IUUL_L. FOR ESTIMPJI THE SIPOPULATION

Ar'1ULTI IALOF AMIGRATI

BY

JUDITH E. ZEH AND DAIJIN KO

DEPARTMENT OF STATISTICSUNIVERSITY OF WASHINGTON

SEATTLE} WASHINGTON98195

BRUCE D. KROGMAN AND RONALD SONNTAG

ANALYTICAL SOFTWARE INC.SEATTLE} WASHINGTON

TECHNICAL REPORT . 33APRIL 1983

A Multinomial Model for Estimating the Sizeof a Migrating l\'hale Population

Judith E. ZehDaijinKo

Department of StatisticsUniversity of Washington

Seattle, Washington

Bruce D. KrogmanRonald Sonntag

Analytical Software Inc.Seattle , Washington

ABSTRACT

This report applies the results of Sanathanan (1972, TheAnnals of Mathematical Statistics 43. 142 - 152) onestimating the number of trials of a multinomial distri­bution to the estimation of the size of the western Arc­tic stock of bowhead whales. Cell totals used in the esti­mate are from a whale census conducted during springmigration. The population size is modeled as the sum ofthe number of trials of several independent multinomialdistributions each of which represents a particular visi­bility condition occurring during the census. The prob­lem of incomplete observation of totals within particu­lar cells as well as the problem of unobserved cells isdealt with. A confidence interval estimate of populationsize is derived. Suggestions are presented for futureresearch to strengthen the data base for estimatingtrends in the whale population.

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1. Introduction

In connection with a particle counting problem in particle phy­sics, Sanathanan (1972) studied maximum likelihood estimates ofthe number of trials of a multinomial distribution based on anincomplete observation of cell totals under constraints on the cellprobabilities. A similar multinomial model is applicable to theproblem of estimating the size of the western Arctic stock of bow­head whales (Balaena mysticetus) from the results of an ice-basedcensus conducted annually during the spring migration. Thisreport presents the statistical details and results of our applicationof the model to the whale census problem.

In this section we describe the basic multinomial model. InSection 2 we discuss maximum likelihood estimates of N, thenumber of whales passing the ice camps, and q, the probability ofmissing a whale, under the modeL We also outline the problems ofunwatched time (leading to incomplete totals within cells) andvarying visibility and other factors influencing q (leading to theneed to use several independent multinomial distributions withdiffering q.)

In Section 3 we discuss our analyses of the estimated probabili­ties q . We examine the variance of the estimates and resultantsample size requirements for computing them. We also use regres­sion techniques to assess the relative importance of the factorsthought to influence these probabilities.

In Section 4 we derive and discuss daily estimates of thenumber of passing whales. Confidence interval estimates of thesize of the bowhead stock obtained from the daily estimates aregiven in Section 5. Finally, Section 6 summarizes our recommen­dations for future research.

Before we can understand the statistical methodology, we needto consider the background and methodology of the ice campcensus. Bowhead whales migrate each spring from the Bering Seato the Beaufort Sea, passing near Point Barrow en route. Monitor­ing of population size from year to year is important for settingharvest quotas which ensure the preservation of the species. Trad­itionally hunted by eskimo whalers but brought close to extinctionby commercial whaling between 1850 and 1915, the population now

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From 1978 to 1981, the National Marine Mammal Laboratory.National Marine Fisheries Service, National Oceanic and Atmos­pheric Administration conducted a visual census of bowheads fromcamps on the ice edge during the spring migration. In 1982, theNorth Slope Borough took over the sponsorship of this census whenfederal funding was cut. The ice-based census takes place duringApril, May. and early June. The objective of this census is not toprovide a complete enumeration of the western Arctic stock ofbowheads. It is recognized that some of the whales pass Point Bar­row before and after the ice camp census effort, and some pass toofar off shore to be seen. The goal of the ice-based census is to pro­vide a minimum population estimate which permits detection ofsignificant year-to-year changes or trends in population size if suchchanges should occur.

Details of the methodology used in the ice camp census effortcan be found in Krogman, Sonntag, Rugh, Zeh, and Grotefendt(1982) and Dronenburg, Carroll, Rugh, and Marquette (1982). Wesketch here only those aspects of the methodology critical todefining the statistical approach to obtaining the minimum popula­tion estimate.

The primary counting station, called South Camp, is a perchcarved on top of one of the highest ice ridges close to the edge ofthe nearshore lead. A lead is a large crack in the ice pack whichprovides open water. The whales follow these open water leads dur­ing their migration. The transition zone between the polar pack iceand the shorefast ice where these leads occur is narrow and closeto the shore near Point Barrow, so researchers are confident that asignificant fraction of the population passes in view of South Camp.

The same whale may surface more than once within view ofSouth Camp. Thus South Camp observers code each whale sightedas new. as duplicate, or, in cases where they are unsure whetherthey have seen the whale previously, as a conditional whale. Therange and bearing of the whale. lead width, visibility. time of sight­ing. height of perch. observers on duty, and other environmentalvariables are recorded for each sighting.

In order to assess the probability of South Camp failing to seeand record a passing whale, a second perch is set up at NorthCamp. approximately 0.5 to 2.0 kilometers north of South Camp.

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They report their sightings to North Camp via a one-way radio link.The mission of North Camp is to look for whales missed by SouthCamp. Each whale sighted at North Camp is coded as a missedwhale, a whale seen by both camps, or, in cases of uncertainty, 'aquestionable whale.

The probability model underlying this experimental design isoutlined in a working paper by Krogman, Breiwick, and Horwood(1982). We assume that the passage of one whale is independent ofthe passage of another though we recognize that this may not bestrictly true. For example, a cow and calf may travel together.However, we need this assumption in order to model the number nl

of new whales seen at South Camp in a given time period out of atotal of N whales passing the camp during that period as a binomialrandom variable. This model allows us to obtain an estimate of N

and the variance of this estimate. We assume that the sighting pro­bability p, one of the parameters of the assumed binomial distribu­tion, is the same at North Camp in the absence of notification of awhale's approach by South Camp. We assume that 0 < P < 1. If n2 isthe number of whales scored as missed at North Camp andN - n t - n2 the number of whales missed by both camps, then thejoint distribution of (n!> n2, N - nl - n2) is multinomial with parame­ters N,p.pq. and q2 where q = i-p. The parameters we seek toestimate are N and q.

2. Maximum likelihood Estimates of N and q

Maximum likelihood parameter estimates under the multino­mial model of Section 1 have been studied by Sanathanan (1972).The observation of nl and n2 yields the likelihood function

L(N; q) = ~l p'nt(pq)'n 2(q2)N-'n t-'n2 (2.1)nl!n2l(N -nl-n2)!

to be maximized. L (N; q) can also be written

L(N; q) = L 1(N; q)L2(q)

where

(2.2)

(2.3)

L 2(q ) =

5 -

(2.4)

is the likelihood based on the conditional probability of (n1,n:;)

given nl+n2. Maximization of the unconditional likelihood isdifficult, but maximization of (2.4) is easy since it does not involveN. To maximize L 2(q ) we maximize its log by setting the derivativewith respect to q equal to zero:

O1nL z(q ) a [ (n1+ n2)! Ia =-;- In I I - n11n(1+q) + nz1n(q) - n21n(1+q)q oq nl.n2'

n1 n2 n2= 0---+---- = a

1+q q 1+q(2.5)

recalling that 1 - q2 =(1 - q )(1 + g) =P (1 + g). Multiplying both sidesof (2.5) by q (1 + q) gives -nlg + n2(1 + q) - n2g = a so n2 = n1q. Hencethe conditional maximum likelihood estimate of q is

(2.6)

Then Sanathanan's Lemma 1 gives the conditional maximum likeli­hood estimate N of N, obtained by maximizing (2.3) with respect toN using g in place of g, as

(2.7)

(2.8)

the greatest integer ~ (n1 + n2)/(1 - (2).

It follows from Sanathanan's Theorem 1 and Theorem 2 that theunconditional maximum likelihood estimates and the conditionalestimates of (2.6) and (2.7) are asymptotically equivalent. AsN ~ co, (.../iT(g - q), (FJ - N)/.../iT) converges to a normal distributionwith mean (0,0) and covariance matrix

1 [g (l - q2) 2g I~ = (1 - g 2q g2(1 + g )/(1 - g)

In view of this asymptotic equivalence, we will use the conditionalestimates (2.6) and (2.7) in the remainder of this paper and referto them as maximum likelihood estimates.

If we had constant watch at both North Camp and South Campthroughout the census with a uniform probability g of missing awhale, an approximate 95% confidence interval for N could beeasily obtained from ii, g, and ~.

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However, watch is not maintained at North Camp during thepeak of the migration when the rate at which whales pass thecamps is highest. At high rates it becomes difficult for North Campobservers to ascertain whether or not a particular whale wasmissed, and a disproportionate number may be scored as question­able.

In addition, even on days when both camps are watching, thereare often missed hours of watch at one or both camps as a conse­quence of poor visibility due to fog, shifting ice which requires mov­ing the perch, illness of observers, etc. Mann-Whitney tests con­ducted by Krogman, Sonntag, et al. (1982) which compared countsof whales in adjacent blocks of watched hours indicated that thelongest time period during which the distribution of passing whalescan be assumed to be constant is of the order of 12 to 24 hours.Thus extrapolation of available data to account for unwatchedhours must be done on a day-by-day rather than a seasonal basis.

The assumption of a uniform sighting probability throughoutthe season is also untenable. Regression analyses described byKrogman, Sonntag, et al. (1982) established that fewer whales perhour were seen under fair or poor visibility conditions on a givenday than during the part of the day when visibility was better. Inaddition to visibility, such factors as perch heights and locations,number and skill of observers, lead width, and the rate and dis­tance at which the whales pass clearly may affect sighting probabil­ity. For example, Dronenburg et al. (1982) note that the whalesmigrate closer to shore near Point Barrow than they do furthersouth, so the probability of sighting them is higher in years whenice conditions permit the location of South Camp and North Campjust northwest of the point rather than to the south.

Perch height and location, lead width, and distance at whichthe whales pass are largely a function of ice conditions during aparticular season and hence tend to vary more between years than'within a particular census period. Observers are also relativelyconstant within a season. Therefore our first simple model forsighting probability expresses it as a function of visibility andobserved hourly rate of whales.

Visibilities were scored as excellent (EX), very good (VG), good(GO). fair (FA), poor (PO), and unacceptable (UN). Since the

Y'o,-nt::> scores too fewwucut.:::s were seen

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the corresponding sighting probabilities. Hence we combinedextreme visibilities to obtain four visibility classes: EX-VG, GO, FA,and PO-UN.

Data for estimating sighting probabilities at high rates ofwhales was limited because of the cessation of North Camp watchat the peak of the migration. We divided the available data into tworate classes, ;£ 10 new + missed whales/hour and> 10, to allow arough test of the hypothesis that g is biased downward at highrates.

We assume that each passing whale in a given year representsan independent trial of the multinomial distribution with parame­ters N i j, »«. »es«. %2 where Pij is the sighting probability andgij = 1 - Pij is the probability of missing a whale corresponding tothe visibility i (i = 1, 2, 3, or 4) and rate j (j = 1 or 2) which existwhen the whale passes. We then compute independent totals ntij

and n2ij of new and missed whales for the ijth class. We use thesetotals for nl and n2 in (2.6) to obtain the maximum likelihood esti­mate gij of the probability of missing a whale at visibility i and ratej for that year. The maximum likelihood estimate .f.li j of the numberof whales passing when both camps were watching at visibility i andrate j is computed similarly from (2.7) for the year.

Because Ni j estimates only the number of whales which passedwhen both camps were watching, we cannot compute the estimateof total population size which we seek simply by summing the Ni j

over visibilities and rates. We will discuss our estimate of popula­tion size in Section 4.

In order to understand the estimate of Section 4, we need toconsider some of the properties of the estimates gij. These are dis­cussed in Section 3.

3. Properties of the Estimates of Probabilityof Missing a Whale for Particular Rates and Visibilities

Throughout this section we will be discussing the probability ofmissing a whale corresponding to a particular subset of the annualcensus effort defined by the rate of whales passing and the visibilityclassification. For notational simplicity we will suppress the visibil­

2mlsslLDR a

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at visibility i and rate j.

We approximate the variance of q of (2.6) for large N by

var(q) R:: 2(1- q2) = q(l + q) (3.1)N (1 - q)2 N (1 - q)

using the asymptotic covariance matrix (2.8). Table 1 shows thestandard deviation of q for various values of q and N.

Table 1. Approximate standard deviations of estimates of q.

Ns.d. q

q =0.2 q =0.5 q =0.8

10 0.173 0.387 0.849

50 0.077 0.173 0.379

100 0.055 0.122 0.268

200 0.039 0.087 0.190

The message of Table 1 is clear. Precise estimates of q must bebased on a large number of whales. Even with N = 200 thecoefficient of variation of q is around 20%.

Correlation and regression analyses were used to examine therelationship between sighting probability and the factors discussedin Section 2 believed to affect it. The explanatory variables con­sidered in these analyses were

visrRATEFAR

NARROW

YEARNPERCHSPERCHONEN

visibility coded 1 for EX-VG, 2 GO, 3 FA, 4 PO-UN1 for rate of whales/hour ~ 10, 2 for rate > 10fraction of new and missed whales in the visibilityand rate class seen at distances ~ 2000 metersfraction of whales in the class seen when the leadwas narrow (s 3500 meters) but not closed78, 79, 80, 81, or 82height of North Perch in metersheight of South Perch in metersfraction of whales in the class seen when therewas one North butwere or more observers

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ONES fraction of whales seen when there was only oneobserver at South Camp but two or more at North

THREES fraction of whales seen with three or moreobservers at South Camp and two or more at North

The correlation matrix among these variables and q is shown inTable 2.

