"tI

This report not to he quoted without prior reference to the Council*

International Council for theExploration of the Sea

C.l\1.1994/ENV:6Ref.: D + E

REPORT OF THE WORKING GROUP ON STATISTICAL ASPECTS OFENVIRONl\IENTAL MONITORING

St. John's, Newfüundland, CanaJa, 26-29 April 1994.

This dücument is areport üf a Working Group of the InternationalCouncil für the Exploration of the Sea and does not necessarilyrepresent the views of the Council. Therefore, it should not he quotedwithout consultation with the General Secretary.

*General SecretaryICESPalregade 2-4DK-1261 Copenhagen KDENMARK

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Section

OPENING OF THE MEETING

TABLE OF CONTENTS

Page

2 ADOPTION OF THE AGENDA .

3 TERMS OF REFERENCE AND TASKS FOR THE 1994 MEETING .

4 REVIEW OF THE 1993 ACl\IE REPORT .

5 MULTIVARIATE METHODS FOR ASSESSING TRENDS I5.1 A Comparison of MANCOVA amI ANCOVA Analyses of aReal Data Set 15.2 Trends in Phytoplankton 2

6 REVIEWS OF THE PERFORMANCE OF MONITORING PROGRAMMES " 26.1 Report of the Sub-Group Meeting Held in February 1994 to Consider the Programme to Inves-

tigate Temporal Trends of Contaminants in Biota '. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 26.2 Evaluations of Sampling Strategies in National Programmes . . . . . . . . . . . . . . . . . . . . . . .. 2

7 DEVELOPMENTS IN GRAPHICAL AND STATISTICAL METHODS . . . . . . . . . . . . . . . . . . .. 37.1 Presenting Statistical Data in Formats Readily Acceptable by Non-Statisticians: Focusing on Key

Aspects of Contaminant Trend Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 37.2 Graphical Aids for Designing Contaminant Monitoring Programmes . . . . . . . . . . . . . . . . . .. 3

7.2.1 Report of sub-group on graphical design aids 47.3 Non-Parametric Tests of Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 67.4 Power Considerations for Setting Targets for Analytical Accuracy . . . . . . . . . . . . . . . . . . .. 6

8 THE USE OF COVARIABLES IN THE EXPRESSION OF CONTAMINANT CONCENTRATIONSAND REDUCTION OF RESIDUAL VARIANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 68.1 Basis for Expressing Contaminant Concentrations in Fish Livers . . . . . . . . . . . . . . . . . . . .. 6

8.1.1 Report of the sub-group on choice of basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 68.2 Effects 01' Biological Variables on Contaminant Concentrations in Musseis . . . . . . . . . . . . . .. 7

9 A COMPARISON OF STATISTICAL TOOLS AND f\IEANS TO RELATE BLOOM OCCURRENCESTO OTHER FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 8

10 APPLICATIONS OF KRIGING TO DATA ON CONTAMINANT CONCENTRATIONS IN MARINESEDIMENTS 8e 10.1 Report of the Sub-Group on Applications of Kriging . . . . . . . . . . . . . . . . . . . . . .. 9

11 TREATMENT AND UNDERSTANDING OF TEMPORAL VARIATION INCONTAMINANT/LENGTH RELATIONSHIPS 10

12 INTERCALIBRATION OF TWO METHODS OF MEASURING CHLOROBIPHENYLS (PCBCONGENERS) 10

13 REVIEW OF A NEW ROBUST l\IETHOD OF ASSESSING TRENDS AS USED IN THE 1993ASSESSMENT BY THE JMG AD HOC MON SUB-GROUP . . . . . . . . . . . . . . . . . . . . . . . . . .. 10

14 ANY OTHER BUSINESS 11

15 SUMMARY AND PROGRESS REPORT FOR ACME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11

16 ACTION LIST ...•................................................... 12

17 RECOI\IMENDATIONS 12

18 CLOSING OF THE MEETING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12

Section

ANNEX 1

ANNEX 2

Agenda .

List of Participants .....

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ANNEX 3 List of Working Papers 16

ANNEX 4

ANNEX 5

Univariate and Multivariate Analyses for Time Trends .

Multivariate Trends in Groups of Phytoplankton Species .....

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45

ANNEX 6 Sensitivity to detect trends in timeseries of contaminant concentrations in marine biota alongthe Swedish coasts . . . . . . . . . . . .. 55

ANNEX 7

ANNEX 8

Focusing on Key Aspects of Contaminant Trend Assessments .....

Graphical aids for designing contaminant monitoring programmes ..

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68

ANNEX 9 Influence of length on elements concentrations in blue musseIs sampled in an unpolluted fiordsystem in West Greenland 80

ANNEX 10 Relationship between length and lead concentration in the blue musse!, Mytilus edulis . . . . . .. 87

ANNEX 11 Shell Length and Metal Concentrations in MusseIs (Mytilus edulis) II . . . . . . . . . . . . . . . .. 99

ANNEX 12 Comparison of statistical tools and means to relate hloom occurrences to other factors

ANNEX 13 Spatial Analysis of Trace Metal Concentrations in North Sea Sediment ..

ANNEX 14 An exploratory graphical display for the analysis of covariance .

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ANNEX 15 Some notes of the intercalibration of two methods, measuring chlorohiphenyls (PCBs) 145

ANNEX 16 A Note on Bias in the EMS from the 3-Point Running Mean Smoother . . . . . . . . . . . . . . .. 151

ANNEX 17 Analysis of variance tables for the new robust method of assessing contaminant trend monitoringdata " 155

ANNEX 18 The power of the new robust method of assessing contaminant trend monitoring data 165

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"1 OPENING OF TUE i\IEETING

The Chairman, Mike Nicholson, opened the meeting at09.00 hrs on 26 April 1994. He welcomed new and oldmembers to the group, and thanked Bill Warren for hisefforts concerning hotel bookings, transportation, andlocal information.

d) review ami report on further progress in the use ofcovariables in the expression or contaminant concen­trations amI rt:duction of residual variance;

e) consider the report being prepared by a Frenchmember on the comparison of statistical tools andmeans to rdate bloom occurrences to other factors.

2 ADOPTION OF TUE AGENDA 4 REVIEW OF TIIE 1993 ACl\1E REPORT

The agenda was accepted and is attached as Annex I. Alist of participants is given in Annex 2. Aseries ofworking papers were presented for discussion. Somewere incorporated into annexes for this report, a list ofthe others is given in Annex 3. As in previous meetings,members Were requested to provide summaries of theirpresentations for the report.

• 3 TERMS OF REFERENCE AND TASKS FORTUE 1994 I\1EETING

WGSAEM considered the 1993 ACME Report andagreed that it gave an accurate reflection of the 1993Report of WGSAEM. WGSAEM noted the recognitionfor its work given by ACME, particularly for its supportof the meeting of the Sub-Group on Temporal TrendMonitoring Programmes for Contaminants in Biota(SGTTC) to reconsider objectives, sampling protocols,sampIe treatment and analytical performance (C.Res.1993/2:7:7).

2) in a multivariate analysis there is an opportunity toassess the interdependence between contarninants,although this may be more useful for data screeningthan for the trend assessment;

I) although the Type I error rate of detecting trends iscontrolled at the 5 % level for the group ofcontaminants assessed within a multivariate analy­sis, this would he inappropriate in the context of theJMG assessments where each data set is of interestin its m\n right;

3) in a multivariate analysis, trends can be interpretedrelative to the known behaviour of the interactionsbetween contaminants within the monitoring organ­ism. These results might be confusing and ambigu­aus, however, unless good quality data on inputsare also availahle. Jaap van Jer Meer JescriheJ ananalysis where parallel trends in fish and sea mam-

Mike Nicholson presented a paper prepared by Dr RajMisra (Annex 4). This gave a detailed development ofthe methodology for univariate and multivariate analysesof variance between two and many groups, and demon­strated a multivariate analysis of trends in 10contaminant/tissue combinations for four years. TheWGSAEM considered that this paper presented a usefultheoretical overview amI satisfied the request from theprevious meeting for a demonstration using a simpleexample based on areal contaminant data set.WGSAEM made the following additional comments:

A Comparison of I\IANCOVA and ANCOVAAnal)'ses of aReal Data Set

l\IULTIVARIATE l\IETIIODS FOR AS­SESSING TRENDS

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5.1

a) review and report on the results of a comparison ofMANCOVA and ANCOVA analyses of areal dataset;

c) to provide statistical advice with respect to othermonitoring issues, as required;

c) review and report on further progress in the presen­tation of statistical data in formats readily acceptableby non-statisticians;

b) review the recommendations of the Sub Groupmeeting held in February 1994 to reconsider theprogramme to investigate temporal trends ofcontaminants in biota;

a) to develop statistical protocols for the determinationof temporal and spatial trends in the concentrationsand distribution of contaminants in marine biota,sediments and sea water;

b) to analyse data for the elucidation of temporal andspatial trends in contarninants in marine biota, sedi­ments and sea water;

The general terms of reference (C.Res. 1986/2:25) forthe Working Group on Statistical Aspects 01' Environ­mental Monitoring (WGSAEM) were:

The specific tasks for the 1994 meeting of WGSAEM(C.Res.1993/2:7:6) were to:

d) to liaise with the Statistics Committee as appropri­ate.•

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mals were analysed to differentiate betwe<.m theavailability and behaviour of contaminants.

WGSAEM also noted that additional graphical tech­niques could be used to provide information and aidinterpretation, and that a more integrative approach ofdata exploration, description, and model formulationcould be more informative than an approach centred onhypothesis testing.

5.2 Trends in Ph)'toplankton

Mike Nicholson went on to present a method given inAnnex 5 for exploring trends in muItivariate data. Thetechnique maximizes the lag-} autocorrelation (the smoo­thness) of a linear projection of the multivariate data,and was demonstrated using a }5 month time series offive major groups of zooplankton and phytoplanktonspecies. WGSAEM considered this to be a potentiallyuseful technique but would have liked to see the displayproduced by various scenarios, for example, whengroups of variables are orthogonal.

6 REVIEWS 01" THE PERFORl\IANCE OF1\10~ITORING PROGRAl\Il\IES

6.1 Rcport of the Sub-Group I\leetin~ Held in Feh­ruary 1994 to Considcr the Programme to Imes­tigate Temporal Trends of Contaminants inBiota

Rob Fryer presented the report of the Sub-Group onTemporal Trend l\tonitoring Programmes forContaminants in Biota held in February 1994 and spon­sored by ICES under C.Res.}993/2:7:7. The SGTTCconsidered the objectives, design, and effectiveness oftemporal trend monitoring programmes, identifying themajor weaknesses in current practice, where more dataare required, and where potential increases in effective­ness could be achieved. In practice these could begrouped under four topics, with main conclusions asfolIows:

Objecthes

Broad monitoring objectives of national or internationalprogrammes need to be supplemented by more detailedand quantified objectives, for example, that a specifiedtrend at a given site should be detected with a givenprobability in astated period after the imposition ofcertain control measures.

Power

Present assessments of the JMG data suggest that impor­tant trends in contaminant levels are unlikely to hedetected in realistie time frames. Simple ehanges insampling and analytical strategy were considered, hut it

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was not possible to fully assess their effectiveness,through lack of data on critical sources of variation.

Choke of tissue/or~anism

The SGTTC eonsidered the necessary eharacteristics ofa monitoring organism and the corresponding parametersthat would need to be estimated for making an objectivechoice. In practice these data were difficult to compile.It was also difficult to find good quality input andseawater data to relate to the corresponding series ofcontaminants in biota.

Choke or ßasis/CO\'ariables

One potential method of improving the precision of trendmeasurements is to exploit additional explanatory vari­ables, or by re-expressing contaminant eoncentration ona more appropriate basis. Some encouraging results wereobtained for some contaminants in livers and herringmuscle, but these need to be repeated with other datasets.

Roh Fryer presented the recommended action list fromthe Sub-Grour report, which includes:

the preparation of a TIMES document glvmgguidelines for the formulation of objectives;

the review of information relevant to the choice ofmonitoring organism;

the proposal to organize workshops together withWGEAMS;

the investigation of components of vanance In

monitoring data; and

the continued assessment of the appropriate basisfor expressing eontaminant concentrations.

WGSAEM generally supported these recommendationsand welcomed the chance of continuing the successfulcollaboration which had taken place with members of theSGTTe.

6.2 Eyaluations of Samplin~ Stratl'gics in NationalProgrammes

There wen~ several presentations of features concerningthe effectiveness and development of national monitoringprogrammes.

A stuuy in whieh the magnituue of Ihe 'ranuom'hetween-)'ear variation was used as a measure of sensi­tivity of various time series had been presented byAnders Eignert at the SGTTC meeting, and was pres­ented again to WGSAEM. The residual variancebetween a reference line (a LOWESS smoother or a loglinear regression line) and the actual recorded geometrie

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means (or mellians) was used to represent the hetween­year variation. This technique is applieable only when itis possible to achieve a proper measure of the part of thebetween-year variation that is not duc to real changes inpollution load. This assumption may, to a certain extent,be fulfilled in the Swedish Contaminant Programmelocated in reference areas not inl1uenced by loealsourees, where relatively smooth long-term changes areexpected. A comparison between various contaminantsshowed that time-series of mereury, sPCB, and sDDTwas less sensitive to detect trends than cadmium, copper,and zinc in herring and that gullemot eggs seemed to bea more sensitive matrix than herring for the investigatedeontaminants sPCB and sDDT. The effect of adjustingfor covariables on the sensitivity was demonstrated andthe possibility to improve sensitivity by using ratios oforganoehlorines was diseussed. The study is presented inAnnex 6.

Otto Swertz presented an outline of the evaluation of themarine monitoring programme from The Netherlands,specifieally the ehemieal programme whieh is intendedto generate information for the preparation amI evalu­ation of water management poliey. The project eonsistsof three phases of whieh the seeond and thin.! are eur­rently being earried out. Swertz referred to agenda item7.2 in which Drs Nicholson and Fryer also worked outsome theory of monitoring design. The first phase of theevaluation, the definition of the information needs,resulted in quantitative monitoring objeetives of qualityeriteria and trend deteetion. In the second phase, differ­ent variation sourees within the programme will bedefined and estimated. Five components are distin­guished: sampling, analytieal, spatial, seasonal, and theresidual population varianee. In the third phase differentdesigns of the programme will be eompared in terms ofeosts and detectable trend, based on a variance modelwith the five eomponents. WGSAEM appreeiated theattempt to balance the eeonomic and the informationalvalue of a programme through the graphieal display ofcosts versus detectable trend. Questions were raisedabout both the estimation of the varianee componentsand about the degrees of freedom in the variance model.Swertz eonfirmed that estimation of the sampling vari­anee is diffieult due to insuffieient data, although theother components can be estimated from historieal data.

Steffen Uhlig presented an overview of the Germanmonitoring programme, BLMP (Bundes-Länder-Mess­programm für Nord- und Ostsee). This had begun in thelate 1970s and had been the suhjeet of evaluation in1992. Since 1993 the proeess of reorganization anddeve10pment had begun. He also presented some of hisinvestigations conceming monitoring design, whichlooked at both the efficieney and the eost of monitoring,aiming to identify those ehanges in the design whiehcould. for example. maximize the ratio of the reductionin the varianee of the estimated trend to the inerease ineosts.

7 DEVELOP;\IENTS IN GRAPIIICAL AND STA­TISTICAL l\JETIiODS

7.1 Prcscnting Statistical Data in Fonnals RcadilyAcceptablc by Non-Statisticians: Focusing onKey Aspecl'i of Contaminant Trend Asscssments

Rob Fryer presented a short paper (Annex 7) deseribinga method which had been suggested at the 1993 meeting.This was a graphical presentation which attempted tocombine four items of information:

the preeision of the trend assessment;

the size of any trend in the most recent part of thetime series;

the current contaminant level; and

the probability that some environmental qualitywould be exeeeded in the immediate future.

It was argued that an index combining these four itemsmight be useful at the management level for allocatingpriorities for remedial action aeross differentcontaminants. Steffen Uhlig noted that whcn data arecollected at more frequent times within a year, moresophisticated time series methods might be more effec­tive at projecting periodic and non-linear eomponents inthe data.

This method generated considerable discussion, andseveral other methods were discussed, including Shewartand CUSUM plots.

Otto Swertz discussed a similar approach for the assess­ments in the Netherlands which focus on eomparinglevels to water quality criteria, summarizing assessmentinformation in some relative quality index and predietingfuture levels. For both inland and marine waters thesethree steps are now being developed. The water qualitycriteria are al ready set out on a Ministerial level; theindices will be based on eomparisons with these andfuture levels will be predieted with numerical models ofthe marine water systems.

7.2 Gmphical Aid'i for Designing Contaminant l\Ion­itoring Programmes

Although it is often theoretically straightforward todesign a monitoring programme, in practice. the situ­ation is generally much more eomplicated. For example:

the objectives are vagUe, or it is difficult to recon­eile a number of different objectives,

there are no estimates of important variance compo­nents,

the estimated costs/constraints are not the realcosts/constraints.

In such situations, it can be useful to explore the effec­tiveness of a range of possible designs, with a range ofplausible variance estimates, costs, and constraints. Thiscan:

open up the debate between statisticians, chemistsand managers,

identify areas where more information is required,or where sources of variation need to be controlIed,

lead to solutions which satisfy a variety of implied,but hard-to-set-down constraints.

Rob Fryer and Mike Nicholson presented two graphicaltechniques for exploring different monitoring designs(Annex 8):

Thc first graphical aid was used to show how theprecision of an estimated mean concentrationdepends on the number of pools that are analysedand how that precision might vary across differentlaboratories and contaminants. This would be usefulwhen, for example, designing a sampling protocolfor a number of laboratories.

The second graphical aid was used to explore thepower of a temporal monitoring programme for arange of sampling and analytical variances. Thiswould be useful when, for example, there is littleinformation about the sampling and analytical vari­ances, and it is important to assess the effectivenessof the programme for a range of plausible variancecombinations.

WGSAEM found the graphical aids potentially veryuseful, allhough they took a while to assimilate. It wasnoted that the effectiveness of different designs can alsooften be readily explored through, e.g., a spreadsheet;however, there are many advantages in simultaneouslypresenting a number of designs on one graph.

WGSAEM noted that the graphs did not incorporate anyinformation about cost, often the critical constraint in thedesign of a programme.

7.2.1 Rcport of suh-group on graphical design aids

A sub-group (Rob Fryer, Benoit Beliaeff, Gunnar Thor­esson, and Dito Swertz) was formed to investigate thisproblem amI two promising graphical aids incorporatingcosts are presented be)ow.

The graphs are presentcd by way of thc following sty­lized example. Suppose we are designing an annualcontaminant monitoring programme lasting IO years.Further, suppose that each year we take a total of R

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sampIes, spread over E sampling expeditions, and anal­yseU in B chemical batches. The % yearly changedetected with 90% power is then given by100(exp(OA08N)-I) where

and ,ry, u2e , ,rb , u2 are four variance components (formore details, see Fryer and Nicholson, 1994; Annex 4of the Report of the Sub-Group on Temporal TrendMonitoring Programmes for Contaminants in Biota).Suppose we have estimates of the variance components(Jy = 0.1, (Je = 0.2, (Jb = 0.15, (J = 0.4. Further,suppose the costs corresponding to taking an extrasampie, analysing an extra batch, or going on an addi­tional expedition are 1, 10, 100 units, respectively, sothe total annual cost of the programme is R + lOB +lODE.

Figure 7.1 shows contours of the % yearly changedetected with 90% power for different combinations ofE and B assuming that R = 25. Thus, taking B = 5 amiE = 2, the programme will detect a yearly change ofabout 9% with 90% pO\ver. Superimposed on thesecontours are the corresponding costs. Thus, the pro­gramme with B = 5 and E = 2 costs 275 units.

Figure 7.1 can be used in a number of ways. Supposewe want to be able to detect a trend of 8 % per year with90% power. The figure shows that this requires at least3 sampling expeditions, will cost over 300 units, and thenumber of batches does not matter very much providedit is 3 or more. Alternatively, suppose we only have 200units to spend. We can then detect a yearly trend ofabout 10 %. If this is not satisfactory, the objectives mustbe changed or more money acquired.

Figure 7.1 can be developed further. For example, thewidth of the contour lines (of % yearly change) canconvey information about the effect of changes in thevariance estimates. This could allow an assessment ofthe robustness of any particular programme design.

Figure 7.2 shows the % yearly change detected with90% power and the corresponding cost for eight combi­nations of E, B, and R. Each combination is representedby something that looks like the frame of a three-poledtent with the canvas badly stretched over it. The bottompole corresponds to B, the upper left-hand pole corre­sponds to R, and the upper right-hand pole correspondsto E. \Vhen the canvas is stretched fully over a pole,then that corresponds to B = 5, R = 25, and E = 2(depending on the pole). When the canvas is only par­tiaHy stretched over a pole (e.g., a quarter stretched),then that corre~ponds to, e.g., on)y a quarter of thevalues ahove. Thus, for example, the very right-handpoint in Figure 7.2 gives the % yearly change and costwhen B = 5, R = 25, E = 2. The point to the left ofthis gives the % yearly change and cost when B = 5, R= 12, E = 2.

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Figure 7.1 Percent yearly change detected with 90% power tor different combinations 01' E ami B.assuming R=25.

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Figure 7.2 Percent yearly change detected with 90% power and the corresponding cost for eightcombinations of E, Band R.

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-w y'\(e Objl!,-L:\J~

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d c-l.lrre.Y\t4J cl.(!.~~1W\

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-ucJ

q0

\00 '2.00

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Thus, to detect a yearly trend of 10%, 2 expeditions arerequired, and it will cost nearly 300 units. Again, givena maximum budget of 200 units, a yearly trend of ahout12 % can be detected with 90% power taking B = 5,R = 25, E = 1.

The figure can highlight the current programme (if oneexists), can accommodate more design variables (inaddition to E, B, R) by increasing the number of polesand can represent any sensible number of combinationsof E, B, R. It is also possible to plot the lowest detect­able trend for any given total cost (the Pareto optimalcurve).

7.3 Non-Parametric Tests of Trend<;

Otto Swertz presented a protocol for trend analysis ofenvironmental variables, specifically, for the detectionand estimation of monotonie trends in quarterly ormonthly data. Following this protocol, one makes thechoice bet\veen an extended parametrie linear regressionanalysis and a non-parametrie Mann-Kendall sign test.Both are tests of a monotonic trend aeeounting forseasonality and serial dependence; the aceompanyingestimator quantifies the size of the trend.

Additional features of this protocol are robust treatmentof outliers, missing values, censored values, and changesin monitoring frequeney.

There was some discussion on how serial dependence isaccounted for in the Mann-KendaIl test ami on the defi­nition of the seasonality parameters ami how theautoregressive parameters in the extended linearregression were estimated. More information is availahlein a forthcoming Netherlands Government report whichcan he obtained from Otto Swertz. He also has informa­tion ahout the PC-software package WQStat containingthe Mann-Kendall test.

A !-hort presentation demonstrating an applieation of theMann-Kendall test was given hy Gunnar Thoresson. Theohjective was to find a procedure for reducing the num­ber of stations in a sampling programme of springspa\ming perch fry sampled by beach seining in theestuary of the River Kyronjoki in Finland. The pro­gramme has eurrently been run for ten years. The analy­sis identified a subset of stations exhibiting a commontrend. The strength of the method in identifying a homo­geneous group of stations was thought to make it anappropriate way to approach this problem.

7.4 Power Considerations for Settin~ Targelli forAnal)"ticli Accuracy

Mike Nicholson presented a simple procedure which hadbccn presented at the February 1994 SGTTC meeting(Section 6.1) whereby the objective 01' maintaining anadequate power provided a framework for setting atarget for analytical accuracy. This would ensure that

problems anSlOg from analytical quality couldsubsequently be discounted when monitoring data arereported and analysed. Incorporating these targets intothe objectives of the monitoring programme mightreduce the waste encountered in, e.g., the JMG assess­ments, where a substantial number of data sets werediscarded, having failed a standard for accuracy imposedat the time of the assessment. Steffen Uhlig noted thatthis approach would help in controlling the quality ofchemical analyses where this had been sub-eontracted tolow-cost/low-quality private sector laboratories.

8 TUE USE OF COVARIABLES IN TUEEXPRESSION OF CONTAI\IINANT CO~CEN­

TRATIO~S AND REDUCTION OF RESIDUALVARIANCE

8.1 Basis for Exprcssing Contaminant Concentra­tions in Fish Linrs

Frank Riget presented an analysis of the relationshipbetween trace metal concentrations and lipid content infish liver. This work had been presented at the meetingofthe Marine Chemistry Working Group in Brest, 1994.The data were taken from the ICES data bank and theGreenland Environmental Research Institute monitoringprogrammes.

It was shown that there is a strong linear relationshipbetween fat fraction and dry matter fraction, suggestingthat the dry matter fraction might replace the [at [ractionwhen the objective is to normalize metal concentrationsin livers. However, as revealed by the leES data anddiscussed by the group, it is necessary to standardize themeasurement of fat fraction. and c1arify how fat contenthas been analyseu.

The reiationship between trace metal concentration anddry matter fraction was analysed on a log seale, indicat­ing for both data sets that concentration expressed on adry weight basis tends to decrease with the dry weightfraction. This effect tended to be removed when concen­trat ions were expressed on a wet \",eight basis. However,these results are preIiminary, and should be appraisedwith other uata. WGSAEM also discussed other ways inwhich the uata might be analysed, for example, toremove possible year effects and exploring alternativetransformations.

8.1. IRrport of thc sub-~roup on basis

During the meeting, a sub-group consisting of AndersEignert. Frank Riget, ami Jaap van der Meer, discussedthe choice 01' a basis for expressing contaminant concen­tration. Organie contaminants are dissolved in fattytissue and, therefore, usually are expressed on the basis01' fat mass. This way, time trends in contaminant levelswill not he affected by f1uctuating fat levels. Thesetluctuations may he due to sources unrelated to contami-

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WGMS amI to WGSAEM. The Chairman encouragedother working group members to explore the method forthemselves, developing their own insights to share withthe rest of the group.

