(
International Council for the ~~. Exploration of the Sea Statistics Committee Ref. B + H
ABUNDANCE ESTIMATION OF HERRING HIBERNATING IN A FJORD
by
Kenneth G. Foote Institute of Marine Research 5024 Bergen, Norway
ABSTRACT
A series of acoustic surveys of the adult component of the Norwegian spring-spawning herring was conducted in Ofotfjorden and Tysfjorden in December 1992. Preliminary results are reported. These include compensation for the effect of extinction when estimating mean abundance, and allowance for autocorrelation when estimating associated variance by means of geostatistics.
RESUME: EVALUATION D' ABONDANCE D' UN STOCK HIVERNAL DE HARENG DANS UN FJORD
Une serie d'evaluations acoustiques de la composante principale du stock de hareng ·norvegien frayant au printemps a ete effectuee dans Ofotfjorden et Tysfjorden en decembre 1992. Les resultats preliminaires sont donnes. Ils comprennent la compensation de l'effet d'e~tinction dans l'estimation d'abondance moyenne et la prise en compte de l'autocorrelation dans l'estimation de la variance associee par methode geostatistique.
INTRODUCTION
In recent years the adult component of Norwegian spring-spawning herring (Clupea harengus) has spent the late autumn - early winter period in the Ofotfjord-Tysfjord system. Since the stock has literally confined itself to a limited geographical region, which is moreover protected from the open ocean, and since the admixture with other species is minimal, conditions for its acoustic surveying must be ideal (Foote 1991). The stock has been surveyed annually in the course of the comprehensive survey of western Norwegian fjords and at other times and places too (R~ttingen 1988). However, the vastness of the annual fjord survey has generally precluded spending much time in any one fjord, and the other surveys of herring have been performed at sea over considerably larger areas.
The cruise reported on here is an attempt to remedy this situation,
denoted denoted 4- and and 6-. 6-.
the the parallel parallel transects transects are are eliminated. eliminated. These These modified modified survey survey grids grids are are
grids grids 4 4 and and 6, 6, a a variant variant of of each each is is considered considered in in which which the the segments segments between between
To To lessen lessen the the chance chance of of biasing biasing the the abundance abundance estimates estimates in in survey survey
analyzed, analyzed, these these are are not not considered considered further further here. here.
and and its its weaker weaker appar~ntly appar~ntly strength strength there. there. As As the the data data have have not not yet yet been been
the the herring herring stock stock in in Tysfjorden Tysfjorden was was much much less, less, owing owing to to limitations limitations of of time time
by by cross cross bars bars whose whose length length is is proportional proportional to to log(1+sA). log(1+sA). The The coverage coverage of of
are are displayed displayed at at the the basic basic resolution resolution distance distance of of 0.1 0.1 nautical nautical miles miles (NM) (NM)
in in Fig. Fig. 1. 1. Values Values of of the the area area backscattering backscattering coefficient coefficient sA sA for for herring herring
details-of details-of these these are are given given in in Table Table 1. 1. The The actual actual survey survey grids grids are are shown shown
Seven Seven experimental experimental surveys surveys were were conducted conducted in in Ofotfjorden. Ofotfjorden. Some Some
set set by by local local fishermen. fishermen.
Tysfjorden Tysfjorden owing owing to to frequent frequent narrow narrow passages passages or or the the presence presence of of gill gill nets nets
speed speed during during acoustic acoustic surveying surveying in in Ofotfjorden Ofotfjorden was was 8 8 knots, knots, and and less less in in
The The platform platform for for the the measurements measurements was was R/V R/V "JOHAN "JOHAN HJORT". HJORT". Cruising Cruising
weight weight measurement measurement and and later later determination determination of of fat fat content. content.
The The usual usual length length measurements measurements were were made, made, with with smaller smaller samples samples taken taken for for
stations, stations, with with five five performed performed in in Ofotfjorden Ofotfjorden and and three three in in Tysfjorden. Tysfjorden.