Table 2. Correlation matrix for explanatory variables and q. i

q V'lSI RATE FAR NARROW YEA..-q NPERCH SPERCH O:N"'EN O:N"'ES

VISI 0.278

RATE 0.043 -0.020

FAR 0.259 -0.005 0.030

NARROW -0.222 -0.038 -0.239 -0.568

YEAR -0.049 0.150 0.113 0.019 -0.529

'N"PERCH 0.176 -0.125 -0.106 0.376 0.195 -0.684

SPERCH 0019 -0.101 -0.103 0.010 0.160 -0.551 -0.089

Ol-l"'EN -0.152 -0.089 -0.167 -0.033 0.242 -0.686 0.302 0.569

ONES -0.157 -0.219 -0.285 -0.147 -0.023 -0.003 -0.325 0.303 0.200

THREES -0.061 0.264 0.109 -0357 -0.242 0688 -0.943 0029 -0.268 0.112 ;

The variables most strongly correlated with q are VISI and FAR.There are strong correlations among the explanatory variables.FAR and NARROW are negatively correlated; when the lead is nar­row, whales are less likely to be far away. YEAR shows a strongpositive correlation with THREES and a negative correlation withONEN; there were more observers in the later years. YEAR is alsohighly correlated with the perch heights since the average heightsfor each year were used in these analyses.

The large number of explanatory variables and their inter­correlations made it impossible to conduct a meaningful regressionanalysis using all of them simultaneously. In order to determinewhich of these variables had the most influence on percent ofwhales the possible subsets" regression program

was s

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A weighted regression using weights l/viir(q) with viir(q) givenby

(3.2)

was done since the estimates q corresponding to different visibili­ties and rates used as outcome variables in the regression werebased on widely varying numbers of whales and thus hadsignificantly different variances. The estimate (3.2) is derived from(3.1) by using estimated in place of true values and noting that(2.7) can be rewritten as

(3.3)

so if nt is the number of new whales counted in a visibility and rateclass and q and N are the estimates (2.6) and (2.7) for that class,N(i - q) ~ nt.

The statistics for the best subset are shown in Table 3. Theexplanatory variables NARROW, VIS!, RATE, and THREES wereincluded in this regression, and all but RATE had significantcoefficients. The positive coefficient for VISI indicates that percentmissed increases as visibility gets worse. The other coefficients arenegative, indicating that the probability of missing a whaledecreases at narrower lead widths, higher rates of passing whales,and larger numbers of observers.

The whales are closer to the perches when the lead is narrow,so the result for NARROW is as expected. We also expect to missfewer whales with more observers, although the importance ofnumber of observers may be somewhat exaggerated in the regres­sion results since THREES was highly correlated with YEAR and maybe serving as a proxy for other year variables such as perch loca­tions which were not included in the model.

The RATE coefficient indicates a higher sighting probability athigh rates of whales, while field experience indicates that sightingprobability is lower at higher rates because observers must spenda greater proportion of the time measuring the range and bearing

the data and a

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provides some support for the idea that fi may be biased downwardat high rates because North Camp observers score more whales asquestionable. However, the lack of significance of the coefficientand its relatively small contribution to explaining the variability offj prevent us from drawing any conclusions. The effect of RATEcould be examined more adequately if more time were spent infuture censuses with both camps watching at high rates of whales.

Table 3. Regression results, best subset of variables for explaining .

Statistics for best subset:

Mallows' Cp 4.32

Squared multiple correlation R 2 0.41

Multiple correlation R 0.64

Adjusted R2 0.31

Residual mean square 3.24

Standard error of estimate 1.80

F -statistic 4.21

Numerator degrees of freedom 4

Denominator degrees of freedom 24

Significance 0.01

Coefficients for each variable:

Variable Regression Standard t-Coefficient Error Statistic

Intercept 0364 0.344 1.06

NARROW -0.239 0088 -2.72

V1SI 0.072 0.026 2,78

RA'MT: -0,067 0,045 -1.50

THREES -0.223 0,073 -3,07

Significance Contribution

toR 2•

0.300

0.012 0.18

0,010 0,19

0,146 006

0.005 023

• The contribution to R 2 for each variable is the amount by which R 2 would

be reduced if that variable were removed from the regression equation.

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replaced in some of the subsets by ONES, YEAR, SPERCH, and/orNPERCH. Fewer observers and lower perches always predictedincreases in percent missed.

Regression analyses were also performed using the Iogit ofestimated sighting probability, In(jJ/q), as the outcome variablewith a corresponding transformation of the weights. The logittransformation is often used in regression analyses of estimatedprobabilities because it tends to linearize the relationship betweenthe outcome and explanatory variables. The best subset of expla­natory variables in the analyses which used the legit as the out­come variable included only VISI and THREES with visibility clearlythe dominant factor. Some subsets rated among the best includedFAR rather than NARROW, again pointing to an increased probabil­ity of missing whales which pass farther from the perches.

Plots of locations of sighted whales also indicate that the dis­tance at which the whales pass is a critical factor in sighting proba­bility. In practice, the largest distance at which whales can beseen is around 3000 or 4000 meters when visibility is good and thisdistance decreases at poorer visibilities. It appears that the falloffin sighting probability begins at distances as small as 1500 or 2000meters when visibility is good.

Additional analyses of the 1982 data were conducted to 'exam­ine the increase in the probability of missing a whale with distance.We concentrated on 1982 because the largest amount of data at allvisibilities with both camps watching was collected in 1982.

We separated the new and missed whales for each visibilityclass in 1982 into two groups. The first contained whales whoseclosest point of approach to the camps (y-coordinate) was less than1500 meters under the assumption that the whales travel roughlyparallel to the ice edge. The second group included whales whoseclosest point of approach was 1500 meters or more. RATE wasignored in this analysis. Probability of missing a whale wasestimated separately in the two distance groups for each visibility.

We obtained q < 0.3 with y < 1500 meters in each visibility class.For y ~ 1500 meters, s> 0.4 in all cases. Relatively few whales wereincluded in the distant groups for EX-VG, FA and PO-UN visibilities,so confidence intervals for q were wide. However, at GO visibility,230 offshore and 544 nearshore whales were counted, giving esti-,"He",,-""-.::> if = if =

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significantly higher estimate of percent missed obtained for thewhales farther out in the lead is evidence that we need to considerdistance in estimating sighting probability.

In order to adequately model sighting probability as a functionof distance and to correct for whales which pass beyond visualrange, we need an independent measurement of distribution of thewhales across the lead. This distribution likely varies from year toyear and even day to day depending on ice conditions. Some aerialsurvey and acoustic location of whales has been done during pastcensuses to get an idea of this distribution. We are at presentworking on the development of a model to correct for distance, butmore data on the distribution of the whales needs to be collected infuture censuses to permit verification of the adequacy of any dis­tance correction.

Since the RATE coefficients in the regressions were notsignificant, we reestimated the q's after pooling the high and lowrate data. The reestimated q's were used in obtaining theminimum population estimates discussed in Section 4. These q'sare plotted by year in Figure 1 as a function of visibility. We haveomitted 1979 from the figure because, for reasons discussed inSection 5, no population estimate was made in 1979.

The plotted 95% confidence intervals based on the asymptoticnormality of the estimates are q ± 1.96.Jvar(q) "With q given by (2.6)and vfir(q) by (3.2). Confidence intervals are truncated at g = °andq = 1 (100 percent missed) in the plots. Figure 1 illustrates anumber of the problems encountered in estimating g.

If either nl = °or nz = 0, it is impossible to compute meaningfulestimates of q and its variance. For this reason, no estimates werecomputed for FA or PO-UN visibility in 1980. In addition, when, asin 1980, very little data is available for estimating g, confidenceintervals may be very "vide. Because they are based on the highlyvariable estimate g, these confidence intervals may also be poorapproximations to 95% confidence intervals. In 1980 they indicatethat more whales are missed when visibility is EX-VG than whenvisibility is GO. We recognize that such reversals of expectedresults might occur in fact due to such factors as the distance atwhich the whales were passing. However, they occurred in thesedata sets only when the counts of whales used in (2.6) to compute

or q were '::>lll.Llll.

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more precise estimate of the average percent missed by poolingdata from adjacent visibility classes.

In Table 4 we present the estimates g for all years and all visi­bility classes along with the numbers of new and missed whales andthe watch time on which these estimates were based. The pooledg's used in 1979, 1980, and 1981 to obtain the population estimatesof Sections 4 and 5 are also given in Table 4.

4. values, for estimates of probability of missing a whale.

Year Visibility New Missed Minutes g S.D.(g) Pooled S.D. of

Whales Whales of Watch~

Pooledq

1978 EX-VG 552 134- 9264 0.243 0.023

GO 318 132 7796 0.415 0.043

FA 141 86 8194 0.610 0.083

PO-UN 16 3 2261 0.188 0.118

1979 EX-VG 58 7 2134- 0.121 0.048

GO 65 26 4661 0.400 0.093 0.40 0.07

FA 51 20 2520 0.392 0.103 0.40 0.07

PO-UN 12 0 685

1980 EX-VG 40 29 2209 0.725 0.177 0.46 0.10

GO 28 3 619 0.107 0.065 0.46 0.10

FA 2 0 242 046 0.10

PO-UN 0 0 0

1981 EX-VG 47 16 962 0.340 0.099

GO 141 87 2960 0.617 0.064 0.57 0.07

FA 58 26 2138 0.448 0.106 0.57 0.07

PO-UN 34- 18 1754 0.529 0.154

1982 EX-VG 214 39 2159 0.182 0032

GO 624 150 10423 0.240 0.022

FA 232 71 4144 0.306 0.042

PO-UN 138 63 3161 0.457 0.069

The estimates for PO-UN visibility are the most variable and

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consequence of the paucity of data at poor and unacceptable visi­bilities. However, we suspect that it reflects a breakdown in theassumptions of the model. The maximum distance at which awhale can be seen may well be so small under PO-UN visibility con­ditions that there is no overlap between areas visible to the twocamps, and it may be much more difficult for North Camp to deter­mine that a particular whale was missed. We have consequentlyexcluded PO-UN data from the population size estimates to be dis­cussed in the next section.

4. Estimation of Number of Whales Passing Daily

In Section 2 we noted that in order to account for unwatchedhours and hours with unacceptable visibility appropriately, we needto estimate numbers of passing whales N on a day-by-day basis,summing over days to get a season total. In Section 3 we deter­mined estimates fj of the probability q of missing a whale underparticular visibility conditions which are based on the entirecensus season. In this section we assume that q depends only onvisibility; that is, q for a given visibility condition is assumed to beconstant throughout the season. Visibility is assumed to be thesame at North Camp and South Camp at any given time so that thebasic multinomial model described in Section 1 can be assumed tohold for each visibility.

We are now ready to derive daily estimates which approximateminimum variance unbiased linear combinations of estimates ofthe form (2.7) for the acceptable visibility classes (EX-VG, GO, FA).The derivation is based on the assumption that the mean numberof whales per minute passing during the day is constant. Forexample, the number of whales passing might have a Poisson distri­bution with a constant rate. We derive approximate variances forthe daily estimates and covariances among them.

We note that our definition of "acceptable visibility classes" isbased on the 1978-1982 seasons. If a season occurred in which thenumber of hours scored as EX and VG was large, they could beseparated into two classes with separate q's. Similarly, if manywhales passed when visibility was PO, PO could be separated from

treated as acceptable, though our analyses indicate that

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The minutes of watch at acceptable visibility during the daycan be divided into categories. We will use the subscript i torepresent visibility class as in Section 3. However, we 'will now use j

to indicate how many camps were watching, j =1 or j =2.

Usually i = 1 for EX-VG, i = 2 for GO, and i = 3 for FA. However,if we pooled visibility classes to estimate s«. we also pool theseclasses in estimating N. Thus in 1980 i = 1 for EX-VG-GO-FA. In1979 and 1981 i =1 for EX-VG and i =2 for GO-FA.

Let

N =~j =nlij =n2ij =qi

Ni j =

true number of whales passing during the day,number of minutes at visibility i andnumber of camps j during the day,number of new whales counted by South Camp atvisibility i and number of camps j during the day,number of missed whales counted by North Campat visibility i and number of camps i,maximum likelihood estimate of qi' theprobability of missing a whale at visibility i,

number of whales which passed during the 'm;.j minutesof watch at visibility i and number of camps i.

and

(4.1)

Since n1ij + n2ij has a binomial distribution with parameters Ni j and1 - qi j , Lemma 1 of Sanathanan (1972) tells us that the maximumlikelihood estimate of Nij is [(nlij + n2ij)/(1 - qi

j)]. Sanathanan'sTheorem 1 tells us that qi converges almost surely to qi, so if qi isbased on a large enough number of whales, (4.1) should be close tothe maximum likelihood estimate of Ni j .

We wish to find a daily estimate of the form

N = LL Cij Ni j ;i j

(4.2)

that a linear combination of estimates for the visibility classeswhich occurred during the day. We impose some reasonable con­straints on the coefficients Cij in this linear combination. Weassume that Cij = 0 if 'm;.j = O. Otherwise we wish to have the form

= = I,

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Since 1440 is the number of minutes in the day and Nij/TTl.;.j is anestimate of rate of whales per minute, the multiplication of Nij by1440/TTl.;.j scales the estimate Nij up to represent the whole dayinstead of only TTl.;.j minutes. With these constraints, we now deriveaij to minimize the variance of (4.2).

We make two assumptions in order to simplify the derivation.These assumptions are required to make (4.2) an approximateminimum variance unbiased estimate given that Cij have the form(4.3). First, assume that gi jFl:1gi j so NijFl:1(nhj+n2ij)/(1-gi

j).