11 TREATl\IEf'I.'T AND UNDERSTANDING OFTEMPORAL VARIATION INCONTAl\IINANTILENGTII RELATIO:,,-/SIIIPS

Jaap van der Meer presented a paper (Annex 14) inwhich he proposed a simple exploratory graphical dis­play for the analysis of covariance. The display is par­ticularly useful when intercepts and slopes differ amongthe levels of the grouping factor. This effect has beenevident in previous assessments of contaminants in fishmuscle, where the regression coefficient of fish lengthhas varied between years. Hitherto either a1l annualregression lines were shown in a single plot, or one orboth regression coefficients were plotted against time.Tbe proposed display is, in fact, a phase diagram of theintercepts plotted against the slopes, estimated aftersubtracting the overall means. The Y-axis of the figuresimply indicates the time trend for a fish of averagelength. In addition, rotation of the axes provides the timetrends of fish of other lengths, e.g., large or small fish.

12 INTERCALIßRATIO:,,-/ OF TWO METIIODSOF l\IEASURING CIILOROßlPIIENYLS (PCBCONGENERS)

Anders Bignert described some of the problems thatarose when a new method (high resolution capillarycolumn gas chromatography) was introduced for thedetermination of PCBs. Tbis is presented in Annex 15.To overcome a problem where the congener compositionvaried with changes in the total concentration, one majorpeak in the low resolution chromatogram was selectedand calibrated against the sum of CB-138 and CB-163 inthe high resolution chromatogram. It was concludeJ thatat least two years of parallel analyses are neeJed toestablish reliable intercalibration factors. Tbe results ofthese intercalibration exercises should be reported toICES before a new analytical method is allowed toreplace an old one.

13 REVIEW OF A NEW ROBUST l\IETIIOD OFASSESSING TRENDS AS USED IN TIIE 1993ASSESSl\IENT BY TIIE Jl\IG ~tD /lOe l\IONSUB·GROUP

Mike Nicholson gave an overview of the history of trendassessments that have taken place within the ICES/JMGprogrammes. These assessments have often been compli­cated by the need to respond to unusual features of thedata, either in the way they were collected, processed,or in their distribution. These complications have led to

the development of a simpler, robust, and more com­plete method of analysing and presenting trends.

Rob Fryer presented abrief description of the newmethodology from a draft TIMES document. The newmethodology essentially consists of the following stages:

When there is no length effe·ct, yeady contaminant levelsare summarized by the median log-concentration. Theseare smoothed and are tested for evidence of alineartrend and any non-linear systematic variation with time.

When there is a length effect, the fish are divided intosmall and large categories, which are then treated separ­ately. Tbe trends for each size group are then formallycompared.

The particular application of this methodology for the1993 JMG assessment meeting was constrained by bothtime amI software availability and although this applica­tion generally worked \vell, more assessment and devel­opment of the method will be necessary.

The presentation led to wide discussion of the advan­tages and disadvantages of various aspects of the metho­dology, such as the need for log-transformation, the useof medians, the type of smoother, the degree of smooth­ing, and adequacy of the F-tests.

WGSAEM endorsed the philosophy of the approach,which had performed well in its first application in the1993 JMG assessments, even in its current initial form.On this basis, it was agreeJ that the draft TIMES docu­ment should go forward for publication, having broughtforward the discussion of the evolutionary/developmentalnature of the current procedures to the overview at thebeginning of the document.

In addition, WGSAEM suggesteJ that a fixed data setshould be selected from the ICES data base and madeavailable for method development, calibration, andcomparison. Tbere mayaIso be the requirement for anupdate to a TIMES document in the light of furtherinvestigations.

l\1ike Nicholson presented the results of aseries ofsimulations investigating bias in the estimated errormean square using the 3-point moving average withdifferent trend scenarios (Annex 16). These resultssuggested that the 3-point moving average performeJwell compared with similar parametrie models and thatbias would be small for trends typical of the marineenvironment.

Rob Fryer presented two papers. Tbe first of these(Annex 17) described analysis of variance tables appro­priate for any linear smoother. Tbe second (Annex 18)considered possible reductions in the power of the testfor a linear trend resulting from the use of the mediancompared with the mean. For the data encountered in the

nation. This approach implicitly assurnes that when anorganism loses fat, it also gets rid of the accompanyingorganic contaminant load, and vice versa. Similarly,metals are mainly attached to proteins in the non-fat partof the body of the organism. Thus, it is obvious toexpress metals on a non-fat mass basis. As the watercontent of the non-fat part may fluctuate considerably insome organisms (e.g., musseis), the dry non-fat rnass(that is dry mass minus fat mass) should preferably beused as the basis for expressing metal concentration. Inpractice, however, fat mass is often not determined. Ifthe non-fat mass shows a constant water fraction (whichis probably true for fish liver) or, in other words, whenthe ratio between water mass and dry non-fat mass isconstant, then metal concentration can be expressed ona water basis, that is on wet mass minus dry mass. Thismay seem counterintuitive, but deserves further study.For example, a possibly large measurement error ofwater content could be disadvantageous. The sub-groupsuggested the continuation of research on the choice ofa basis for expressing contaminant coneentration in linewith the points made above. Some sampie data sets(e.g., livers of Dutch flounders and Swedish and Norwe­gian eods) will be analysed intersessionally and the sub­group plans to present areport at next year's meeting.

8.2 Effl'Cts 01' niolo~ical Variables on ContaminantConccntrations in l\Iusscls

Frank Riget presented two papers exploring the effect ofshell length on contaminant concentrations in musseIs.

The first of these (Annex 9) considered data on 20elements colleeted at four stations in an unpolluted fjordsystem in West Greenland in each of three years. Oneaeh sampling oceasion, musseIs were colleekd andpooled in 12 to IS length groups with an interval of 3mm. Thc relationship between log concentrations and loglength was analysed in a 2-way ANCOVA on year andloeation including all first and second order interaetions.Shell length was significant for most of the elements,together with a varying mixture of significant loeationand/or year effeets.

Examination of the individual loeation/year regressionsshowed that some elements (Na, Pb, Br, Sr, La, Ce, andEu) tended to have a positive association, while others(Sc, Fe, Co, As, Se, Rb, Cu, Cs, and Th) tended tohave a negative assoeiation. Some (Cr, Zn, and Hg)showed no clear pieture.

WGSAEM noted that this is a valuable data set givinginformation about the effect of shell length over anextensive range of elements. The data offer a goodopportunity for further analysis. One approach might bcto refine the analysis by including information on thcnumber of musseIs in each pool.

The second paper (Annex 10) looked more closely at therelationship for lead using data from three West Green-

land fjord systems: one affected by lead/zine mining;another affeckd by cryolite mining; and a third whiehwas free from pollution. The same two-way analysis ofcovarianee was employed, showing a signifieant shelllength effeet in all three areas. For the two pollutedareas, shell length was dependent on loeation within thearea, but not on year of sampling. In one of the areas,the second order interaction between loeation, year, andshelliength was signifieant.

Examination of the individual loeation/year regressionsshowed that the regression slope was generally positivewith an average value in the range (0.8, 1.0) in thepolluted areas, and about 0.4 in the unpolluted fjord.

At a stationjust outside the fjord eontaining the lead/zinemine, approximately 40 km from the pollution source, 4to 8 sire groups were sampled throughout the monitoringperiod. The time trend of the slope at this loeationshowed an inerease from 1982 to 1987 followed by adeerease. A possible explanation of this pattern may befound in the history of inputs, as reflected in the corre­sponding trends of dissoh,ed lead in water, whichshowed a signifieant decrease during the late 1970s. Inthe period with inereasing slope in the shell length rela­tionship, large musseIs may be 'remembering' the period\vith high levels of dissolved lead, whereas small mus­sels have only been exposed to the recent (to them) lowlevels. The period of deereasing shelliength slopes couldthen be explained by the extinction of the large 'remem­bering' musseIs. This interpretation is consistent withinformation about the slow grO\vth rate of musseIs atWest Greenland compared to more southerly areas, witha mean length of about 4 cm at age 8, and about 6 cm atage 12. A similar time trend could not be seen at any ofthe cryolite mine locations, where the level of inputs isbelieved to have been relatively constant over a longtime perioJ.

Norman Green and Birger Bjerkeng submitted a paper(Annex 11) deseribing their investigations of the effeetof biological covariates on metal concentrations in mus­sels. For their data, concentrations of cadmium, lead,and mercury were not systematically influeneed by shelllength. However, a signifieant proportion of thebetween-replicate variance is explained by combinationsof shell length, shell weight, and soft body dry weight.This suggests that normalization might be important fortrend analysis. WGSAEM thought that the results \vereinteresting and noted that one of the combinations ofeovariates, labelIed as degree of shell filling (a measureof eondition), was more important in two out of threeeases than a combination corresponding to general size.

•

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•

9 A CO:\IPARISO:--l OF STATISTICAL TOOLSAND l\IEANS TO RELATE BLOO~I OCCUR­RENCES TO OTIIER FACTORS

Generally speaking, a phytoplankton bloom may bedefined as an algal proliferation, whether toxie or not.We may distinguish between regular blooms (e.g.,diatom spring blooms in temperate seas) and unusual orunexpected blooms. Regular blooms are weil doe­urnented: for example, vertieal stability of the watermasses is kno\\,n as the essential triggering factor fordiatom spring blooms. Nutrient depletion then acts as alimiting faetor.

Benoit Beliaeff presented a paper (Annex 12) describingsome potentially useful statistical methods for relatingblooms to environmental variables. These ean begrouped as folIows:

S~mcntation mcthods: detection of discontinuities anddetermination of homogeneous intervals, using eitherunivariate (cumulative funetion) or multivariate time­series (D2 index or ehronologieal c1ustering).

Ordination tcchniqucs: deseription of large-seale gradi­ents in large data sets (observations x variables). Classi­eal methods are prineipal eomponent analysis, assuminga linear model, and Correspondence Analysis, allowingnon-linear relationships and using either quantitative orqualitative variables.

R~rcssion anal,)'sis: canonieal correlation has been usedby several authors. Canonical coefficients are sensitiveto multicollinearity between independent variables and tomeasurement error, and the results may be diffieult tointerpret. Multiple Linear Regression may be a poorpredictor, although it has sueeessfully been used eoupledwith the Alternative Conditional Expeetation algorithm,providing an optimal transformation of the originalvariables to detect non-linear relationships among vari­ables and an objective determination of thresholds.

Spcctral anal,)'sis: decomposition of a quantitative signalinto its constituent periodicities. Coherence analysisprovides an effieient means of relating speetra between,e.g., a biologieal variable and an environmental vari­able.

Finally, a good choiee of method depends on a goodquestion being addressed by biologists to statisticians.Data quality may suffer from a poor sampling design:for example, variables aeting in different temporal sealesare sampled with the same frequency. Further methodo­logieal contributions may foeus on:

Methods to dctcct a bloom: eould some observedincrease in algal cell density be considered as a bloom?Some analogies may be found wilh epidemiologicalstudies.

S~m.iti,·it.}' of mcthllds, such as segmentation methods,to the ehoiee of a partieular taxonomie resolution.

10 APPLICATIONS OF KRIGING TO DATA O:--lCO:'ll'TAl\IINANT CONCENTRATIONS INI\IARINE SEDIMENTS

Dr W.G. Warren prescnted his paper, 'Spatial Analysis0/ Trace Metal ConceJltratiol/s in North Sen ScdimeJlt'(Annex 13). In aeeordanee with a recommendation oflast year's meeting, this paper was submitted to theFebruary 1994 meeting of WGMS, and represented arevision of the paper presented at last year's meeting.While some improvements were made to the methodol­ogy, the principal difference was that, in the revision,traee metal eoncentrations were normalized to alumin­IUm.

The study examined the effects ofusing different optionsin the statistieal analysis, namely, whether or not toattempt to allow for 'drift' in the mean eoneentration,whether to use all data loeations to interpolate the con­centration at an unsampled loeation or solely the dataloeations within a 'kriging neighbourhood', i.e., a re1a­tively small region about the unsampled loeation. Theconclusions are essentially the same as given in thereport of last }'ear's meeting (C.M. 1993/ENV:6). Asstated in that report, a main value of the study was theinsight given into the use of kriging as a tool for spatialinterpolation and how the estimates may be affeeted bythe interaetion between sampling design and options inthe statistieal analysis. In terms of the actual coneentra­tions, in contrast to last year's report, after normaliz­ation to aluminium, not all metals showed similar spatialpatterns.

In diseussion, the question arose as to whether kriging isan 'exact interpolator'. In the absence of measurementerror, kriging is, indeed, an exaet interpolator in that theestimate at a data loeation is the observed value. How­ever, if there is measurement error and an estimate ofmeasurement error variance is available, a 'smoothed'estimate may be preferred, i.c., one that is more inaecordanee with the values at neighbouring loeations,while taking inlo aeeount the magnitude of the measure­ment error. In the study, a direet estimate ofthe measur­ement errar varianee was available for the Norwegiandata since replicate measurements were made at mostdata loeations (it is important to distinguish betweenmeasurement error and mieroscale spatial variation).

It was also pointed out that, for the purpose of eonstruet­ing a variogram, there are designs that are superior to aregular grid, although observations on a regular grid\....ould be preferred for the interpolation step. In mostapplieations, however, as in this study, one has to usethe same set of dala localions für holh the conslructionof the variogram and the interpolation.

9

Jan Rene Larsen, who had presented Dr Warren's paperat the WGMS meeting, reported on the reaction ofWGMS to the paper. It was feit that WGMS had misin­terpreted the results, perhaps because of an ineompleteunderstanding of some of the technical terminology. Inaddition to the above clarifying description of the tech­nique, the sub-group addressed some of the questionsthat had been directly raised by WGMS.

10.1 Report of thc Suh-Group on Applications ofKriging

Tbc sub-group emphasized that kriging is first of all atool to estimate l an unknown value of a variable in aloeation based on measured values in neighbourhoodloeations. Moreover, the teehnique estimates the errorassociated with the estimated value. Finally, the parame­ters, namely, the sill, the nugget, and the range of thevariogram estimated in the proeess of kriging ean readilybe interpreted in terms of eovariance between loeations.In this respect kriging has an advantage over other inter­polation or mapping methods.

Thc WGMS had eritieized thc assumption of secondorder stationarity, stating that this was unrealistic. Tbesub-group emphasized that this applies to the underlyingstochastie process and does not imply the oversmoothingin the interpolation of a particular realization of theproeess, the actual data being from one such realization.It was also noted that the doeument demonstrates that themethod is faidy robust to a violation of this assumption.

In reviewing the technique, the WGMS had reiteratedthat spatial studies are usually performed in order toidentify areas with elevated eoncentrations, 'hot spots',input sourees, ete. WGMS feit that in ealculating a'new' value in an area where a high (or low) value hadal ready been measured, kriging would tend to 'smoothout' extreme values from the data set and thereby pre­venting the proper identifieation of areas/values of par­ticular interesl. Tbe sub-group eommented that in thispartieular use of the technique, the original value wouldalways be 'retumed', unless it is desired to makc allow­anee for measurement errors.

The WGMS was skeptieal to the proposal of applyingthe teehnique to a larger geographical area, for instance,the entire North Sea. They argued that differences ingeochemical eomposition and particle size distribution inthe region make it unrealistie to use the same measuredor normalized value to map the geographical distributionof a particular contaminanl. The sub-group had threeeomments to these objeetions:

I) Tbe technique ean be used on any measured orderived (normalized) value.

2) Tbe teehnique ean be applied on a regional as weilas on a subregional seale. thus allowing separateanalyses to he done on any suhset of data.

iO

3) It will generally be possible to allow for abruptehanges in the level of the measured parameterresulting from, e.g., differences in substrate typethrough whieh subregions ean be identified. Tbemeasured values in one suhregion will only havelillle, if any, influenee on the estimated values inthe other.

Tbe WGMS feIt that the requirement of data from atleast 150 stations for kriging to work satisfaetorily wasunrealistie. Tbey argued that the UK data set (whiehfulfilled the requirement) had been eollected for a par­tieular purpose (the NSTF assessment) and that it wasimprobable that a routine sampling seheme would be thatextensive. Tbe sub-group aceepted the prineipal objec­tions but argued that the requirement only applies to theconstruetion of the variogram. Onee this is eonstrueted,the kriging ean be done on the basis of far fewer sta­tions, probably 50 to 60. Moreover, if it can be assumedthat the spatial eorrelation strueture is eonstant overseveral years, whieh seems reasonable for sediments, thevariograms can be constructed on the aceumulatedamount of measurements over years. Finally, the sub­group concurred that the technique would probably notprovide much new information in the UK example.

The sub-group feit that the kriging technique providesgood estimates for input into time trend analysis. Tbcestimated value would tend to be closer to the 'true'value, thereby (hopefully) reducing the betwcen-yearerror variance.

The implications for sampling design could be summar­ized as folIows:

I) For construction of the variogram, 150 measure­ments are desirable. These data could, however, beeollected over several years, provided that the'constant spatial eorrelation strueture' assumption isfulfilled. Once the variogram is constructed, it maybe that, depending on the form of the variogram,no more than, say, 50 measurements are requiredto do the analysis.

2) It is desirable to place sampling stations on a reg­ular grid. The distance between the stations willdeterminc the magnitude of the estimated variance.

3) In the Norwegian example, where duplicate sampIeshad been taken at a large number of stations, betterestimates would have been obtained if instead twiceas man)' stations had been sampled, but withoutduplieate measuremenl.

The sub-group presented its report and a number ofquestions were raised conceming the specifie details ofthe treatment of measurement error, particularly inrelation to non-exact prediction of observations. BillWarren cIarified these points using an informal presenta­tion which will he developed for a 1995 presentation to

•

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JMG assessments, the results suggested that the reduc­tion in power was smal!.

14 ANY OTJIER BUSINESS

Rob Fryer reported some comments received informal1yfrom the Chairman of WGEAMS, who had also attemledthe 1994 meeting of the Sub-Group on Temporal TrendMonitoring Programmes for Contaminants in Biota. Themembers of WGEAMS had been very positive about theSGTTC, and will encourage the arrangements of a jointmeeting between WGSAEM and WGEAMS in the nearfuture to discuss the design and analysis of spatial moni­toring programmes. WGSAEM agreed that such a meet­ing would be beneficial, but noted that spatial monitoringof biota is unlikely to be useful except for effectivelystationary organisms.

15 SU;\I:\IARY AND PROGRESS REPORT FORACl\IE

a) Re\'iew and report on the resull'i 01' a compari­son 01' I\IANCOVA and ANCOVA anal)'scs 01' areal data set.

A theorctical overview describing the differences andsimilarities between multivariate and univariate methodswas presented, and satisfied the request for a demonstra­tion of these techniques using a simple example based onareal contaminant data set.

h) Rel'iew the recommendations 01' the Suh-Groupmeeting held in Fehruary 1994 to reeonsider theprogramme to imcstigate temporal trends 01'eontaminants in biota.

The report of the Sub-Group on Temporal Trend Moni­toring Programmes for Contaminants in Biota held inFebruary 1994, and sponsored by ICES underC.Res.1993/2:7:7, considered the objectives, design, andeffectiveness of temporal trend monitoring programmes,identifying the major weaknesses in current practice,where more data are required, and where potentialincreases in effectiveness could be achieved. In practice,these could be grouped under four topics: specificationof monitoring objectives, the power of trend detection,the choice of monitoring organism, and the choice ofbasis for expressing concentrations.

The recommendations of the Sub-Group were essential­Iy:

to prepare a TIMES document giving guidelines forthe formulation of objectives;

to review the information relevant to the choice ofmonitoring organism;

to hold workshops together with WGEAMS;

to investigate the components of variance in moni­toring data;

to continue assessing the appropriate basis forexpressing contaminant concentrations.

WGSAEM supported these recommendations and wel­comed the chance of continuing the successful col1abor­ation which had taken place with the members 01' theSub-Group.

e) Rel'iew and report on further progress in theprcsentation 01' stati'itical data in fonnats rcadilyaceeptable hy non-statistician'i.

Various techniques wen~ presented am.l extended duringthe meeting. These included:

a method for integrating information oncontaminant level, trend, variability and manage­ment objective to produce an index for al10catingmanagement priorities across contaminants;

graphical aids for the interaction between statisti­cians, chemists, sampIers and managers during thedesign of a monitoring programme;

non-parametric methods for assessing trends;

a method of generating targets for analytical qualitycompatible with monitoring objectives.

d) Re\'iew and report on further progress in the U'ie01' eomriables in the expression 01' contaminantconeentrations and reduetion 01' residual mri­anee.

Preliminary investigations were presented on the appro­priate basis for expressing contaminant concentrations infish liver and on the effects of biological covariates onconcentrations in musseis. Thc rcsults suggested that forcontaminants in musseIs, there is a potential improve­ment to be gained from incorporating biological covar­iates into the analysis. Thc results for musseis gavesome insight into the roles of water, fat and proteincontent, but more work will be done intersessionally todevelop further understanding. In particular, linksbetween covariate effects and inputs wil1 be exploredusing some example data sets, and the results will bepresented at next year's meeting.

e) Considcr the report hcing prepared hy a Frenehmcmher on the eomparison 01' statistical toolsund meaos to rc1ate bloom occurrenccs to otherfaetors.

A comprehensive review of statistical methods foranalysing phytoplankton bloom data was presented. The

.. ...~.L

methods were grauped according to major areas ofapplication and the advantages and pitfalls of eachmethod were described. Possible areas for future workinclude methods for detecting blooms at an early stageand the sensitivity of statistical methods to the choice oftaxonomie resolution.

16 ACTION LIST

I) Create four fixed data sets of (a) contaminant timeseries, (b) fish liver data, (e) sediment spatial data,(d) phytoplankton, for use in method development,calibration, and comparison. Jall, Mike, Frank,Benair

2) Analyse some example data sets on contaminantconcentrations in fish livers. Frank, Jaap, Anders

3) Explore the effect of biological covariates on con­centrations in musseIs. Frank, Mike, Roh, Bill

4) Evaluate alternative smoothing strategies for assess­ing trends in contaminant time series. Str:jfim, Jaap

5) Extend the robust method of analysing trend data toincorporate seasonal effects and compare with theMann-Kendall test. Bellair

6) Compare the use of the median with other measuresof loeation in the robust method of analysing trenddata. Ouo

7) Prepare an explanatory example deseribing the useof the Mann-Kendall test for the assessment oftrends when there is seasonality and serial depend­enee. Ouo

8) Assess the sensitivity of statistical methods foranalysing phytoplankton data to the ehoiee of taxo­nomie grouping. Belloit

9) Report to the WGMS to clarify the uses of krigingfor contaminants in marine sediments. Bill

10) Investigate data sets to provide estimates of sampl­ing and analytical components for alternative trendmonitoring strategies. Rob, Mike

11) Develop more realistic examples of the graphicalaids for monitoring design. Otto, Belloit, Rub, Mike

12

17 RECOl\ll\lENDATIONS

WGSAEM recommends that:

1) Members of WGSAEM liaise intersessionally withmembers of the WGMS amI WGEAMS to build amutual understanding of plausible objectives forsediment monitoring programmes and statisticalmethods to address these problems.

2) The paper describing a robust method for analysingcontaminant trend monitoring data be published inthe TIMES series.

3) Members of WGSAEM ereate and distribute inter­sessionally a number of fixed data st:ts that ean beused for model development, ealibration, and eom­parison.

4) WGMS respond to Bill Warren's response toWGMS' response to Bill Warren's paper on krigingfor contaminants in sediment.

5) WGSAEM med for 5 days in early/mid-April 1995in AbenJeen to report and review on investigationsconcerning:

a) the appropriate basis for expressing contaminantconcentrations and the effect of biological cova­riates on contaminant eoncentrations;

b) methous for assessing temporal trends;

e) methods for analysing phytoplankton data fortemporal trends;

d) methods for analysing spatial sediment data;

e) the design anu effectiveness of monitoringprogrammes, including graphical aids.

18 CLOSING OF TUE MEETING

There being no other business, the Chairman thanked theparticipants for their hard work and enthusiasm, BillWarren for being a gooJ host, and Dr Larry CoaJy forallowing us to meet in St John's, and closed the meetingat 15.15 hrs on Friday 29 April 1994.

•

ANNEX 1

Working Group on tht: Statistical Aspt:cts of Environmt:ntal MonitoringSt John's, Newfoumlland, 26-29 April 1994

AGENDA

Opening of the meeting and organization of the work.

2 Adoption of the agenda.

3 Terms of reference and tasks for the 1994 meeting.

4 Review of the 1993 ACME report.

5 Review and report on the results of a comparison of MANCOVA ami ANCOVA analyses of areal data set.

6 Review the recommendations of the Sub-Group meeting held in February 1994 to reconsider the programmeto investigate temporal trends of contaminants in hiota.

7 Review and report on further progress in the presentation of statistical data in formats readily acceptable bynon-statisticians.

8 Review and report on further progress in the use of covariables in the expression of contaminant concentra­tions and reduction of residual variance.

9 Consider the report being prepared by a French member on the comparison of statistical tools and means torelate bloom occurrences to other factors.

10 Applications of kriging to data on contaminant concentrations in marine sediments.

11 Treatment and understanding of temporal variation in contaminant/length relationships.

12 Intercalibration of two methods of measuring chlorobiphenyls (PCR congeners).

13 Review of new, robust method of assessing trends as used in the 1993 assessment by the JMG Ad hoc MOll

sub-group.