Biological Biological measurements measurements were were made made at at a a total total of of eight eight pelagic pelagic trawl trawl
(Foote (Foote et et al. al. 1987), 1987), in in advance advance of of the the cruise. cruise. Conditions Conditions were were good. good.
calibration. calibration. This This was was done done according according to to the the ICES-recommended ICES-recommended procedure procedure
Secondary Secondary acoustic acoustic measurements measurements on on standard standard targets targets effected effected a a
in in a a database. database.
backscattering backscattering coefficient, coefficient, and and storage storage of of the the results results of of the the interpretation interpretation
according according to to scatterer scatterer type, type, computation computation of of the the corresponding corresponding area area
data data in in echograms echograms on on a a workstation workstation screen, screen, classification classification of of echo echo traces traces
1991), 1991), or or BEl, BEl, for for postprocessing. postprocessing. This This included included retrieval, retrieval, display display of of the the
strength strength were were stored stored by by means means of of the the Bergen Bergen Echo Echo Integrator Integrator (Foote (Foote et et al. al.
also also at at other other frequencies. frequencies. Preprocessed Preprocessed values values of of mean mean volume volume backscattering backscattering
EK500 EK500 echo echo sounder sounder system system (Bodholt (Bodholt et et al. al. 1989), 1989), operating operating at at 38kHz 38kHz but but
The The primary primary acoustic acoustic measurements measurements on on fish fish were were made made with with the the SIMRAD SIMRAD
MATERIALS MATERIALS AND AND METHODS METHODS
to to describe describe the the various various survey survey grids grids and and respective respective abundance abundance estimates. estimates.
and and repeatedly, repeatedly, by by means means of of several several experimental experimental designs. designs. The The goal goal here here is is
In In fact, fact, the the herring herring stock stock in in Ofotfjorden. Ofotfjorden. and and Tysfjorden Tysfjorden was was surveyed, surveyed,
biologist biologist in in surveying surveying this this and and other other stocks. stocks.
the the aim aim has has been been to to develop develop methods methods and and instruments instruments to to assist assist the the fishery fishery
a a formal formal obligation obligation to to perform perform a a survey survey in in the the conventional conventional manner. manner. Rather, Rather,
by by allowing allowing more more time time to to be be spent spent on on surveying, surveying, but but - importantly importantly - without without - 2 -
part). part). (First (First 1. 1. Fig. Fig.
18.0 18.0 . .
17.5 17.5 . .
17.0 17.0 . .
16.5 16.5 . . 16.0 16.0 . .
68.3 68.3
68.4 68.4 . .
68.5 68.5 . .
68.6 68.6
68.3 68.3 . .
68.4 68.4 . .
68.5 68.5 . .
Survey Survey gridl~ gridl~
68.6 68.6 . .
68.3 68.3
-· -· ----- _ _ .. .. ._____._L__ ._____._L__
68.4 68.4 . .
68.5 68.5 . . ···-
gridll. gridll. Survey Survey
68.6 68.6
vertex vertex other other every every connecting connecting
6, 6, grid grid on on based based Zigzag Zigzag 3044.2-3081.9 3044.2-3081.9 0656 0656 11/12 11/12 0211 0211 11/12 11/12 7 7
4 4 grid grid of of version version Truncated Truncated 0210 0210 2989.7-3044.1 2989.7-3044.1 11/12 11/12 1906 1906 10/12 10/12 6 6
transects transects mid-fjord mid-fjord Two Two 2910.3-2940.3 2910.3-2940.3 0736 0736 10}12 10}12 0347 0347 10/12 10/12 5 5
transects transects parallel parallel Equidistant Equidistant 2849.6-2910.2 2849.6-2910.2 0346 0346 10/12 10/12 1947 1947 9/12 9/12 4 4
time-limited time-limited severely severely Ad-hoc, Ad-hoc, 2451.3-2507.0 2451.3-2507.0 1547 1547 7/12 7/12 0927 0927 7/12 7/12 3 3
2349.3-2437.5 2349.3-2437.5
night night but but 1 1 grid grid of of Repetition Repetition 2319.7-2333.4 2319.7-2333.4 0802 0802 7/12 7/12 1841 1841 6/12 6/12 2 2
day day zigzag, zigzag, slack slack Large-scale, Large-scale, 2215.6-2317.7 2215.6-2317.7 1746 1746 6/12 6/12 0625 0625 6/12 6/12 1 1
Type Type hour hour date date (NM) (NM) hour hour grid grid date date
log log Vessel Vessel End End Start Start Survey Survey
1992. 1992. December December in in Ofotfjorden Ofotfjorden
in in applied applied grids grids survey survey experimental experimental seven seven of of parameters parameters Some Some 1. 1. Table Table - 3 - - 4 -
. 68.6
. 68.5
. 68.4
. 68.3 . 68.6 Survey gridl.2_
. 68.5
. 68.4
. 68.3 . 68.6 Survey grid!.§.