Second, assume that Nij R: TTl.;.jN/1440 on the basis of our earlierassumption that the mean number of whales per minute passingduring the day is constant. If the number of whales passing is Pois­son with fixed rate, then the conditional distribution of Nij given N

is binomial with parameters Nand TTl.;.j/1440 so E(Nij ) = N TTl.;.j/1440

and our second assumption is reasonable.

It follows from these two assumptions and the binomial distri­bution of n hj + n2ij that

(- 1 TTl.;.j N. .

varNij)R:( ')2 1440- gi'(1-gi')1 - gi'

and

var( ~ ~ Cij N ij ) = ~ ~ ai/ [~Orvar(Nij)

g,jR: 1440 N I; I; ai/ (t j)

i j TTL;.j 1 - gi(4.4)

Minimizing (4.4) subject to the constraints given by (4.3) is justfinding the infimum of a quadratic d'A d, where d is the vector ofcoefficients aij and A is a diagonal matrix with the correspondingg/ / [TTL;.j(1 - gi j ) ] on the diagonal, subject to the constraint 1'd = 1

where I' =(1, 1, ... , 1). Rao (1973), p. 60, shows that the desiredinfimum is attained at ex = A -11 [ I' A -1 I t 1 1, i.e. for

(4.5)

Even if the assumptions required to make (4.2) a minimumvariance estimate with Cij defined by (4.3) and (4.5) do not hold, theaij of (4.5) are reasonable. They give more weight to counts based

- 18-

probability 9i of missing a whale is large. Data obtained when bothcamps were watching gets more weight than data from only onecamp if the number of minutes watched and the visibility are thesame.

We now derive an approximate variance for N of (4.2). We treatthe Cij of (4.2) as constants although they are determined by usingqi in place of 9i in (4.5) since their variability is negligible relativeto the variability of Nij . Thus

var(N) =L [Ci1 2 var(Ni 1) + 2 cil Ci2 COV(Ni 1• Ni2) + Ci22 var(Ni2)]. (4.6)t

Note there are no covariance terms involving different i in (4.6)since data from different visibilities are assumed to be indepen­dent.

If nlij + n2ij and fli were independent. then it would follow from(4.1) that

var(N.. ) = var(nl" + n2") var[-_1-.]tJ tJ tJ 1 ~ ,- qi J

+ var(nlij + n2ij) E 2[ 1~ .11- q/

+ E 2(n lij + n2ij) varlf

1~ .11 - qi J

(4.7)

See, for example, Hogg and Craig (1970), p. 168. When j = 1, therequired independence holds since qi is based only on counts madewhen both camps were watching. When j =2 there is some correla­tion. However, if qi is based on a large number of new and missedwhales, its correlation with the new and missed whales counted ona single day should be negligible. We therefore assume that (4.7)provides a reasonable approximation to the variance of Nij .

We know from the assumed binomial distribution of nlij + n2:i.j

that

(4.8)

and

(4.9)

We assume that

1

- 19 -

and we use a first order Taylor series expansionapproximate variance for 1/(1- iIi l ) as follows:

1 d [ 1 1(- )Fl:: +_. .- ,1 J. d- 1 - J' qt qt- qi qi - qi

[ 1 1 [1 1 12

vaT . R:: E . - .1 - g/ 1 - giJ 1 - giJ

~ [~, [1 -\,; IJ'vor(gi)

i.e.

to derive an

(4.11)

with vaT(gd defined by (3.2).

It follows from (4.7) - (4.10), substituting estimated for trueparameters, that

VaT (Nil) = Nil gil (1 - g/) [VaT[ 1 _\il 1+ 1 1(1 - g/)2

+ Ni/ (1 - gi j)2 VaT[1_\7] (4.12)

where VaT[ 1_ j ] is defined by (4.11).1 - qi

Using the same assumptions as those from which (4.12) wasderived, we obtain cov (Nit. Ni 2) as follows:

since counts when only one camp is watching are independent ofcounts when both camps are watching, and both are assumed to beindependent of gi' Now

1 ..: gi 1 _1iIi i] = 1 ..: gi 1 _1qi E [ 1 - \i 2 ]

1= -- 1J!Tr'I---1

- 20-

(4.14)

so from (4.8), (4.13). and (4.14) we obtain

(4.15)

so (4.6) becomes

var(N) =~[ciI2var(Nil) + 2 CiICi2CDV(Nil' Ni2) + ci22var(R:i2)] (4.16)\

with var(Ni l) and var(Ni2) given by (4.12) and cDv(Ni l• Ni2) given by(4.15).

Now suppose N =2.:2.: 9ij FJij and N' =2.:2.:ci;,Ni;, are the daily esti.~ j i j

mates (4.2) for two different days. We need to determine cov(N. FJ')since the variance of the estimate of total number of whales pass­ing during the season will involve this covariance. Because countson two different days are independent and data from different visi­bility classes are independent, the derivation is essentially identi­cal to that of (4.15).

cov(N. N') = 2.: [Cil Cil' cov(Nii • Nil') + Ci2 Ci2' COV(Ni2• Ni2' )\

i.e.

x (1 - qi) (1 - qi2) covl 1 1 ~ , 1 )I- qi 1 - fji 2

so using (4.14) we obtain

COV . II') = 2.: rCil Cit' Flit Nil' (1 - §i)2 Va1"!-'--t L

- 21 -

(4.17)

with vaT(fj.} given by (3.2) and vaT[ l_ JIby (4.11).1 - qi

5. Estimating Population Size from the Daily Estimates

A minimum population estimate for the western Arctic stock ofbowheads is obtained by summing the daily estimates (4.2) over allwatched days. We define a day as "watched" if there is at least anhour of watch under acceptable visibility conditions. A "missedday" is a day which is not "watched". We do not compute (4.2) formissed days since the fJ obtained would be either 0 or based on solittle data that, considering the Mann-Whitney test results dis­cussed in Section 2, the extrapolation to the rest of the day wouldbe suspect.

If we write T for the season total estimate, the minimum esti­mate is

T = ~ fJwatched days

(5.1)

where iJ is given by (4.2). We are making the implicit assumptionthat no whales passed on missed days.

Note that if visibility were constant throughout the season andboth camps were watching all 1440 minutes of every day, T givenby (5.1), if an integer or if truncated to the next smallest integer,would be identical to the estimate (2.7) as we would hope.

Suppose we believe that whales passed on some fraction 1m ofthe number of missed days rn . If w denotes the number of watcheddays, then we can compute a correction factor

F =(w + 1m m }/ w (5.2)

and a scaled up estimate F T of the season total which is equivalentto filling in the fraction 1m of the missed days with the averagedaily estimate.

In order to avoid downward bias in the average daily estimatecaused by including days watched before whales were seen, we

as a urnala was

- 22-

seen and the last watched day as the last on which a whale wasseen. Missed days would generally include only those between thefirst and last watched day although others could be added toaccount for migrations believed to have begun before the firstwatched day or to have continued after the last watched day.

Because of the variability in the distribution of whales overperiods of more than 24 hours, the correction for missed daysdescribed above will be biased unless the missed days are ran­domly distributed among days representing the varying rates ofthe migration. In years such as 1979 in which a large block of dayswas missed at the height of the season, the estimate F T of totalwhales, even though it includes a correction for missed days, willinevitably be too low. On the other hand, the estimate F T will betoo high in a year with no missed days at the height of the migra­tion but many missed days when rates are low. These biases cannotbe accounted for in our variance estimates, and thereforeconfidence intervals computed for different years may not overlap.Clearly, a meaningful confidence interval for total whales cannot becomputed for a year such as 1979 in which large numbers of dayswere missed.

Although there is certainly variability involved in thespecification of (5.2), it is hard to quantify. We therefore treat F asa constant. Then

and if

var(F T) = F 2 var(T)

S =.Jvfir(T)

(5.3)

(5.4)

is an estimate of the standard deviation of the season total esti­mate T, then an approximate 95% confidence interval for T is

(T - 1.96 S, T + 1.96 S)

and the corresponding confidence interval for F T is

(F f - 1.96F S, F f + 1.96F S).

(5.5)

(5.6)

These confidence intervals are exact if T is normally distri­buted. The assumption that f is approximately normal wouldclearly be appropriate for (2.2) in view of the asymptotic normality

1

- 23-

For T given by (5.1) we could appeal to the Central LimitTheorem to guarantee approximate normality if the N wereindependent or, under some conditions, weakly dependent. Thecovariance between N and N', given by (4.17), clearly becomesnegligible asymptotically since gi -+ qi almost surely. Even for smallsamples, daily estimates based on different visibilities are indepen­dent, so a Central Limit Theorem argument has validity.

We also note that T of (5.1) is a linear combination of the esti­mates iJi j of (4.1) and is therefore normal if each Ni j is normal. SeeRao (1973), p. 519. The numerator nlij + n2ij of Nij is asymptoticallynormal since it is binomial. The denominator 1 - gi j converges inprobability to the nonzero constant 1 - q/ since gi converges to qi

and by assumption 0 < qi < 1. Therefore Nij is asymptotically nor­mal. See, for example, Rao (1973), p. 122.

To obtain the confidence interval (5.5) or (5.6), we need an esti­mate var(T) of the variance of the T defined by (5.1). This estimateis

var(T) = var(~N) = ~var(N) + ~cov(N. N') (5.7)

where var(N) is defined by (4.16) and ciiu (N. N') by (4.17). The sumof variance estimates is over all watched days, and the covariancesum includes all pairs (N, N') with N and N' representing differentdays.

In Section 1 we mentioned conditional and questionable whales,those which observers are unable to score as new, duplicate,missed, or seen by both camps. These conditional and questionablewhales can be used to obtain less conservative minimum populationestimates than the low minimum estimate (5.1). Although we neveruse conditional or questionable whales in estimating sighting pro­babilities, the user of the program which computes the daily andyearly estimates of numbers of whales is allowed to specify a frac­tion Ie of conditional whales which he/she believes should be addedto nlij, the number of new whales, in (4.1) and a fraction I q of ques­tionable whales to add to the missed whales n2ij' That is, the pro­gram (which appears with sample output in the Appendix) permitsclassification of the group of whales which observers were unable tocategorize as new, missed, duplicate, or seen by both camps. Weused I m =r, =f q =0.5 to get a "middle" minimum population esti­

areciassined as

- 24-

new and missed, the computations of this section and Section 4proceed as before.

In Figure 2 we plot the low, middle, and high estimates. Theapproximate 95% confidence intervals shown in Figure 2 are givenby (5.5) for the low estimate and (5.6) for the middle and high.Table 5 gives the exact values of the estimates. Table 5 values areslightly different than those presented by Krogman et al. (1983)since the laUer were made using q's based on watched periods hav­ing RATE ~ 10 whales per hour to avoid any possible bias due tohigh rates. For purposes of comparison, the low minimum esti­mates for 1978 and 1980-1982 in Krogman et al. (1983) were 2598,2423, 2397, and 2606, respectively. After completing the analysesreported in Section 3, we concluded that the possible bias causedby including high rate data in estimated q's was offset by the gainin precision of the q's provided by basing them on a larger numberof new and missed whales.

Table 5 Estimated whale numbers f. standard deviations. and approximate 95% confidence intervals.

Year Watched Missed Low Estimate Middle Estimate High Estimate

Days Days f ± s. d (f)(confidence interval)

1978 41 6 2615 ± 88 3193 ± 105 3823 ± 122

(2443. 2788) (2988. 3398) (3583. 4063)

1979 19 17 542 ± 28 Not computed because extrapolation

(488. 597) to missed days invalid.

1980 13 0 2066 ± 203 2284 ± 225 2502 ± 246

(1668. 2484) (1844. 2724) (2020.2985)

1981 36 11 2620 ± 344 3376 ± 442 4226 ± 553

(1946. 3295) (2509.4243) (3143. 5309)

1982 26 8 2545 ± 51 3397 ± 66 4372 ± 84

(2446. 2645) (3267. 3527) (4208.4535)

(5.8)

- 25-

We turn, then, to the low estimates of Table 5 and Figure 2. The1978, 1981, and 1982 estimates, with a mean T of 2593, do not differsignificantly. The 1980 estimate is significantly lower. The 1979estimate is included only as an example of the impossibility ofobtaining a population estimate for a year in which a significantnumber of days at the height of the migration are missed; we willnot consider it further.

The 1980 census differed from the others in several respects.First, it was the only year in which the ice camps were locatedsouth of Barrow. As noted in Section 2, whales pass further fromshore at that location and are more likely to be missed.

Second, in 1980 an ice blockage prevented the migration frombeginning at the normal time. When it did begin, the rate at whichwhales passed was higher than in other years; all the whalescounted passed during a 13-day period. The migration period dur­ing the other years was 1 to 1)f months long. As a consequence ofthe high rates in 1980, the two-camp watch with one-way communi­cation was abandoned for most of the season, and very little datawas available for estimating qi'S. Thus we were forced to use thesame q for all visibilities as noted in Section 3.

We can compute a sample standard deviation

[1 1

1

/2s = -- ~ {f - T )2n-l n years

of the estimates f of (5.1) where T = (~ f)/n and n = 3 (if we omit1980) or n = 4. We obtain s = 41.9 when we omit the anomalous1980 value and s = 265.9 when we include 1980; the estimates Scomputed from (5.4) are of the same order of magnitude. Sincethe estimates f indicate that the population is neither increasingnor decreasing rapidly with time, the rnean of the 1978, 1981. and1982 values also estimates the population size. Thus the compara­bility of s and S is evidence that the variance estimate (5.7) pro­vides a reasonable representation of the variance of the annualestimates.