14 Any other business.

15 ACME summary and progress.

16 Action list.

17 Recommendations.

18 Closing of the meeting.

13

ANNEX 2

LIST OF PARTICIPANTS

Name Address Telephone Fax

Benoit Beliaeff IFREMER +3340374158 +3340374073BP 1049, Rue de l'I1e d'YeuF-44037 Nantes Cedex 01FRANCE

Anders Bignert Swedish Museum of Natural History +46 86 664115 +4681 52013S-104 05 StockholmSWEDEN

Roh Fryer SOAFD +44 224 295502 +44224295511Marine LaboratoryP.O. Box 101, Victoria RoadAberdeenUNITED KINGDOM AB9 8DB

Jan Rene Larsen ICES +45 33 154225 +45 33 934215Palregade 2-4DK-1261 Copenhagen KDENMARK

Mike Nicholson MAFF +44502562244 +44502513865(Chairman) Fisheries Laboratory

Pakefield RoadLowestoftSuffolkUNITED KING DOM NR330HT

Frank Riget Greenland Environmental Research +45 35 821415 +45 35 821420lust.Tagensvej 135DK-2200 Copenhagen NDENMARK

Otto Swertz RIKZ +31 703744606 + 31 703 282059Postbus 209072500 EX Den HaagTHE NETHERLANDS

Gunnar Thoresson National Board of Fisheries +46 17331305 +46 17330949Institute of Coastal ResearchGamla Slepv. 19S-74071 ÖregrundSWEDEN

Steffen Uhlig Institut fur Statistik und Okonometrie +49 30 8384777 +49 30 8382129Freie Universitat BerlinGarystr. 2114195 BerlinGERr..,1ANY

Jaap van der Meer NetherIands Institute for Sea Research + 31 22 2069357 +31 222019674P.O. Box 59NL-1790 AB Den BurgTHE NETHERLANDS

14

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William Warren Department of Fisheries & OceansP.O Box 5667St lohn 's, NewfoundlandCANADA

+ I 709 7724835 + I 709 7722156

15

ANNEX 3

LIST OF WORKING PAPERS(not included in the Report)

Asmund, G., Riget, F, F., Pedersen, B. and Larsen J.R. The relationship between trace metal concentrations and lipidcontent in biological tissue.

Fryer, R.J. and Nicholson, M.D. Can simple changes in sampling and analytical strategy improve the power of theICES Cooperative monitoring Programme.

Nicholson, M.D. and Fryer, R.J. A note on setting targets for analytical accuracy in trend studies.

Swertz, O. Evaluation of the marine chemical network from the Netherlands.

Swertz, O. A protocol for trend analysis of contents and fluxes of pollutants.

I. Some authors, e.g. Cressie, use the term 'prediction' instead of 'estimation', since, strictly speaking,estimation is related to the true parameters of a model and not to the realizations of a stochastic process. •

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16

Introduction

ANNEX 4

Univariate and Multivariate Analyses for Time Trends

by

R.K. Misra

Marine Chemistry DivisionDepartment of Fisheries and Oceans

P.G. Box 550. Halifax. Nova Scotia. Canada B3J 257

and

M.D. Nicholson

Ministry of Agriculture Food and FisheriesFisheries LaboratoryLowestoft. Suffolk

NR33 OHTUnited Kingdom

WGsmtAnnex4

This paper supplements the paper by Misra et ale (1989). In analysing

for trends we investigate measurements made on several (p) variables

(contaminants) taken on a number of individuals each year. Misra et ale

(1989) noted that statisticians find that labeling statistical techniques as

"univariate" or "multivariate" is illogical.

Here. the analysis of variance is referred to as a univariate analysis

(ANOVA) when data on p variables are analysed one at a time. in contrast to

~ the multivariate analysis (MANOVA), which analyses the data jointly. Thus,

when da ta comprise p variables, Yi, i=1, ... , p measured on nj individuals of

year j, p separate ANOVAs are required, but only one MANOVA. Analyses of

covariance (ANCOVA and MANCOVA, equivalently) are special cases of k~OVA and

MANOVA where one ar more measured variables, e.g. length, are emplayed as

covariables sa that the year-means of Y can be compared and analysed with

increased precision.

The ICES guidelines far investigating trend monitoring data by

univariate procedures have been established (Anon 1986, 1987a). WGSATM (Anon

17

1987b) and Misra et al. (1989) recognized the utility of multivariate analysis

and agreed that the use of both approaehes is superior to the use of either

one alone. Misra et al. (1989) showed how (i) the multivariate analysis eould

provide additional trend information that cannot be retrieved by univariate

analysis. and (ii) the univariate analysis ean sometimes be misleading.

Understanding the simi1arities and differenees underlying the two approaehes

is required to enable their proper application. particularly for managers in

instanees where the results of both are seen to be conflicting. Here we offer

additional support to that supplied by Misra et al. (1989) for employing both

procedures.

Data

We used the data on Canadian Atlantic cod (Gadus morhua). deseribed in

Seott et al. (1978. 1983) and Misra and Uthe (1987). Misra and Uthe (1987)

analysed three years of this data by MANCOVA. Here. we employed four years of

data. 1977. 1978. 1979. and 1985. Coneentrations of 10 (=p) eontaminants in

either liver (L) or museie (M) tissues were determined (Yi. i = 1•...• 10.

after transformation to their common logarithms). These were Y1 (Zn-M). Y2

(As-L). Y3 (Cd-L). Y4 (Cu-L). Y5 (Hg-L). Y6 (Se-L). Y7 (Zn-L). Y8 (PCB-L). Y9

(a-HCH-L), and Y10 (HCB-L). Log length was used as the covariate X.

The text for this presentation was drawn mainly from Hair et al. (1992).

Johnson and Wiehern (1988). Morrison (1976), and Harris (1975).

Data Summary

Data on n individua1s for a year with p variables measured on each

individual can be disp1ayed as a reetangular array (matrix) Y of p rows and n

eolumns. where

•

•

measurement on Y from the mean of Y. This statistie is the "varianee" and

supplementing the sampie variances (5) with sampie covariances when we da

(3 )

( l)

(4 )

(2)

Y21 Y22 Y2n

Yp1 Yp2 Ypn

y =

Sampie means:

1 nY = -. ~ Y

1 n j=1 1jand

1 ns = - • ~ (Y _ Y )2

11 n-1 j=l 1j 1

Sampie variances: s11' s22' ...• spp (5)

However. Y variables are frequently mutually correlated. This requires

provides a measure of variation in the measurements. Thus, for the first

Y , Y ••••• Y1 2 P

whieh we show as the vector Y' with p elements (Prime denotes a row vector,

unprimed vectors are column vectors.)

measure of loeation (the mean for a Y variable) that serves as the "eentral

descriptive statistics to provide summary numbers for assessing the data. For

data that are normally distributed, the deseriptive statisties are (i) a

value" for all measurements on Y, and (ii) an average squared distanee of eaeh

contaminant (Y1), the sampie mean Vl and the sampie varianee si (we denote as

s11) are given by

For theoretical reasons, the divisor used in (3) is n-1. not n. The sampie

standard deviation is given by (s )!. For p ANOVAs, where one variable at a11

time is analysed, the descriptive statistics are:

Data set (1) is bulky. To extraet pertinent information, we employ

•

MANOVA, where we analyse p variables jointly. Consider n pairs of

measurements on two variables Y and Y. These are (Y ,Y ),1 2 11 21

A measure of linear association is provided by(Y ,Y ), ... , (Y ,Y ).12 22 In 2n

the sample covariance s ,where12

1 n - -s = ---. ~ (Y -Y)(Y -Y)

12 (n-1) j=1 1j 1 2j 2

1 n - -Note that s = ---. ~ (Y -Y )(Y -Y)

21 (n-l) j=l 2j 2 Ij 1

so that s = s12 21 •

as theand s22

not significant. If we analyse

use s11

If large values for Y are associated with large values for Y ,s will1 2 12

be positive. A negative s will occur if large values for Y are associated12 1

and, if there is no particular association between Y1

with small values for Y2

and Y s will be approximately zero, i.e.2, 12

data on Y and Y by two separate ANOVAs, we1 2

descriptive statistics for variation, i.e.

S = (6) •but if we analyse Y and Y jointly, i.e. MANOVA, we use the matrix

1 2

S = (7 )

20'

Instead of the matrix S of (6). S is called the variance-covariance matrix or

simply the covariance matrix. Equation (6) is a special case of (7) that

occurs when s12 = O. If we change the scale of measurements of Yl and Y2 by

- !replacing their original values by the standardized values (Y1j -Y1)/(sll) and

(Y2j -V2)/(S22)!' respectively, then the 5ample coefficient of correlation r 12

between Y1 and Y2, which is sI2/(Sil S~2)' becomes s12' i.e. r 12 = s12 (recall

that a standardized variable has variance = 1, i.e. sll and 522 both = 1).

Thus the sample correlation coefficient is a standardized version of the

sampie covariance. The correlation coefficient offers the advantage of

~ evaluating the strength of the covariance between Yland Y2 easily, because the

value of r 12 must always range +1 to -1. The covariance matrix (7) now takes

the form

R = (8)

which is commonly known as the correlation matrix.

Graphical Displays

To visualize the information that is retrieved via these descriptive

statistics, the 1985 data on Y1 (Zn-M) and Y2 (As-L) for 35 (=n) individuals

was analysed.

For Y1: Yl = 3.5564, sll = 0.003981,

For Y2: Y2 = 0.3489, s22 = 0.028459,

and r 12 is approximately zero (-0.0392) (9)

21

,-------- --- - -----------,

The correlation matrix, which is the covariance matrix of standardized Y1 and

Y2 , is

R =[

1 -0.0392]

-0.0392 1(10)

Figures 1A & B show the marginal dot diagrams, i.e. plots for Y1 and Y2 when

these variables are considered separately. Figure 2 shows their scatter

diagram. i.e. the two-dimensional plot for Yl and Y2. In Figure 2 a curve was

superimposed. Probability specified (by us) for it was 0.90, so that if the ~

data were bivariate normal, we would expect to find about 90% of the points

inside this curve. Figure 2 shows that 32 out of 35, i.e. 91%, are inside the

curve.

The scatter diagram indicates a complete lack of orientation of the

points, suggesting that the Yl measurements vary independently of the Y2 ones,

i.e. the correlation (covariance) is about zero. The curve in Figure 2 is

approximately circular. To see what happens when Yl and Y2 are correlated we

changed the data structure to generate a significant correlation coefficient

(r12 = 0.9316; high and positive) by arranging the Y1 and Y2 values in

ascending order. Figures 3A & B show marginal diagrams for the shuffled

values of Yl and Y2. Figure 4 shows their scatter diagram. The marginal

diagrams did not change, i.e. Figures lA &Bare identical to Figures 3A &B,

implying that VI' V2, s11' and s22 also did not change. The scatter diagrams

(Figures 2 and 4) changed considerably. The orientation of points changed

with the change in the correlation (covariance) value. Therefore univariate

analyses on YI and Y2 separately will give the same results because they

ignore the correlation. However, multivariate analysis can be expected to

yield different results because the covariance is taken into account.

22

•

For the vector Yof (11), the univariate expression (13) is extended to

4It (y_g),~-l(y_g) (14)

MANOVA is an Extension of ANOVA

(13)

(12)

The study of variation in

normally distributed data is often based on distances. The term (Y1­

~1)2/011 of (12) measures the squared distance of Y1 to ~1 in standard

deviation units. It can be rewritten as

where c is a (univariate normalizing) constant.

vector has only one element, it would make an ANOVA.

Y' = (Y1' Y2, ... , Yp ) (11)

with elements that are variates defined in several (p) dimensions. If the

where L is the population analog of the sample covariance matrix Sand

23

replaces the distance (13) used in the univariate analysis.

The MANOVA is a straightforward extension of ANOVA. To illustrate:

vector Y = (PI' P2, ... , pp)'

3. The multivariate generalized distance (14) for the multivariate analysis

4. In the univariate analysis, we test hypothesis pertaining to PI as follows:

(i) (Y1-P1)2/(011/n) = xi (chi square) (15)

with degrees of freedom (df) = 1 when all is known (In practice 5 11

from a large sample size is used to approximate all')

2. Consider the univariate normal distribution for an element, e.g. Y1.

Corresponding to the sample mean (Y1) and variance (sll) values, the

population values (~1 and all' respectively) give the univariate normal

distribution as

1. MANOVA deals with the continuous random variable Ywhere the vector

•

(ii) (V1-~1)/(s11/n)! = t n- 1•

i.e. at-test using df = n-l. or equivalently

- • -1 - 2n(Yl-~1) sI1(Yl-~I) = t n- 1 (16)

Expressions (15) and (16) are the univariate squared distances of the

sampie mean V1 to the population mean (test value) ~1' The

multivariate extension of (15) is

n(Y-~)k-l(y-~) =X; (17)

i.e. a chi-square with df = p. Vector Yis the mean vector

(V1• V2 ...• Vp)' The multivariate extension of (16) is •(18)

i.e. Hotelling's T2 with parameters p and n-l.

5. In the univariate analysis to test the hypothesis

HO: ~i1 = ~i2 (19)

that two years (year 1 and 2) have equal means for Yl' we compute t (or t 2)

on the data from sampies of nj (j = 1 for year 1 and 2 for year 2) as

- - -1 - -tl = (n1n2/[n1+n2 ]) (Yi1-YiZ)s11(Yi1-Yi2) (20)

where s11 is the pooled within-sample variance and we use the suffix i in t 2

to remind us that this t 2 is for variable Vi' Recall that testing (19) by a ~

t-test is equivalent to testing it by ANOVA. because F (of ANOVA) = t 2.

The MANOVA analog of (19) is

HO: ~1 = ~2 (21)

This is the same as saying that the two years have equal means for each of the

10 (p) variables and we test it by T2 (compare with 20) where

- - • -1 - -T2 = (n1n2/[n1+n2])(Y1-Y2) S (Y1-Y2)

where Y1 and Y2 are mean vectors for years 1 and 2.

24

(22)

There is Something Different About MANOVA

1. If, for example, we test HO of (19) for thc eod data (p = 10), using the t­

test of (20) ten times, i.e. one for eaeh Yi , Type I error (signifieanee

level), which is erroneous rejeetion of a true hypothesis, gets inflated

over multiple t-tests. That is, if we ehoose a significance level of 0.05

(0 = 0.05) the probability of falsely identifying the difference between

two year-means of at least one variable will be inflated from 1-(1-0.05),

ie. 5% to 1-(1-0.05)10, i.e. 40%. Hotelling's T2 guarantees that the 0

level (here 0.05) will not inflate irrespeetive of how large pis.

~ 2. Hotelling's T2 will compare years in their means for any linear combination

of variables, i.e. the year-means of L given by

•

L = C1Y1 + C2Y2 + ••. + CpYp (23)

where Cl' C2 , .•. , Cp are eonstants chosen by the user. We eompute LI and

L2 for the two years and test the significanee of LI - L2 by T2. This

feature has interesting implieations. Numerous values for Land L1 -L2 ean

be generated by assigning values to the constant Cl' C2 , ... , Cp in (23).

HO of (19) defines only one of these values of LI - L2• For example, by

assigning Cl as 1 and the remaining Cs as zero, the t-test of (20) will

test the significance of this specific value LI - L2. Ten separate ANOVAs

test only 10 particular values for LI -L2• It is easy to visualize data

sets where none of the 10 (or p) separate ANOVAs will rejeet hypothesis

(19) that years have equal means, even though the two years may be

different. The difference was not deteeted by the univariate analysis

simply because the user chose the wrong values for the eonstants Ci of

(23). Hotelling's T2 will rejeet this hypothesis if LI - L2 is signifieant

(not zero) for any set of Ci values. If T2 is not signifieant, one ean be

sure that the differenee LI - L2 is not signifieant for any of the possible

values it can take. Again, Type I error is never inflated.

25

3. Above, we gave the covariance matrix S for two variables in two forms, viz.

equation (6) where the covariance was ignored (not significant) and

equation (7) where it was not ignored (significant). In the general case

where p ~2 the form of (6) of the covariance matrix is extended as

S = o s22

o

o

The correlation matrix is

R =

1

o

o

o

1

o

o

o

1

(24) •when the correlations are not significant and, when they are, it is

R =

1

1

(25)

Separate ANOVAs utilize form (24) where the correlation (covariance)

structure of p variables is ignored. In presenting T2 to analyse a data set

where p = 4 for camparisan on means of two samples, Morrison (1976) states:

"It would not be proper to test four individual mean differences by

univariate t statistics, for we must have protection against the effects of

positive correlations among the subsets as weIl as the tendency for

individual differences to be significant merely by chance as more responses

are included in the variate vectors." Johnson and Wiehern (1988) state

that the alternate (to T2) approach of constructing confidence intervals

based on the use of t is "somewhat misguided."

4. Null hypothesis HO of (21) can be written as

HO: l!1 - l!2 = Q (26)

and is a comparison of mean vectors of two years. This comparison is a

special case of a linear comparison (contrast) of several years. The

general form of the linear comparison where K (years) ~ 2 is given by

where

K~ = ~ a l!

j=l j j(27)

K~ a = 0 (28)

j=l jTo retrieve the form (26) from (27) we assign values K = 2, a

1= 1, and a

2= -1 in (27). Any linear comparison of K years can be tested by T2.

Because time trend over K years can be defined as a linear comparison of K

year-means, whether or not years are equally spaced, the earlier text on

comparison of means of two years is relevant to the investigation of time

trend.

27

A number of post hoc procedures are

MANOVA for the General Case

For the general case where the number of years K ~ 2, the univariate

analog of H of (19) isoHO: llil = lli2' ... , = lliK (29)

for the ANOVA of variable Y. The multivariate analog of H of (21) isi 0

HO: J!1 = J!2' ... , = ~ (30)

for the ~~OVA that analyses all p variables jointly. In the ANOVA, we employ

F statistic to test H of (29).oavailable, e.g. the Scheffe's test, to do a follow up investigation of

specific year-mean differences, including time trend. These procedures will ~

control Type I error rates ac ross multiple tests.

Four multivariate procedures for testing H of (30) are in use. All useobetween year (B) and the pooled within year (W) matrices of sums of squares

and sums of products. Two are commonly used, one that employs Wilks lambda

likelihood ratio statistic and the other the union-intersection procedure that

uses the greatest characteristic root (gcr) statistic. We note (Hair et al.

1992; Morrison 1976; Harris 1975) that many investigators may prefer the gcr

statistic because of "its greater heuristic and didactic value" (Harris 1975)

and for the following reasons. After rejecting H , we may wish to investigateomultiple comparisons (i) of years, (ii) of contaminants, and (iii) of

combinations of years and contaminants. The nature of construction of the gcr

procedure leads directly to simultaneous confidence bounds on double linear

compounds of years and contaminants. One can test multiple comparisons of

years and of contaminants. Comparisons of combinations of years and

contaminants, which are not conveniently handled by other procedures, are a

special feature of the gcr. The gcr statistic also guarantees that the

specified value of , say a = 0.05, will not inflate irrespective of how many

comparisons are tested. In fact Hotelling's T2 is subsumed as a special case

28

•

•

of the ger proeedure (Hair et al. 1992; Harris 1975). Numerous eomparisons

are possible. The eod study employed the ger to examine the time trend

(reeall that the time trend ean be expressed as a linear eomparison of year-

means) and to identify individual eontaminants that led to the significanee of

the time trend. We also note (Morrison 1976; Harris 1975) that when the first-1

eharaeteristie root of the matrix B·W is mueh larger than the others, whieh

was the ease with the cod data, the ger is the preferred method.

Analysis of Cod Data for the Time Trend

MANCOVA and ANCOVA are special eases of MANOVA and ANOVA where metrie

independent variables (~ 1), referred to as eovariates, are ineluded in the

MANOVA and ANOVA.

The ICES guidelines for analysing time trend by eonventional ANCOVA

(Anon 1986) expeeted that model 2 (which employs one eovariate, e. g. fish

length) would be appropriate for most data sets. Using a single eovariate

leads to easy applieation and interpretation (Nieholson and Wilson 1987). In

the MANCOVA of the eod data, we employed log fish length as the eovariate.

The eoeffieient of regression (b) of Y on X in ANCOVA is replaeed by a veetor

~ of Q of 10 eoeffieients of regression, i.e. one for each of the 10 Y

variables, in the MANCOVA. The null hypothesis H ß = 0 (where _6 is theo -veetor of parameters of Q) was rejeeted (probability level of signifieanee P <

0.001), indieating that MANCOVA was warranted, i.e. years should be eompared

based on their mean Y. adjusted for variations in the values of the covariate1

X among individuals. These adjusted year-means are the same for ANCOVA and

MANCOVA (Table 1).

The H of (30) of no differenee between years on the veetors of theoadjusted mean eontaminant eoneentrations was tested. Charaeteristie roots of

29

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

1

-1the matrix B·W were 4.6231, 1.1163, and 0.2504. The first eharaeteristie

root is mueh larger than the others. H was rejeeted (P < 0.001), indieatingothat years da not all have equal vectors of adjusted means of Y. We tested

the signifieanee of the linear eomparisan of years far the time trend and

identified individual contaminants that contributed signifieantly to the time

trend. The time trend in the MANCOVA (ger) was highly signifieant (P <

0.001). The significanee of the contributions of individual contaminants to

the time trend was tested through their 95% simultaneaus confidence intervals

(CIs). Table 2 lists the CIs for each Y. (Note: If the confidenee limits

(CLs) for a CI are of the same sign, i.e. da not contain zero, the •(Zn-M), Y3

(Cd­

identified as

contribution of that Y to the time trend is significant.) Yi 1

L), Y (Cu-L), Y (Hg-L), Y (PCB-L), and Y (HCB-L) were all4 5 8 10

significant. Ten separate ANCOVas also showed the time trends were

Y , and7

results

signifieant (P < 0.001) for Y , Y , Y , Y , Y , and Y ,but not for Y , Y ,1 3 4 5 8 10 2 6