. 68.5
. 68.4
68.3 68.6 Survey grid I 7
. 68.5
. 68.4
. 68.3 . 16.0 . 16.5 . 17.0 . 17.5 . 18.0
Fig. 1. Seven experimental survey grids applied in Ofotfjorden in December 1992, with values of acoustic density indicated by cross bars of length proportional to log(l+sA). Scales are degrees of latitude north and degrees of longitude east. - 5 -
DATA ANALYSIS
The three salient parts of this involve correction for extinction, abundance estimation, and variance estimation. A further, hidden component, which is also important, is checking and cross-checking to guarantee the quality of the interpreted values of area backscattering coefficient sA'
Extinction correction The magnitude of some values of sA, exceeding 100000 units of square meters of backscattering cross section per square nautical mile, denoted m2/NM2, suggests the need to compensate for the effect of extinction. This was done according to the method described by Foote (1990), but for the cumulative echo quantity per 0.1 NM, as resolved in depth in 10-m thick intervals. Briefly, if the result of echo integration over the j-th depth layer [zj,zj+~zj] is described by sa,j=sA,j/(4n18522), then the extinction-compensated value is
,.. n-1 s s exp [ 2 L: p . cr . ] (la) a,n a,n j=l a,J e,J where Pa .=pA j/18522 is the estimated area fish density over the j-th depth layer, anrl cre:j is the extinction cross section associated with the scatterers in the j-th layer. The area fish density for this layer is given by
1 ,.. p . = - ln [ 1 - 8ns . cr . I ab . ] a,J 2 cr . a,J e,J ,J (1b) e,J where crb . is the respective backscattering cross section. Compensation for extinct~3~ is effected by employing equations (la) and (lb) as a recursion, where it is understood that the exponential term in equation (la) for n=l is unity. The value of crb, assumed constant over depth, is derived from the standard equation for clupeoids (Foote 1987),
TS = 20 log t - 71.9 = 10 log (crb/4n) (2) where TS is the average target strength for a herring of mean length t. Each of three values of the extinction cross section have been examined (Foote et al. 1992), according to the ratio cre/crb: 1.17, 1.7, and 2.24, which like crb is assumed to be constant independent of depth.
Abundance estimation The pattern of coverage in the seven experimental surveys is quite irregular or limited in some instances, for example, survey grids 3 and 5, and more uniform in others, although with potentially significant differences between the zigzag design in survey grids 1, 2 and 7, and the sets of equidistant parallel transects in survey grids 4 and 6. In addition, analysis of the extinction-compensated data with a basic resolution in sailed distance of 0.1 NM and the need to attach a specific geographical coordinate to each suggests the need to perform a preliminary averaging over blocks. This has been done over squares with a side length of 0.2 NM. Averaging of these block-averaged data yields a number which is assumed to
blocks blocks
of of
side side length length 0.2 0.2 NM NM gives gives the the results results shown shown in in Table Table 3. 3.
analyses. analyses.
Combination Combination
of of the the density density values values after after averaging averaging over over square square
The The extinction-compensated extinction-compensated
values values for for sA sA were were used used throughout throughout the the reported reported
of of fish fish by by
about about 5%, 5%, assuming assuming the the mean mean extinction extinction coefficient coefficient oe=1.7ob. oe=1.7ob.