More significant between-year differences are indicated by themiddle and high estimates. It may be that the population whichpasses the camps does in fact differ from year to year. Alterna­tively, it may be that the variability introduced by including frac­tions of missed days and conditional and questionable whales

- 26-

6. Suggestions for Future Research

In this section we summarize recommendations for futureresearch which would strengthen the data base available forestimating population trends in the bowhead whale stock. The icecamp census and other recent studies indicate that the presentpopulation is considerably smaller than it was before commercialwhaling began in 1850. There is no clear evidence that the popula­tion is either growing or declining, but large counts of calves in1982 are a cause for optimism.

Our first recommendation is that the ice camp census be con­ducted each spring for the next several years whenever ice andvisibility conditions do not preclude the collection of usable data.The following points need to be kept in mind in locating and staffingthe perches:

1. The model used in estimating sighting probability assumesthat North and South Camp observers have the same pro­bability of seeing a whale. To insure that this assumptionholds, the two perches should be reasonably close together(probably within a kilometer of each other) and as similaras possible in terms of height, location relative to the lead,etc. To avoid biases due to the skills of individualobservers, it would be wise to rotate observers betweencamps.

2. We have not examined differences among observers in ouranalyses. As far as we know, shift assignments in previouscensuses have not been made using an experimental designwhich would facilitate such analyses. As well as rotatingobservers between camps, they should probably be rotatedamong times of day to avoid time-of-day biases. This rota­tion must be done in a manner that avoids observerfatigue. An appropriate experimental design for accom­plishing this goal could be developed.

3. There is some evidence that more whales are missed whenthere is only one observer at a camp and fewer are missedwhen there are three or more observers. We recommendhaving at least two observers at a perch at all times.

- 27 -

4. It is extremely important to maintain two perches withone-way communication (South to North) for a significantpart of the season so that estimates of the probabilities ofmissing whales under the different visibility conditionswhich occur during the season will be precise and will berelatively uncorrelated with the counts of whales on anyparticular day. Several hundred whales must pass withboth camps watching at a given visibility to obtain a goodestimate of percent missed for that visibiity,

5. If it is desired to study effects of high rates of whales orpoor visibility on the estimates of percent missed, moredata must be collected at both camps under these condi­tions.

6. The precision of the census results could be improved ifobservers could be trained to make more accurate deci­sions as to whether whales are new, missed, or duplicate. Adecrease in the number of whales scored as conditional orquestionable would mean more reliable estimates of per­cent missed and total numbers and would perhapsdecrease the need for making separate low, middle, andhigh population estimates based on assumptions about theconditional and questionable sightings.

Second, the analyses of Section 3 and the work of Clark (1983)and Cummings et al. (1983) indicate the need to incorporate thedistance at which the whales pass in our sighting probability model.If the ice camp census is to account for whales which pass beyondvisible range, independent data must be collected using acousticand/or aerial surveys to establish the distribution of whales acrossthe lead on a daily basis. A report addressing these issues ispresently in preparation.

This research was supported by the North Slope Borough (NSB),Barrow, Alaska, and by NSF Grant MCS80-02167. The experimenlaldesign and collection of data which permitted our analyses camefrom many years of cooperative research effort by the NSB and the

Mammal Marine

- 28-

Administration, Seattle, Washington. We have gained invaluablehelp from all the scientists engaged in bowhead research. In par­ticular, we are grateful to Lee Eberhardt, Jeff Breiwick, and JoeHorwood for contributing to the basic idea of the percent missedcorrection. We thank Mayor Eugene Brower, Tom Albert, and RayDronenburg of the NSB and Mike Tillman and Howard Braham of theNMML for their contributions to the cooperative effort. David Rughand Geoff Carroll played principal roles in the experimental designand collection of field data. Richard Grotefendt assisted with dataprocessing and analysis. Finally, we thank Paul Sampson for callingour attention to the paper by Sanathanan and Michael Perlman forreviewing this report.

REFERENCES

Clark, C. W. (1983). The use of bowhead vocalizations to determinethe distribution of whales within the lead (1979 and 1980).Presented at the second conference on the biology of the bowheadwhale, sponsored by the North Slope Borough, March 7-9, 1983,Anchorage, Alaska.

Cummings, W. C., Holliday, D. V. and Ellison, W. T. (1983). Usingbowhead underwater sounds to determine spatial distribution ofthe migratory whales. Presented at the second conference on thebiology of the bowhead whale, sponsored by the North Slope Bor­ough, March 7-9, 1983, Anchorage, Alaska.

Dixon, W. J. and Brown, M. B., ed. (1979). BMDP-79 Biomedical Com­puter Programs PiSeries. Berkeley: University of California Press.

Dronenburg, R. B., Carroll, G. M., Hugh, D. J. and Marquette, W. M.(1982). Report of the 1982 spring bowhead whale census and har­vest monitoring including 1981 fall harvest results. PaperSC/34/PS 9 presented to the IWC Scientific Committee, Cambridge,June 1982.

(1970). Introduction to Mathematical

- 29-

Krogman, B. D., Breiwick, J. M. and Horwood, J. W. (1982). Correc­tion factor for percent missed: bowhead whales. Working paperPS/WP 2, D2 presented to the IWC Scientific Committee, Cam­bridge, June 1982.

Krogman, B. D., Sonntag, R, Rugh, D., Zeh, J. E. and Grotefendt, R(1982). Ice-based census results from 1978-81 on the western Arc­tic stock of the bowhead whale. Paper SC/34/PS 6 presented to theIWC Scientific Committee, Cambridge, June 1982.

Krogman, B. D., Sonntag, R, Rugh, D., Zeh, J. E. and Grotefendt, R(1983). Minimum population estimates of the western Arctic stockof the bowhead whale from ice based census results 1978-82.Presented at the second conference on the biology of the bowheadwhale, sponsored by the North Slope Borough, March 7-9, 1983,Anchorage, Alaska.

Rao, C. R (1973). Linear Statisticallnjerence and Its Applications,2nd ed. New York: John Wiley and Sons.

Sanathanan, 1. (1972). Estimating the size of a multinomial popu­lation. The Annals oj Mathematical Statistics 43. 142-152.

- 30-

EX-YG GO FA PO-UN

VisibilityI

1978 1980

i- -'I

i1I

t,I!

1:

o L_..EX-VG GO F/\ PO-UN

Visibility

.J

T..i

1

r1I

100 r~-

u 80 ~(l)0)0)

;: 60 r+>~ 40o'-~ 20 l-

Io L_

1981 1982

EX-VG GO F/\ PO-UN

Visibility

• ..1

TII1

+>!:(l) 40 io'-~ 20 l-

Io L._

EX-VG GO Fr, PO-UN

Visibility

T

1i~I

1

T

1

Io L

100 r---­iI

!

+>~ 40 ro'­(l)

0.. 20 -r

U 80 i

(l) r0) ;

0) ,

;: 60 I-

10....;

e 1.. er e t lsse 1 95i~ CI

- 31 -

82 83

1

,i1

i1

1

High Estimates

,

1000 L.-I. -.1 1 - - 1

77 78 79 80 81

Year

4000

L 5000 ..-tJ.....~

(fJQ)

t"""'l

oL 3000 i­3:

!I

4- io .2000 ~

!L ICD I

..0EJ

Z

~

U 5000~Ln(J)

82 83

11:"--,

"

r-I I

! I

L __.__ .1__._...L . .L.__ .1._J1000

77 78 79 80 81

Year

4000 r4­o

5000

All Estimates

(fJ 5000(I)

t"""'l

oL3:

iL 3000 ;-Q) !

..0 ,E 'J

"- 2000

8S

$*Ii

.J'

iI

I

4000 -

5000 ~s:-tJ.....~

(fJQ)

t"""'l

oL 3000 ­3=

~liddle Estimates

4-

o 2000LQ)

..0E 1000 L __-t ..1. l.J.J

77 78 79 80 81

~

LJ 5000

~in(J)

82 83

TI

Il'J,

Low Estimates

r---I

i

4000 -

4-

o 2000

~

f!J(l)

t"""'l

os: 3000 :..3:

~

U 6000~Ln(J)

5000s:-tJ',-1

t.(I)

.J)E 1000 -.1 ••_ • .1 _.,.__l._--U

J77 78 79 80 81

ear ear

.1 .. 1 e

- 32 -

APPENDIX

Program used for computing estimates and sample output.

"---- "- - ----"-----

----- --------

20

-33-

------t'lroGIU" GET"C'''''Nr-------------------C PROGRAM TO CALCULATE 'ERCEMT KiSSED 0 fOR VARIOUS VISIBILITY

"-- ---C-AtlD-RATt-I:LASSrr-TRUPffiORTH AND SOUTH leE ClMP DiTA AND"',--,F""'fj"O""Kr-----­C Q AND THE DATA, A CONFIDENCE INTERVAL ESTIKATE N FOR TOTAL WHALES

----------cmRKCTU---cIRD* eoINTEGER NDAy,KDAy,NRATE,NVISI,KVISI,NCAKP,KCAK',KDISTINt EGEI( NLEAD, NCE AD, Noes, t, IHRO l>" IV IsO t 2), lHOO t 2), I!SR EVPARAKETER CNDAYal00,NRATEaZ,NVISIa5,NOBSa~1

--------...PA-RA~e-R-rRCl!'1Pa3,H CAKPaz ,Nt £10a4 IREAL fRACC31,TI"EKOCZ),TIMF.CNVISI,NRATEI,TIKEMCNVISI,NCAKP,NDAY)

-------~I~N~r~E~G~ER~IUKl61,IOs,IOBSOlzl,tYR~~I,HONOtZI,IOiYO(ZI,JOAYCCZIINTEGER IDIST(Z),LEADlNOAY),IVRlNDAy),KCNCNDAYI,IDAYCNDAYIINTEGER JOIVlNOAV"toBsNlNOAY),tOBSSINOAV"tVISCNOAYIREAL NWHALECZI,NEWCNDAYJ,KISSeD(NOAYI,NEWFARCNDAYJ

------~RE~A~l~FARINDAY',NHtNYISI,NCIHP,~JY~)~,~N~H~F'J~R7tnN~V~ls~I~,~~~Rr.lnTnE~)-------REAL KRATE,NTOTCNVISI,NRATEI,KTOT(NVISI,NRATEJ

------~R~ElnL~lEIDtNVISI,NRATE,NlEAD',RH08StNVISIIN'~R'J~T?E-,rnNO~BSrrl------­REAL TIKEL(NVISI,NRATE,NLFAOJ,TIKEOINVISI,NRATE,NOBSIREAL O(NVISI,NRITE),VARQ(NVISt,NRATE'REAL WLEADCNLEADI,TLEADCNLEAO),WOBSCNOBSI,TOBSCNOBSJREIL OCONl(NVISI,NCIHPI,OCONztNytSr,NCAHP),QCON3lNVISI'REAL NHATCNVISI,NCAK"NOAYJ,CCNVISI,NCAKP,NOAYI

-----.D~A~T~N/I,Z,3,4,8,q,

OPENCUNITaIUNCll,fILE-tIN$t)OPENtUNITaIONtzl,FIlEaffNRfJOPEN(UNITaIUNC3J,fILE-tOUTtJ

-------------~ornp~ENTuNIT-IuNI4J,FILEafOOTTEMflOPEN(UNIT atUN(51,fILE-tOUTHTStJ

--"--------uPElITUNIf-IUN (6), FILeafINPOTf)REAOCIUNCbl,.IMRATE,KVISI,MOIST,KLE~D,CFR~CCI),I-1,3J

--------...C..-L.,.,.uSF( ON It- ION (6' ,- ----------OPENCUNITaIUN(61,fILE-tINOtJ

----...,.C--,NlT1ALHATIuN AND HERGING OF NORTH INC SlJUTR1NTtJltKJlFnt---------CALL GETQNICIUN,fRAC,KDTST,KDAV,IOS,CARD,ICBSO,IYRO,KONO,IDAYO,

1 JDAVO,IARO,TIMEMo,IVIsn,LEAOD,IOI)l,NWHAlE,IYR,KON;l~ly;J]~A~Y~,~--­Z IP~EV,NDAY,TIMEK,10BSN,InBsS,IVIS,LEAD,NEW,KISSED,NEWFAR,

3 flISFARI00 10 l allZ

10 CLOSEtUNITaIONII'JC CALCULATE TOTALS AND BUILD ARRAY Of DAYS

ClLL GEIQNI (NVISI,HRAlE,NRITE,NCA~~tAnI~NUBSIN~A~,N~,1 TIMEM,NKLEAD,TIKEL,NMOBS,TIKEO,NTOT,KTOT,TIKE,NKFAR,IUN,10S,2 ITR,MON,IOlY,JOIY,flOIYI

C CALCULATE ESTIKATED Q'S ANO NtS, WRITE OUT FILE----~ CILL G~ElION,NVISI,NRATE,NCAHp,NLEID,NOBs,HVISI,HRATE,MCiHp,

1 KLEAO,KDlST,FR~C,NTOT,KTOT,TIKE,NKFAR,NKLEAD,TIKEL,NKOBS,

----------~Z~T~I~OAy,IyR'HON,IOAT,JDAY,TIHEH,NK,a,VIRO,3 WLEAD, HEAD, WOBS, TO BS,ecON1, aCONZ, CCON3, N"'AT,C )