Y (P: 0.09-0.51). However, there is no reason to expect that the9

from separate ANCOVAs will be so consistent with those from the

•they are displayed

in aseparate figure

The trend was upward (both CLs positive) for Y3

and downward (both CLs negative) for Y (Zn­1

Because the adjusted year-mean values were

~~~COVA with other data sets.

(Cd-L), Y (Cu-L), and Y (Hg-L)4 5

~1), Y (PCB-L), and Y (HCB-L) .8 10

gene rally very elose to each other for each Y. (Table 1),1

in expanded scale by plotting adjusted means against year

for each Yi

(Figure 5 [1] - Figure 5 [10]). Adjusted means vary along a zig­

zag line, indicating that a linear time trend, if signifieant, will explain

the temporal variation only partially. The findings in Table 2 are consistent

with Figure 5, with one exception. Figures 5 (3), 5 (4), and 5 (5) showa

clearly increasing linear time trend underlying the zig-zag line, while

Figures 5 (1), 5 (8), and 5 (10) showa deereasing time trend. Figures 5 (2),

5 (6), and 5 (7) do not show a elear trend.

30

For Y (a-HCH-L), Table 2 suggests no trend, while Figure 5 (9)9

indieates a possible linear trend. Adjusted year-means are more elose to eaeh

other for Y than for any other Y variable (Table 1); the differenee between9

the highest and lowcst means is only 0.0503. Threfore thc underlying trend

seen in Figure 5 (9) is probably an artifaet from the expanded seale used to

plot the data. Confilieting results ean oecur in data sets, but ean bc

determine this variability. MANOVA does not ignore these correlations. When

Correlations of variables will, therefore,

MANOVA employs a linear eombination Z = A Y + a Y + •••1 1 2 2

The variability of Z is given by A'RA (or A'SA) where R+ A Y of variables.p p

is thc eorrelation matrix (25) .

readily explained.

•variables are intereorrelated, a variable Y will eontribute to the time trend

iin three ways: 1. A eontribution that is unique to the variable; 2. A

eontribution that is not unique, but is made through its eorrelations with the

other variables; and, 3. A eontribution resulting from both 1. and 2. MANOVA

employs a linear combination of variables that maximizes the differenees

between years to produee the most reliable evidenee of year differenees. The

extreme ease ean also occur where no individual variable is identified as

•signifieantly eontributing to the time trend, whereas the eombination of

variables is a highly signifieant eontributor (Misra et al. 1989). Misra et

al. (1989) used the simple ease where two variables with two years of data

were analysed by MANOVA and two ANOVAs three times: 1. The original data where

Here, the outcomes of the MANOVA and the two ANOVAsr was near zero.12

yielded the same results pertaining to differences between the year-means of

( r = 0.98)'12 '

-0.97). The

outcomes of the ANOVAs did not

Y and Y ; 2. Shuffled data to raise the value of r positively1 2 12

and 3. Shuffled data to raise the value of r negatively (r =12 12

change in either of the shuffled eases, because

ANOVA ignored the eorrelations between variables. MANOVA of the shuffled data

31

sets identified differences between the year-means in both eases as highly

significant (P < 0.001). Graphieal display was used to explain why this

disparity between ANOVA and MANOVA outeomes will inerease with inereasing

eorrelation between variables.

It remains that a number of ANOVAs test only a few of the numerous

eombinations of Y variables that eould identify differenees among year-means

and the time trend. If none of these ANOVAs identifies a significant

difference, it does not mean that years do not necessarily differ in their

means.

Correlations among Y variables are real, probably beeause contaminant

concentrations are measured on the same individuals. Correlation and

covariance matrices of Y variables eharaeterize both the manner in which these

contaminants are associated with each other and the degrees to which they vary

and covary in fish. Thus, a realistic examination of the time trend must be

based on the combined effects of unique and joint eontributions of the Y

variables. ~OVA does this. However, the importanee of analysing data by

separate ANOVAs remains. Data on individual eontaminants are important

eomponents of the multivariate distribution of the eontaminants. Analysing

data on a eontaminant is meaningful. We see separate ANOVAs and one ~OVA as

procedures which complement, not compete with, each other.

Here we identified individual variables in the eod study that

contributed significantly to the time trend. This does not imply that these

variables did not also eontribute via their eorrelations with other variables

or that variables identified as not signifieant eontributors in Table 2

contributed nothing to the time trend.

Other procedures are available that cireumvent the problem of handling

mutually correlated variables while examining their unique contributions.

One ean, for example, replaee Y variables by their prineipal eomponents (pes).

32

•

•

•

•

PCs are uncorrelated with each other and ANOVA for each PC can be done.

Unfortunately the original correlation structure for the Y variables is

destroyed and one does not know if the PCs have any meaning in the real world

from which the data arose (Draper and Smith 1981). Alternately, one could use

the "stepdown analysis" procedure (Hair et al. 1992). This is similar to the

popular stepwise regression procedure and is believed by Draper and Smith

(1981) "to be one of the best variable selection procedures." It can be used

to examine whether or not a variable contributes uniquely to the time trend.

Unfortunately, the reliability of the results depends on the order in which

the investigator enters the Y variables (Hair et al. 1992). As the number of Y

variables and their intercorrelation level increase, isolating the unique

contribution from the joint contribution becomes formidable.

In conclusion, we suggest that the ICES guidelines continue to recommend

ANOVA for time trend investigations and that they be extended to recommend the

use of MANOVA as weIl .

33

Referenees

Anon. 1986. Report of the meeting of the Ad Hoc Group of Statistieiansassisting the Working Group on ~arine Pollution Baseline and MonitoringStudies in the North Atlantie on Trend Monitoring. ICES C.M. 1986/E:39

Anon. 1987a. Report of the ICES Advisory Committee on Marine Pollution, 1986.International Couneil for the Exploration of the Sea. Coop. Res. Rep. No.142: 128 p.

Anon. 1987b. Report of the 1987 meeting of the Working Group on StatistiealAspeets of Trend Monitoring. ICES C.M. 1987/E:24.

Draper, N.R., and H. Smith. 1981. Applied Regression Analysis. John Wiley &Sons, lne. New York, NY.

Hair, J.F., jr. R.E. Anderson, R.L. Tatham, and W.C. Blaek. 1992.Multivariate Data Analysis. MaeMillan Publishing, New York, NY.

Harris, R.A. 1975. A Primer of Multivariate Statisties. Aeademie Press~ NewYork, NY.

Johnson, R.A., and Wiehern, D.W., 1988: Applied Multivariate StatistiealAnalysis. Prentiee Hall, Englewood Cliffs, NJ.

~isra, R.K., and J.F. Uthe. 1987. ~ethods of time trend analysis applied toeontaminant levels in Canadian Atlantie eod (Gadus morhua). Can. J. Fish.Aquat. Sei. 44: 859-865.

Misra, R.K., J.F. Uthe, C.J. Musial, and C.L. Chou. 1988. The analysis oftime trends in eontaminant levels in Canadian Atlantie eod (Gadus morhua).5. Time trends, 1977-1985, employing a multivariate linear model. ICESStatutory Meeting, Paper C.M. 1988/E:4.

Misra, R.K., J.F. Uthe, and W. Vynke. 1989. On multivariate and univariateanalyses of varianee. ICES C.~. 1989/E:13, Annex 7.

Morrison, D.F., 1976. Multivariate Statistieal Methods. MeGraw-Hill BookCompany, New York, NY.

Nieholson, M.D., and S.J. Wilson. 1987. ldentifieation of trends in levels ofmetals in fish musele: Appraisal of the statistieal analysis and of dataquality. ICES C.M. 1987/E:24, Annex 3.2.

Seott, D.P., J.F. Uthe, and C.L. Chou. 1978. Regression analysis of heavymetal and organoehlorine residue eoneentrations in a statistieally sampledpopulation of Atlantie eod (Gadus morhua). ICES Statutory Meeting, PaperC.M. 1978/E:16.

Seott, D.P., J.F. Uthe, and C.L. Chou. 1983. Choiee of variables inestimation of time trends in eontaminant levels in fish. Paper presentedto the leES Working Group on Marine Pollution ßaseline and ~onitoring

Studies in the North Atlantic, Copenhagen, 1-4 February, 1983.

•

•

•

Table 1. Adjusted Year-Means of Yi• i = 1•...• 10

I I Year

IYj • i =

1977 I 1978 I 1979 I 1985

1 3.7002 3.6949 3.7485 3.6357

2 -0.2689 -0.3427 -0.2065 -0.2314

3 0.5449 0.8909 0.5577 1.1188

4 -0.0686 -0.0812 0.1069 0.1517

5 -0.1328 -0.1313 -0.2291 0.2372

6 2.1725 2.2457 2.3547 2.2032

7 0.9908 0.9785 1.0620 1.0228

8 -1.8401 -1.7466 -1.7813 -2.0274

9 2.5127 2.4909 2.4840 2.4624

10 1.5505 1.5741 1.5400 1.2471

Table 2. Confidenee limits far Individual Contaminants in the Time Trend Basedon 95% Simultaneous Confidenee Intervals (ger Proeedure).

I IConfidenee Limit

Y.• i =1 Lawer Upper

1 -2.5 -0.4

2 -1.8 4.0

3 5.4 13.8

4 0.3 8.1

5 4.1 12.0

6 -3.3 2.4

7 -1.3 2.4

8 -7.5 -2.0

9 -3.2 1.6

10 -9.7 -3.3

35

FIG.1 ..Ä.. Zn-~\/l ' ORIGIf\JßL D.AT,.:l, ; ~'v,t.:l"R,GI~,JA.L DIAGR.,.:l,k'l

,..., R0 0 od 2m 0 8:3 dBaE 0:1 •

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•

36

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•

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•-1

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39

40

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41

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FIG.5(ö). TI~'v"lE TREj\JO FeH Se-L OF: \"'(6)

2.4.C· ,----,.----,---....,......--.,....--..........,

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10

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•

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•

•

ANNEX 5

Wc.-king Paper WGSAEM StJohn's 1994

Multivariate Trends in Groups of Phytoplankton Species

Andy Solowl and Mike Nicholson2

Introduction

In environmental studies, interest may centre on temporal changes in the joint

distribution of a group of variables such as contaminants (Misra et al, 1989) or species

abundance (Solow, 1994). Intuitively, the group of variables may jointly exhibit a trend

not evident from simple plots of the individual variables against time. The problem is

how 10 extract and assess this underlying trend. Here we apply a non-parametric

method used by Solow (1994) for extracting this trend 10 groups of phytoplankton

observed over a 15 month period at two stations in the North Sea.

Theory

The technique is based on a method of trend extraction for multivariate time series

proposed by Shapiro and Switzer (1989), modified for application to compositional

data (c.f. Aitchison, 1983).

Let X={X/t), i=l, ..,p} " t=l, ..,n be a multivariate time series ofp variables observed

on t occasions. The trend will be constructed for some linear transformation of X i.e.

Y(t)=a'X

chosen 10 maximise the lag-one autocorrelation in Y(tJ (Shapiro and Switzer, 1989).

Intuitively, this criterion is equivalent to maximising the smoothness of Y(t).

1Woods Hole Oceanographic Institution, Woods Hole, MA 02543. 2MAFF Fisheries Laboratory,Lowestoft, Suffolk NR33 OHT.

45

The technique (Minimum/maximum Autocorrelation Eactor analysis) is similar to

principal component analysis in the sense of producing aseries ofp solutions for Y((),

such that Y1{t) has the largest lag-one autocorrelation, Y2{t) has the second largest lag­

one autocorrelation orthogonal to the first, and so one. Write D for the (n-J)xp matrix

whose columns are the first differences of X and assume that X has been centred by

subtracting the column means. The covariance matrices of X and D are Yx = (X'X)/n

and VD =(D'D)/(n-l) from which the lag-one autocorrelation of Y(t), r, satisfies

(a'Vva)/(a'Vxa) = 2(J-r).

Hence to maximise r, 01 is proportional to the eigenvector of Yx·1YD corresponding to

the smallest eigenvalue, equal to 2(J-rJ. A specific solution for a1 can be taken to give •

Y1{t) unit variance and a positive coefficient of Xdt).

If the data have been expressed as percentage composition at each time, Solow (1994)

suggested the following modification, proposed by Aitchison (1993) for principal

component analysis of compositional data. Construct the matrix Z defined by

Because the rows of Z have zero sum, the smallest eigenvalue of Vz will be zero. The

corresponding eigenvector is discarded, and the analysis proceeds as above. An

algorithm for this analysis is given in Solow (1994).

Application to Groups of PhJioplankton from the North Sea.

The data analysed here were collected as part of the British NERC North Sea Project

(Charnock et al, 1994). Phytoplankton were sampled at fourteen areas (Figure 1) and

we will analyse data from two of them. Densities (cells/mI) of five groups of

phytoplankton

•

•

Dinolagellates

Diatoms

Flagellates

Ciliates

and

Others (Cyanobacteria in Area 1)

were recorded at roughly monthly intervals between August 1988 and September

1989. Figure 2a shows the individual time series of log densities for each area. Zeroes

were replaced by a value of half of the smallest observed density (0.05 for Ciliates and

50 for Others). Figure 2b shows the corresponding plots forthe relative densities of

each species group. In each plot a scatterplot smoother has been superimposed to

capture the basic time-flow of the data.

The following table gives the lag-1 autocorrelations of the original series together with

that of MAF-1:

Log Density Relative Density

Species Area 1 Area2 Area 1 Area2

Dinoflagellates -0.16 -0.20 -0.43 -0.12

• Diatoms 0.46 0.18 -0.06 0.18

Flagellates 0.57 0.33 0.03 -0.03

Ciliates -0.24 0.23 0.49 -0.18

Others 0.24 0.01 -0.31 0.07

MAF-1

PC-l

0.77

0.35

0.70

-0.02

0.64

-0.38

0.29

-0.07

\.For interest. the table also shows the lag-1 autocorrelation of the first principal

component. which is seen 10 be considerably less smooth than MAF-l.

,....---------- ----

To test the significance of the lag-1 autocorrelations, a randomisation test was used.

All were significant at the 5% level except that for the relative density in Area 2. In no

case was MAF-2 significant.

The following table gives the correlations between the original series and MAF-1:

l

Species

Log Density

Area 1 Area 2

Relative Density

Area 1 Area 2

Dinoflagellates

Diatoms

Flagellates

Ciliates

Others

0.60 -0.16 0.34 -0.34

0.71 0.13 -0.38 0.90

0.78 -0.53 0.56 0.09 •-0.04 -0.70 -0.92 -0.56

0.73 -0.38 0.41 -0.23

showing the variate contributions to each MAF-l. Finally, Figure 3 shows MAF-1

plotted against Day for each area and presentation of the data.

Conclusions

The following impressions can be drawn:

• MAF is clearly better at extracting a smooth underlying trend than principal

component analysis.

• For both areas the first MAF's reveal similar trends in both log and relative density

(see Figures 3 and 4), although in Area 2 MAF-1 was not significant.

• For both log and relative density, the trends in each area are different (see Figures 3

and4).

• For log density, MAF-l reflects the general time-flow of most of the species

groups, omitting Ciliates in Area 1 and Diatoms in Area 2.

•

•

•

• For relative density, the trend tends to be in the contrast between

(Dinoflagellates+F1agellates+Others) and (Diatoms+Ciliates) in Area 1, and

between (Dinoflagellates+Ciliates+Others) and Diatoms in Area 2.

References

Aitchison J. (1983) Principal component analysis of compositional data. Biometrika 70

57-65.

Charnock H., Dyer KJ., HuthnanceJ.M., Liss P.S., SimpsonJ.H. and Tett P.B.

(1994) Understanding the North Sea S)'stem. Chapman & Hall, London.

Misra R.K., Uthe J.F., Scott D.P., Chou C.L. and Musial CJ (1989) Time trends of

chemical contaminant levels in Canadian Atlantic cod with several biological

covariables. Mar. Poilut. Buil. 20227-232.

Shapiro D.E. and Switzer P. (1989) Extracting time trends from multiple monitoring

sites. Technical Report 132, Department of Statistics, Stanford University.

Solow A. R. (1994) Detecting change in the composition of a multi-species

community. In press.

50

:l6°N

~~P: r:r ep C1l

~oNCE ~.

~f{ ~

~'" J7.~ ~ •:l4°N o(X)

~

~ ~

:l:l>°H

Mooring •• erD A at es• c~'"' &. meeTing 3 at CK.u

x core C at DM

0 ?hytc:Jlar.:<!c;, 33:7':pJlr1'; J at 58

~reas_.

:~S- .::.

= at .~.C

Figure 1 :-tor...h Se3. SUril:"J staecn posltior.s pius IrXXlr1n.g s!tes.,~r~"1g si:= ar:d kry a..-:::3..S O!?r.yw?!arl.kton study

Figure laArea 1 Area2

1000.00 100.0.. 100.00 + ..~ .. ~

~ 10.00 ~ 10.0~ ~

~ 1.00 + + ~.Ei .53 1.0Cl 0.10 Cl

0.01 0.1100 200 300 400 500 600 100 200 300 400 500 600

Date Date

Area 1 Area2100 1000

§ § 100

• .~ 10 .~

Cl .. Cl+ 10

1 1100 200 300 400 500 600 100 200 300 400 500 600

Date Date

Area 1 Area2100000 100000

.. 10000 ..~

~10000

~ 1000~ ~

~ ~ 1000 .. ..100 .. ..10 100

100 200 300 400 500 600 100 200 300 400 500 600Date Date

• Areal Area210.00 100

8l 1.00 :n.~ .S 10::I ::IU 0.10 U

0.01 1100 200 300 400 500 600 100 200 300 400 500 600

Date Date

Area 1 Area210000 1000

.... ..II 1000 II8 -S 100

0 .. .. ..100

10 10100 200 300 400 500 600 100 200 300 400 500 600

Date Date

51

Fi~ure in

Area 1 Area230 8

i i 7

120 ::1 6.. 5tlO 4

~1O ~3.S ~2Cl

10

...0

100 200 300 400 soo 600 100 200 300 400 soo 600

Date Date

Area 1 Area27 306

eS e20g4 gi53 i5 lO •2

10 0100 200 300 400 500 600 100 200 300 400 500 600

Date Date

Area 1 Area2100 10090

!l 80

~90

70::I 60 80gj, 50 gj,

~ 40 .. ~30 702010 60

100 200 300 400 500 600 100 200 300 400 soo 600Date Date

Area 1 Area21.2 1.2 •1.0 1.0

Ifj 0.8 Ifj 0.8

~ 0.6 ~ 0.6u 0.4 U 0.4

0.2 0.2 ..0.0 0.0

100 200 300 400 500 600 100 200 300 400 500 600Date Date

Area 1 Area290 308070

t 60 .. t 20

-5 50 .. 804030 1020100 0100 200 300 400 500 600 100 200 300 400 500 600

Date Date

52

Figura 3MAF-1 against Day

2

Area 1 Area2

?;- .?;-"iil 0 "iilc: c:8 8 0g g.J .J

·1-1

-2100 200 300 400 500 600 200 300 400 500 600

2 Day 2 Day

Area 1 Area2

?;- ~"ü\ "in

0c c8 8~ 0 ~"" "oPcu cuQ) Q)CI; Cl: -1

·1

-2

100 200 300 400

Day

500 600 200 300 400

Day

500 600

Figure 4Relationships between MAF-1 s

2.0

••

2.01.5

•

•

Relative density

1.0

•

•

•

1.5

-2.5 -2.0 ·1.5 ·1.0 -0.5 0.0 0.5

2 Area2

1.0

0.5

-1.5

·1.0

ctlQ) 0.0...«

-0.5

.....

2

•

Log density

•

1.5

1.0

0.5

.- 0.0CO(J)L-

et -0.5

-1.0

-1.5

-2.0·2 -1 0

2.0 Area 2

1.5

1.0

~'iij 0.5c:(J)"0(J) 0.0 •>~(J) -0.50:

•

~'iij

a3 0"0Q)

>.~

ä) ·1c:

•

•

•

-1.0

·1.5 •Area 1 -2 Area2

-2.0 ·1.5 -1.0 -0.5 0.0 0.5

Log density

•1.0 1.5 ·1.5 ·1.0 -0.5 0.0 0.5

Log density

1.0 1.5 2.0

•

•

ANNEX 6

Sensitivity to detect trends in timeseries of contaminant concentrations inmarine biota along the SvJedish coasts

Anders Bignert, Swedish Museum of Natural History .

IntroductionSince 1967, the Swedish Museum of Natural Histo:sr has beeninvolved in monitoring activities along the Swedish coasts. In1978 the Swedish Environmental Protection Agency started theSwedish Environmental Monitoring Programme (PMK) and part ofthe early programmes th.:lt started during the 1.960 I S wereincluded in the new monitoring activities. This means thatseveral timeseries of between 10 to 20 years are availabletoday.

In the present study, these timeseries are used to cornparedifferent matrices, sites and treatment in terms of theirsensitivity to detect trends.

The possibility to statistically verify a time trend depends onthe magnitude of the trend, the length of the timeserie butalso on the random variation between the years. The lar;rerrandom variation in the time serie, the less sensitive ~t is toverify a true trend.

The between-year variation in a timeserie may be due to actualchanges in pollution load. It may however, also be caused by amore or less random variation or by uncontrolled factors thatinfluence the concentration even though pollution load isccnstant. It is hardly possible to distinguish betweenvariation due to actual chan$es in antro~ogenic pollution loadand other factors in timeser~es of the k~nd dealt with in thepresent study. Provided that random variation constitutes amajor ~art of the between-year variation, a measure of thisvariat~on would serve as a tool to cornpare various timeseriesin t~rms of their sensitivity to verify trends.

Possible techniques for assessing between-year variation aresuggested by Fryer & Nicholson, 1990. As a measure of thebetween-year variation, the residual variance of the time serieeornpared to a referenee line is estimated. The reference lineis eonstrueted by fitting a nonpararnetric srnooth curve throughthe annual geometrie means by using a method for sumnarisingtrends with loeally-weighted running-line srnoothers deseribedby Fryer & Nieholson, 1991..

The residual variance (Rv) ean be used to estimate the power ofa trend study, a low residual varianee yields a high power. The

55

power increases as the number of years or trend slope increasesand as the residual variances decreases.

In a similar approach the 'standard error of estimate' of asimple linear regression of logged median concentration valuesis used to estimate the number of years required to verify atrend at a specified magnitude of the trend or vice versa toestimate the required magnitude of a trend for a specifiednumber of years.

Also the within-year variation, represented by the 'Coefficientof Variation' (Vc), has been used to compare variouscontaminants and to study possible differencies betweenconcentrations expressed on dry and fresh weigth basisrespectively.

It should be stressed that the between-year and within-year ..variation is only one part of factors to consider in the choiceof an adequate sampling matrix.

Species and tissuesYoung specimens of herring (Clupea harengus) has been used inopen sea locations. Young herring is known to be vagrant withina limited area whereas adult stages of the species migratesubstancially. Herring can be collected in the entire area fromthe Skagerrak to the Gulf of Bothnia and it is an importantfood for man and a major food for manypredators such as sealsand guillemot.

Another sl?ecies used in open sea is cod (Gadus morhua). Young,sexually ~mature and less migratory specimens are analysed. Codcan only be collected in waters along the Swedish west coastand in the Baltic proper. '

In coastal Baltic areas perch (Perca fluviatilis) is used. The ttspecies has since lon~ been used in ecological as weIl as inphysiological monitor~n~ programmes and in experimentalstudies . Along the Swedish west coast common dab (Pleuronecteslimanda) and flounder (Platichtus flesus) are used. Theselection of these partly migratory species is a compromisesince stationary fish species big enough for individualanalysis has been difficult to obtain.

Blue musseI is used at the Swedish west coast and in the Baltic~ro~er. Because of the small size, especially in the Baltic,~ndividual analysis of organochlorines is not possible and thuspooled samples are analysed.

Guillemot eggs are collected from the central Baltic proper.This matrix has been shown to have many advantages as a speciesfor trend monitoring studies. It is a species nestling in

•

colonies, feeding on co~aratively few prey species and, basedon bird ringing data, fa~rly stat~ona~ within the Baltic. Thecollection of eggs also gives a possib~lity to use eggshell~arameters as effect ~arameters. Only eags collected during the~nitial egglaying per~od are used since~our studies onguillemot eggs show that replacement eggs have statisticallysignificant higher concentrations of contarninants and lowervalues for egg size parameters.

Tissue analyses, which is used in the present ~rogramme, giveinformation on the actual proportion of cont~nants which havepassed through biological membranes. The tissue concentrationsrepresent some sort of integration of the conditions prevailingduring a certain tirr~ in the actual environment .

Each sample normally consists of several individual specimen:autumn catched perch and herring from the Baltic of 20 (perehfrom 1986 and forward 10), spring catched herring from theBaltic and herring, cod, dab and mytilus from the Swedish westcoast from 1983 and forward of 2S and guillernot eggs of 10-20specimens.

Table 1. Tissues used for chemical analysis of varicus species.

•

Species

Herring, Dab, Flounder

Cod

Perch

Blue musseI , l?ooled sarrple~ndividuals

Guillemot

analyte tissue

organochlorines museIeHg musc1eCd, Cu, Zn, Pb liver

organochlorines liverHg museIeCd, Cu, Zn, Pb liver

organochlorines museIe

organochlorines soft tissuemetals soft tissue

organochlorines egg

Sampling sites.The sampling sites are choosen to represent la~er areas, notlocally influenced. In open sea, one sampling s~te in the northand one in the south of the Gulf of Bothnia, Baltic proper andSwedish West coast respectively are used. Guillemot eggs aresampled in the nestling area in central Baltic proper and codat a sampling site south east of Gotland. The coastal areas areselected in areas not locally influenced by major riverdischarses, industrial or urban activities or dense humanpopulat~ons and in areas not crossed by main navigation routessince such areas imply a certain risk for accidental disposals.

57

Preparation and chemical analysisPreparation methods follow the recommendations given withinlCES and Helcom monitoring programnes. Replicates from the sametissue sample has been analysed in herring rnuscle and guillemotegg. The errors are found to be within the limits of theanalytical error.

The chemoanalytical results are carefully controlled byinternal and external standards. The analytical error,estimated through replicate analyses, is however quite seldomassessed, hence the true range of the analytical error isunknown.

Ccmparison of various contaminantsTable 2 I?resents the nurnber of years required at a fixed powerof 90~ (~.e.90~ chance) to detect linear trends of various •metals and organochlorines for 1, 2 and 5~ slopes. A similarinvestigation was carried out for CMP data at lCES (Nicholson &Fryer, 1991). The nurnber of years required to detect trends forCM:P data is the average nurnber for these 25 series. The Swedishdata is apart of the CMP data but includes additional years.The maximum Rv values (worst case) is often e...'Ctrem values, farapart fram the average.

Table 2. Number of years required for detecting trends with 90% power inherring, caught in auturnn at five different sites. Max (worst site) and min(best site) values for various contarninants for an annual change of 1,2 and5% respectively. Comparative data from ICES in the right colurnn.

