change in the angle to the approaching ship's bow, as reflected in 

the general tendency for the replicate angles to increase. Thus the 

replicates do not yield information on the precision of the measurement. The 

relation between the first of the replicate wire angles and the radar angle is 

quite good (Figure 8). 

The tendency for the radar angles to be greater than the a1 idade angles, 

noted above, is detectable in these data also. Greater variability is 

ref1 ected in these observations, which is consistent with the general 

difficulty of obtaining a1 idade angles consistently during the experiment. 

Also during Experiment 2 the distances to the approaching ships were 

measured using the radar and using the binocular reticles (Table 5). 

Measurements were difficult to make using the reticles due to the vessel 

motion and the rate of changes of distances as the two vessels passed. The 

mean reticle counts show the same general relationship to actual distances 

obtained from the radar as seen in Figure 2. The predicted distances froln 

these mean reticle counts using equation 7, with standard deviations from 

equation 8 where mu1 tiple reticle readings allowed estimating the variance of 

the mean reticle, are also shown in Table 5. 

During Experiment 3 visual estimates of both range and angle, and wire 

measurements of angle were obtained for five sightings of cetaceans 

(Table 6). The sightings were of a few to many animals of 4 different 

species, and were made at ranges visually estimated to be 2 to 5.7 nm. The 

wire angles were replicated 2 to 6 tiines. The replicate angles tend to 

increase consistently, suggesting a change in the angle due to the ship's 

motion, and perhaps, in part, due to the cetacean's motion. The two Tursiops 

schools eventually approached the ship, and no information is available on the 

possible movement of the Grampus school. 

There is general agreement among the visual estimates of the bearing to 

the cetaceans, except for the Grampus sighting (Figure 9). The field notes 

suggest that this group of ani5G'hTas only observed briefly, then lost to 

sight. Another sighting was made very soon afterward, so it is possible that 

the estimated and measured angles are for two different sightings. 
19 

120' 

100' 

80' 

60' 

40' 

20' 

0. ' 

0 0 

0 

'v 

0 

0. 

p 

a 

O0 20° 40° 60' 80' looo \20° 

BEARING FROM RADAR 

Figure 7. Relationship between angle measured from wire attached to 25x 

binoculars and bearing to buoy measured on radar. 
20 

40 

30 

20' 

W 

-I 

(3 

z 

a 10' 

W 

U - 

0" 

tv) 

U - 

LL 

Fi 

I I I I 1 

330" 340" 350" 0" I 0" 20" 30" 40" 

RADAR ANGLE 

gure 8. Relationship between the estimated angle to the bow of 

approaching ships using a wire attached to the 25x 

binoculars and the angle as measured by radar. 

equality line is shown. 

The 
21 

Table 4. Angular measurements (degrees) to bow of passing 

ships, with multiple replicates of the wire angles. 

Radar A1 i dade Wire Angle 

1 2 3 4 5 6 7 

351 

354 

357 

27 

7 

350 

345 

355 

3 38 

35 

346 

353 

352 

24 

--- 

340 

--- 

35 

349.9 

355.5 

355.9 

27.5 

6.8 

349.4 

340.5 

358.4 

328.9 

38.9 

350.4 

356.4 

355:9 

28.4 

7.4 

349.4 

341.1 

358.9 

330.2 

39.3 

350.4 

356.6 

356.6 

29.2 

8.4 

349.4 

341.1 

358.9 

330.4 

39.6 

350.7 

356.9 

356.9 

29.7 

8.9 

349.9 

341.4 

359.1 

330.9 

40.4 

351.1 351.4 352.4 

357.3 357.5 357.9 

357.9 358.6 358.9 

9.5 

349.1 350.4 

341.9 342.6 343.1 

359.5 

330.9 331.4 333.4 

40.8 41.4 41.9 
22 

Table 5. Reticle measurements (number below horizon) to bow of 

approaching ships with radar measurements of distance. 

Means, standard deviations (SD) and predicted distances 

(D) with standard deviation (SD(D)) are given. 