The The overall overall
effect effect of of extinction extinction was was to to reduce reduce the the apparent apparent quantity quantity
RESULTS RESULTS
Table Table 2. 2.
is is no no
structure. structure.
The The chosen chosen variogram variogram model model parameters parameters are are presented presented
in in
function, function,
which which is is judged judged to to
be be the the least least distance distance lag lag beyond beyond which which there there
h~a h~a and and
1 1
for for h>a. h>a. The The quantity quantity a a describes describes the the range range of of the the spherical spherical
where where the the amplitudes amplitudes
sum sum to to unity, unity, AN+As=1, AN+As=1,
and and S(h)=1.5h/a-0.5(h/a) for for
3 3
y(h) y(h) = = ANN(h) ANN(h)
+ + AsS(h) AsS(h) (5) (5)
vanishes. vanishes. Explicitly, Explicitly,
variance variance
at at all all
distance distance
lags lags except except at at the the very very sampling sampling point, point, where where
it it
1990, 1990, Foote Foote
and and Rivoirard Rivoirard 1992). 1992). The The nugget nugget term term represents represents a a constant constant
an an
intrinsic intrinsic
nugget nugget
term term and and a a spherical spherical function function term term (Guillard (Guillard et et
al. al.
values. values.
The The
convenient convenient
model model adopted adopted for for use use represents represents y y as as the the
sum sum
of of
other other
by by
characteristic characteristic
points points of of the the imposed imposed block block grid grid for for averaging averaging
sA
set set
of of points, points,
the the one one
by by the the represented represented intervals intervals of of sailed sailed distance, distance,
the the
t t
for for
transect transect
and and
v v for for volume volume or or total total area. area. Each Each is is defined defined by by
a a finite finite
averaging averaging
is is performed performed
over over two two sets sets of of points, points, designated designated by by the the subscript subscript
y y is is the the
average average
of of the the model model of of rhe rhe experimental experimental variogram, variogram, where where
the the
values values
of of
sA sA at at different different
points points with with respect respect to to the the distance distance between between
these, these,
where where
y y denotes denotes the the
variogram, variogram, or or expectation expectation of of squared squared differences differences in in
E E = = Ytv Ytv
- ytt ytt
- Yvv Yvv
2 0
(4) (4) - 2
formula formula
for for
the the estimation estimation variance variance is is (Matheron (Matheron 1971, 1971, Cressie Cressie 1991) 1991)
correlation correlation
due due to to sampling sampling in in the the estimation estimation of of variance. variance. The The basic basic
twice twice
the the
resolution resolution
distance. distance. It It offers offers a a consistent consistent method method of of treating treating
the the
matter matter
of of
averaging averaging
the the extinction-compensated extinction-compensated data data in in small small blocks blocks
at at
Variance Variance
estimation estimation
Geostatistics Geostatistics has has already already exerted exerted its its influence influence in in
fjord fjord area area to to the the fish. fish.
relative relative
to to the the bottom bottom
depth depth and and bottom bottom topography, topography, or or accessibility accessibility
of of the the
delimited delimited
area, area,
which which is is determined determined by by observation observation of of the the fish fish distribution distribution
Multiplication Multiplication
of of
pA pA
by by the the total total area area gives gives the the total total number number of of fish fish in in
the the
for for this this is is just just the the fundamental fundamental equation equation of of echo echo integration. integration.
PA PA =sA/ob =sA/ob
(3) (3)
cross cross section section ob, ob, the the area area density density pA pA results, results,
represent represent
the the sought sought global global average. average. When When divided divided by by the the backscattering backscattering - 6 - - 7 -
Table 2. Variogram model parameters for analyzed experimental survey grids in Ofotfjorden.
Survey a grid ~ As (NM) 1 0.20 0.80 1.5 2 0.20 0.80 2.4 3 0.11 0.89 2.4 4 0.14 0.86 1.9 4- 0 1.00 2.5 5 0.12 0.88 3.0 6 0.13 0.87 1.8 6- 0 1.00 1.8 7 0.20 0.80 1.8
Table 3. Results for the abundance and associated estimation variance for the experimental survey grids. The standard error of the mean density is included as a statistic without regard to correlations, denoted se.