DO 20 Ia3,6

CLOSECUNITaIUNCIl1--- ------CAt:l:l'KOLOAD

STOP-------"E!W- --" -------------- -"-

-----------SUijROUTINE GETQNOlcIRO,IDIST,IOSrC GET SIGHTING DISTANCE fROM CARD FOR GETON

------ -----CllUACTER CARlr*.'),8LJNOl --INTEGER IDlST lOS

-34-

SURROOTIRE G£TQNElIUN,NvISt,NRITE,NCIMp,NlEIO,HuBS,MVlsI,M~AlE,

1 "CAMP,MLEAO,MOlST,FRAC,NTOT,MTOT,TIME,N"FAR,NMLEAD,Tl"EL,----------~2-n~S,JIHEQ,KU~tMON,IOAT,JOIY#TTMEM,NM,~,vlRa,

3 WlEAO,TLEAO,WOBS,TOBS,OCON1,QCON2,QCON3,NHAT,CIINTEGER MOAY'NRATE,L,LL,NVT~TITSTt~'N~C~inM~pr,~M~C~i~H~P~,~M~DTlrSTr---------~INTEGER NlEAD,"LEAO,NOB~,I,J,K,M,IUN(6)

REAL QCUNIlNVISI,NCAMPJ,OCOR'-IRvISI,NCIMpi,NMINVISI,ACIMp,MOIV)REAL QCON3(NVISII,NHAT(NVTSI,NCAMP,MOAVI,CCNVISI,NCA"P,"OAVIINTEGER JDAYIMDIYJ,IVRIHOIVJ,HONlMOIYi,IDIYlHOAYJ,HIsoREAL NTOT(NVISI,NRATE),"TOT(NVISI,NRATEI,NMFAR(NVlSI,NRATE)REAL NHlEAOINYISI,NRITE,ALEIOJ,NH06S(AvISI,ARATE,HOBSIREAL FRAC(31,TEMP,TI"E(NVISI,NRATEI,TIMEM(~VISI,NCA"',"OAVIREll TIMELIRyISI,NRATE,NlEIOJ,TIHFOIRVISI,NRITE,NOBSJREAL Q(NVISI,NRATEI,VARQ(NVISI,NRATE),OAVN,VARN,VEARN,VEARVREAL WLEADlNlE1D),tlE10lNlEIOJ,W08S1N08S),lOSSIN08SJREAL FAR,TI"A,TIM',SO,QL,QU,QN,NOAYN,"RATE,CQ,CDVN

C CALCULAtE ESIIHAJED Q'S INO A'S, wRITE FILE DOTCHARACTER LABELR(21.~,LABELV(51.7

DITA L1BElR'fLOWf,fHIGA"DATA LABElV/~EX/VG~,~GOOO~,~FAIR~,tPO/UN~,tUNKNOWNtl

IFlHRATE.GT.2.0R.NVISI.GT.5.0R.HCIKp.CT.ZiCO TO 90WRITE(IUN(31,IIIFRAC(II,FRAC(21,"OIST,"RATE,"LEAO

11 FQRMATlfFRACTIUN OF C t~EITEO IS N ·',F5.2,f Q AS H .~,F5.ZI

1 ~FAR GT~,I5,5X,~HIGH RATE GT~,F5.1,5x,tOPEN LEAD GTt,I51Z 'vISIBILITY RATE NEW HISSED MIRUtES Q f,3 tVARIANCE SO CItl

---~4~T FRACTIONS FlR WAllES CLOSED LEAD NARROW LEAD f,5 ~OPEN LEAD UNKNOWN LEAOtletA fOlD BY 0as ERV·...E"l>"R-CrLT'AS..,S...,"r,...,4'""'{",•..--...,WrDArTl'L....E....S-""T'1"11HRlE!"'lf..,JnJ.---------------­

C FIRST Q'tS--------UlJZ'.,..O--.-1=--.1,...,''""'NV1 ....STl---------------------------------

00 20 J·l,NUTE----~FINTOTll'J).EO.O••O~TlI,JI.Ea.c.)TAEN

Q(1,JI·l.YUQlI,J) ·2.

ELSEJEflIP-NJ OJ t hJ JQ(I,JI-MTOT(I,JI/TE"P

----------vARQ I h J ) • Q(11J)Ttr;·~+-Q~I~h-J~r~"~T~E~H~P~----------------------ENO IF

--------.S.....O.S QRt tv Alll I#J'TlQL·Q(I,JI-l.Q6·SDQu·a(1,JI+l.Q6·SDTIMP·MAX(TI"E(I,J',1.1TEHP·HAX(NTOTCI,J)+KTOTlT,JJ,l.JFAR-NHFAR(I,JI/TE"'

-----OU-rO K.l,NLElOWLEAO(KI·NMLEAO(I,J,KI/TE~P

10 tlEAOtK)·IIHELtl,J,K),JIHP00 15 K-l,NOBS

------- - ----vOlJSTTO"'iil'l11'01f)t~I-,~J~,K"..)r·'~t""E"'flI"'p'----------------------------

15 TOBS(K)·TIHEO(I,J,K)/TI"P--------vRTTETlUNl:;-l,n'lT;Ul!£[VlTJ""iJ'LAB'~fINlOlrr;-J), HTOT II, J), -----­

1 TIHE(I,JI,Q(I,JI,VARQ(I,J),SO,Ql,O~,FAR,(WLEAO(KI,TLEAO(KI,

-------..,z-vK-;_'1-=-,UNL""El:"ArnO"'-VlTB S IK) , TOil SrKT;1<. I. NO 13 S IC IF NOT USING ANV CONDITIONALS OR QUESTIONABLES, SAVE Q(I,J)

-- TFTfUCnT;EQ~-O~;lND-;tnc(Zl~EQ.O.I tA;;.E:.;.N,.-.........-.-,........rr-r-IiiR llETIIDl 16 j,*JRTOn II J J iKTOTC I, J), TIHE( h J I, Q( lin,

1 VUQ(l,JI,FARWR1TEnUN16Ti'3'3'~)~1 ~W~lE-l...O....llITilITl:D IK), K·1, N(UD ),

1 (WOBS (KI,TOBS(K) ,K-hNOBS I---~C..---..Ir?'FlJnNG FRACTTOlrtrF-COllOYTTON1LS OR OUtsTfOlUBlES, RTIIHEvE 0H,J)

C WHICH 010 NOT USE THEMELSE

1

-35-

c Nor~ns useD F'ORQ""TIUT[Vy....S.....xs..---·----­IFlMCAI1P.GT.HRATE.OR.I1VISl.GT.HVISI)GO TO 90DO 205 1·1,"9ISIQCOH)lI)·VARQlI,l)/(l.-O(I,I')··Z

------l"£OO--ZU""5~CA"P

QU·QlI,I) ••Jla·I.-auTEK'·VARQ (l,lt .lFLOAHJ ).(QU/Q (I, U )/QLUZ )UZaCCNZ(I,J,·QC"Z'(EKPQCONllI,J)·QU*QL.ll./QL**Z+TEH"

ZU5----CUR TIROEYEARN·O.

-----~nv-o.

I'I1S0·0-------,O.,.,O........5"'Or-wK"""·...I"i1'l·,.,'C'a"Yy-------·---------------------

TEI1'·C.IIKa·o.00 Z5 I·l,I1VISI

---"'C-1:"F"T"I",x--cFOR..,-q~IODWREN-suuTJ1ANlJNORTH CAMP OUI III 1M SOUTH FILEIFlIYRlK'.EO.60.AHO.HONlK'.EQ.5.AHO.IOAYlK'.'E.Z~.

------.,.I-r1ANlJ."TU"AT (K, • tE • Z, Jf HE NNIH I,Z,K) .HHU.,Z,K )+HI1 n,I,K)

-------- --- --,......"rt("I"7,"Tl"7,VR"T'"'·l"£O-.------------------------TIHEHll,Z,K).TIHEl1lI,Z,K'+TII1EHlI,I,KJ

-----------~---rrK£I'I(X,l,K '·0.END IF00 25 J·I,MCAMP

C IF HAve POOLED 0, THEN POOL DAILY DATA AS WELLIF(~~ISI'THEN

L·I+lIF (er:I....,,...,I....'-.r""Eg-;ar(rrrr,rJTr'H'71EI:1N..------------------

TIKEHlL,J,K'·TIKEHlL,J,KJ+TIHEH(I,J,K'--------------.,.T.,.I~"FH(l,J,K)·O.

NI1(L,J,K'.NKlL,J,K)+HK(I,J,K)-----,H1\1-I1-J,"1ITito. ...:..::.:.-.;..~..;,..------------

END IF----- --~t:NU.,F~- ~--.----.-----~---~ ~--~---

CU,J,K) ·0.NHA' ( I, J ,1(..,)'......0......--·-----------·---------------QU·QlI,l)UJ

----"otar;-,;;-gu---- ---------------.. -------------InF~IT1MEI'I(I,J,I<'.LE.O.'GOTo z5

TII1A·TIHA+TIHEHlI,J,K)----.111£( 1, J' .TI"K£1ITlT~tfl7QrTU--------------------

TEMP.TEI1P+TIHElI,J)25 CONTINUE

OAYH·O.VARN·O.COVN·O.NOATN·O.IF(TIHA.GE.60.)GO TO ~o

C "ISSEO OAYKISO·KISD+lGO TO ,.q

33 FORI1AT(16F5.Z)------r;lf--O-----.....,,~ 5 IiI, 11 VISI

DO 45 J.l,KCA"'au·o(x,I,UJQL·I.-QUON·NI'\( 1.,3,1< J I QtHHAHI,J,K)·OH

-----~UAYfCiilfOAY~--.J-,I(.,.,-J----------------

IFlTII1EKlI,J,K'.LE.O.JGO TO 45-C1r,~-,r< ) • If If'!Et I, JlTTEM,,*.H7tcr.7T Il1E PI ( X, hI(n--------­

co-erI,J,K).QNDllN·OUN+CQVARN·VARN+ClI,J,K'.CO.(OCONIC!,J)+ON·QCONZlI,J)'

-------.I."F-1'( JO£Q ;Zlvnw.VAl{N+--z;TCTrilIl{l.NHllTIIll'IrJ~otnrnrn-

ll-l(-l--'-~~·----rFll1.--;·rr;1f)G1TItr itS

00 405 l·l, II----------cuvlfli.--cO~-cQ.CrI; J ,t ,tNHlnT;J;TUO-cmaTI, J ,

!F(J.EQ.Z COVN·COVN+ C f,l,1( +NHAn 11 lo.e I,Z,1. *"'H.HI,Z,-~~'---~ --"1-."tl:l*CTn-l,

4j05 CCNTXNUE

-36-

YEARK-YEARN+OAY~------T'~El~ViiT'EARV'""'+....vTlR..,N.,.,+...Z.-.......C'"'OVK-------------------

~q SO-SQRT(YARN)C WRI1E fILE fcrR~GRA"S

IF(K.EQ.l)WRlTE(lUN(5),55)"ON(K),IOAY(K) (K)------ft1ifrtlITITllflT

I-K/6O"-1*100+"-1*60

-NINHOAYN)

C END OF DO 50 lOOP--WRI1E OAT DlTA TO ".IN OUTpUT FILE50 WRITF.(IuN(3),55)lYR(K),KON(K),IOAY(KI,JOAY(KI,NOAYN,Tl"A,OAYN,

55

5 fRO CAMPf,5CF6.1,F1.111C NOw FINISH GETTING YEAR ESTIMATES

----------s1Ja:;-oRTTf£TRVl

66

71

9099

QL - YEARN-l.96*SDau - YEARN+l.96.S0WRITF.(10RC3J,66JY·~E~lR~N~,V~EnlnR~vr,~S~D~,or;oUIIYRCHClYJ,HDly,HISOFaRMAT(~NUMBER OF WHALES -~,F6.0,3X,~YARIANCE -t,F9.2,

1 3X,fSTANDARD DEVIATION -t,F7.lIt~5~CONFIDENCE INTERYAL ;-'n,2 F6.0,~,t,F6.0,tlt/IZ,t SEAS"N,t,I~,~ DAYS LONG WITH~,I3, •.3 , HISSING DIYS'ltESTIHATes SCALED UP FOR HISSING DlyS ARE})TIl1P-HOAY-HISO .tIKI-YEARNlTIHpTEl1P-(TIHP+FRAC(3).FLOAT(KlSO)/TIHPTEARR-TEMPtYEARNYEARY-TEl1P·.Z·YEARVSO-SORf( YEARY»aL-YEARN-l.96*SOQU-YElRN+I.96*SDWRITE(IUN(3),66)YEARH,YEARV,SD,QL,Q~

WRITEC!UN(31,17JTIHA,FRAC(3JFaRMAT(~"EAH PER DAY -~,F7.2,t USED FOR fRACTIONt,f~.3,

I f OF MISSING OIYS',RETURNWRITE(IUN(3J,99JfORKAT(~SUBRaUTIHE GETQHE CANNOT HANDLE VALUE Of PARAKETERtl ~

1 f "VISl, NVISI, MCAMP, OR NRITEfJSTOPEND

-37-

SUBROUtINE GETONFlHVISI,HTOT,NTOTIUIVIRQ,LJ8ELV,lURIC fIX QtS If NECESSARY TO 8E SURE HAVE 0 LT 1 AND C fOR .ORSE vISI8ILITY

----rC~~S~-,nTER vtSI BIlITYINTEGER I,J,K,",IUNC6J

--------,,-REl:'"lnL----rorrlrwrsn-,-vn-.";O:';"lH';"';;'V';'IS..-.I.....,-,-T-£....I1 ....P,-O....Or-, MTOTfKV IS II , NTO H "VI SI ICHARACTER lA8ELVC"VlSII*C*J