Ret i cl e 

Di stance Measurement 

(nm) 1 2 3 Mean SD D SD(D) 

4.5 0.25 0.20 0.20 0.22 0.03 5.0 0.18 

3.4 0.50 0.60 0.55 0.07 3.6 0.22 

2.3 0.90 0.80 0.85 0.07 2.8 0.14 

1.8 1.80 1.60 1.70 0.14 1.8 0.11 

1.3 3.30 3.30 --- 1.1 --- 

1.1 3.50 3.50 --- 1.0 --- 

0.9 4.20 4.20 --- 0.9 --- 
23 

W 

m 

v) 

aJ 

V 

aJ 

P 

m 

*r 

m 

a 

0 

cr) 

m 

0 

e 

m 

m 

0 

m 

m 

(u 

h 

m 

m 

v) 

0- 

0 

v) 

L 

3 

I- 

.r 

rb 

4 

4e 

?? 

4-I 

L? 

m 

e 

’? 

b * 

h0 

mw eN 

?? 

mm 

*-J 

L?? 

(u(u 

00 

mm 

mo 

hW 

44 

4-3 

00 

’5”; 

me 

mw 

cu 

m 

m 

m 

W 

m 

W 

99 

ew 

(u 

9? 

mr- 

(u 

99 

mm 

mo 4 

4m 

W 24 
24 

W 

A 

(3 

z 

W 

Q1 

a 

- 

3 

100" 

80" 

60" 

40" 

20" 

0" 20" 40" 60" 80" 100" 

VISUAL ANGLE 

Figure 9. Angle to sighting measured by wire on binoculars versus visual 

estimated angle. 
25 

D ISCUSS ION 

The experiments on the R/V D. S. Jordan suggest that improvements in 

estimating range and bearing of ceTacGnsTk$Eed during surveys are possible 

with new measuring devices. It is not clear, however, what the limits of 

precision are which can be obtained by technique and equipment refinement, but 

at the very least one could expect some improvement with estimates and some 

information on the variability of the estimates. This would be a substantial 

aid in evaluating the precision and bias in absolute or relative abundance 

estimates which may be derived from shipboard sighting survey data. 

The ultimate limitation in reducing the variance of the estimates of 

distance to sighted cetaceans is the variability of the reticle readings 

themselves. The coefficient of variation was around 28% on sightings under 

ideal conditions, and can be anticipated to be higher under less than ideal 

conditions, especially where the sighted object may be visible for only brief 

periods and where the horizon may be difficult to determine due to vessel 

motion and surface swell. Some improvement can be anticipated by having the 

reticle scales rearranged for easier use. For instance, for the closer 

objects many reticle marks must be counted; so sequential nunbering or 

otherwi se distinguishing the successive marks may make counting easier. A1 so, 

some observers had difficulty seeing the reticles because they are to the side 

of the field of view. The possibility of placing the marks in the center of 

the eyepiece should be explored. 

The precision of the estimated bearing to sighted cetaceans can be 

improved by using a measuring device. This has already been explored in a 

preliminary fashion on a subsequent sighting cruise aboard the R/V D. S. 

Jordan. The binoculars Mere mounted on stands with an etched angular-scare 

XfZEFed. The angles to the sighted cetaceans were read from these scales 

rather than vi sua1 ly estimated. Unfortunately the scales were etched to only 

five degree increments, but the results are encouraging. The frequency 

distribution of the actual recorded values for this latter cruise and for a 

comparable earlier cruise are shown in Figure 10, where it is clear that there 

is a reduced tendency for estimates to clump at favored values. 

It is possible to use larger and more finely calibrated angular scales to 

further reduce the clumping aspect of these observations. However the ability 

of the scientist making a sighting actually to read an angular scale is 

limited due to the necessity to maintain visual contact on the animals and due 

to the motion of the ship. Repetition of angular measurements over several 

seconds, at least, would reduce variability. 

There are some possibilities for equipment improvement which may help 

reduce the variability of the measurements of bearings and ranges. For 

angul ar measurements the most obvious i s to determi ne mechanically the angle 

of the binoculars and enter this into the ship's computer. Additional 

information such as the compass heading, the engine revolutions, the time and 

the ship's position from satellite fixes and extrapolations could also be 

entered for assistance in computing exact sighting geometry. It would be 

important for the scientist to be able to trigger such recording, and also to 

have such information recorded automatically at intervals to study searching 

patterns. 
26 

5 % 

4% 

v) 

W 

f 

9 2 % 

P 

18 4% 

I 

2W 

ANGLE OF OBSERVATION ( 0 is ahead 

Figure loa. Frequency of specific angles recorded without a 

measuring device as estimates of angle to sighted 

cetaceans. 