Survey grid (NM2) n N(109) crE(%) se(%) 1 103.9 573 1.94 17.6 11.8 2 103.9 608 2.09 14.5 9.2 3 66.9 313 4.16 23.2 12.2 4 71.4 339 3.18 10.5 8.7 4- 71.4 255 2.71 14.3 10.5 5 66.1 159 2.09 35.7 13.6 6 64.7 283 3.92 10.4 7.5 6- 64.7 217 3.17 13.9 9.9 7 64.7 203 2.33 18.2 10.3
has has however however failed failed to to significantly significantly change change the the cr~estimate. cr~estimate.
which which is is allowed allowed because because of of the the subjective subjective nature nature of of their their determination, determination,
computing computing crE may may be be violated. violated.
Use Use of of alternate alternate variogram variogram model model parameters, parameters,
2 2
the the sampling sampling is is wanting, wanting, i.e., i.e., is is non-representative, non-representative, a a condition condition for for
the the covariance covariance properties properties of of the the subject subject fish fish distribution. distribution. Insofar Insofar as as
fish fish distribution distribution by by transects transects in in relation relation to to the the area area to to be be covered covered and and
lies lies in in the the nature nature of of crE2. crE2. This This depends depends on on the the degree degree of of sampling sampling of of the the
It It is is easy easy to to find find possible possible explanations explanations for for this this discrepancy. discrepancy. One One
higher higher than than the the estimates estimates for for crE crE in in Table Table 3 3 for for the the particular particular grids. grids.
the the mean, mean, since since the the overall overall average average is is (2.45 (2.45 0.50) 0.50) 10 ± ± • • This This
number number is is
9
result result is is that that the the corresponding corresponding standard standard deviation deviation is is 22.3% 22.3% relative relative to to
estimation estimation of of a a variance. variance. Based Based on on survey survey grids grids 1, 1, 2, 2, 4-, 4-, 6- and and 7, 7, the the
Repeated Repeated surveying surveying of of the the herring herring in in Ofotfjorden Ofotfjorden permits permits indep~ndent indep~ndent
Variance Variance estimation estimation
and and substantially substantially higher higher estimates estimates of of survey survey grids grids 4- and and 6-. 6-.
roughly roughly midway midway between between the the rather rather low low estimates estimates of of the the first first two two surveys surveys
Survey Survey grid grid 7, 7, surprisingly surprisingly perhaps, perhaps, gives gives an an estimate estimate that that is is
survey survey grids grids are are designated designated 4- and and 6-. 6-.
and and more more realistic realistic estimates estimates of of abundance abundance are are obtained. obtained. These These modified modified
that that link link the the parallel parallel transects,, transects,, it it is is believed believed that that biasing biasing is is avoided avoided
the the north north side side of of the the fjord. fjord. By By eliminating eliminating the the segments segments of of the the two two grids grids
skewed skewed fish fish distribution, distribution, with with tendency tendency toward toward higher higher concentrations concentrations along along
give give relatively relatively high high abundance abundance estimates, estimates, which which may may be be attributed attributed to to a a
distribution distribution observed observed in in the the preceding preceding surveys. surveys. Both Both survey survey grids grids 4 4 and and 6 6
The The fourth fourth survey survey grid grid was was designed designed by by G. G. A. A. Rose Rose based based on on the the fish fish
survey survey grids grids is is interesting interesting for for further further discussion discussion here. here.
the the quite quite large large estimates estimates of of crE crE in in Table Table 3. 3. Consequently, Consequently, neither neither of of these these
poor poor coverage coverage that that is is evident evident from from Fig. Fig. 1 1 is is reflected reflected in in both both cases cases in in
to to sail sail to to the the end end of of a a fjord fjord and and out out again, again, without without crisscrossing. crisscrossing. The The
frequently frequently used used minimalist minimalist approach approach to to surveying, surveying, when when there there is is only only time time
of of the the fifth fifth survey survey grid grid is is also also poor. poor. Its Its choice choice derived derived from from a a
limited limited time time period period dictated dictated by by a a mid-cruise mid-cruise stop stop in in Narvik. Narvik. The The coverage coverage
structure, structure, as as suggested suggested by by the the first first two two survey survey grids, grids, but but in in a a rather rather
was was motivated motivated by by the the desire desire to to learn learn something something more more about about the the spatial spatial
Clearly Clearly the the coverage coverage of of the the third third survey survey grid grid is is poor. poor. Its Its design design
which which it it did. did.