C CHECK Q'S, GO 10 220 wHEN O.R.IFCI1VISI.EO.l.AND.OClJ.GE.l •• 0R.OCll.lE.0.IGO TO ZZ5IFlHVISI.EO.l'GO TO 220"-Z

ZOO DO 205 I-H,KVISIJ-I-lIF(Q(IJ.GE.l .. OR.Qul.LE.O.'GO TO z10IfCOCII.LT.QCJIIGO TO 210

Z05 CONtINuEGO TO Z20

C COMBINE vISIBILITy CLASSES If NOT O.K.~

C FIRST BE SURE "VISI LE 3 SO THIS CODE WILL WORKZ10 IFlHVISI.GT.3)GO TO Z25

NTOTCII-NTOTCII+NTOTCJII1TOTtI'-HIOTlI'+HTOTlJ'IFCNTOTCII.EO.O •• OR."TOTCYJ.EO.O.ITHEN

CO-I.ELSE

tEHP-NIOTH,CU-KTOTC II/TEI1P

EHDIFIF (I.EO." ITHEN

IFlOU.GE.l.'~~~~

K-lElSE

K-JIFlQU.GE.l••OR.QU.lT.OII"THEN

K-lNTO TC IJ -NTOT l I 1+NTNl1JI1TOTCII-I1TOTCII+I1TOTCllIFtNIOT(I'.LE.O ••OR.HTOTtt'.LE.O.IGO fO 225TEttP-NTOT CIJCU- KlOTl I I ITEHPIFCOU.GE.l.IGO TO 2Z5

ENDIFENDIFQt I)-COVAROCII-OU*Cl.+QUI/TEI1PDO Zl5 H-R,JNTOTt I1I-HTOT CIJ11 IOf( HI -In OTC 11QCI1I-aUVAROOO-VARQn,

IFCI1.lE."VISIIGO TO zooZZ~InlIUNC 3' ,ZZZlTOT1T;VAlfQTIT;lABtrVTIl, t-l, HVISt IZ2Z FORI1AT(tO AND VARIANCE FOR eSTIMATING N BY VISI8ILITyt/

1 ( F5• Z, Fq • 5, IX, A "RETURN

---""'Z'""'Z-"-5 -'Rll·"'ET'C!"UnNrTC""-]T,"C"l,."',ttUNlJIFTNDlf'tlil1R1BlE EST IffITr"'O....F--.r.Cfr------STOPEND ---

-38-

SU!~O~~tTQNGIJDAY;lYR,MON,IDAYJ

C GET DAY OF "ONTH fROM JULIAN DAY-----------rINTtGER JDATiTT1fillUlfiTDAYI1'IDnTSTI.....I ....3,~2...,J.-----

DATA "DAYS/0,31,5q,qO,lZO,l5l,lel,Zl2,2~3,Z73,30~,33~,365,

I a, 31,60,911121,152.182,2 13, 244, 274, 305. 335, 3661IOU-lIFIIITR/4'.4.EQ.ITRJ IOlV-z00 I/) "ON-l,12IFIJOI'.GT.KOIYSIMON,lDIVJ.IND.JDAT.LE.MDAYSIMON+I,XOIYJ)

1 GO TO 2010 CON t IHUE

"ON-OlDIT-ORETURN

-----..,.ZO,,----..I""orrAYIfJlrlY-KOIY$ I KON'-,"Tl....DT'lf....'r---------------­RETURNEHD

SUBROUTINE GETQNRT1P~tVlMOAy,NOAY,IUN#~YR,MON,IDAY.JDly,IRR,

1 TIME~,IOBSN,IOBSS,IVIS,lEAO,NEW,"tSSEO,NE_F.R,"ISF.R)

--~ FINISH PROel:SSTNbllFIlR EVIaurlIDUf«(Wl'-A H,--n ANY; I N.nXnPTCTITArLIr"Z....E..--..R...-EX"'"'T..-rA""O"'U....R­INTEGER IPREV,"DAY,NOAY,IUN,IYR,MON,IOAY,JCAY,lHR,1

-------..;;INTEGElflO1fSRTffOAYT;lOB"S""S I NO n J, I vrsrserrrrrrrerNrnD~AnyT1)r--------­REAL NEWINOAY),"ISSEO(NOAy),NEWFARI~OAY),"ISf.R(NOAT)

-------"Rn:E"T".....l-..-,r1I,,'"'"EKTNl) AT ), I RATEIFIIPREY.LE.O)GO TO 50

C IF THERE WAS A PREVIOU~S~H~D~U~R-,~t~O~¥U~ RATE AHO WR1TE ITS REcORDSIRATE-O.00 10 I-l,IPREV

10 IRATE-IRATE+NEW(I)+MISSEO(I)t SET "OAT - FIRST JULIAN DAY WITH WHALES

IF(IRATE.GT.O •• ANO.JOAY.lT.MOAY)MOAY-JOAY00 20 I-l,IPREV

ZO WRITE(IUN,ZZ)IYR.MON,10AY,JOAY,IHR,TI"E"(lJ,ICBSN(IJ,IOBSS(I),I IVISIIJ,tEADIIJ,IRATE,HEW(IJ,HISSEDIIJ,NEkfAR(II.HISFAR(IJ

ZZ FORMAT( HZ, 14, 13,FIO.Z.3IZ, I6,5F8.3)IAR-IAR;lIF(IHR.GE.Z~)THEN

IHR-OJOAY-JDAY+l

END IFIOBSNIIJ-IOBSNtIPREvJIOBSS(1)-10BSS(IPREV)IvlSIIJ-IvISIIPREVJlE40(lJ-LE4DIIPREV)GO 10 '10

C FIRST HOUR50 IAI( -0

108SN(l) -0IO!lSS 11'-0IVIS(U-5tEAOI U--l

qO TIMEM(1)-FLO.TIl~~O.(JDAY-lJ+60.1HR)

NEWlI'-O.MI55E0(1)-0.NEWFARI U -0."ISF4R(l)-O.IPREY-lRETURNEND

-39-

-------- -s1JllROUTINl: -lil:rCRIC IUN, FRAe, 110 rsT;1oItflY;I 0);CAR 0, lOBSO, IYRlr;KONOi"·- - -_._­1 IOAYO,JOAYO,IHRO,TII1EI10,IVT~O,lEAOC,IOIST,NWHALE,IYR,11ON,10AY,

---2---;JOAY it PREV, NOAY, TIIHI1, lOB SN, nUSS,"lVlS,TEjO, NEW,KHSED,NEwF AR'-"·:3 I1ISFAR,

C IR IT rrrt UTItJtrROUnu---r:OR--P1HrGUI1-Ge-nJr­CHARACTER CARO.l.'IRfEGE~ NDIT,MOIT,KOIST,t,J,IHROtZl,IVISOtZI,lEiDOIZl,IPREYINTEGER IUNI5',IOS,108S0IZ',IYRO(Z,,110NC(Z',IOAYO(Z',JOAYO(Z'

----,..1HTE"GFR 1DIST12 h tel 0 nUrIYT,THlfIIYRI1f01fi1 nTY,J0 lY,TIHlr,n"EC---------INTEGER IoeSNlNOAy,.IOBSSlNOAy,.IVIS(NOAY'

-----,R~E~AL~Hllet2J'NEwtHDIY',l1tSStnTNOiTl,NEWFiR1NKDTiVyTl-----------­REAL FRAC(ZI,TII1EI10IZ"TtI1EMINOAYI,I1ISFAR(NOAYI

C GEl IND DUIPO' FIRS' REIDER CIRD IN SOOTH CiMP FILE 11-11 ANDC NORTH CAMP FILE (I-Z' AHO GET FIRST DATA CARD FCLlOWIHG HEADER

------,roAY-366 .JOlY-MOAY

---------OO;;....,2..,O.r--.I~-.;1r:,,..,2.------------------

10 REAOlIUNlI,,11,IOSTAT-IOS,ERR-qO,END-qO'CARO

------------

1ENOIF

II FORMAT tA ,IFlCAROlZtZ,.NE.~l~'GO TO 10

----WlITrrr3lU l CAR 0I08S01I,-0

---------c-Al.""LG"rra"'"HRIrr'(l"onH"I'"YI,-'-,TIITONrrrllln lr-, "FU CITOS, ·CiR0, IYlll1n I ,ffCllrOTllll-lflnn,..,---­1 JOAYO(l),IHROll),IHIH,ISEC,TII1E"IOIl),IOBSOII',IVISCIII,2 LEIDOIIJ,IDISTtI',NWHilFtt'J

IFl10S.NE.O,GO TO 90---- lFITllfE"MlJ1 rr;n;OTGO-To"'-'e"'o"'"

IFlJOAYOlII.lT.JOAYITHEN---- --;)un-."JOA'YO t lJ

IYR-IYRO (l'---------11[]NaHtlmrrn

IOAY-IDAYO(U----._--..-.. -.. -.- '--rlJREV-O -_.---- --------------- ~_._-_._-

CALL GETQNHlIPREV,110AV.NOAY,IUN(4',IYR,110N,IOAY,JOAY,1RR, THfElf,TOnRil1lBSS ,TVTS#ltllr.;lrnl,ll1"S)£O, REW FjRllfIs FAffr-----

--------------- ._---

20 CONTINUEC MAKE TEMPO~ARY FILE OUTTEM WITH "FRGED SOUTH AND

----r----r-IRUE~ OF CIMP WItH EARLrBTITI1E,-r-rlTtST-25 IFlTIMEMOI1'.lE.TII1EI1012"THEN---- I-r

J-Z

NORTH CAMP DATA

ELSE

J-l ---- .-----------END IF

27 -rFTJn-AnyTt'O"('"YI'"TJ-.'lr'"E-.J71o"'lroY".J7'GO-,.O..,-., - - - - - - - - - - - - - - - - -C FILL IN I1ISSING PART OR WHOLE DAY30 CILL ~TQNHIIPREY,HDAVINO~A~Y~,~IU~NIT(r.~nl~,~I~Y~Rr-,~H~o~N;roAY,JolY,IRR,tIHEH,

1 I08SN,I08SS,IVIS,lEAD,NFW,I1ISSFOtNEWFAR,~lSFARI""---"-TFCll..nnZ1,27,30 .----- ---. ----- ----

35 IF(JDAYO(J,.LT.JOAV.OR.IHR.GT.IHROIl)'GO 70'C-- Hl(lN I'IISsnfG-lil)URr----

36 IF(IHR.EQ.IHRO(II'GO TO 40--------CATI CelONA tIPREViHtrn,lIDlYllUf,l14 J, nR,HONi"!UAY; -------

1 JOAV,IHR,TII1EI1,108SN,IOBSS,IVTS, E NEWt~ SSEO,NEWFAR,MISFAR'GO-.,.O"""3o---- - .

-40-

-----..C~NDIll:l"KI'T"1fl'SIfIGmtmURsO CHFCR DTRg-)1'U""FF~-­~o IF{l.EQ.l'THEN

----.-.- lHHlBSOln-;£Q.-lDlJ)SnPRtVr;n~IVI SOUT;flf;lV1S r"'IP....R....e'TlYTJ-.----I ANO.LEAOOCl).EQ.LEAO{lPREV»THEN

----..---- -------,;j£1ffUU VJ.NFIllIPlfEVTI1UiHlIHIlElSE

IpR£V·IPREV+llOBSSCIPREV)·I08S0{1)

..- ---- ---I1nrSlffIP-lfEVl. rOBSN( I ISR rv=r IIVlSCIPREVI·IVISOCI'

---------rno I I PR EVJ.LEIDlJTYT-·TI~E~CIPREV'.TIME~OCI)

NEWIIpREYJ·NwAllEftlMISSEOCIPREV'·O.NEWFAR(IPREvl·O.HISFARCIPREV'-O.

END IFIflIOISTCII.GT.HOISTINEWFARlIPREVI-NEWFARCIPREVI+NWHALECII

ELSE IFlI.EQ.ZJTAENIFlIOBSOCII.NE.IOBSNlIPREVIITHEN

IPREV-IpREV+lIOBSS(IPREV'·I08SSCIPREV-l'IOBSNliPREvl-IOBSOfIlIVISllPREVI·IvtSCIPREV-l)lEAOIIPREYJ·lEloIIPREV-IJTIMEMlIPREV)-TIMEMOlI'NEW I IPRE VI .0.HISSED U PREV).O.NEWFARIIPREvl·o.MISFARCIPREV)·O.

END IFMISSEOlIPREV)·HISSEOlIPRfV)+NWHALElI)

-----------TI~F~I~XC~ISTlt'.Gf.HOIST'MISF1RII~EV'.KISF~~~+NWHILEftJEND If

C GET lNOT~ECORD FROM UNtT ICALL GETQNRlIUN(I),IUN(l),FRAC,IOS,CARO,IYROCI),HONCCII,

1 IDATO(I',JDA~OIII,lARO(t"IMtN,ISEC,TtHEHOlI',IOB··~s~or(InJ~,---------2 IVISOlX',LEAOO(I),IOISTlT"NWHALEl 1)1 ___

IF(IOSI60,50,QO50 IFlTl"E"Oll»80,25,25C END OF FILE OtrlJNTT&·~UN~(rI'-I-------------------- -----------60 TI"EHOlll.~9999q.