5% 

4 % 

v, 

0 

+ 

I 

W 

5 

v, 3 

LL 

0 

W 

0 

+ 

z 

0 

E 

W 

a 

a 

w 2% 

I 

0 I. _' e 40.500 

ANGLE OF OBSERVATION (0 is ahead 1 

1000 1500 I800 

Figure lob. Frequency of specific angles recorded with a 

calibrated ring as estimates of angle to sighted 

cetaceans. 
27 

One approach for improving the reticle measurements would be to mount a 

camera into the binocular optics to record photographically what the scientist 

is seeing. It may be possible to measure the angle below the horizon froin the 

photographic image. An alternate approach would be to mount a camera with a 

separate optical system on the binoculars to accomplish the same end. The 

feasibility of this would, of course, depend on the visibility of the sighting 

cue which is being observed. The human eye is capable of focusing on a 

particular portion of the image in the binoculars and detect cetaceans which 

may not be detectable in the photographic image. One possible approach might 

be to mount a camera external to the binocular optics with an even higher 

power lens, a1 though this may result in aiming problems. 

An alternate approach to improving the reticle measurements is to 

gyrostabilize the binoculars themselves, thereby establishing a horizon 

reference point. It would then be possible to input the vertical angle of the 

binoculars relative to this horizon directly into the computer. The 

feasibility of this is unknown, but would depend in part on the response times 

of a gyrostabilizer of size sufficient for the 50 to 70 kg weight of the 25x 

binoculars. 

Improved equipment of these types would probably result in greatly 

improved estimates of range and bearing to sighted cetaceans. In addition, 

such equipment could allow other questions to be approached. Automatic 

recording of the bearing of the binoculars could be used to examine the search 

pattern employed by the scientists. Doi (1974) demonstrated the need to 

understand this process. Best and Butterworth (1980) discuss the 

possibilities at some length, without being able to determine the relative 

searching effort expended by the fishermen at different points of the compass 

from the sighting data. Additional information was collected aboard Japanese 

sighting vessels in 1980, suggesting that most searching occurs forward of 45' 

(Doi, Kasamatsu and Nakano, in press). 

The trend in the replicate measurements of the angle to approaching ships 

and to sighted cetaceans by the wire device, suggests the possibility of using 

the ship itself as a range finder, as it progresses along its trackline for a 

short period after sighting. Using the vessel for this purpose would be 

greatly enhanced with the automatic recording of the angle of the binoculars. 

One problem with using the ship as a range finder is the possible 

movement of the sighted cetaceans. This has been identified as a possible 

problem in general with application of line transect theory, especial ly i f 

such inovement is directional with respect to the ship. Au and Perryman (in 

press) initiated work on this problem from a helicopter associated with a 

research vessel. Using equipment as described above, it may be possible to 

continue such investigations, at least in terms of movement after sighting, 

from ships alone. 

CONCLUSIONS 

1. Visual estimates of the range to a buoy at sea averaged over several 

individual s are reasonabl e, but the range of estimates among individual s i s 

large. There is a slight tendency to overestimate, as measured by the mean 

estimates, at distances less than 3 nm. 

I 
28 

2. Range to sighted objects can be estimated from measureinent of the 

angle below the horizon through 25x binoculars over a range of 0.3 to 5.0 

nm. Actually making these measurements is difficult in practice, especially 

in less than ideal visibility conditions. 

3. The relationship between reticle marks in the optics of Fuji 25x 

binoculars and the distance to the object is given in equation 7. The 

equation does not fit the available data very well, and needs additional 

study. It was validated while the ship was underway by estimating distances 

to the bow of approaching ships. 

4. Prediction of the distance to an object from the reticle measurelnent 

is given by equation 9. It was tested using reticle measurement and radar 

measurements to the bow of approaching ships. An expression for the variance 

of the predicted distance s given (equation 10) in terms of the variances of 

the estimates of the parameters f and g, the covariance of these two 

estimates, and the variance of the actual measurement of the reticle. The 

statistical properties of this estimator need to be examined further. 

5. The binocular wire angle can measure the bearing to a buoy with high 

precision. The variability is independent of the actual bearing and the 

distance to the object. 

6. The radar on the R/V D. S. Jordan has an approximate 3 degree angle 

measurement error, independent Cf angle. 