whether whether the the first first result result could could be be repeated repeated under under night-time night-time conditions, conditions,
survey survey grid grid design design is is a a repetition repetition of of the the first, first, intended intended to to determine determine
in in November November 1992. 1992. It It includes includes the the midday midday period period of of twilight. twilight. The The second second
The The first first survey survey grid grid design design is is based based on on that that used used by by I. I. R~ttingen R~ttingen
Abundance Abundance estimation estimation
DISCUSSION DISCUSSION - 8 - - 9 -
Another explanation may lie in the backscattering cross section ab in equation (3). Any error in this will have a first-order effect on PA' hence on the overall abundance. It is not hard to imagine dependences of ob that are being neglected, for example, those of depth or lighting, not to mention the known one of physiological state through fat content (Ona 1990). It is indeed hard to imagine equation (2) applying in any arbitrary situation, yet that is precisely what is done here, to a series of successive surveys. Even if equation (2) were applicable, a nominal range of variation in this would boost the overall estimation error.
It is observed that the estimate for aE in Table 3 is larger than the standard error of the mean, which is a pure statistic that regards each measurement sA to be an independent estimate of the mean. This result is due to the field size being much larger than the range of the data (Petitgas and Rivoirard 1991).
Another way to compute the estimation variance for survey grids 4- and 6- would be to consider the result for each transect as a sampling unit. A geostatistical analysis could then be conducted on the set of transect results in one dimension (Petitgas 1990, 1991). This has not yet been done.
Summary estimates
All in all, survey grids 4- and 6- seem most applicable for abundance estimation of the herring stock in Ofotfjorden, if only providing partial coverage. The mean of the respective results is 2.93 109 animals, with estimated variance of about 20%.
Structural analysis
Interestingly, the variograms for survey grids 1 and 2 reflect the basic day-night differences already observed for 0-group herring (Foote and Rivoirard 1992). The daytime structure is more clumped and variable than the night-time structure, when the fish tend to be more uniformly distributed. This is seen quantitatively through the variogram model parameters in Table 2, with longer range for the night-time data.
Additional analyses
It is apparent from Fig. 1 that survey grids 1 and 2 achieve the most comprehensive coverage of Ofotfjorden. These suffer inevitably from a rather weak coverage of the region of highest fish concentration. Survey grids 4 and 6, specifically their derivatives 4- and 6-, represent a second-tiered coverage of the fjord region of highest concentration. The results from analysis of grids 4- and 6- should be supplemented by results from the other fjord areas that are covered by grids 1 and 2. Only a rather small difference, however, is expected. Grid 7 should be similarly treated. Comparison of the results through a repeated-survey estimate of variance will yield new abundance and variance estimates.
the the calibration calibration exercise exercise and and for for performing performing the the data data interpretation. interpretation.
well well
as as
cruise cruise preparations. preparations. K. K. A. A. Hansen Hansen is is especially especially thanked thanked for for leading leading
H. H. P. P. Knudsen Knudsen
are are thanked thanked for for diverse diverse contributions contributions to to data data collection collection as as
whereabouts whereabouts
of of herring herring in in advance advance of of the the cruise. cruise. A. A. Romslo, Romslo, B. B. Kvinge, Kvinge, and and
I. I.
R~ttingen R~ttingen is is thanked thanked for for communicating communicating detailed detailed information information on on the the
ACKNOWLEDGEMENTS ACKNOWLEDGEMENTS
realistic realistic measures measures of of certainty certainty should should be be a a goal goal of of abundance abundance estimation. estimation.