>20

Rv 1% 2%

Hg in musclemax 0.200 >50 41min 0.026 33 21

Pb in livermax 0.139 50 36min 0.015 28 18

Cd in livermax 0.054 41 27min 0.007 21 14

Cu in livermax 0.067 44 28min 0.008 23 15

zn in livermax 0.022 31 20min 0.009 24 15

sDDT in musclema..-x: 0.318 >50 47min 0.060 42 28

sPCB in musclemax 0.256 >50 44min 0.030 34 22

58

lCES (CMP)5% 5%

2313 13

2111

158

169 11

129 14

2716

2513 15

•

Guillemot eggs from St. Karlsö from the same timeperiod.sDDT 0.034 36 24 14sPCB 0.021 31 20 12sDDT/sPCB 0.016 28 19 11

•

The table indicate that the average between-year variance formercury in the present prograrrme might be greater than for CMP­data (where 60%" of the worst cases were excluded). The othercontaminants show equal or lower between year variance.

Organochlorines seems to show a larger between-year variationthan PB, Cd, 01 and zn and guillemot eggs seems to be a moresensitive matrix than herring to study time trends oforganochlorine concentrations .

A comparison of the median Vc (Coefficient of variation) of thefive herring sites, to illustrate the within-year variation forthe different metals, ranks as folIows: Zn(21), 01(26), Pb(32),Cd(35), Hg(40). This result shows almost the same pattern asthe between-year variation, except that lead seams to be worsethan cadmium if the between-year variation is considered.

Camparisons of various contaminants, sites and betweenconcentrations expressed on dry and fresh weight basisrespectively.A ccmparison between dry and fresh weight concentration for Hg,Pb, Cd, 01 and zn does not indicate any consistent difference(Table 3) .

Table 3. Residual variance (Rv) for various contaminants. Heavy metalscompared on a fresh and dry weight basis respectively.

Pb dry 0.146fresh 0.129

Cu dry 0.022fresh 0.008

Cd dry 0.057fresh 0.027

Fla0.0320.039

0.1510.139

0.0590.054

0.0740.067

0.0100.009

0.134

0.056

0.0420.044

Utl0.0350.040

0.0320.042

0.0340.038

0.0090.016

0.074

0.065

Lan0.0560.054

0.0130.015

0.0080.007

0.0340.039

0.0170.022

0.060

0.030

Äng0.2250.200

0.0400.032

0.0490.051

0.0210.031

0.0090.012

0.081

0.066

Har0.0300.026

dryfresh

Zn dry 0.008fresh 0.010

sDDT fat w. 0.318

sPCB fat w. 0.256

Hg•

59

Table 3 indicates problems to ass~ss trends in Pb atHarufjärden and Fladen and Hg at Angskärsklubb and demonstratesa comparatively low between-year variation for zink at allsites.

To compare the within-year variation between metal concen-trations on dry and fresh weight basis respectively and betweensites, comparable samples of herring have been used. Herring isthe only species which has been possible to analyse at allsites for all contaminants.

The median Vc of about ten years at the five herring sites,seems to be slightly lower for fresh wei~ht concentrationscompared to dry weight, expressed as a difference in percent,for cadmium (-18%, -20%, -5%, -8%, 0%), copper(O%, -24%, -13%,-9%, +4%) and zink (-10%, -42%, -40%, -22%, +19%).

Carq;>arisons of different speciesIn order to comnare different species collected at the samesite the same years, herring, cad, dab and blue musseI framFladen were choosen. Data were missing from blue musseI 1985and 1986 and were subsequently excluded from the other speciesto get them comparable, see Table 4.

•

GO

Table 4. Different species at Fladen comoared for residual variance (Rv).Mercu....vy and oroanochlorine are analysed ln rrnlScle tissue for herring anddab, for cod in liver. Lead, cadmium, copper and zink in liver tissue.

Hg Pb Cd Cu Zn sDDI' sPCB

Herring 0.037 0.183 0.064 0.072 0.009 0.171 0.035

Cod 0.023 0.226 0.163 0.111 0.032 0.059 0.003

Dab 0.070 0.061 0.155 0.027 0.027 0.288 0.158 •Mytilus 0.019 0.417 0.052 0.017 0.029 0.219 0.016

Table 4 indicate problems to analyse lead in blue musseI & codand sDDT in dab & blue musseI. The interpretation of Rv-valuesfor the DDr's should be cautious because of an increase inconcentraticn in 1983-84 due to the use of DDr in former EastGermany.

Carq;>arison of adjusted versus unadjusted timeseriesTo reduce both the within year and between year variation, ashomogeneous sample populatlons as possible are used i.e. theannual samples are collected in the same area at the same timeof the year and it is endeavoured to collect the samples fromcomparable populations with respect to sex, age etc. In

•

practise, this is only possible to a certain a~ent. Hence,factors, other than changes in antropogenic pollution load,might explain a significant I?art of the variation inconcentration. Factors contributing significantly to thevariation in concentration of both metal and organochlorinescan be used as adjustment variables. Due to the great co­variation among the biological variables registered, mostfrequently one variable is considered to be enough. Theresression lines of the current concentration versus thead]ustment variable is estimated for each year. If theregression coefficients between years do not differsignificantly, an Analysis of Covariance (ANCOVA) is carriedout. The annual adjusted geometrie mean values are estimated atthe 'grand mean I of the adjustment variable (Nicholson &Portmann, 1985 and Anon., 1986, Model 2 for a detaileddescription). For the time series of spring catched herring,where the fat content varies considerable the adjustment of DDTand PCB for fat has proved to be aPI?ropriate, e.g. a 5% annualchange is possible to detect in a tlmeserie 4 years shorter forboth sDDT and sPCB from the Karlskrona archipelago in the southof the Baltic Proper after adjustment. Also for metalconcentrations in cod liver this adjustment is efficient, seeFigure 1. Since the biological variation concerning age,length, weight etc is kept to a minimum however, the adjustmentgenerally does not decrease the between-year variation.

Table Sa. Resiual variances (Rv) and nurnber of years (yr) required fcrdetecting trends with 90% power and 5% annual change in spring catchedherring fcr DDT and sPCB before and after adjustment for fat centent .

Ängskärsklubb Karlskrcna

sDDI' sPCB sDDT sPCB .• Rv yr Rv yr Rv yr Rv yr

Unadjusted 0.102 19 0.095 18 0.136 20 0.060 16

Fat adjusted 0.078 17 0.064 16 0.065 16 0.020 12

Table 5b. Standard error of estimate (SEE), nurnber of years (yr) requiredfor verifying trends at an annual change of 5% in cod liver for Pb, Cd, CUand Zn before and after adjustment for fat content. The lowest annualchange (%) possible to ver~fy for the current timeseries, 11 years long, isalso reported.

Gotland Fladen

SSE yr % SSE yr %

Pb unadjadj

0.362 14 7.810.359 14 7.74

0.593 17 12.790.519 16 11.20

61

Cd unadj 0.247 12 5.33 0.594 17 12.81adj 0.169 10 3.65 0.446 15 9.62

Cu unadj 0.220 11 4.75 0.471 16 10.16ad] 0.196 11 4.23 0.341 14 7.36

Zn unadj 0.172 10 3.71 0.306 13 6.60adj 0.154 10 3.32 0.194 11 4.18

Adjusting concentraticns of cadmium, cCPl?er and zink in cod. liver forvarying fat content increases the sensit~vity of the timeseries Le. rnakesit possible to detect a trend with 3% smaller annual change or shorten thenumber of years required with up to two years compared to the unadjustedtimeserie.

Camparison of raw and selected data and of ratios versus •concentration values .Various biological variables such as age, sex, weight, lengthand sexuell rnaturity are determined. These measurements can beused to exclude individuals in the tails of such a variablesdistribution, see table 6.

Individual physiol~ical variation mi$ht cause differencies inuptake and ellminatlon rate of lipophllic components causingvariation in concentration of organochlorines e.g. sDDT andPCBs. If chemical partition is an important factor controlingthe concentration, the relative concentration of variouscontaminants should however be more or less constant havingsimilar lipophilicity and percistency.

While the concentration of sDDT varies notable between springand autumn it is no noticeable difference in the ratiosDDT/sPCB fram spring and autumn respectively. In general, thewithin-year variation as weIl as the between-year variation ismuch smaller in the ratio than in concentration between two fat •soluble components e.g. sDDT/sPCB. Provided that the twocontaminants constituting the ratio sterns from differentsources and change at different rates over time, studies onratios might improve the pssibility to detect trends.

Table 6. Timeseries of PCB-10 and DDE in herring muscle during 1980-87. Thesecend row in the first two columns reports the result after exclusicn ofthe specimens in the tails of the age classes sarnpled and specimens withfat content < 1.9 %.

PCBIO DDE DDE/PCBIOSSE yr % SSE yr % SSE yr %

Harufj ärdenraw 0.214 10 8.08 0.279 11 10.54 0.131 8 4.95selected 0.153 9 5.78 0.196 10 7.40

82

•

Ängskärsklubbraw 0.323 12 12.20 0.339 12 12.80 0.128 8 4.83selected 0.305 12 11.52 0.291 12 10.99

Landsortraw 0.154 9 5.82 0.308 12 11.63 0.147 9 5.55selected 0.134 9 5.06 0.298 12 11.25

Utlänganraw 0.308 12 11.63 0.353 13 13.33 0.235 11 8.87selected 0.298 12 11.25 0.351 13 13.26

Fladenraw 0.308 12 11.63 0.390 13 14.73 0.291 12 10.99selected 0.303 12 11.44 0.386 13 14.58

Table 6 indicates an improved sensitivity for timeseries whereextreme specimens, with respect to age and fat content areexcluded. Up to 3% less annual chan~e were required to detect atrend. If it is possible to use ratlOS, an annual change of 5%rather than 13% would be possible to detect for DDE atÄngskärsklubb.

References

Anon., 1986. Guidelines for analysing trend monitoring data. Annex 4.Report of the meetin~ of the ad hoc group of statisticians assisting theworking gr0U!? on marlne pollution baseline and monitoring studies in thenorth Atlantlc on trend monitoring. lCES C.M. 1986/E:39.

Fryer R. & M.D. Nicholson. 1990. Part 2. Testing for Trends in Annual MeanContaminant Levels. Report of the Working Group on Statistical Aspects ofTrend Mcnitoring. lCES C.M.1990/Poll:6.

Fryer R. & M.D. Nicholson. 1991. Surnnarising Trends with Locally-WeightedRunning-Line Smoothers. Report of the Working Group on Statistical Aspects

~ of Trend Monitoring. lCES C.M.1991.

Nicholson M.D. & R. Fryer. 1990. Part 1. Assessing the Power of ContaminantMonitorin~ Studies . Report of the Working Group on Statistical Aspects ofTrend MOnltoring. lCES C.M.1990/Poll:6.

Nicholson M.D. & R. Fryer. 1991. The Power of the lCES CooperativeMonitoring Prograrrme to Detect linear Trends and lncidents. Report of theWorking Group on Statistical Aspects of Trend Monitoring. lCES 1991.

Nicholscn M.D. & J.E. Portmann. 1985. The Precision of Estimated MeanLevels of Metals in Fish Tissue. lCES 1985/E:32.

eh·Copper and Zink (ug/g dry w.) • in cod liver~

Cu, Cod, Gotland tat adj. Zn, Cod. Gotland tat adj.-.8% yearly 8.6% yearly 100 -3.0% yearly 100 1. 7% yearly

40 SEE = .220 40 SEE = .196 SEE = .172 SEE = .154r2-.02 r2-.69 * r2=.30 r2 .... 14

80 80

30 30 00 0 60 60

020 0 0 20 o 0 0 0o 0 0 40 0 400

~Oo 0 .0-

0 <Jo00 0o '0 0

10 10 00 020 20

0 0 0 082 84 86 88 90 82 84 86 88 90 82 84 86 88 90 82 84 86 88 90

Cu, Cod, Fladen tat ad j . Zn, Cod, Fladen tat adj.-2.0% yearly 7.0% yearly -8.3% yearly 1.0% yearlySEE == .471 SEE = .341 SEE = .306 SEE == .194r2=.02 60 r2=.33 . 160 r2=.52 *

160 r2==.0360

o 0

0 120 1200 0

40 400 0

0 0o 0

0--0 80 800 o 0

~ 020 0

0-0 20

00 40 0 40

0 0

0 0 0 082 84 86 88 90 82 84 86 88 90 82 84 86 88 90 82 84 86 88 90

pie - 94.02.10 13: 59

•

•

ANNEX 7

WGSAE.\{ StJohn's 1994 Wa-king Paper

Focussing on Key Aspects of Contaminant Trend Assessments

M.D. Nicholson, R.J. Fryer and N.W. Green

In its working group reports, the ICES Working Group on Statistical Aspects of

Environmental Monitoring has presented aseries of discussion documents suggesting

methbds for increasing the interpretability of results from contaminant trend

assessments. The useful information in a contaminant time series consists of:

(a) .whether the level is changing systematically with time,

(b) the current level,

and(c) the variability ofthe data.

Current assessments focus mainly on (a). However, for management purposes, great

use can be made of all three types of information. For example, a situation in which

levels are varying erratically at a 'high' level, but with no systematic trend, would be of

more immediate concern than one in which there is a clearly defined upward trend, hut

at 'low' levels. Further, sensible management decisions require that such information be

integrated across tissues, areas and, possibly, contaminants. 'VGSAEM have proposed

ways in which (costly) trend data might be more fully and usefully exploited. These

include:

(d) comparing trends against some "management" or "guidance" level,(e) in connection with (d) constructing a standardised index which can be compared

across media, tissues, contaminants or areas,

(j) predictingfuture levels

and

(g) evaluating the effectiveness and efficiency ofmonitoring methods.

One potentially useful technique is shown in Figure Ia. Here we see a three-year-ahead

forecast of mercury levels in flounder in one of the JMP areas. In the context of JMG

Purpose d, forecasting is not of direct interest, and, as used here, is simply a way of

producing an index incorporating trend, level and variability. The fullline through the

data in conveys the systematic change in levels across time for year 1 through to the

current year 8. The dashed lines around it convey the precision of this trend. The line

65

~~- --~----------~

marked 'projection' is the projected trend in the next three years. The line marked

'upper limit' is the upper 95% confidence limit for an observation made in each of these

thrce years. The dotted Une coresponds to some management level. In this case we

have used a level of 0.3 mglkg wet weight for illustration. The choice of management

guidelines has recently been considered by the OSPARCOM workshop on assessment

criteria for chemical data of the JMP.

Figure 1b shows a similar plot for copper in flounder from the same area, with a

management level of 20 mg/kg wet weight.

The upper 95% confidence limit for the forecast three-years-ahead, expressed relative

to the management level, provides a standardised index which can be compared across

data sets. Hence, for the data sets above, the index is approximately 1.1 for mercury

and 0.05 for copper. Although there is evidence of a systematic change in the copper

levels, the indices suggest that this data set gives less cause for concern than that of

mercury, even though mercury shows no evidence of trend.

This technique is directed mainly at (d)-(f). A simple extension wouId be to summarise

explicit information about the qua/ity of the results i.e. information about (g), the

effectiveness and efficiency of monitoring. This information is invaluable when revising

guidelines and developing new monitoring strategies.

Summary

The resuIts of large monitoring programmes of a large number of contaminants

observed in a large number of areas can be overwhelming. Information-fatigue quickly

sets in. The technique suggested here offers one method of integrating and possibly

clarifying the significance of large sets of results. Providing suitable management

levels are available, a meaningfuI index can be constructed which is independent of

contaminant and tissue. Trus index can be used to rank data sets. An important

statistical henefit is that the ranking is equally valid regardless of the length of the time

series or the variability in the yearly signal. Uncertainty is penalised by increasing the

index. This recognises that important management decisions include maintaining the

length and quality of monitoring data sets.

For this or similar methods to be useful requires a comprehensive data base of

assessment criteria to be established. lt also requires clarification and an explicit

statement of monitoring objectives.

•

•

a)

0.4

upper limit0.3 :,: ~ management

-- 0 ~~

<>

----- proJectlono

---,..

<><>

...... _----­ ---Q

,.,..----------~-----~- -~-

0.2

0,1

~~

Ol~

"-0)

Ec0~

COL-......C(])ÜC0()

>-L-:::J()L-(])

e ~

0.01 2 3 4 5 6 7 8 9

Now +110+2

11+3

Year

b)

20,0 - managementlevel

5:5:0)

• ..Y:"-OlEc0~COL-........C(])ÜC0Ü

L-(])Cl.Cl.0

0

1.0

0.5 - - <>

<>=--=~-=--~<>~-=-:-=-=----=--=...::;.-=-~;..:-=---:-.-::-;:--:-=~~ 0 2. __ -<r- -

~upperlimit

______ projection

0.01 2 3 4 5 6 7 8 9

Now +110+2

11+3

Year

67

ANNEX 8

Working Document for WGSAEM 1994

Graphieal aids for desigllillg cOlltamillallt Illonitorillg progmmmcs

Mike Nicholson and Rob Fryer

Introduction

It is often theoretically straightforward to design a contaminant monitoring programme. Allwe need to know is:• the objectives of the programme• estimates of the variance components• sampling and analytical costs and constraints.

However, in practice, things are generally much more complicated:• the objectives are rather vague, or it is difficult to reconcile a number of differentobjectives• estimates of the variance components are nowhere to be seen• the given costs and constraints turn out not to be the real costs and constraints, or aremore complicated than first envisaged• statistical idealism proves to be completely incompatible with chemical pragmatism andfinancial realism.

In such situations, it can be useful to explore the effectiveness of a range of possible designs,with a range of variance estimates, costs and constraints. This can:• open up the debate between statisticians, chemists and managers• identify areas where more information is required, or where sources of variation need tobe controlled• lead to solutions which satisfy a variety of implied, but hard-to-set-down constraints.

Here, we present two graphical aids for designing a contaminant monitoring programme.Although they look a bit strange at first, they convey a lot of useful information. They arepresented by way of two examples (in which we shall skip over some of the statistical theory,to concentrate on the graphical techniques).

•

•

Designing to achieve Cl specified precision fOl' an estimated mean contaminant level

General problem

We wish to estimate the mean concentration of a population. We can pool individualorganisms. How do \ve allocate sampling and analytical effort?

Confidence [ünits jor pooled sampIes with replicale ollalyses

Assurne that we can take a total of IP individuals and divide them into P pools each of Iindividuals. Suppose R replicate analyses are made on each pool. Let cpr be the measuredconcentration in chemical analysis r of pool p. The mean concentration 1J. is estimated bythe sampie mean

P R

- I '" '"c = LLcPR 1'=1 ,.=1 pr

Then, given some assul11ptions, the 95 % relative confidence limits for 1J. are

[ ]

1/2_ 2 2C as aa-+1 . --+--1J. - 0.975,1-1 IP1J.2 RP1J.2

where• to975 /'-1 is the 97.5 percentile of the t-distribution with P-l degrees of freedom• a~2 i~ the sampling variance• a} is the analytical variance.

Why use a graphica[ aid?

In principle, we could optimise the choice of number of individuals, pools and replicateanalyses. For example, if SAMPLING COST is the cost of obtaining an extra individual andANALYTICAL COST is the cost per chemical analysis, then an objective solution can be foundby stating the problem in terms of minimising the TOTAL COST of estimating the populationmean concentration with a given confidence interval. For example, if we desire confidencelimits to be 50% or better, we minimise

TOTAL COST = IP SAMPLING COST + RP ANALYTICAL COST

subject to

[a; a~] 1/2

100'0.975,1'-1 IPj.L2 + RP1J.2 :::;; 50%

89

However, in practice• there may be constraints on the minimum amount of material required in a pool forchemical analysis• there may be a limit on the number of individuals that can be collected, or on the numberof chemical analyses that can be made,• sampling costs may be difficuIt to obtain, or be borne by different, possibly competingbudgets, or be shared across a variable number of chemical determinationsetc.• the programme may be designed for a number of different laboratories, all with differentcosts and analytical variances.

Although such thoughts might be incorporated into some much more complicatedoptimization problem, there may be no solution, the process may be too complex to be easilyunderstood and accepted, or the solution may still be feIt to be too restricting.

An alternative is to demonstrate how the confidence intervals are affected by different •combinations of I, P, R, Cf/, Cf/; this may be more useful than simply presenting a cost-minimised optimum solution. We can demonstrate this using typical published trend andAQC data.

How big is Cf1J1. likely ro be?

Fryer and Nicholson (1993) report average values of 100Cf/f' for data collected as part oftheICES CMP for measuring trends in trace metal concentrations in fish muscle. These provideestimates of 1OOalf' for

• I

• each metal average over species and tissues

Copper35%

Zinc21 %

Mercury39%

Cadmium49%

Lead48% •

• each species averaged over metals and tissues

Cod37%

Dab42%

Flounder46%

Herring32%

Plaice39%

Sole40%

Whiting32%

• each tissue averaged over metals and species

70

Liver40%

Muscle36%

•

How big is a/JJ. likely 10 be?

Like1y values of ajJJ. can be obtained from the seventh ICES intercalibration for trace meta1sin biota (Berman and Boyko, 1986, 1987). This provides estimates of within laboratoryvariability for a range of levels of different contaminants analysed for eight sampies. Fromthese results, the average 10, 25, 50, 75 and 90 percentiles of ajJJ. from about 50partieipating laboratories were ealculated and are given below:

QlO Q25 Q50 Q75 Q90

Copper 0.9 1.3 3.0 5.2 11.3Zine 1.1 1.8 3.2 5.3 8.8Mercury 2.9 4.2 7.3 10.9 21.9Cadmium 1.4 2.2 4.1 7.4 12.1Lead 3.6 5.9 11.1 20.7 38.5

Graphical design enve/ope

One method to give some fee1 for the effect of varying P, I, R, a/, a} is to plot theconfidence limits against one 01' these and to use the width of the plotted line to incorporateinformation about Olle 01' the others.

For example, Figures 1a-e, show

[ ]

1/22 2

as aa{O.975.P-l IPJJ.2 + RPJJ.2

plotted against P for IP = 25, R = 1 and 100a/JJ. for each metal averaged over species andtissues, using the width 01' the line to demonstrate the additional effect of variation in aa:• the outer edges 01' the solid black line correspond to the upper and lower quartiles of ajJJ.for each meta1• the outer lines correspond to the 10 and 90-percentiles.Hence, these plots give some guide to the expected range of confidence limits timt would beachieved by those laboratories participating in the ICES intercalibration trial.

Figures 2a,b give a similar picture of the overall range of confidence limits that would beexpeeted for all metals with IP = 25, 50 respectively:• the edges of the solid band correspond to the most and least variable metal measured bya laboratory with median precision• the outer lines show how much worse and how much better the confidence limits wouldbe if the laboratories with the 90 and 10 percentile precision did the business.

71

Designing to achieve a specified power for tl'end detection

General Problem

To design a 10 year temporal monitoring programme to detect a given % yearly increase inconcentration with 90% power. The programme will involve a number of contaminants and,possibly, a number of participating laboratories.

% yearly increase detected wirll 90% palI/er

Fryer and Nicholson (1994) describe a monitoring programme in which I individuals arecollected each year. In each year, the I individuals are collected on E sampling expeditions,say a week apart, and are analysed in B chemical batches, again say a week apart. Thereare therefore I1E individuals taken on each expedition and I/B individuals analyzed in each •batch.

Fryer and Nicholson (1994) show tlmt, given various assumptions, the % yearly increase inconcentration detected with 90% power in a 10 year monitoring programme is given by

% yearly increase detected with 90% power = 100(exp(0.4087,,!t) - 1)

where

72

and• a/ is the random between-year variance• a/ is the random between-expedition variance• ab

2 is the random between-batch variance• if- is the random within-batch-and-expedition variance.

Loosely,• a2 represents the sampling and analytical variability at any one snap-shot in time• a/ represents the additional analytical variability that occurs if we take measurementssome time apart• a} represents the additional sampling variability tl1at occurs if we take sampIes some timeapart• a/ represents the additional analytical and sampling variability that occurs if we take andanalyse sampies years apart.

The important thing to note is that the % yearly increase detected with 90% power dependson four components of variation.

•

lVllY llSe a graphical aid?

• there are many plausible combinations of I, E, B to consider• the variance components might vary between contaminants and laboratories• we might not know some of the variance components, but be able to give a range ofplausible values• we might want to know how small some of the variance components must be for theprogramme to satisfy its objectives

Again, we can demonstrate the effect of I, E and Band the different components of variationon power by using typical published trend and AQC data.

Sampling / analylica/ sch('lJI('s

Suppose that we have the capacity to analyse a total of I = 25 individuals. Consider foursampling schemes which explore the range of possible allocations of individuals toexpeditions and batches.

SI: E = 1, B = 1

S2: E = 1, B = 25

S3: E = 25, B = 1

S4: E = 25, B = 25

all individuals are taken on one expedition and analysed in onebatch

all individuals are taken on one expedition, but each individualis analysed in a different batch

each individual is taken on a different expedition, but allindividuals are analysed in one batch

each individual is taken on a different expedition and analysedin a different batch

Estimates oi the variance components

• 100a

• 100a..100ay

estimates by contaminant, species and tissue based on ICES CMP data aregiven in Fryer and Nicholson (1993) and suggest a median value of about40% with most estimates lying between 20 and 80%

estimates are hard to find; a variety of sources and personnel chit chats(Fryer and Nicholson, 1994) suggest timt for a good laboratory, values of10% might be reasonable for most trace metals and 20% for organics.

estimates of both these quantities are very hard to find; Fryer and Nicholson(1994) show that, for the ICES CMP data, values of a/ + a/ can beanywhere between 10 and 100%, but they could not disentangle the twocomponents of variation.

73

Graphical design [ree

Figure 3 shows the % yearly increase detected with 90% power for sampling strategies SI ­S4 for some combinations of a/, a/, ab