7. The binocular wire angles underestimate the radar angles, after 

correction, slightly, especially at angles greater than 60 degrees. A simple 

mu1 t i p 1 i c a t i v e constant is sufficient to correct for this. 

8. Development of new equipment to improve 

of angle and di stance measurements, including 

improve the possibilities of aplication of 1 

sighting data. 

the precision and reliability 

possible automation, should 

ne transect theory to ship 
29 

ACKNOWLEDGEMENTS 

This work was the result of collaboration among several individuals. The 

most important were the sighting survey team, consisting of Tom Duffy, field 

party chief, Bob Pitman, Mike Graybill, Scott Sinclair, Mike Newcomer, and 

Gary Friedrichsen. The crew and the captain of the R/V D. S. Jordan assisted 

us greatly in the extended maneuvering of the ship whicrwas-ed. This 

study was 1 argely exploratory, and benefited greatly from at sea discussions 

with and data collection by Drs. Lee Eberhardt, Robert Clarke, Phil Hammond, 

Nancy Lo and Rennie Holt. It is to be hoped that similar interactions will 

continue as work on sighting methodology is pursued. 

I 
30 

LITERATURE CITED 

Au, D. and W. Perryman. (in press) Movement and speed of dolphin schools 

Best, P. D. and D. S. Butterworth. 1980. Report of the southern hemisphere 

responding to an approaching ship. 

minke whale assessment cruise, 1978/79. Rep. Int. Whal . Commn 30:257-203. 

-- Fi sh. Bull. (U . S.) -- 

---- 

Bowditch, N. 1966. American practical navigator. U. S. Govt. Print. Off., 

Washington, D.C., 1524 pp. 

Doi, T. 1974. Further development of whale sighting theory. In Schevil, 

W. E. (ed) The Whale Problem, Harvard U. Press, pp. 359-3'w. 

Doi, T., F. Kasamatsu, and T. Nakano. (in press) A simulation study on 

sighting survey of minke whales in the Antarctic. Rep. Int. Whal. Commn. 

32. 

---- 

Heineman, D. 1981. A range finder for pelagic bird censusing. -- J. Wildl. 

Manage, 45(2) :489-493. 

Horwood, J. W. 1981. Results from the IWC/IDCR minke whale marking 

and sightings cruise, 1979/80. ---- Rep. Int. Whal. Commn. 31: 287-313. 
RECENT TECHNICAL MEMORANDUMS 

Copies of this and other NOAA Technical Memorandums are available from the National Technical 

Information Service, 5285 Port Royal Road, Springfield, VA 22167. Paper copies vary in price. 

Microfiche copies cost $3.50. Recent issues of NOAA Technical Memorandums from the NMFS 

Southwest Fisheries Center are listed below: 

N 0 AA-TM- N M F S-SW F C- 1 0 

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Albacore trolling and longline exploration in eastern North Pacific waters 

R. M. LAURS, R. J. LYNN, R. NISHIMOT0,and R. C. DOTSON 

(March, 1981) 

Observations of albacore (Thunnus alalunga) fishing off California in 

relation to sea surface temperature isotherms as measured by an airborne infrared radiometer. 

during mid-winter 1981. 

J. L. SQUIRE, JR. 

(May, 1981 1 

Stock assessment activities within the National Marine Fisheries Service. 

(June, 1981) 

Planning double-tagging experiments. 

J. A. WETHERALL and M. Y. Y. YONG 

(May, 1981 ) 

Histological gonad analyses of late summer-early winter collections of 

bigeye tuna, Thunnus obesus, and yellowfin tuna, Thunnus albacares, 

from the Northwest Atlantic and the Gulf of Mexico. 

S. R. GOLDBERG and H. HERRING-DYAL 

(June, 1981) 

Status reports on world tuna and billfish stocks. 

STAFF, SWFC 

(July, 1981) 

An evaluation of tagging, marking, and tattooing techniques for 

M. J. WHITE, JR., J. G. JENNINGS, W. F. GANDY and L. H. 

COR NE LL 

(November 1981 ) 

Local stability in maximum net productivity levels for a simple model 

T. POLACHECK 

(April 1981) 

Environmental data contouring program EDMAP2. 

L. EBER 

(April 1982) - 

The relationship between changes in gross reproductive rate and the 

current rate of increase for some simple age structured models. 

T. POLACHECK 

(May 1982) 

small delphinids. 

of porpoise population sizes.