estimates estimates from from coverage coverage to to coverage coverage should should be be addressed. addressed. Obtaining Obtaining
planned planned
for for December December 1993 1993 and and January January 1994, 1994, the the problem problem of of consistency consistency in in
The The described described additional additional analyses analyses should should be be performed. performed. In In cruises cruises
Future Future work work
measurements measurements at at different different frequencies. frequencies.
frequency, frequency,
as as by by application application of of an an acoustic acoustic scattering scattering model model to to simultaneous simultaneous
would would
be be (4) (4) use use in.specifying in.specifying the the in·situ in·situ target target strength strength at at any any survey survey
mixed mixed in in
species species or or size. size. additiqnal additiqnal An An attraction attraction of of multi-frequency multi-frequency data data
and and (3) (3)
increased increased power power of of discrimination discrimination of of scatterers, scatterers, especially especially when when
(2) (2) the the possibility possibility of of finding finding errors errors by by checking checking data data across across frequency, frequency,
(1) (1) valuable valuable redundance redundance 1n 1n the the usual usual single-frequency single-frequency operation, operation,
integration integration surveys surveys can can hardly hardly be be overestimated. overestimated. These These can can offer offer
The The potential potential for for using using multiple-frequency multiple-frequency data data in in ordinary ordinary echo echo
relative relative stability. stability.
numbers numbers
are are thus thus not not independent, independent, hence hence the the present present emphasis emphasis on on their their
38kHz, 38kHz,
using using the the values values for for ob ob determined determined by by Foote Foote et et al. al. (1993). (1993). The The
themselves themselves
show show a a stability stability to to within within ±10% ±10% of of the the respective respective estimate estimate at at
frequencies frequencies other other than than 38 38 kHz kHz is is poorly poorly known known if if at at all, all, the the numbers numbers
estimate. estimate.
Although Although the the backscattering backscattering cross cross section section of of herring herring at at
In In a a number number of of instances instances these these are are sufficient sufficient to to form form an an abundance abundance
also also
collected collected
simultaneously simultaneously at at 18, 18, 120 120 and and 200 200 kHz kHz for for much much of of the the time. time.
The The present present work work has has reported reported on on measurements measurements at at 38 38 kHz. kHz. Data Data were were
Multiple-frequency Multiple-frequency data data
duration duration of of the the cruise. cruise.
consistent consistent
with with the the variograms, variograms, whether whether a a stability stability is is observed observed over over the the
the the
so-called so-called point point or or near-point near-point measurements measurements are, are, whether whether they they are are
vicinity vicinity
of of a a common common point. point. It It would would be be valuable valuable to to know know just just how how comparable comparable
the the
pooled pooled data data and and a a study study of of data data from from different different survey survey grids grids in in the the
Two Two
related related analyses analyses of of some some interest interest would would be be an an estimation estimation based based on on
data. data.
fish fish
abundance abundance
in in Tysfjord Tysfjord should should be be computed computed and and presented presented with with the the Ofotfjord Ofotfjord
is is also also
distributed distributed in in Tysfjord, Tysfjord, whose whose data data have have not not been been analyzed. analyzed. The The
The The adult adult component component of of the the stock stock of of Norwegian Norwegian spring-spawning spring-spawning herring herring
- 10 10 -
pp. pp. 211 211 France. France. Fontainebleau, Fontainebleau,
Paris, Paris, de de Mines Mines des des Superieure Superieure Nationale Nationale Ecole Ecole applications. applications.
its its and and variables variables regionalized regionalized of of theory theory The The 1971. 1971. G. G. Matheron, Matheron,
410-414. 410-414. 189: 189: Mer, Mer, Explor. Explor. int. int. Cons. Cons.
Reun. Reun.
P.-v. P.-v. Rapp. Rapp. Annecy. Annecy. Lake Lake of of example example the the lakes: lakes: in in geostatistics geostatistics
of of use use The The 1990. 1990. J.-M. J.-M. Chautru, Chautru, and and D., D., Gerdeaux, Gerdeaux, J., J., Guillard, Guillard,
[mimeo]. [mimeo]. pp. pp. 8 8
1993/B:30. 1993/B:30. C.M. C.M. ICES ICES herring. herring. mature mature of of strength strength target target of of dependence dependence
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