2, ~. A schematic explanation of the plot is given

in Figure 4.

Figure 3 has three groups corresponding to 100ay = 0, 10, 20 %. These are chosen toexplore a range of possible values of 100ay. We could, of course, consider values higherthan 20%.

Each group is sub-divided into three liDes for each of the four sampling strategies. Theselines show how the power of the different sampling strategies depends on the othercomponents of variation.

The 'central' mark in each line denotes the % yearly change detected when 100ae = 20%,100ab = 15%, lOOa = 40%. The values of 100ab and 100a are chosen to represent some'average' contaminant. The value of 100ae is a guess at a likely value for an averagecontaminant. The 'central' mark thus denotes the performance of the sampling strategy foran average contaminant.

In each set of three lines• the upper and lower points of the left line denote the % yearly change detected when100ae is doubled (to 40%) and halved (to 10%) respectively, (with the other variancecomponents held constant)• the upper and lower points of the middle line denote the % yearly change detected when100ab is doubled (to 30%) and halved (to 7.5%) respectively (with the other variancecomponents held constant)• the upper and lower points of the right line denote the % yearly change detected when100a is doubled (to 80%) and halved (to 20%) respectively (with the other variancecomponents held constant).

Thus, the left line shows the effect of mis-guessing 100ae• The middle line shows the powerfor a laboratory / contaminant with very good (ie low) between-batch variability and for not­so-good (ie high) between-batch variability. The right line shows the power for the rangeof values of 100a found in the ICES CMP data.

Figure 3 shows that

• Sampling scheme SI never does very weIl.

• When a/ is large, none of the sampling schemes do weH, in the sense tImt % yearlychanges of 10% or more are unlikely to be detected.

• As a/ reduces, the benefit of additional expeditions and batches becomes cIear.

• A laboratory must ensure that it has sma11 bet\veen-batch variability or analyse in severalbatches

• If the programme is designed to investigate a 11l1mber of contaminants with a range ofbetween-expedition variances lOOae then several expeditions would be sensible.

References

Berman, S.S. and Boyko, V.J., 1986. Report on the results of the seventh intercalibrationexercise on trace metals in biota (part 1). Cooperative Research Report No 138.

Berman, S.S. and Boyko, V.J., 1987. ICES seventh round intercalibration for trace metalsin biological tissue. ICES 7/TM/BT (part 2). Unpublished.

Fryer, R.J. and Nicholson, M.D., 1993. More on the power of the ICES CooperativeMonitoring Programme. Report of the Working Group on Statistical Aspects ofEnvironmental Monitoring.

Fryer, R.J. and Nicholson, M.n., 1994. Can simple changes in sampling and analyticalstrategy improve the power of the ICES Cooperative Monitoring Programme? Report of theSub-Group on Temporal Trend Monitoring for Contaminants in Biota.

75

Confidence Envelope ror CuCL4400

300

200 1

100

90

70: ,

60

50

10

ob=========!2 3 4 5 6 7 B 9 10 1112

P

Confidence Envelope ror ZnCL4400

300

200

100

90

BO

70

60

50

40

o~~==~==~=~2 3 4 5 6 7 B 9 10 1112

p

Confidence Envelope for HgCL4400

300

200

100

90

10

O~==========!.2 3 4 5 6 7 8 9 10 1112

p

76

Confidence Envelope for CdCL4400

300

200

100

90

BO

70

20

10

OF'<='<=""""==~~~~~2 3 4 5 6 7 B 9 10 1112

p

Conridence Envelope for PbCL4400

20

10

o~=====""""'==i""";2 3 4 5 6 7 8 9 10 1112

p

OverallCL4200

:L 8 0

:L 60

:L 4 0

e :L 2 0

:L 00

80

60

40

20

02

Confidence Envelopc vvit.h N=25

:L 0 :L:L :L 2

Overall Confidence Envelope vvi t.h N = 50

•C:z:...4200

:LSO

:L 60

:1..20

:LOO

80

60

40

20

..,:I?

8

77

78

- -- ---- ---------------1

Summary of desigll tree

High variances

100ae = 401000"b = 151000" = 40

100ab = 301000". = 201000" = 40

lOOa = 801000". = 201000"b = 15

.Medium variances

100ae = 20, lOOab = 15, 100a = 40

Low variances•lOOae = 101000"b = 151000" = 40

100ab = 7.51000". = 201000" = 40

100a = 201000". = 201000"b = 15

Summary of sampling strategies

51: E=I, B=1 52: E=I, B=25 53: E = 25, B=1 54: E=25, B=25

Working Paper

ANNEX 9

leES WGSAEM 1994

Influence of length on elements concentrations in blue musseis sampledin an unpolluted fiord system in West Greenland.

by

Frank Riget

Greenland Environmental Research InstituteTagensvej 135

DK-2200 Copenhagen N, Denmark

Background

At last years meeting in the Working Group on Statistical Aspects of TrendMonitoring it was decided to continue assessment of the effects of shell lengthon contaminant concentrations in musseis.

In trend monitoring it is desirable to isolate effects of human impacts ofpollutants from effects of natural phenomena. Knowledge of natural variationsis needed to properly assess impact on the environment. Therefore, GreenlandEnvironmental Research Institute (GERI) has studied element concentrationsin blue musseIs sampled in an unpolluted fiord system in West Greenland.

The main aim of the project was to quantify the magnitude of natural year toyear variation and geographical variation in order to establish criteria forproving time trends in element concentrations. The objective of the presentwork is to quantify the influence of mussei length on element concentrations.

80

•

•

•

Data

BIue musseIs were sampled at four stations in Godthabs Fjord near Nuuk, WestGreenland each summer during the period 1980 to 1982 (fig. 1). The musseIsampIes were obtained by dividing collected musseis into shell length intervalsof 3 mm. Table 1 gives mean shell length and number of individuals in eachgroup. Musseis were cut out of their shells and the soft parts were frozenimmediately. SampIes were analysed at Sentralinstitutt for Industriell Forskning(SI) in Norway and at Isotoplaboratoriet in Denmark (lD). At SI the sampieswere analysed for Cu, Cd, Pb and Zn by atomic absorption spectrophometry, andat ID the sampies were analysed for Na, Sc, Cr, Fe, Co, As, Se, Br, Rb, Sr, Cs,La, Ce, Eu, Hg and Th by instrumental neutron activation analysis. Results wereexpressed on a dry weight basis.

Statistical analyses and the rcsults.

In order to evaluate the variability of element concentrations the followingmodel of ANOVA is used:

log(element concentration) =

Y + L + S + Y*L + y*S + L*S + Y*L*S + E

where

•log(element concentration)

YLS

Y*L, y*s and L*SY*L*S

E

= logaritmic value (base e) of elementconcentration

= year= locality= logaritmic value (base e) of shelllength= first order interaction effects= second order interaction effect= residual

Table 2 summarizes the results of the ANOVA. The R2 values are relatively highfor all elements except for Hg. Elements as Ce, Hg and Pb have high relativestandard deviations. The shelllength effect is significant at the 1% level for 17elements out of a total of 20. However, for most elements the influence of shelllength is dependent on the locality and for some elements also on the year ofsampling. For 11 elements the picture is further complicated by the secondorder interaction effect which is significant at 1% level.

For each combination of locality and year of sampling the influence of shelllength on element concentrations has been evaluated by a regression of log-

81

concentration on log-shelllength. The estimated slopes from the regressions areshown in Table 3.

Elements as Na, Pb, Sr, Sr, Cd, La, Ce and Eu have in general positive slopesand in most cases significant different from 0 at the 5% level. This means thatthe higest concentrations are found in large musseIs. For the heavy metals Pband Cd significant slopes were found in 7 and 11 combinations of locality andsampling year out of a total of 12 and with a range of -0.46 to 0.81 and -0.11 to0.86, respectively.

The elements, Sc, Fe, Co, As, Se, Rb, Cu, Cs and Th generally have negativeslopes and in most cases significant different from 0 at 5% level. Theconcentrations of these element are highest in the small musseIs. For Cu theslope was signifikant in 9 out of 12 combinations and a range of -0.06 to -0.51.

Cr, Zn and Hg show no clear picture of the length dependence and theconcentration seems to be independent of the length of the musseis.

•

ö4

Table 1. View of sarnpies of blue rnusseis at four loealities in Godthab Fjordat West Greenland In the years 1980, 1981 and 1982. Length 1S rnean shellIength (ern). n is nurnber of rnussels.

Locality I Loca1ity 21980 1981 1982 1980 1981 1982Length n Length n Length n Length n Length n Length n1.42 213 1.40 215 1.42 189 1.41 189 1.41 145 1.41 1231.70 264 1.71 235 1.71 226 1.71 246 1.71 198 1.71 1501.99 232 2.00 227 2.01 223 2.00 247 2.00 222 1.99 1402.30 230 2.30 243 2.29 205 2.29 195 2.30 210 2.28 932.64 217 2.63 294 2.64 229 2.62 174 2.63 215 2.65 1683.05 198 3.03 173 3.04 167 3.04 157 3.04 166 3.06 1663.45 169 3.46 152 3.45 158 3.45 172 3.43 171 3.44 1633.85 135 3.85 123 3.84 152 3.84 130 3.84 134 3.84 1434.23 94 4.23 75 4.22 96 4.24 102 4.24 102 4.26 1064.63 75 4.63 27 4.67 42 4.64 80 4.67 82 4.68 845.19 26 5.28 19 5.36 10 5.15 50 5.18 37 5.22 48

5.68 37 5.66 30 5.69 396.28 28 6.38 31 6.32 307.41 11 7.37 27 7.75 28.45 6 8.07 6

Locality 3 Locality 4 •1980 1981 1982 1980 1981 1982Length n Lenglh n Lenglh n Lenglh n Lenglh n Lenglh n

1.41 116 1.41 182 1.41 217 1.42 199 1.40 199 1.39 2131.69 167 1.70 245 1.69 232 1.70 189 1.71 191 1.71 2172.00 171 2.01 246 1.99 153 2.00 205 2.00 218 1.99 2222.29 164 2.29 202 2.30 98 2.30 167 2.29 172 2.30 2012.61 175 2.65 211 2.66 172 2.65 238 2.65 230 2.65 2153.05 126 3.03 172 3.04 168 3.03 172 3.04 178 3.03 1703.45 123 3.45 173 3.45 167 3.44 149 3.44 154 3.45 1543.85 101 3.85 155 3.84 147 3.84 153 3.83 151 3.85 1334.23 82 4.25 101 4.26 108 4.25 102 4.24 96 4.27 1074.68 48 4.67 109 4.70 86 4.70 77 4.69 82 4.68 875.19 61 5.17 75 5.16 60 5.17 51 5.15 51 5.17 415.66 30 5.65 39 5.71 32 5.81 17 5.65 32 5.63 236.34 30 6.27 19 6.55 30 6.25 20 6.25 147.23 7 7.35 31

•

•

Table 2. Analysis of variance. Effects are Y =year of sampling, L = locality,S = shelllength. YxL, YxS and LxS first order interaction effects. YxLxS secondorder interaction effect. The significance level (p < 0.01 * * *, 0.01< P < 0.05 * *,and 0.05< P < 0.10 * are based on the partial su ms of squares (Type 111, SASannon., 1990). Re!. S.D. = relativ standard deviation.

EffectsY L S YxL YxS LxS YxLxS R2 ReI.S.D.

Na *** *** *** *** *** *** 0.93 1.11Sc *** *** *** *** *** *** *** 0.94 1.13Cl' * *** ** * 0.63 1.24Fe *** *** *** *** *** *** *** 0.91 1.11Co *** *** *** *** *** *** 0.90 1.07Zn *** *** *** 0.79 1. 11Pb ** *** *** *** *** 0.67 1.32As *** *** *** *** *** *** 0.87 1.08Se *** *** *** *** *** *** * 0.92 1.07BI' *** *** *** *** *** *** * 0.92 1.09Rb * *** * * 0.68 1. 11Cu *** *** *** *** 0.80 1.11Sr *** *** *** 0.63 1.21Cd *** *** * ** *** ** 0.76 1.21Cs *** *** *** ** 0.64 1.28La ** *** *** *** *** *** 0.96 1.25Ce *** ** ** *** *** 0.78 1.50Eu *** *** *** ** * *** ** 0.96 1.18Hg *** 0.43 1.33Th *** *** *** *** * *** *** 0.94 1.14

ö5

Table 3. Estimated slopes dcrived from regressIOn analysis. For each elementand each cornbination of year and locality log-koncentration has been regressedon log-shell length. * slope differs frorn 0 at 5%-level.

Na Sc Cr Fe Co Zn Pb A. Se Br Rb Cu Sr1980 loc.l 0.40' -0.28' -0.09 0.05 0.04 0.07' 0.51* -0.11 -0.20* 0.36* -0.16* -0.50* 0.60*

2 0.23* -0.26* 0.24 -0.28* -0.11 * 0.10* 0.55* -0.08 -0.31* 0.19* -0.18* -0.39* 0.25*3 0.08* -0.53* -0.19 -0.65* -0.36* -0.11* 0.38 -0.24* -0.58* 0.02 -0.37* -0.34* -0.174 0.51* 0.03 -0.05 -0.09 0.10* -0.03 0.28 0.07 -0.21* 0.39* -0.28 -0.11 0.49*

1981 loc. 1 0.68* -0.44* -0.10 -0.23* 0.01 0.01 0.12 -0.07* -0.23* 0.48* -0.16* -0.48 * 0.50*2 0.40* -0.28' 0.02 -0.21* -0.13* 0.13 0.75* -0.01 -0.31' 0.22* -0.09* -0.09 0.34'3 0.05 -0.54* -0.08 -0.52* -0.16* -0.03 0.24 -0.10 -0.45* 0.02 -0.13' -0.37* 0.044 0.43* -0.47* 0.20 -0.58' -0.13 -0.03 -0.19 -0.01 -0.31* 0.30* -0.17* -0.44* 0.47*

1982 100. I 0.53* -0.79* -0.22 -0.29* -0.11* 0.11 0.35' -0.11' -0.33* 0.26* -0.10 -0.24* 0.49*2 0.16 -0.32' 0.17 -0.27* -0.10* 0.06 0.81* -0.01 -0.33* 0.04 -0.15* -0.06 0.123 0.29* -0.10 0.20 -0.16* -0.22* 0.19* -0.46' -0.08* -0.69* 0.04 -0.20' -0.25* 0.174 0.46* -0.43* -0.04 -0.49* -0.13* -0.17* 0.68* -0.15* -0.35* 0.11* -0.25' -0.51* 0.16

Cd C. La Ce Eu Hg Th1980 loc.l 0.67* 0.02 -0.84* -0.12 -0.15 -0.57*

2 0.78* -0.36 1.13* 0.84' 0.80* 0.34 -0.35*3 0.42' -0.63* 1.06* 0.62* 0.49* -0.31* -0.64*4 0.41* -0.49* 1.14* 0.92* 0.88* 0.15 -0.01

1981 loc. / 0.30* -0.23* 0.22 -0.59 -0.03 0.03 -0.53*2 0.67* -0.53' 0.80* 0.35 0.47* 0.11 -0.33*3 0.47* -0.30 1.11* 1.15* 0.65* 0.16 -0.72*4 -0.11 -0.55* 1.14* 0.87* 0.66* 0.06 -0.52*

1982 10c.1 0.40* -0.20 0.34 1.36 -0.06 0.08 -0.60*2 0.86* -0.39* 0.63* 0.7/ * 0.36* 0.12 -0.39*3 0.31* -0.19* 0.84* 0.53' 0.56* 0.07 -0.54*4 0.46" -0.53* 0.76* 1.02* 0.53* -0.12 -0.48 *

•

ANNEX 10

Working Paper leES WGSAEM 1994

Relationship between length and lead concentration in the bluemusseI, Mytilus edulis.

by

Frank Riget

Greenland Environmental Research InstituteTagensvej 135

DK-2200 Copenhagen N, Denmark

Background

At last years meeting in the Working Group on Statistical Aspectsof Trend Monitoring it was decided to continue assessment of theeffects of shell length on contaminant concentrations in musseIs .

Greenland Environmental Research Institute (GERI) has used bluemusseIs as a monitor organism for a number of years in areasaffected by heavy metal pollution from mining and GERI also hasstudied variation of trace metals at unpolluted locations.

Two data sets from two different mining areas and one data setfrom an unpolluted location have been analysed in order to lookcloser at the relationship between musseI length and leadconcentration.

Data

sets have been analysed with respect to thebetween length of the musseIs and leadOne of the sets is from an area affected by aand the another set is from an area affected by aThe third data set is from an unpulluted area.

Three datarelationship·concentration.lead-zinc minecryolite mine.

...' 7ö

t:$8

Maarmori1ik

The impact of a 1ead-zine mine loeated at Maarmorilik in mid WestGreenland has been monitored by ana1ysing metals in speeies offish, prawns, seaweed and musseIs. The lead-zine mine operatedduring the period 1973 to 1990.

From the intertidal zone of a number of fixed stations elose tothe mine and up to 40 km from the mine blue musseIs have beensampled. Sampling has taken plaee in September eaeh year. MusseIswere pooled in size groups aeeording to shell length, eaeh poolnormally eonsisting of 20 individuals. The number of size groupssampled varied from one to eight. Looking only at oeeasions wheretwo or more Iength groups has been analysed leave data to eomposeof 189 eombinations of year and stations in total (Table 1).

In most oeeasions two size groups (size groups 6-7 em and 7-8 emor 8-9 em) has been sampled (Table 1), but at three stations withquite different degree of pollution at' least 4 size groups weresampled eaeh time during the period. Data from these stationsgive good opportunities to study the relationship between musse1Iength and lead eoneentration. '

Table 1 shows the data used in the fo1lowing analyses.

Ivittuut

Mining for eryolite in southern Greenland started on a smallseale in 1854 and eontinued unti1 '1987. The eryolite oretypieaIIyeontains 0.2 to 0.5% galena (PbS). The mine is an openpit loeated at the shore of Arsuk Fiord. Environmental studieshad not been earried out until 1982, sinee then fish, seaweed andmusseIs from the fiord had been monitored.

From a number of fixed stations in the Arsuk Fiord blue musseIshave been sam1ed in June/Ju1y eaeh year since 1982 exeept in 1991where no samp1ing were made. At eaeh station it is attempted tosampIe 40 individuels in size group 2-3 em shell 1ength, 20 •individuels in size group 6- 7 em, and 20 individuels in sizegroup 7-8 em. However, in many oeeasions it was diffieult to getmusseIs in the largest size group (Table 1).

Kobbbefjorden

From 1987 to 1990 blue musseIs were sampled regulary at aloeation in Kobbefjorden near Nuuk, West Greenland in order tostudy seasonal variation of traee metals ~ The fiord is unaffeetedby Ioeal inputs of pollutants. '

At each sampling time two sampIes eaeh eomposed of 10 individualsin eaeh of the size groups 2-3 em, 4-5 em and 6-7 em (shellIength) were sampled. A total of 17 samplings were made duringthe three year period.

statistical analyses

Influence of musseI length on lead concentration

The following statistical model are used in the analyses of theMaarmorilik and Ivittuut data sets:

logPb =Y + P + y*p + ß-logL + Y*ß-logL + P*ß"logL + Y*P*ß"logL + c:

and for Kobbefjord data:

logPb = S + ß"logL + S*ß"logL + c:

•where

logPbYPy*pß10gL

Y*ß"logLP*ß"logLY*P*ß"logL

SS*ß-logL

c:

= logaritmic value (base e) of Pb concentration= year= place= interaction between year and place= regression variable= logaritmic value (base e) of shell length= interaction between year and ß= interaction between place and ß= interaction between year, place and ß

= sampling= interaction between sampling and ß= residual

The analyses of variance are summarized for the three data setsin Table 2. Type 111 sum of squares (also called the partial sumsof squares) tests the influence of an effect when all othereffects are included in the model. The calculation has been donewith the SAS package.

There is high significance of the parameter ß for all three datasets. Lead concentrations seem therefore to be dependent on thelength of the musseI.

For the Maarmorilik and Ivittuut data sets which include bothyear and place effect, the interaction effect between ß and placeis highly significant while the interaction between ß and year isnot significant. This indicates that the relationship between thelogaritmic values of musseI length and lead concentrations ismore dependent on the locality than on the year of sampling.However, the picture is more complicated by the second orderinteraction between year, place and ß which is significant at 5%level for the Ivittuut data and not significant for theMaarmorilik data.

For the Kobbefjord data there is no significance of theinteraction between sampling and ß. This means that therelationship between the logaritmic values of mussel length andlead concentration is the same for all samplings.

89

EstimatioD of ß

The following statistical model is used to estimate 8 for theMaarmorilik and Ivittuut data:

logPb = Y + P + y*p + ßlyo Pl "logL + E;

and for Kobbefjord data:

estimation of a common ß:

logPb = S + 8"logL + E;

estimation of separate 8:

For the Maarmorilik and Ivittuut data this nested model isessentiel the same as used before but it gives an estimate of 8and a test for 8=0 for each combination of year and place. Forthe Kobbefjord data a commen ß for the total data set isestimated as a concequence of a not significant interactionbetween sampling and 8.

Results

Maarmorilik data and estimated ß

A plot of the estimated ß vs Pb concentration calculated as thegeometric mean of the size groups sampled is shown at the top offigure 1. A few outliers are omitted from the figure. In mostoccasions 8 is estimated to be positive and no negativesignificant 8 is found. There seems tO,be a tendency of a highervalue of 8 with low Pb concentrations than with high Pbconcentrations. The mean 8 is found to be 0.8 (Table 3) whichmeans that Pb concentration increase with mussel length in power0.8. The Pb concentratioD are lesser than would be predicted ifconcentration were direct related to lenght.

When only two size groups have been sampled the estimation of 8may be uncertain. In figure 1, mittel 8 is plotted versus Pbconcentration for cases where three or more length groups weresampled. Compared with figure at the topof figure 1 many of thenegative 8 disappeared together with some of the extreme values.The tendency of smal 8 values for high Pb concentrations is still.clear. The mean ß is found to be 1, e.i.a direct proportionalitybetween Pb concentration and mussel length.

As mentioned ealier musseIs in fourto eight different sizegroups have been sampled at three different stations throughoutthe monitoring period. The degree of pollution is quite

9C

•

different at the three stations and this data set is probably themost reliable data set when looking at the relationship betweenß and the level of pollution. Figur 1 at bottom shows theestimated ß versus Pb concentration for these three stations. Themean ß is now 1.3 (Table 3).

The high values of ß at low Pb concentrations derive from st. L,which is astation located about 40 km from the pollution sourcejust outside the fiord. It is used as a reference stationalthrough it is clearly affected by the mining activities. Thecontamination of the fiord waters has changed during the miningperiod. In figure 2 the time trend of the amount of dissolved Pbin fiord waters is plotted together with the time trend of ß atst. L. From 1973 to 1977/78 the amount of dissolved Pb were at avery high level. Then it droped to a lower level during 1980's.It decreased further from 1991 after the closure of the mine. Thevalues of ß increase from 1982 to 1987 which could be explainedby large musseIs at the station "remernbering" the period withhigh amounts of dissolved Pb in the water and small musseIs notexisting at that time. When ß then decrease from 1987 and onwardit could be explained by the extinction of the large"remembering" musseIs.

This explanation of the findings of high ß values at st. L. couldalso be thrue for other high values of ß in the dataset. In factthe values of ß at st. 17 show a similar trend pattern, whereasno time trend in ß is seen at st.36.

Ivittuut data and estimated ß

In the case of the Ivittuut data set only few ß are estimated tobe negative; on1y one significantly (figure 3 at the top). Incontrast to the findings for the Maarmori1ik data no values of ßgreater than 2 is found, and there is no tendency of a smallervalue of ß with high Pb concentrations. These differences betweenthe results of the two datasets may be exp1ained by thevariability of the contamination. The contamination of Arsukfiord from the mining is in contrast to the contamination of theMaarmorilik area believed to have been re1atively constant duringa long time period. MusseIs in the Arsuk fiord have thereforegrown up under relatively same degree ofcontamination oppositeto the mussels in the Maarmorilik area.

The mean ß is found to 0.7 close to the value tor the totalMaarmorilik data set (Table 3).

When looking only at cases with three size groups analysed allvalues of ß tor high polluted stations disappeared except for one(figure 3 at the bottom). The mean ß increaseq to 0.8 (Table 3).

91

Kobbefjord and estimated B

For the Kobbefjord data all of the separately estimated ß waspositive except one, and only two were found significantlydifferent from 0 (figure 4). All values of B were below one. AsB was not found to be significant different between samplingperiods a comrnon B of 0.38 was estimated (Table 3). This value isweIl below the values estimated for the two other data sets.

Conclusion

From the analyses of lead concentrations in musseIs at two areacontaminated by lead and one area unaffected at West Greenland itmay be concluded, that

Lead concentration increase significant with musseI length.

The relationship between musseI length and lead concentrationdepend both on locality and year of sampling, the former seemsmost important.

When lead contamination is relatively constant during time,the lead concentration increase with length of the musseIs bapower of 0.7 - 0.8.

When a pronounced decrease of lead contamination occure ~time it may result in high differences in lead concentrationbetween small and large musseIs (high B, upto 4).

At an unpoluted area the lead concentration increase withlength of the musseIs only in apower of about 0.4.

Table 1. View of the Maarmorilik and the Ivittuut data

Maarmorilik data

Number of stations per year with two or more length groupsanalysed:

1982 83 84 85 86 87 88 89 90 91 92 total

20 11 14 13 18 17 22 19 20 17 18 189

Frequency of number of size groups analysed:

number of size groups: 2 3 4 5 6 7 8

number of stations: 89 53 14 16 10 4 3

Frequency of sampled length groups:

length group:3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 cm total

5 29 72 169 169 108 41 2 1 596

Ivittuut data

Number of stations per year with two or more length groupsanalysed:

1982 83 84 85 86 87 88 89 90 92 total

19 18 20 17 17 17 17 16 17 17 175

Frequency of number of size groups analysed:

number of size groups: 2 3 4

number of stations: 104 69 2

total8-9 cm7-86-75-6

Frequency of sampled length groups:

length group:2-3 3-4 4-5

179 6 4 14 156 56 15 430

93

Table 2. Results of the ana1yses of variance for the three datasets.

Maarrnori1ik

Effect DF Type 111 S5 Pr > F R2

Y 10 0.65 0.072 0.996P 34 23.86 <0.001y*p 145 7.00 0.044ß 1 2.16 <0.001Y*ß1nL 10 0.48 0.234P*ß1nL 34 5.28 <0.001Y*P*ß1nL 145 6.75 0.071

Ivittuut

Effect OF Type 111 S5 Pr > F R2

Y 9 1.63 <0.001 0.998P 30 75.11 <0.001y*p 134 7.23 0.008ß 1 15.26 <0.001Y*ß1nL 9 0.54 0.070P*ß1nL 30 2.37 0.001Y*P*ß1nL 134 6.37 0.034

Kobbefjord

Effect OF Type 111 SS Pr > F R2

S 16 0.88 0.329 0.824ß 1 1.14 <0.001S*ßlnL 16 0.65 0.570

Table 3. Mean values of ß.

n Mean S.O. minimun IIBXinunMaarrnoriliktotal data set 189 0.79 1.21 -3.00 4.95>2 size groups 100 1.00 0.94 -1.49 3.61St. L, T17, T36 33 1.30 0.88 -0.36 3.61

Iyittuuttotal data set 170 0.71 0.38 -0.84 2.07>2 size groups 70 0.83 0.23 0.18 1.31

Kobbefjordtotal data set 17 0.36 0.31 -0.22 0.86

alldata

10 100 1000 10000

three or more length groups analysec

o

B~l ••3 ~ • • • •.'.., . ..021 •••• • <) • ~ 0

01 ]i-------~ ~L.(~°-.Q<)-~-·_·~·~~?!-g~~~--°..Q....----o ".'6 ,-' 00;,.0 ~O

o 0 0 0 &"~ 000 <) <)

j0<)00 0 V

<> <>:. :TI--'--'-~-"-",I,','TI---r--"-I-,.-,-r-"T"IT"'Tl'1---,---,,....-r-T..,Ir-Ir;'r-r"I--..,.--~~-,.-""T..,...,."T""T'"I I t 11

10 100 1000 10000

Beta4

•3 •'.2 •

• • •••

0

-1

10

Pb-mglkg cI.w•

• • • significant 000

••• •o

o· ·

100

not significant

•.....~00 ..

<>

Si: L T17 and T36

1000

Figure 1. Plot of ß vs Pb concentration. Maarmorilik data.

Pb tons , Beta35 :

j1- 4

• "I

30 ~, , r, ,

1 , ,, Ii , , ,

25 -;, , ~3.. , I

j . -- I~ : , i20 i . , , - ,. ,

j. 'lI , I,, r2

15 ~ , I,

1 ,

1~

,, I101 .,

l1j ,,

l51

o ~I

I I I ~OI ,i I I iI

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 19 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 97 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 95 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2