IFITLHEHOlJ'.LI.TIHEMOIIl'GO TO z,62 CALL GETQNHlIPREV,"OAy,NOAY,IUNl~I,IYR,HON,IOAY,JOAY,IHR,TIHEH,

1 tOBSN,IOBSS,IYIS,LEIo,NEw,HtSSED,NEWFAR,HlsFlRJIflIHR.GT.O)GO TO 62

C REWIND TEMPORARY FILE1-"REWIND(UHIf·IUNII',IOSflf·toS,ERR·QOlRETURN

------c--enUR IF RECrrR1lsrrnr-mll""rrJR 0EIt70 WRITElIUN(3),77)JOAYOlII,IUNlI)

---n FOR1'ilTltOATl-rUJrJUlUfn:rlY~tlITT\]fORDER OR!JNIT t, 12)STOP

C ERROR IN DAfE OR fiME ON INPUT FILE80 WRITElIUN(3),88IIYROCII."ONOCI),tOAYO{II,

END

-41-

S08RaOTI~btTQNJIIYR,HON,rDlY,JDAY,IHR1THIN'ISEC,TI~~E~H~Ir---------------­C GET JULIAN DAY AND TI~E IN ~INUTES Fn~ PROGRA~ GETQN

----- ---lNT EGE R IYR, HON., ItrlYIJDl'I'., IRR., IMIR#I~D ITs C13I ----------­REAL TI~EI1

IFIHON.LE.O.OR.KON.GT.lz.nR.IOIY.lF..0.OR.IDlY.GT.1 (I1DAYSOION+II-I1DAYSCI10NII)THEN

JDlY--l

C NOTE TIMEH SHOULD BE DOUBLe PReCISION ON 1 less lCCURITE COMPUTER THIN CDCDATA I10AY5/0.,31,59,QO,120.,151,181,212,243,273,304,334,3651

ELSE

IflrIYR741'4.EO.IYR.lNO.HON.Gl.Z1JDlY_JoAY+1END IF

JDAY-HDAYSCHON1+rOAYC CHECK FOR LEAP YEAR (THIS CODE WILL SUFFICE TILL THE YEAR 21001

IFlIHR.LT.O.OR.IRR.GT.Z4.0R.IHIN.lT.O.OR.IHIN.Gl.bO.1 OR.JDAY.LE.OITkEN

TIHEH--l.ELSE

END IFtIHEH-FLOAfI1440'IJOAV-t'+60'IRR+IHIN'+FlOATIIsEC'760.

REfORNEND

SUBROUTINE CETQNRCION,tsoOTH,FRlC,ICS,CARO,lVR.,110N.,IDAY,JOAY,1 IHR,II1IN.,ISEC,TII1EI1,I08S,IVIS,LEAO,IOIST,NWHAlEI

------..-C-R..-'O..,U"'T....I.-rN"..E---.-TCflrrADAlrITACl Rf'I 0N UNIT 10N F0R PRO GRAtI GEfON'.--.A:-i:N"'O..------­C RETURN 10 5TATUS IN lOS, DATA IN APPROPRIATE VARIABLES

CRARACTER CIRDiril,OFLlGil.,DCTil,SPECIE.Z,H8Q il.,VIS.2INTEGER IUN.,ISOUTH,IOS,tYR,110N,IDAY,JDAY,IHR,II1IN,ISECINtEGER I09S,IvIS,lEID,IOIST.,IloUlT,IcllFREAL TII1EI1.,FRACCZI,NWHALE

10 REAOIION,II.,IOSTAT-IOS,ERR-QO,ERD-QOJCIRD11 FORHATCA I

IFlCARO(2:Z'.NE.f3fJGO TO 10REAOCCARO,22.,IOSTAT-IOS,ERR-QOIOFLAG,IHR,II1IN.,ISEC,IADULT.,

1 OCT.,ICllF.,$PECIE.,IOISf,MBO,VtS,LEAO,lrR,RON,IDAY22 FORHATC5X.,Al,3IZ,I3,Al.,IZ.,A2,18X.,I4,A1,A2.,2X,I5.,22X,3I21C GET JULIAN DAY AND TIME IN MINUTES

CALL GETQNJ(IYR,110N,IOAY,JOAY,IHR,IHIN,ISEC.,TIHEI11IFrIRR.EO.Z~'TREN

IHR-OJon -JOAT+lCALL GETQNGCJDAY,IYR,HON.,IDAYI

END IFC INCREMENT OR DECREMENT NUM8ER OF OBSER~ERS IF RECUIREO

IFIOFLAG.EQ.fSfJIOSS-IOBS+lIFIOFLAG.EQ.tFt.AND.IOBS.GT.OIIOBS-I08S-1

C GET vISIBILIty CLASSIVIS-5IFrto9S.NE.OITREN

IFIVIS.EQ.tExt.OR.VIS.EO.tVGt IVIS-1

c rNEGJI1VEJ IF BLINk

-42-

SUBROUTINE GETQNT(NV1St.HRITE.NRITE.RClHp.HLElo.NLE.O.NCAs. ,1 HDAY.N".TI"E".N"LEAD.TI"El.N"OBS.TI"EO.NTOT."TOT.TIKE.HKFAR~

-~-~lUNiTOS#TYR. ''lONdOAV. JOlY. "DlY , .~ .C GET ALL TOTALS II' GOING THROUGH OUTTE" AND BUILD ARUY DF DAYS t ...:,.

--------~____rRTEGER NOIT.HDIT.NRiTE.NVtSt.NlE1D.KLEID.NCJHP.N085.1 •INTEGER IUN(5'.IOS.IYR(NOAYJ.110NfNO.YJ.IDAY(NDAYJ.J.K.IHR ~.

INtEGER JOATtNDAY',ROBSN,NOaSS,IVISI.llEID,IVl.1lE.IRI.N(I.RO$REAL NK(NVISI.NCA"P.NDAYJ.N"fAR(HVISI,NRATEJ.INEWF.II1ISF.KRATE

--------------~R~ETlrL~XK~,~InR~lrTTflRTUTtNVIS1,NRlTE'.KTDTCHV1Sl.NRiTE'.INEW.1M1SSRE AL N"LEAO OIV IS I,NRATE ,NlEAO" NKOB SHIV lSI .NUTE,NOBSJ : J ••

REll TIHEI,TIHEtNVISI,NRITE'.lrTMrKTNVISI,NCIKP.NDIY'REAL TII1EP,TI"El(NVISI.NRATE.NLEADJ,TII1EO(NVISI,NRATE.NOBS'Cill P"OOOKP00 20 I-l.NVlSI

5

10

15NI10BSCI,J,K'-O.TIKEOf I,J,K '-0.

',. ~,

REIOtION(~I.Z2.IOSTAT-IOS.ERR-qO.END-qo'IYR(I'."ON(I',IOIY(I'.

1 JOAY(lJ.IHR.TIKEI.NOBSN.NOBSS.IVtSI.ILEAD.IRATE.INEW.I"ISS,ZlZO

NIOTt hJ'-O.I1TOHI,J'-O.

---------.rNKf:lln 1, J I -0.TIKE( I,J'-O.

ZZ2 INEWF,II11SFfOR"AT(3IZ.I4.I3,Fl0.Z,3IZ.16.5F8.3'IF t J 0AnI' .LI .1'I000000;:'G;'O~1O:':':Z;":1;-=-::':'::":"":::':':"':"'------------------------------------

1-1C GET I~OICES IN IRRAYSZ5 IVI-IVISI

Z7

Z8

Zq

11I1EP-III1EIIF(ILEAO'Z7.ze,Z9llE-~

GO TO 30ILE-1GO TO 30

30

ELSE IFtNOBSN.Gl.0.1ND.NoaSS.Gf.OITFENNCA-Z

----------If t NOBSN. EO .1. AND. Moass. Gr-;nTHEN

NOB -1--.....E...,L~S...E..-,I""F-rtN1JB"S~-;AtfCJ.NnBSS-;E C-;l1TIfElr-

NOS-ZELSE IFtNoaSN.GE.Z.1No.NoaSS.GE.3'THEN

NOS-3

ElSE

ELSE

END IF

END IFXK-INEW+1I'IISSNHtIVI,NC1,l'-NHtIwl,NC1.I'+XKIF(NCA.EQ.Z'THEN

NTOTtIVI.IRA'-NfOTtIVI.IRIJ+INEW"TOT(IVI,IRAI-"TOTfIVI.IRA'+I"ISSNl1tElat lVI, IRA, ILE )-NP'llE AD t IVI, IU. HE 1+Xl<NMOSS(IVI.IRA,NOBJ-N"OB$(tvI.IRA,NOB'+XK

-43-

IFUOSt3lt,H,~O

34 lI"El atlP1EP

11P1ELClvI,lRl,lLE'attPlEltlvl,lRl,llE,+IIMEPTIHEOCIV1,IRA,N08t aTIHEoeIVl 1 N08t+TIHEP

IfeIOS.NE.otTHEN------------ -------;ra1'l1rn--------------------

00 It5 lal,J-----------D~(rtv....l=al.....,....N-v....nTI------------r-

00 40 NCA al,NCAHP-------------~FT'NPfnVtIN_clll1Dn,_;GT .0.' RETl.1RN---- ----.

40 CONTINUEIt 5 ~trlYoi-all1P\orr:lnTr:-:YI------------------·

WRITEelUN(31,ltitl44 FORPlAICtNO WHlLESt,

STOP-----~Nrno--r-lc:-F----------------

IFeJOAyeJt.GT.JOAYCI»THENl a J00 50 IVIal,NVISl00 50 NClaI,NCl"PNPH IVI,NCA,1).0.

50 TIHEHClvI,NCl,I)aO.ENO IFGO TO 25

~O WRITEelUN(3),~qllUNe4),10S

99 FORP\4TCfUNEXPECTEO ERROR OR EOF ON ONIT t,Iz,5X,tl0Sfll at,151STOP

----e"N1)

--------"S.,..,U"'B,,-Rl"rOurrTrlnN:r<E"-"G~ETcmIIT10 N,ISOOTR, IA DOlTiD'tr, I Cj(F, s PEClt,1'f8"'Q'\:,-------­1 FRAC,NWHAlE I

C GEt COORt NI/AALE OF WAALES ON CARo,nc BY GETONR FOR'bOONC ASSUHING FRACTION FRAC OF QUEST OR COND REALLY NEW OR HISSED

CHARACTER OCT.C."SPECIE~~~1,8[lNK.lPARAHETER (BLANKat t)INtEGER lUN,lS001A,IIOOlT,ICllF,IREAL FRAcez),NWHALE,lWHAlENWHlLEaO.IFISPECIE.NE.BLANK.ANO.SPECIE.N~.t8KtlRETURN

lWHALE-lI0ULT+ICllFC SOUTH ClK'

IFCI0R.EQ.ISOOfRlfHeNIFIOCT.EQ.8LANK)THEN

NWHIlE-IWAIlEELSE IFCDCT.NE.tOt.AND.DCT.NE.tTtlTHEN

IFCFR1CCll.GT.O.11 NWHAUaFRACU )+IWHALE

ERO IFC NORTH CAK,

ElSE

KWH lLE- HlAIl EELSE IFCHBQ.EQ.tQtlTHEN

301

ERO IF

IFCFRACCzl.GT.O.1NWHALE-FRAC c:n*lWHALE

CONTINUe

-44--------------- ---"--

11 0 ARCTIC WHAlE URROW COI'l81NE CAI'IP 800H7Zl 0 NHRL-tftRTH-CIll'---S TO N lO~~21) METERS 80~o5~z;-1--FRACTION OF C TREATEO AS N • 0.00 Q AS 1'1 • 0.00

CIUNkNOWN l UO

WHAlES TII'IE( .318, 1.0n)o.oco 0.000

FAR GI lqqq ALGA RAIE GY 60.0 OPEN LEAD Gf 3500VISIBILITY RATE NEW KISSED "INUTES Q VARIANce SO

FRAt lION S FAR WA AU S CLO se 0 Le m-lfRR1O<DTTw- Ln e""'A"O'--"'Orwpr"EN...lnE",A"'O..----nTTlT1n-1'n"Tn-.,......,."..-'------AND BY 08SERVER CLASS WHALES TI"E WHALES TI"E WHAles TII'IE

1 EX /VG 1 LOW Ito. a Zq. 0 ZZO'1"Iq-.....o-.....7n2n5,---...0"'31'"'zn6n",---.TI ...7....7 -r--'-oo:-n--::..r-,..,...,....-----.783 0.000 0.000 0.000 0.000 1.000 1.000

rUK ESt1KAtlNG N BY VISIBILITYEX/VG

0.000

0.000

0.000

I -.020, .235)O.OCO C.OOO

0.000 0.0000.000 O.COO1-1.772, 3.77Z)0.000 0.000

0.000 0.000O.OCO 0.000

o.OCO o.COC0.000 0.000

.cnl .'in(-1.772, 3.772.0.000 O.COOo.COO 0.000

0.000 0.0000.000 0.000

1.000 .856(-1.772, 3.772.

(-1.772, 3.7721O.OCO 0.000

0.000 0.000(-1.772, 3.172.

0.000 0.000 '(-1.772, 3.772.

1.000 .971(-1.772, 3.172.