Figure 2. Time trend of dissolved Pb in fiord waters and of ß atst. L.

. l

Beta3

aU data

2 •• 0

~... .", •_. : '. . • • A.0° • 0 00· •

0

0 0 0 . S':>O! 0 000 00 ??o 0

0 0 0& 0 0

•-1

10 100 1000 10000

o

three length groups analysed

•

••• .-. ~,

• • p •••

:~t.~. "..­•••o

••

Beta1.41.31.21.11.00.90.80.70.60.50.40.30.2

0.1 t,---r-_r_-r-..........,r-T""'1n---.---r---......,..-,-...--r-....---r----.-~_r__r_T",...,...

1 10 100 1000

Pb-mglkg d.w•

••• significant 000 not significant

Figure 3. Plot of B vs Pb concentration. Ivittuut data.

S7

<>

• ••

0 0 0

0_ 0v

00 0

0

0

... 0

BetaJ0.9 J~

~:~l~0.6

0.50.4

0.3

0.2jO.111 -!L_~ _=___

0.01-0.11

-0.21-0.3 ~L!!----..,..-----,.----.--,---,---,--,--,'--.-1----r----.,..--,---,-.,....-,-,,..-,-,"TI

0.1 1.0 '10.0

Pb-mglkg d.w.

••• signiflcant 000 not significant

Figure 4. Plot of ß vs Pb concentration. Kobbefjord data.

ANNEX 11

International Council for the Exploration of the Sea,\Vorking Group on the Statistical Aspects of Environmental Monitoring

25-29.April 1994, St lohns

SHELL LENGTH and METAL CONCENTRATIONS inMUSSELS (Mytilus edulis) 11

Birger Bjerkeng and Norman GreenNorwegian Institute for \Vater Research

PB 173 KjellsasN-04110SLO

Summary

The results from about 90 musseI (MytilllS edillis) sampIes indicate that the concentrations ofcadmium (0.35-120 ppm d.wt.), lead (0.09-460) and mercury (0.02-7.0) in soft tissue are notsystematically influenced by shelllength (20-50 mm). About 45% of the between-replicate§variance for lead and about 20% for cadmium and mercury is explained when the data isnormalized by principal component factors for shelllength, shell weight and soft body dryweight. This indicates that normalization might be important far trend analyses for thesemetals especially lead.

Introduction

This report is part of the continued assessment of the effects of shelllength and contaminantconcentrations in musseIs and evaluation of the importance of length in the preparation ofpooled sampIes (cf. 1993 \VGSAEM annual report, action list). Below the effect of shelllength on cadmium, lead and mercury concentrations are discussed.

Analysis of blue mussei data

Data for metallevels and chlorinated hydrocarbons in blue mussei have been collected from47 different Iocations around the Norwegian coast in the years 1981 to 1983. The databasecontains data on 572 samples. Each sampIe was prepared from 20-100 individual shells, formost sampIes from within one of 3 different length groups: 2-3 cm, 3-4 cm and 4-5 cm.

The data do not by any means make up a complete multifactor design; the year by stationmatrix is quite unbalanced, with a lot of empty cells, and sampIes from different areas anddifferent years have been analyzed for different subsets of pollutants. Chlorinated hydro­carbons and corresponding extractable lipid content have only been analyzed for about 300sampIes and will be treated later. Most of the sampIes have data on shell and tissue weight.

§ Replicates in this context means sampIes from the same loctttion and date, hut not from thesame length group.

,----------- -

ANNEX 11

Proccdure of nnnlJsis:

The statistical analysis here is restricted to data on the three metals cadmium, lead andmereury. All metal eoncentrations were converted to dry weight basis, only data where thiswas possible were used in the analysis. First the data were scrcened, and suspect values whercomited. Valucs bclow detection limit were designated th'e detection limit.

j

Then the data were inspeeted visually. Box-whiskers plot aeross loeations (Fig. 1-3) were uscdto select locations with consistent or occasional above-baekground levels. The results aresUl1UTIarized in the table below:

Overall distribution parameters Stations category according to metallevels:(ppm dry weight):

Min: Max.: Median: Mode: High in general: Occasional high!intermediate:

Cd 0.35 120 1.2 1.2 51,52,56,57,63,65,69 1,2,14,30,71,84

Pb 0.09 460 1.4 1.2 51,52,56,57,63,65,69, 22,25,28,30,79 71,80

Hg 0.02 7 0.08 0.05 1,2,51,52,56,57,63,65, 3,25,30,31,35,69,71,79,80 74,76,82,84,87

On the basis of this table a subset of locations were selectcd for further study. The selection ismarked by bold type in the table, and consists of all high-Ievelloeations and most of theoceasionallintermediate occuring twice in the table. The seleeted locations are (FigA):

1,2,3,30,31,51,52,56,57,63,65,69,71,79,80,84

To get a visual indieation of whether there is a systematic variation across length groups,mean interation plots were produced (Fig. 5-7). The plots show how the mean value variesacross length groups with one curve for each year, in aseparate subplot for each loeation.

The plots do not show a convincing picture of systematievariations with length. Thedifferences between years are as large or larger than the variations across length groups, andthe length variations have various patterns, giving no clear trend. Only a few of the subplotsshow a eonsistent pattern across years. The sampie in length group 2-3 cm for 1990 at loeation56 seems suspicously low and should probably be discarded. For locutions with low-Ievelvalues there is very little variation with length groups. .

Length is not necessarily a sufficient measure of size or age. As Fig. 9 shows, the tissueweight can vary considerably for u given shelllength, and the dry shell weight also varies for agiven length.

An attempt was made to normalize the data by using a combination of physiological variables:mean length, mean shell weight and mean tissue weight. Since these measures are more orless correlated with each other, principal component factors hu.ve been extracted as linear

100

..-----------------------------------------

ANNEX 11

cornbinations of 10g(Iength), log(rnean dry shell wcight) and log(rncan soft tissue wet wcight).This leads to three factors, viz.:

Factor 1 Factor 2 Factor 3

10gloCshelI length) 0.964832 -0.172565 -0.198295

10glQ(dry shell weight) 0.967106 -0.109024 0.229826

10glO(dry tissue weight) 0.958354 0.283752 -0.032289

Proportion of total 0.928212 0.040727 0.031061variance explained

Interpretation: General Size Seasonal state regarding Age? (relative thicknessspawning and feeding? ofshell)(Degree of shell filling)

Below are summarized the within cell regression results of MANCOVA analysis on 10g(Cd),10g(Hg) and 10g(Pb), with sarnpling occasion (Ioeation and date) being used as a singlerandorn faetor, and with the three extracted factors used as linear covariates.

STAT.GENERALMANOVA

Regression results, dependent variable: LOG_PB (myt_fact.sta)Multiple R: .6759972 R-square: .4569722

F(3,88) = 24.68477 P = .00000

Standardvariable

FACTOR1FACTOR2FACTOR3

B-weight.131946

-.083423.113020

Error.025954.048256.049253

beta.609978

-.182452.217130

t(88)5.08381

-1.728772.29468

p-level.000002.087357.024131

STAT.GENERALMANOVA

variable

FACTOR1FACTOR2FACTOR3

Regression results, dependent variable: LOG_HG (myt_fact.sta)Multiple R: .4519799 R-square: .2042858

F(3,88) 7.530826 p = .00015

StandardB-weight Error beta t(88) p-level

.008840 .022430 .057245 .39414 .694434-.133474 .041702 -.408898 -3.20063 .001908

.055079 .042564 .148218 1. 29401 .199049

.oll 0-1.... ..L

STAT.GENERALMANOVA

variableFACTOR1FACTOR2FACTOR3

ANNEX 11

Regression results, dependent variable: LOG_CD (myt_fact.sta)Hultiple R: .4590625 R-square: .2107384

F(3,88) 7.832206 P = .00011

StandardB-weight Error beta t(88) p-level

.049200 .029455 .241613 1. 67031 .098412-.122257 .054765 -.284041 -2.23238 .028128

.103934 .055897 .212113 1.85939 .066313

102

The "B-weights" are the regression coefficients (slopes). It is seen that lead is the metal forwhich the within-cell variation is best described by these three factors (r-squared for lead was0.46 compared to 0.20 and 0.21 for mercury and cadmium respectively). In this tentativeanalysis there was no selection of factors, but simply all were included in the regression.

Figures 9 and 10 compare lead values as function of length group and year for station 57 and63 before and after correction for the physiological factors. It is seen that for these data thecorrection in general brings the values for different length groups closer together, and thusincreases the ability to depict changes in time. However, some of the largest discrepancies(mostly 1987-88) are not reduced significantly; a problem that is likely influenced by therelatively poorer analytical quality prior to 1989. Because of this, the data should possibly bereanalyzed, using only the data from 1989 and later to establish relationships. This needs to belooked into.

Another problem that should be addressed is the fact that the same number for dry weight %has been used to calculate both mean dry weight and metal concentrations on a dry weightbasis for part of the data. If dry weight % values are not accurate this could lead to misleadingresults. (Regressing y/x on f(x).). Perhaps one should use wet weight of tissue instead of dryweight in these cases.

e -

0.1

0.25

1007550

10.75

0.5

;J>zZm~...........

LOCATION

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2 13 15 23 25 27 30 32 36 52 57 65 71 74 77 80 82 84 86 88 92 94 96 98

......

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>zZtrJ~............

VJ-aö'=::lVJ

e

LOCATION

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I I I I I I I i I I' I I I I I I I I I I I I I I I . .

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1 I. I . i I I I i I I I I I I i I I i! I I I I i j ! I I I I I ! i !

1 3 14 22 24 26 28 31 35 51 56 63 69 73 76 79 81 83 85 87 91 93 95 97 992 13 15 23 25 27 30 32 36 52 57 65 71 74 77 80 82 84 86 88 92 94 96 98

LOCATION

106

ANNEX 11

\

"-

--- ..... - ......\\,

\

I

~;II

I,

\1rt E.

Ficr 4 Lo .t>.. catIOn of seleeted mussel stations.

•

ANNEX 11

Plot of Means

Cd (ppm dry weight)

-0-- YEARG- 1:84

.....0-.... YEARG- 2:85

-0-- YEARG- 3:86

'--A--' YEARG_4:87

....•... YEARG- 5:88

........... YEARG- 6:89-- YEARG- 7:90

······4····· YEARG- 8:91

_.-+-- YEARG- 9:92

'--lI--- YEARG- 10:93234

G_16:84

m· .I I

234G_15:80

I i I I II . '1--I .l ~ I I I*"'"*. .-'.:.o;;:~:-=.- I 1

1. Imt++

! I I

I I II I Ie······oI I I

234G_14:79

! I I

J I I

I I I+++

._l. . !~.-.- ... _.-..--~---i

l Li I

234G_13:71

100 --~-+--L-

~.:~10 -i:::-- i !-

I-~.-+---1--

I I

100 r J

10 ----

Fig. 5. Mean interation plots of cadmium concentrations in mussei soft tissue across three sizegroups 2-3 (2),3-4 (3) and 4-5 (4) cm. Station number rs indicated after plot numberG_l to G_16.

1(;7

r-------- ----

ANNEX 11

Plot of Means

Hg (ppm dry weight)

9...... 0 ......9t-' 1I

• rtJ....·:~

I I I

--0-- YEAR •G- 1:84·····0···.. YEAR

G- 2:85--<>-- YEAR

G- 3:86'--A--' YEAR

G_4:87....•... YEAR

G- 5:88......... YEAR

G- 6:89--+- YEAR

G- 7:90 e······4··..- YEAR

G- 8:91-+-- YEAR

G- 9:92...-...-. YEAR

G_10:93

Ll_1I II

Ii

I I~·_.-1 I1iI. I ._~

-f?5i2~"" [---,", .' .. -

I I I

234GJ:52

234G_15:80

·····.1 II ::6"'J"~1i"'~' i -1-I--=-r-- .-

I

I III

I_.e.

I I I

J.~~___~JI . I

10 ~--'----"T""--'

~!---+---1_'~ 1

0.1 -~.;~;~:,;~--=:::i-~~~. , :.:~.:~ i..._..•._..-.

0.1

0.01 L.-.J.-_...l...---l---1

0.01

Fig. 6. Mean interation plots of mercury concentrations in mu~sel soft tissue across three sizegroups 2-3 (2), 3-4 (3) and 4-5 (4) cm. Station numberis indicated after plot number0_1 to 0_16.

iü8

ANNEX 11

Plot of Means

Pb (ppm dry weight)

100

10

,-

L1- .~-, ...... I I

J -m-I .r---r--r- I I I~_...mtl":::::!! -~-, ....•. , I j······o 6

I I I-r I Ii=::~. . .~~-::.

-1-1-'-

-0-- YEARG_1:84

·····0····· YEARG_2:85

-0- YEARG_3:86

._-~--- YEAR.G_4:87

....•... YEARG_5:88

....•..... YEARG_6:89

--- YEARG_7:90

............... YEAR

G_8:91--+_•. YEAR

G_9:92.-+--- YEAR

G_10:93

I II

J I III I I~'-I- ~~. "~~i-

i , I

I LJ-I I I1 I I1

i I

I iI,

I I I

234G3:52

234G_15:80

........ I It ............~........+ ..........I .'I ...j"'---,•..- I I

I ........ i .t

I .I I

234G_14:79

-1.-;-J9 - ~H' I

~I~............... '_. -~:... . ~~-.~-';. - -T . _-~-

_.~ -..-. --U_I .::....-;: ,....::::.,I I I

U-__l-&-_-4- ,.I I .,'........I ,

r1

100 ~j~L _I 1 I J I I10 I I I ITT 1 I I

I I I +····· ..1 1 , , I~

. •• i Q...... 1:]-., = I i1 -I .::-'-:•. ,~ .._- . - +-r-r- --l.---.I-.L

T······ I ······1 I' I I I

Fig.7. Mean interation plots of lead concentrations in musseI softtissue across three sizegroups 2-3 (2),3-4 (3) and 4-5 (4) cm. Station numberis indicated after plot numberG_I to G_16.

1U~

ANNEX 11

-1..c.......0>C(])

CCO(])

~

....--EE-...-

oC\I

o(0

oCO

oo,-

<CI •000

II i 1, I___ ._0 : J I__ . .;

I ~ I

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I : I I I I1 I i I I I I

I 1 1 1 01.00 1I1 II ~<CIO '11 I I

i I <CI I '<CI 10 9~~ I 0 I I I II ~I·---·-J ----o----T-ll-i---1I I 1 !, I ,

I <> 0 . 0 ODJ<CI ! I I I! <>~ ~Oi,'

;I!" <CI I' """~ 0100~TI i

I I I <CI I :1' II! I I <CI I !'" I ' , I! 0: <> <CI! !! 1 I . cJ.aa eo clcacl 0 !! I I 0 <n> '. CoCb 00I ' I~ 0 0 ~ <CI b d, ! I i I 0 I : I. Ii I I I <CI I ! <> iI I ! I ,! I i ~ : 0

1 <CI..~,- ..--.----,----..--1'-.+.--,-j----L--------r- l--;-- ---;---

I 1

1: 'I I 1 i I I I I II ' . I I I 'I' I . ,

! ! I ,. I i'I ! I I !! II , I I . I

! ! i! 10

I I I 1 .

I i I I II I :0! ,

I

coCI)CI)(])~

0>(])~

~

CO(])C

I

CoZ

CD,o,-

(])CI)CI)

:::J

E(]):::J

CO

.......CI)

COoücCO L.()0> ,­(]) (0

~ COo 11Z S(])..c.......Eo~-

C\I ,-00 (0 ~. .00 0

C\I.o

,.-00 (0 ~

'00 0o . .00 0

oC\I"­o.o

(5) M l1l5!aM AlP anSS!l UBaV\j.Fig. 8. The relationship between mean length and mean tissue weight in musseis.

110

ANNEX 11

94939291908988

I I I i i I 0 Lgroup=2

-t r'- 1--- 1------1- : :,I-~~~~~:~------------r--------- ,-----------1,- I ----i-------f---------- j---- ------

I I I I--------- r-- ----- --1-- ------ --------~r-------- -------+---------- ---; -- - --I I' ! I01 0 I------r--- I A ---i---r----t--- ------

-------I!------~----- -t------l------!------1--- -------- ~----- --I , ' i '-_. ... t.. . . ~--- J___ Ai i ,I,I I; ---I------r-----------i------------

-----1-----1------1------1-1----1---t-0.6 ~--~--_L.------L_--.i...-----L_--L----L_----J

86 87

2_: __~~= l=~-=::r__~ __-I_ ~_~=I~=_==:I===~ =-=_ :=~;:~:~1.8

1.6 --------11----------CO I -------- --------r---- -~-------I------

§' ;-: =--=.=:~=r-.-·-t-----[-- __t_-l-==-1 j·_---!-----t--j--J--J----i----- ---

::: ~----[----l_- r --- ------_-1---_---------

86 87 88 89 90 91 92 93 94

YEARA

2.2

2

1.8

1.6Ü

ICO• 0.. 1.4

ICD0 1.2-l

1

0.8

B YEAR

Fig.9. Lead concentrations in mussei from station 57 (Sy;rfjord) as a function of size group 2­3 (2), 3-4 (3) and 4-5 cm (4) and year before (A) and after (B) correction forphyciological factors.

~11

ANNEX 11

94939291

t I I 0 Lgroup=2

----- - - 1- --I - - : :=r;~~~:~----------- -------- ----------- ---1------ ---- r----- -- --- -------- ------1---------- -r---- --------------r-------- ------t----- --.---- -----I------t----

--1---'---- ----+-----j----r~---- -- ------T-- __J----- --------A -------- 1------· --- -I' -- ----

------ ----I----I---A1-------j---+----~----- ----i I I !

I r---t-----r----j---j----------t---------0.6 L-.-~~____L_~~~L_...~~__'_~_ ____.Jl-....._~__'_~~_______.I~~~__'__~~__.J

86 87 88 89 90A

YEAR

2.2

2

1.8

1.6CDa..

1.4I(90-1 1.2

1

0.8

•

9493929190

YEAR

898887

2.2 ,--.-~-....--,-~-~_,_-~~_r_~~-,_._~----.~-~__._-~~_r_~~-.--,I I I iI I I 1 j 0 '_group:::2

2 - ----------1----------- i-- -. ---. --- i ----·---i ----------T -- , - l_group:::3

I I I I i A '_group=4! - I l I ,I I ' i------- ---------1_ -----------------r------ -- .. ----- -------------- -----------1·-·-------------:------- ----- -

_.-----.--r-----~--I--l I ~------I----I i I I I--.----.------- ------I-----------I-----------r--------l----------,---------------t--------

, I I I I j I- ----1- .---.i------ --·T------------T-·-- --.-..-----,,-------- j ---- ---.- T-- -- -- ---

I I ! - ! ~ :. -- -- -- - --- 1----- -- -- -- - -! - - - - -- - - -1--- --- - --- ~ ----.. ---..-- -/.. --- ..--------- -r-- ------------ - -- i -- -- -- - - - -

l!l ,~, I

I j ! t 1 I :------- -. --r------------,---- --·----1- --------- -1--------------1-·-----------r--------- ------.---I, I'!0.6 L-__-'- -L ..l- l.-__---l. --'- ...l.-__--l

86B

1.8

1.60

ICDa.. 1.4

I(90 1.2-1

1

0.8

Fig. 1O.Lead concentrations in mussel from station 63 (Hardangerfjord) as a function of sizegroup 2-3 (2), 3-4 (3) and 4-5 cm (4) and year before (A) and after (B) correction farphycialogical factors.

112

CIEM/WGSAEM94

ANNEX 12

St Jchn's, 1994 April 25-29th

Camparison of statistical tools and means to relate bloamoccurences to other factors

BELIAEFF Benolt, BELIN Catherine and RAFFIN BernardIFREMER, DEL/QM, rue de lilIe d1Yeu, BP 1049, 44037 Nanteseedex 01, Franee

What is abloam?

Adefinition of a blocm is given by Sournia (in !?ress). Thisauthor distinguishes the term of "red tides", whl.eh irnpliesthat algal proliferation'is so intense as to modify theusual appearanee of the sea surfaee as pereeived by thehuman eye, frcm "plankton blocms 11, more vague as these wordsmay irnply or nct the latter as!?eet."Blooms" may be found in the llterature, when speaking of aregular, seasonal growth in ternperate waters (e.g. Sourniaet al., 1987), and on the other hand when speaking of anunusual phenomenon. The former ease is mueh better studiedthan the latter due to its predietable nature: dataeolleetion may be planned. On the other hand, studies onunusual algal blooms are hard to fund beeause they are sounpredietable. The standard j oke : the best way to preventthe reapparenee of a toxie bloom is to fund someone to studyit (Culotta, 1992). In this eontext, data aequisition duringa blocm period might only be feasible in ease of regularevents, unless a monitorl.ng phytoplankton network eoveringthe eoastline with sampling frequeneies suited to usualblocm drnamies exists (See exarnples of data from the FrenehMcnitorlng Network [REPHY] in annex) .

• Algal bloams determi.nism

Regular blocrns in ternperate seas are weIl documented.Vertieal stability of the euphotie zone is often reported asthe key parameter for the eontrol of seasonal variations inphytoplankton populations (Legendre, 1981; Weeks et al.,1993), and nutrients appear to be limiting faetors (e.g.Sieraeki et al., 1993), but do not seem to aet as the basisfaetors of the phytcplankton onset, espeeially fordinoflagellates pcpulations (Lassus et al., 1988).Lassus et al. (1988), Delmas et al. (1992) and Delmas et al.(1993) stressed the major role played by physieal offshoreproeesses to explain blooms of Dinophysls sp. off thesouthern Freneh Atlantie eoast. Aeeording to Lassus et al.(1988), "same seeondary prceesses may aet as promotingfaetors in bays and estuaries, but nutrient levels astriggering faetors are unprcbable". Besides, it is to be

113

noted in this study the absence of a significant correlationwith simple parameters (temperature, salinity, N03, etc.).Actually, it seems that bloom chronological data cannot beconsidered as similarly weighted along temporal axes:initiation is the crit~cal phase in bloom dynarnics. We havethe feelin~ that once favorable physical conditions arereached, w~th no nutrients limitat~on, nothing could stop abloom unless climatological conditions become desastrous,for instance. As Beltrami & Cos~er (1993) wrote, bloom has acertain inertia, requiring the ~nteraction of favorableconditions for a threshold to be reached that triggers theonset of anomalous growth. However once triggered, the bloomis refractory for a time and can be sustained even if theconditions which caused it abate. This point is essential tobe noted to understand potential failures of statisticalmethods.

Methods

Not a method alone can answer to all questions related to analgal bloom. We divided i t into method families, which maynot be regarded as chronol~ical steps in a bloom analysis,but as answers to some part~cular questions:

- Temporal detection of a bloom: univariate ormultivariate time-series seamentation.

- Reduction of great multIdimensional data tables:ordination techniques.

- Periodicities detection: spectral analysis.- Prediction: regression analysis.

Segmentation

Determining homogenous periods in a chronological seriesallows to select periods choosen to calculate correlationsbetween phytoplankton and "environrnental" data or moregenerally to confoud time decomposition between biological •and environrnental descriptors. Cornelius & Reynolds (1991)emphasized the need of segmentation methods to elucidate thestructure and function of ecological boundaries.

The Cumulative Function (CF) method (Ibanez, 1993) allows a~artition of an univariate time-series. It simply consists~n constructing the cumulative function from theobservations, by successively adding the differences betweenan observation and a reference value (generally the mean ofthe entire series). Results brought by this so-easy-to-useCF method are:

- detection of great variations of·the mean level,- determination of hcmogenous periods,- estimation of homogenous intervals means.

Moreover, correlations mar be calculated between biologicaland environmental cumulat~ve functions, the significance ofwhich is tested using a randomization procedure.

•

•

Ibanez (1984) proposed the lY index to identify anobservation (observations-vector) significantly differentfrom the n preceding observations in a multivariate(phytoplar:kton spec:l;es) chronologi<;:al series and gave a meanto detenmne an opt~mal temporal w~ndow corresponding to themagnitude of n; this last procedure is called the auto-lYfunction (Ibanez, 1976) and is analogous to anautocorrelation function under the lY Mahalanobis metric.Contrary to CF, this method uses all the infonnationavailable in the phytoplankton cormnmity, which seernsreasonable consider~ng the various biological interactionsand the phytoplankto~c succession. It allows detection of"extraordinary" events during the phytoplanktonic seasonalevolution.

The chronological clustering method (Legendre et al., 1985)describes disjunctions during an ecological succession,contained in a multi-taxa chronological series. Rapidlyresurned, the different steps involved in the method are:

- computation of a (samples x samples) distance matrix,- clustering of samples with the time contiguity

constraint,- performance of an aposteriori randomization test to

verify the validity of clustering,- removal of singletons.

This last step allows the elimination of "aberrant"observations, e.g. corresponding to temporary shifts ofwater masses at a fixed station in a aquatic ecosystem.Those extreme variabilities may perturb the data series inan unpredictable and non significant manner.The exce~ted result of the use of this method is a nonhierarch~cal partition of the series into non overlappinghomogenous groups, which may represent the ste~s of theecological succession. The authors present an ~nteresting

comparison of the chronol?$ical clustering with ordinationmethods. A key point in th~s context is that the latter onesdo not give criteria for assigning samples to groups,contrary to the former which prov~des clear even ifarbitrary rules.

A complement of segmentation methods may be found inCornelius and Reynolds (1991). The split moving-windowboundary analysis is presented by these authors along withtwo methods of temporal discontinuities statisticalsignificance.

Ordination techniques

Ordination consists of ~lotting n points (observations) in aspace of fewer than p dimensions (where p is the number ofvariables) in such a way that most of the important featuresof the p-dimensionnal pattern are retained (Pielou in Gould,~986). It helps in determining the major components ofvariation in a large data set. According to Greig-Smith et

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116

al. and Mackas & Sefton (in Gould, 1986) these techniquesare more appropriate when there arelow levels of variationand when the changes between samples are gradual, notdisjunct; this may forbidden the use of these techniques todescribe a sudden onset of phytoplankton growth like analgal bloom.

Principal component analysis (PCA) seems to be the most usedordination technique for the description of data set underour concern. Geometrically, the principal component axes,allowing a better visualization, result of the rotation ofthe original coordinate system to select a new onerepresenting the directions with maximum variability. PCAtransforms the original correlated variables intoorthogonally rotated uncorrelated variables.According to Matta & Marshall (1984), interpretation ofpatterns, using PCA, is quite difficult if several majorsources of variation are present and PCA may be efficient toselect subset of data which will be useful ln subsequentanalysis. The author recomnands to use this method when dataare collected from a small geographie area or from a narrowspectrwn of time. Thus a suggestion is to remove the long­term temporal variation prior to the detection of strongseasonal and geographical patterns in phytoplanktonpopulations.

Matthews et al. (1991) found correspondence analysis (CA) tobe superior to PCA for detecting large-scale ~adients, likespatial stratification and seasonal chan~es, lnphytoplankton data. CA consists in descrlbing a contingencytable (sI?ecies x environmental variables, both underdisjunctlve coding) . A cell in this table corresponds to thenumber of times that a taxa belongs to same abundance class,simultaneously within a particular environmental descriptorcategory at the same date.Using CA Ryckaert et al. (1987) described the main features •of the annual changes in a phytoplankton ccmmmity dominatedby diatoms. Advantage of CA are non negligible: use ofquantitative or qualitative variables or both and itsability to study non-linear relationships betweendescriptors (contrary to PCA) are the major ones. Drawbacksare a chronological succession not explicitly taken intoaccount by the analysis and the necessity of descri~tors

categorization to determine frequencies ln the contlngencytable. This last point could be considered as an attractiveresult, too: there is a need of pertinent thresholds in suchstudies.

Regression analysis

Multiple linear regression (MLR) was used as a predictivetool by several authors (e.g. OUchi A., 1982; OUchi et al.,1983). Matta & Marshall (l984) criticized the use ofregression techniques: "regression of individual species on

•

•

environmental parameters [ ... ] involves a false assumption,i.e. that the response is linear and monotonie". Moreover,to explain a single phytoplankton speeies drnamies withouttaking into aeeount possible inter-speeies lnteraetions maylead to ininterpretable results: red tide is not a simpleconcept of a blocm of a primary producer, bur rather aspecial event in natural phytoplankton suceession. Moreover,it is predietible that a model eonstrueted for a set of datawould reveal itself a bad predictor with further set of dataeolleeted on the same loeation.