(-I.17Z, 3.17Z)0.000 0.000

3.0 61Q.O .107 .004Z37 .0650.000 0.000 0.000 O.OOC 1.000 1.0eo

0.000 .029 0.000 0.000 0.000 0.0000.0 0.0 1.000 2.000000 1.41it

0.0 0.0 1.000 2.000000 1.4140.000 0.000 0.000 0.000 0.000 0.000

0.000 .065 0.000 0.000 0.000 .0790.0 0.0 1.000 2.000000 1.itlit

0.000 0.000 0.000 0.000 0.000 0.0000.000 0.000 0.000 0.000 0.000 0.000

0.0 Z42.0 1.0CO z.oooooo 1.4140.000 0.000 0.000 0.000 1.000 1.000

0.000 0.000 0.000 0.000 0.000 0.0000.0 0.0 1.000 2.000000 1.~lit

0.000 0.000 0.000 0.000 0.000 0.0000.0 0.0 1.000 2.000000 1.itlit

0.000 0.000 0.000 0.000 0.000 0.0000.000 0.000 O.COO 0.000 0.000 0.000

0.0 0.0 1.000 2.000000 1.4140.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.0000.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.0000.000 0.000 0.000 0.000 0.000 0.000

0.0

0.0

0.0

0.0

0.0

0.0

z.o

0.0

Z8.0

GOOOFAIR

LOW.871

HIGH

HIGH

HIGH

HIGH

LOw0.000

HIGH0.000

LOW0.000

LOW0.000

0.000

.it6 .00952

.~6 .00952

1 ex/VG 2

Z GOOD 1

2 GOOD 2

3 FAIR 1

3 FAIR 2

.. PO/ON 1

it POIUN 2

5 UNKNOWN 1

5 UNKNOWN 2

Q lNO VARIANCE.46 .00952

80 5ZZ 1.. 3 37.0 WAALES At ACCEpTABLE vISIBILITY IN 1440.0 "INUTESDAY ESTI"ATE. 46.78. OR - 6.35 VARIANce. .403292E+02COVARIANCE IERK· .261093E+Ol WAlLES AND tIKES 8Y VISIBILITY1 CAI'IP 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Z CA"PS 0.0 0.0 0.0 o.o~.o 1440.0 0.0 0.0 ~NO CAMP 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

80 521 1~2 2.0 WHALES

0.0 0.0 0.0 0.0 0.0 0.0 0.0

OR POOLED VISIBILITY0.00.00.0

OR pOOLED VISIBILITY0.00.00.0

AT ACCEPTABLE VISIBILITY IN lititO.O "IHUTESOR - 1.51 VARIANce. .228511£+01

WHALES AND TII'I£S BY VISIBILITY0.0 0.0 0.0 890.0 0.0 0.0 0.00.0 0.0 Z.O 550.0 0.0 0.0 0.0

NO CAKP 0.0 0.0

OA' ESll"AIE. ...39 +COVARIANCE TER" • O.1 CA"P 0.0 0.02"CAMPS 0.0 0.0

80 523 144 72.0 WHALES AT ACCEPTABLE VISUIlITY IN H40.0 "INUTESOAt £5II"IIE • 102.\2 + OR - 13.82 VARIANCE ••190810£+03COVARIANCE TER" ••729078E+02 WHALES AND TI~E~ BY VISIBILITY OR POOLED VISIBILITY1 el"' 0.0 0.0 0.0 0.0 9. o-,oo-;-o-----o.o-tr.1J--o;g--...,o..-ree:2 CAI'IPS 0.0 0.0 0.0 0.0 63.0 1080.0 0.0 0.0 0.0 0.0NO Cl"P o. a o. 0 --o-;a-- -1).cr---v;o O.-0- o. 0 0..-0-- "0..-0 O. 0

POOLEO VISIBILITY0.00.00.0

leA"' 0.0 0.0 0.0 0.0 c.o 0.0 0.0 ~O.O 0.02 CA"'S 0.0 0.0 0.0 0.0 2Z'.0 1380.0 0.0 0.0 0.0NO eA"' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

80 524 145 225.0 WHALES .T ACCEPTABLE VISIBILITY IN 1380.0 "INUTESDATE 5II IU 1E • 296. 81 + OR - 34. 68 VARIA"NC~E~•...-='-::.'1..,ZilojZT8Z~E+iion4:-=-=---------COVARIANCE TERM. .6159Qge.03 WHALES AND TI"ES BY VISIBILITY OR

-45-

80 525 146 448.0 WHILES It ACCEPtl8LE VISI8ILITY IN 1355.0 KINOTESDAY ESTIKATE • 601.8q + OR - 6q.11 VARIANCE. .477658E+04COVARIANCE lERK· .352025E+04 VHALES AND tI"ES 8' Vl$18I(lt, OR1 CAKP 0.0 0.0 0.0 0.0 0.0 0.0 11.0 85.0 0.02 CA"PS 0.0 0.0 0.0 0.0 448.0 1355.0 0.0 0.0 O.tNO CAKP 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

VIS lBILITY

80 526 1~7 171.0 WHALES AT ACCEPTA8LE VISIBILITY IN llQ4.0 MINUTESOXf ESII"XIE i 260.12 + DR - 30.19 VIRIINCE ••q4BZ53E+03COVARIANCE TER". .351Q76E+04 WHALES AND TI"ES 8Y VISI8ILITY1 CA"P 0.0 0.0 0.0 0.0 0.0 0.0 10.0 246.0 o.a2 CAKPS 0.0 0.0 0.0 0.0 171.0 l1Q4.0 0.0 0.0 0.0NO ClAP 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

OR POOLED VISI8ILITY0.00.00.0

OR POOLED VISIBILITY0.0

80 521 148 194.0 WHILES Xl ICCEpTIBLE VISIBILIty IN 117z.0 "INUtESDAY ESTI"ATE • 301033 + OR."'I 35.40,. VARIANCE •• 125342E+04CO VARIANCE tE RK. • 5066 t; 0"ETlR VHIL ES I"O":':';';T-;'1U.HE""'S"-'Bn;ynJVTI T$TlarT.IlnI....T;,;yr--PI~Tl'f;I":T1""""ITTTT15"Tl,."r.:;-1 CAKP 0.0 0.0 0.0 0.0 0.0 0.0 0.0 268.0 0.02 CAMPS 0.0 0.0 0.0 0.0 19'.0 1172.0 0.0 0.0 0.0NO CAKP 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.00.0

80 528 149 51.0 WHALES AT ACCEPTABLE VISIBILITY IN 1344.0 "INUTES

DR POOLED VISIBILITY0.00.00.0

OR pOOLED VISIBILITy0.00.00.0

OR POOLED VISIBILITY0.00.00.0

OR peOlED vISIBILITy0.00.00.0

OR POOLED VISIBILITY0-;00.00.0 -_._------

0.0 0.0 0.0 0.0 0.0

63.0 1086.0 1.0 354.0 0.00.0 O.~ 0.0 0.0 0.0

NO CAMP 0.0 0.0 0.0 0.0

NO CA"' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

80 530 151 63.0 WHALES ATOAf ES1I"AIE • 153.88 + URCOVARIANCE TER". .778515E+03

Olf ESII"llE • 100.66 + OR - 20.52 VIRIINce ••420927E+03COVARIANCE TERK. .204072E+02 WHALES AND TIKES BY VISIBILITY

I CA"P 0.0 0.0 0.0 0.02 CAMPS 0.0 0.0 0.0 0.0

1 LA"' 0.0 0.0 0.0 0.0 51.0 13".0 0.0 96.0 0.02 CAKPS 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

80 5Z9 150 27.0 WHALES A1 lCCEPI1BLE VISIBIL1l' IN 1440.0 "INUTESDAY ESTIKATE. 49.7~ + OR - 11.10 VARIANCE ••123117E+03C0 VlR IANCE 1ER". • 111 7ft 7E +a 3 WH1LE"SA"N"'"0-'-1TliH.nE~SC"1IBrVY---VVTtsrnIBrInl...,I.,T....Y~lr"1In'!l'frl:"'""I:1T~rrt.."..,,'"1 CAKP 0.0 0.0 0.0 0.0 27.0 14~0.0 0.0 0.0 0.0

COvlRIANCE IERM • • 332514£+03 WHilES INO tIMES BY VISIBILITY1 CAMP 0.0 0.0 0.0 0.0 18.0 1440.0 0.0 0.0 0.02 CAMPS 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0NO A"P 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

80 6 1 153 53.0 WHALES AT ACCEPTABLE VISIBILITY IN 1440.0 "INUTES

2 LA"PS 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0NO CAKP 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

80 531 152 l~.O WHILES At ACCEprlBLE VISIBILITY IN 1440.0 MINUTESDAY ESTIKATE. 33.16 + OR - 8.02 VARIANCE. .643266E+02

DAY EStIMAtE. 97.63 + OR - 19.ez VARIINce. .39Z66qE+o3COVARIANCE TERK. .108361E+04 WHALES AND TIKES 8Y VISIBILITYI CA"' 0.0 0.0 0.0 0.0 53.0 1"0.0 0.0 0.0 0.02 CAMPS 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0NO CAM' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 O~-'Or.~Or---~r-

VISIBILITY

80 6 Z 154 Q.O WHAlES AT lcce-TABLE VISIBILITY IN 1HO.O MINUTESDAY ESt I"AI E· lo;-s8-.-0lf-----..~-83---VAUDlC"E. • B2877E+02- '-----------COVARIANce TeRK· .236276E+03 WHALES AND TIMES BY VISI81LITY OR POOLED1 CAMP 0.0 0."'0 0.0 0.0 9.0 IHO.O 0.0 ---o-;o--O-;O'--"""10"';.::';O<-=~":"'::"'::':::'::"'::":::':::"':''':'''-'

2 CAMPS 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0NO LA"' 0.0 0.0 '-,,-;-0 0.0 0.0 0.0 0.0 0-;0----0;0 - ....0..:.,.0.<----------NUMBER OF WHALES • 2066. VARIANCE. ~1223.QO STANDARD DF.VIATION. 203.095% CONFIDENCE IN1ERVAl • ( 166&., Z464.J80 seASON, 13 DAYS LONG WITH 0 "ISSING DAYS

203.0ESIInllES SCXLED OP FOR KISSI~G DI1S IRENUM8ER OF WHALES • 2066. VARIANCE. ~12Z3.90 STANDA~D OFVIATIDN •95% CONFIDENCE INTERVAL • « 1668.~ 2464.1

"EIN PER Olf • 158.92 USED FOR FRlctlOR C.OOO OF HISSING ~lVS

-46-

UJACVU. 83/03/Z3. U. W. CYBER 170-750 Hes 1.~-5~3/552.

(JOll HAS BEEN ENHAN EO. THE NEW FORMUlA~A~~~U~TS FOR THE PRIORITYOF THE JOB AND THE T KE OF DAY FOR DjjCOU T. OBS WIll NOW GfT AN~SRO LI"II- WHEN THE PROCESSIRG COST TTKE RTORTTT~F~l~CTrt~R~~~-----------REACHES THE JOB DOLLAR LIKIT. AT THIS POINT REPRIEVE PROCESSING,AS PROVIDED BY THE EXIT CONTROL $TATE"ENT OR RECOVR SUBROUTINi, WILLBE GIYEN AN ADDITIONAL 8 SRUS. 0322TilE NEW S UHSHCAl PACKAGE eeNSl:IlflHS SFFlee US ANtttWNNe-ee~Oo-fftHHf'folH'f'E-----­MARCH NEWSlETTERIFWILL OPEN ON WEDNESDAY, KARCH 23. THE OFFICE,ROOK ~4A, IS STAF ED BY SALLY ZITZERL PHONE 543-705i1- AND WIll

--.roJ(1'1ALlY BE OPEN FRO" 1 P.H. TO 5 P.R. HON.,TUES.,THURS.,Am:rF"'wR"YX-.------------WITH THE SCHEDULE FOR WED. TO BE ARRANGED. 0322WE NOW SUPPORT SCREEN EDITING ON THE HP2645A, VT-52 AND ANSI

_

-ICi+iO~I'\HP+-,A;.::T-HlB.f.L .:.E~Ef.lR~K;:.:I;.;.N~A'GLftS~. f-fiC~U;;.:R.:.jS~O;...R~Pf.0f.S ..lT~HN~NHlf..£:Ae:ND;.....:S~Cf+RK=E~E.etiNEDIT I NGR76R KE't5ARE -NOT- SUPPORTED FOR TH SE T RMINALS. 0217

EXECIlIE I1SGLOG' FOR I10RltE:..".JI~Nl.tEc1JOIJCRZlM.AA.I..T.I..Iu:ONN.1.1------------------------------­0314 DISK HARDWARE PROBLEKS.0218 PLOTREO,DEy-CALCOKP TO CENTRAL SITE.

IZ.59.~S.IO(JEZ0450,J

12.59.49. PASSWORD NOT MODIFIED SINCE 83/01/26. (VALIOIO.IZ.'9.'I.ON(FAFZOOZJ12.59.'l.ATTACH,ICEDATA/NA.IZ.'9.'Z.FS,ICEOAIA.12.59.52. FILESET NAKE IS ICEOATAlZ.'9.5Z.GF,INS,FINAL/S80LIN.l2.59.54.GF,INN,RAW/NPRCH80.lZ.'9.54.AIIACH,JuDfSEI/KaK,NA.12.59.55. JUDYSET 8USY, AT 0001Z1.IZ.59.".FS,JODfSEI.12.59.58. FILESET NAKE IS JUOYSETIZ.'9.,6.GF,GETUN.12.59.58.FTN5,I-GETQN,OPT-Z,lO.13.00.24. 63100 eK SIORAGE USED.13.0C.24. ~.434 CP SECONDS COKPILATION TInE.I3.00.24.LUAO,LGU.13.00.24.NOGO,EXEON.I3.00.Z6.RF,EXEUN.13.00.28. EX EON REPLACED13.00.26. EXEUN.13.01.04•• PKO NOT CONTROL CARD ENABLED-IGNORED.Il.OI.I3.'PHD NUl CONIRO' CARD ENASLED-IGNORED'13.01.13. STOP13.01.13. '2100 HAXlKU" EXECUTION Fl.13.01.13. 11.699 CP SECONDS EXECUTION TInE.13.0I.I3.SKIP,AAI.'13.01.13.ENDIF,AAl.I3.0I.Il.kF,UOI,UOI80.13.01.14. OUT80 REPLACEDI3.0I.I4.RF,OOlrEK,IEn80.13.01.16. TEK80 REPLACED13.01.I6.kF,OOIHIS,HIS80.13.01.17. HIS80 REPLACED13.0I.I/.RF,INU,INuao.13.01.17. IN080 REPLACEDI3.01.18.REWIND,OOI.13.01.18.COPYSF,OUT,OUTPUT.

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