Contrary to MLR, canonical correlation (CC) is a techniqueused for studying interrelationships between two set ofvariables. It extends simple correlation for relating twovariables and multiple eorrelation for relating a singlevariable to a group of variables (Gould et al., 1986). ceconsists in finding linear eornbinations of the two set ofthe ori$inal variables (weights are called canonicaleoeffic~ents), such that the simple eorrelation between thetransformed variables is maximum. The major benefit is theassessment of relationships between sets of of variables ofecologieal interest, without disregarding information oninterrelationships within the response set. On the otherhand, onee more, it cannot deteet non-linear relationships,and canonical coeffieients values are sensitive tomultieollinearity (high degree of eorrelation betweenindependent variables), sampling size and measurement error.Many applications of CC may be found in the literature (e.g.Munawar & Wilson, 1978; Varis 0., 1991; Gould et al., 1986).

To deal with cbvious non linear relationships betweenpatterns of phytoplankton dynamies and drastie wind-indueedwater äotions, Millet & Cecehi (1992) used the alternatingeonditional expeetation (ACE) algorithm, deseribed elsewhere(Breiman & Friedman, 1985). ACE Computes optimaltransformations for multiple regressions of eeologiealparameters. The dependent variable and all predictorvariables are replaeed by funetions to maximize thecorrelation coefficient ln the linear model; ACE algoritbmconverges toward a single solution that is e~irieally

defined and does not require previous assumpt~ons coneerningpatterns of distribution. This method allows an objectivedetermination of thresholds for environmental deseriptors,whieh could be regarded as triggering parameters.

Spectral analysis

A key point in the use of speetral analysis is that itrequ~res a great nurnber of data equally sI?aeed. Le$endre etale (1985) noted that this method along w~th techn~quessI?eeifieally designed for the identification of cycles intlme or space data series, such as periodograms andeorrelograms are not relevant to the study of succession

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118

since any constant periodicity is clearly hypothesized otherthan the trivial annual cycle.Spectral analysis was used to estirnate plankton patches size(Platt et al., 1970; Mackas & Boyd, 1979) or more generallyto study plankton distribution at different spatial scales(Platt, 1972). Coherence analysis provided mean to correlatedistribution of the phytoplanktonic and environmentaldescriptors (Platt et al., 1970; Demers et al., 1979).As suggested by Platt & Denman (1975), the variable ofinterest may show simultaneous fluctuations at manyfreauencies, through dynamic interaction with otherosc{llating components of the system. Thus, with semi­continuous record, spectral analysis may be the adeguatetechnique to deco~ose the data record to discover ~ts

constituent period~cities. It agrees with Gould et al.(1993) when they underline that one must be aware of thedifferent frequencies in'a quantitative signal when applying •analytical techniques to help discern patterns in the data.

Conclusion

To statistically relate a bloom to environmental factors isall but a narrow field of theoretical investigations. Use ofsegmentation techniques, for either univariate or rathermultivariate chronological series allows objective detectionof blooms. Non-linear relations, co-linearity betweenexplicative variables, poor s~lin$" designs constitutedifficulties for the use of ordinat~on techniques andregressions. To be fully exploited, spectral analysis areasking a ~eat number of data.Due to ep~sodic physical forcing, a bloom rnay be seen of aseries of discontinuous bloom events within various watermasses rather than a single event (Weeks et al., 1993;Sieracki et al., 1993). This makes questionable a samplingdesign based on data collection at a single point. A betterunderstanding of bloom dynarnics is tributary of a consequent •spatial grid at different scales.Helps in understanding relationships between biological andphysical factors rnay come from the use of numerical modelswh~ch are able to s~mulate bloom modification in front of anexternal factor intervention (Beltrami & Cosper, 1993;Asciotti et al., 1993; Gallegos et al., 1992). See also aninteresting attempt of a typological study of red tidesphenomenon or "qualitative" modelling in Seliger (1993).

•

References

Ascioti F.A., Beltrami E., Carroll T.O. and C. Wirick, 1993.Is there chaos in plankton dynarnics? J. Plank. Res., 15:603-617.

Beltrami E. and E. Cosper, 1993. Modelling the temporaldynamics of unusual blooms. In: "Toxic Phytoplankton Bloomsin the Sea", T.J. Smayda and Y. Shimizu (eds.) , ElsevierScience Publishers, pp. 731-735.

Breiman L. and J.H. Friedman, 1985. Estimating optimaltransformations for multiple regression and correlation. J.Am. Stat. Assac., 80: 580-619.

Cornelius J.M. and J.F. Reynolds, 1991. On detennining thestatistical significance·of discontinuities within ordered

4t ecological data. Ecology, 72: 2057-2070.

Culotta E., 1992. Red menace in the world's aceans. Science,257: 1476-1477.

Delmas D., Herbland A. and S.Y. MaestrinL 1992.Environmental conditions which lead to increase in celldensity of the toxic dinoflagellates Dincphysis spp. innutrient-rich and nutrient-PQOr waters of the FrenchAtlantic coast. Mar. Ecol. Prog. Ser., 89: 53-61.

Delmas D. Herbland A. and S.Y. Maestrini, 1993. DaDinophysis spp. come from the "open sea" along the FrenchAtlantlc coast? In: "Toxic Phytoplankton Blooms in the Sea",T.J. Smayda and Y. Shimizu (eds.), Elsevier SciencePublishers, pp. 489-494.

Demers S., Lafleur S.P.E., Legendre L. and C.L. Trump, 1979.Short-tenn covariability of chlorophyll and terrperature inthe St. Lawrence Estuary. J. Fish. Res. Board can., 36:568-573.

Gallegas C.L., Jordan T.E., and D.L. Correll, 1992. Event­scale response of phytoplankton to watershed inputs in asubestuary: timing, magnitude and location of blooms.Lirnnol. Oceanogr., 37: 813-828.

Gould R.W. Jr., Balmori E.R. and G.A. Fryxell, 1986.Multivariate statistics applied to phytoplankton data fromtwo Gulf Strearn wann core rings. Limnol. Oceanogr., 31: 951­968.

Ibanez F., 1984. Sur la segmentation des serieschronologiques planctoniques multivariables. OCeanologicaActa, 7: 481-491.

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Ibanez F., Fromentin J.-F. and J. CasteI, 1993. Applicationde la methode des sorrmes cumulees a l'analyse des serieschronologiques oceanographiques. CRAS/Sciences de la Vie,316: 745-748.

Lassus P., Bardouil M., Berthome J. - P., Maggi P., Truquet P.and L. Le Dean, 1988. Seasonal occurrence of Dinophysis sp.along the French coast between 1983 and 1987. Aquat. LivingResour., 1: 155-164.

Legendre L., 1981. Le contrrle physique de la ~roductionphyto~lanctonique a 8chelle courte et interm8diaire.Oceanls, 7: 119-129.

Legendre P., Dallot S. and L. Legendre, 1985. Succession ofspecies within a comrnunity: chronological clustering, withapplications to marine and freshwater zooplankton. Am. Nat.,125: 257-288. 4tMackas D.L. and C.M. Boyd, 1979. Spectral analysis ofzooplankton spatial heterogeneity. Science, 204: 62-64.

Matthews R.A., Matthews G.B. and W.J. Ehinger, 1991.Classification and ordination of limnological data: acomparison tools. Ecological model1ing, 53: 167-187.

Matta J.F. and H.G. Marshall, 1984. A multivariate analysisof phytoplankton assemblages in the western North Atlantic.J. planke Res., 6: 664-675.

Millet B. and Cecchi P., 1992. Wind-induced hydrodynamiccontrol of the phytoplankton biomass in a lagoon ecosystem.Limnol. OCeanogr., 37: 140-146.

Munawar M. and J.B. Wilson, 1978. Phytoplankton-zooplanktonassociations in lake superior: a statistical approach. J.Great Lakes Res., 4: 497-504. •

Ouchi A., 1982. Prediction of red tide occurence by means ofmultiple linear regression model. Bull. Jap. Soc. Sci.Fish., 48: 1245-1250.

Ouchi A., Kusuki Y. and H. Takayama, 1983. Multipleregression equations of diatom red tides and clustering ofobservation area. Bull. Jap. Soc. Sei. Fish., 49: 867-873.

Platt T., 1972. Lecal phytoplankton abundance andturbulence. Deep Sea Research 11, 19: 183-187.

Platt T. and K.L. Denrnan, 1975. Spectral analysis inecology. Annual Review of Ecology and Systematics, 6: 189­210.

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Platt T., Dickie L.M. and R.W. Trites, 1970. Spatialheterogeneity of phytoplankton in a near-shore environment.J. Fish. Res. Board Can., 27: 1453-1473.

Ryckaert M., Gros P. and E. Erard-Le Denn, 1983. Successionsaisonniere des populations phytoplanctoniques des eauxc6tieres de la Manche. Oceanologica Acta, Proceedings 17thEuropean Marine Biology Symposium, Brest, France, 27September-1 October, 1982, 171-175.

Seliger H.H., 1993. Red tide mechanisms: spatial andterrporal scales. In: "Toxic Phytoplankton Blooms in theSea", T. J. Smayda and Y. Shimizu (eds.), Elsevier SciencePublishers, pp. 819-824.

Sieracki M.E., Verity P.G. and D.K. Stoecker, 1993. Planktoncommunity response to sequential silicate and nitratedpletion during the 1989 North Atlantic spring bloom. DeepSea Research II, 40: 213-225.

Sournia A. (in press). Red tide and toxic marinephytoplankton of the world ocean: an inquiry intobiodiversity. Paper submitted for the proceedings of the 6thinmational conference on toxic phytoplankton, Nantes, 1993October 18-22.

Sournia A., Birrien J. -L., Douville J. -L., Klein B. and M.Viollier, 1987. A daily study of the diatom spring bloom atRoscoff (France) in 1985. I. The spring bloom within theannual cycle. Estuarine, Coastal and Shelf Science, 25: 355­367.

Varis 0., 1991. A canonical approach to diagnostic andpredictive modelling of phytoplankton communities. Arch.Hydrobioi., 122: 147-166 .

Watanabe M., 1983. The modelling of red tide blooms. In:"Application of Ecological Modelling in EnvironmentalManagement", Joergensen S. E. (ed.) , Dev. Environ. Modelling,pp 421-454.

Weeks A., Conte M.H., Harris R.P., Bedo A., Bellan I.,Burkill P. H., Edwards E. S., Harbour D. S., Kennedy H. ,LlewellYn C., Mantoura R. F.C., Morales C. E., Pomroy A. J. andC.M. Turley, 1993. The physical and chemical environment andchanges in community structure associated with bloomevolution: the Joint Global Flux Study North Atlantic BloomExperiment. Deep Sea Research II, 40: 347-368.

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ANNEX I3

Spatial Analysis of Trace Metal Concentrations in North Sea Sediment

William G. WarrenSeience Branch

Dept. of Fisheries and OceansP.O. Box 566;, St. John's, NF

Canada AIC 5XI

SUMMARY

Spatial interpolation by means of kriging is illustrated for the concentrations of several tracemetals in North Sea sediment. The underlying methodology is briefly outlined; more emphasis isgiven to the nature of choices that have to be made in carrying out the analysis than to the theoryper se; for example, s1:J.ould one attempt to allow for drift in the mean, should the data betransformed, should aIl the data be used or only the data at locations in the neighbourhood of thepoint of interpolation? Comparisons of these options are made on some data sets; for the most •part, the results appear little affected by the option chosen.

Introduction

Various methods have been developed for mapping the density or amount of a material ororganism throughout a region, based on data obtained at point locations, or what are effectivelypoint locations, within the region. Kriging is one such method. While the collection of techniquesknown as kriging first achieved prominence in mining applications, the methodology has recentlybecome a focus of attention in marine and fisheries science. Although it has been used for theestimation of abundance and the mapping of several fish stocks, it would appear better suited forrelatively sedentary species such as crab and shellish; indeed, its viability with the more mobilespecies is cIearly questionable. However, the mapping of concentrations of metals in marinesediment is more akin to the initial application in mining. Thus, following an outline of themethodology, this report will describe the application of kriging to interpolate, and hence map, theconcentrations of several trace metals in sediment in the North Sea.

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Methodology

Let Z(s) be the trace metal concentration at a point s in the region of interest; s can beindentified by coordinates corresponding to latitude and longitude. Z(s) is regarded as arealization of some underlying stochastic process such that E[Z(s)] = j.L, andVar[Z(s + h) - Z(s)] = 2/(h), that is, the expeeted value (or the average over all possiblerealizations) of Z(s) is the same at all points in the region, and the variance of the differencebetween the concentrations at two locations is a function solely of the distance, h, between thelocations. The function feh) is known as the (semi)variogram.

Suppose that concentrations are measured at locations S1, S2, ... , Sn and it is wished to estimatethe concentration at some unsampled location, So. Suppose also that the estimate is

n

2(so) = L AiZ(Si)'i=l

Indeed. in most interpolation methods the estimate will be of this form, Le. a weighted average ofthe concentrations at the sampled locations. (A simple special case has the estimate as Z(Sj)where where Sj is the sampIe location that is dosest to so). In kriging the weights, .Ai are chosen soas to minimize the mean square prediction error, E[(Z(so) - Z(sO))2], that is the expected value(ar average over all possible realizations) of the square of the difference of the actual (hutunknown) concentration and the estimated concentration. Thus, if the assumptions of the previous

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paragraph hold then, in this sense, 2(so) is an optimal estimator of Z(so). The (minimized) meansquare prediction error, denoted by I1"k (so) can also be calculated.

'Ne will not here go into the detail of how the Ai and I1"I;(SO) are obtained, other than toremark that they are readily obtained from the variogram, l(h). The key step in the process is,therefore, the construction and estimation of l(h).

The dassical estimator of the variogram is

where N(h) is the set of location pairs (Si, Sj) such that the distance between Si and Sj is handIN(h)1 is the number of distinct pairs in N(h). In practice, unless the sampie locations have beenaccurately gridded, h must be interpreted as a distance döSs, i.e. all h between h - 8/2 andh + 8/2 where 8 is the dass width. A IJlore robust (to contamanation by outliers) but less intuitiveestimator is given by

i(h) = ~ [IN~h)1 L IZ(si) _ Z(SjW/2] 2/(OA5i+OA94/IN(h)l)N(h)

(Hawkins and Cressie 1984). This latter, with distance dasses, was used in the examples thatfollow.

Ideally the "Hh) so calculated will fall, apart from random fluctuations, on a smooth curve.The next step is the to fit an appropriate functional form the i(h). The so-called spherical model

,(h) =0, h =0,

= Co + c.(3/2 - (1/2)(h/a)2)h/a, 0< h :s a,

= Co + c., h ::::: a,

is often satisfactory and, along with the linear model

l(h) =0, h=O,= Co + blh, h > 0,

has been used for the examples of this report. The quantity Co is referred to as the nugget; Co + c.is known as the sill and a as the range. Note that concentrations at locations at distances greaterthan the range are mutually independent or uncorrelated.

For estimating the parameters of ,(h) we have chosen to use weighted least squares with theweights proportional to the IN(h) I, i.e. to calculate the Co, c. and a (or Co and bl ) so as tominimize I:i wi[,(h;) - .:y(hi)F. With the IN(h;)1 being variable, and relatively small for thesmallest distance dass, this strategy would appear to be better than unweighted least squares.Further refinement to generalized least squares or the robust estimator

appears to offer no particular advantage in the examples that follow, particularly in relation to theextra effort needed in their calculation.

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

Data

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

The trace metal data available consist of the concentrations in sediment of several metalssampled in 1990/91 at several hundred sites in the North Sea and English Channel. These datacan be grouped by contributing country with most being provided by the Uni ted Kingdom andNorway. There is little overlap in the areas covered by each country; for this reason and others thatfollow, spatial analyses were undertaken separately for the data from each of these two countries.A cursory examination of the U.K. data set indicated that the spatial properties of the EnglishChannel component differed noticeably from those of the North Sea data. The English Channeldata, specifically from sites south of 51°N, also made up only a relatively small part of the U.K.data and were, therefore, excluded from the spatial analysis, as were a few scattered sites north of56.5° and a single site east of 3.5°E. A further complication arises from some of the Norwegiansites being in fjords. It is understood that each of these was in proximity to a point source, such asa smelter; the concentrations were, in general, considerably greater than those in the remainder ofthe data base. Accordingly these sites, north of 600 N and east of 5.8°E, were also omitted.

For the Norwegian data there were usually two observations for each site; there are a fewinstances of three observations or a single observation. The differences between eoneentrations at asite can be regarded as measurement error. The U.K. data have a single observation at each site;accordingly no direct estimate of measurement error is then possible. (This has an impact on theestimation of the variogram and subsequent interpolation. Kriging has been described as an exactinterpolator in that the estimate at data location is the observation at that loeation. IIowever, inthe presence of (known) measurement error, it may be preferable to allow for the fact that themeasured concentration is subject to measurement error and thus obtain a "smoothed" estimatethat is more eonsistent with the estimates at neighbouring points. For a full discussion see Cressie1991, Section 3.2.1).

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The sites of the U.K. data are located more or less as a rectangular grid but with two griddensities, the higher density being towards the U.K. coastline, and the lower density, atapproximately double the mesh size, further off shore. In contrast, the Norwegian data sites havethe appearence of being randomly loeated with highly variable intersite distanees. There aresubregions eontaining several data sites and others, of comparable size, devoid of such sites. Thesedifferences in sampling procedure work against any attempt at a combined spatial analysis of theU.K. and Norwegian data. Added to this is the fact that different laboratories were involved in thechemieal analysis, giving rise to the possibility of interlaboratory differences.

Of the trace metals for which there are sufficient sites to warrant spatial analysis, the U.K. and •Norwegian data sets have four in common, namely aluminium, chromium, lead and zine. Inaddition, the U.K. data set contains a reasonably large number of sites with iron eoncentrations,and likewise the Norwegian data set contains sites with eopper and nickel concentartions. Thegeographie distribution of metals in sediment is usually found to reflect strongly the distribution offine-grained material. The need for normalization of whole sediment analytical data to reduce oreliminate the influence of differences in grain size has been clearly established within ICES.Accordingly, the concentrations of all metals have been normalized to aluminium (ICES 1993).(Only a relatively small proportion of the data in the available data base had been normalized forfines per se).

Implemcntation

In theory, .2'(so) is a weighted average of the concentrations at all sampie locations. Inprinciple, its calculation involves the inversion of an (n +1) x (n +1) matrb: where n is the numberof data loeations. Large values of n may make this eomputationally prohibative. The estimate is,however, infiuenced predominantly by the observations at near locations with little weight beinggiven to obervations at the more distant loeations, particularly at distances greater than the range.

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Accordingly, it is customary to define a kriging neighbourhood, i.e. a region about the location atwhich estimation is desired, with the es timate formed as a weighted average of concentrations atdata locations solely within the neighbourhood. In Cressie's (1991 p.159) example, interpolation isat the node of a grid at which no observation was made, but with observations at the surroundingnoues. In such circumstances it is easy to define neighbourhoods that contain the same number ofdata locations for each node at which estimation is being undertaken. While, for the U.K. data theobservations to some extent fall on a grid, the mesh size changes and the locations of the Norwegiandata are irregularly dispersed. In these circumstances two strategies seem available, (i) define aneighbourhood with respect to distance from point of prediction, or (ii) for a specified integer k,use up to the kth observation locations nearest to the point of prediction. In the examples here amodification of (i) was employed. The neighbourhood was taken to be ±do of latitude and ±2do oflongitude from the point of predietion. (At the latitudes involved, 10 of longitude corresponds toapproximately one half the distance of 10 oflatitude). The difference between using suchneighbourhoods and using all data locations was examined for chromium concentrations of boththe U.K. and Norwegian data. In the remaining CasC3 all uata uata locations were used.

In constructing the variograms, the dass width for distance was taken as 0.1 0 of latitude (6nm) for the U.K. data and 0.20 of latitude (12 nm) for the Norwegian data. The reason for thedifferent dass widths is that the Norwegian data contain approximately one quarter the number ofdata locations as the U.K., but spread over something like twice the area. For fitting thevariogram, the first 26 points were used for the U.K. data and the first 16 points for the Norwegiandata. These choices comply approximately with the recommendation of Journel and IIuijbregts(1978) that the fit should be only up to half the maximum possible lag and one should use onlylags for which IN(hj)1 > 30.

A linear variogram, ,(h) =Co + bzh can arise when, instead of E[Z(s)] =J.1. throughout theregion, the process contains "drift". For example, as a simple alternative, one might assume thatthe process mean changes linearly with latitude and/or longitude, i.e.E(Z(s)] =J.1.(s) =ao + allt + a2lg where lt and 19 denote latitude and longitude, respectively. Inthe presence of drift, extensions of the method, namely universal kriging and IRF-kriging (IntrinsicRandom Functions of order k) are available. These are not without difficulty. A simplisticapproach is to assurne a functional form for the drift, as that above, start with an ordinaryleast-squares estimates of the parameters and construct a variogram from the residuals. Thecovariances so obtained can be used to obtain generalized least squares estimates of the regressionparameters and, thence, a variogram constructed from the new residuals. The process can berepeated until convergence. In theory, the results would still contain some bias but, for reasonablylarge n, the bias should be negligible. In some of the examples below this approach was followedand the results compared with those obtained by using a linear variogramj the estimates after thesecond iteration differed negligibly from those after the first.

In some cases the variogram based on the actual concentrations appeared to be adverselyaffected by one, or sometimes two, seemingly outlying concentrations. A closer examination of thedistribution of concentrations suggests that such concentrations were not so much outliers butobservations from the tail of a positively skewed distribution. The variogram based on thelogarithms of the concentrations may then turn out to have a better-defined form. One could theninterpolate the logarithms of the concentrations, however the antilogarithms (or exponentials) ofthe values give biased estimates of the concentrations themselves. An adjustment to remove thebias can be applied, however, if ,*(h) denotes the variogram of the logged data, then thevariogram of the actual data is given by

,(h) = ]([1- exp(-,*(h))]

where ]( is a constant, i.e. does not depend on h. Although ]( could be estimated, one can, infact, use 1- exp(-,*(h)) for ,(h); the Aj in L:j AjZ(Sj) are unaffected by the value of J{. Thisavoids the problem of backtransformation and gives the interpolated values of Figs. MA, M.5 and

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M.11. lIowever, a value of J{ is needed for estimation of the kriging errors. These have not beenealculated but their pattern should be sirnilar to those obtained for the other metals.

For the U.K. data, interpolation was made at the eentre of rectangles of dimension 0.25° oflatitiude and 0.5° of longitude from 51°N to 56°N and from 2.5°W to 3.5°E (land massesexcluded). For the Norwegian data, interpolation was sirnilarly made from 55.25°N to 61.25°N andfrom OOE to 12°E (land masses and the Kattegat south of 53°N excluded).

Results

In this section the results obtained for the several several eombinations of metal and region areoutlined. Explanations for the observed behaviour are given in the Diseussion Section that follows.

1. Aluminium - U.K. Data.

The estimated variogram is plotted in Fig. 1. There is no evidence of a flattening off, or sill,even when lags greater than 156 nm a~e plotted. Thus a linear variogram was fitted. This led to •the interpolated eoneentrations of Fig. :\1.1 and kriging errors of Fig. E.l.

Under the assumption that the linear nature of the variogram was due to drift, theconeentrations were regressed on latitude and longitude. The eoeffieient of determination forregression was R2 = 35%, and the regression parameters indicated an increase in eoneentrationfrom south to north and a decrease from west to east.

The variogram based on the regression residuals in given in Fig. 1a. A spherieal model wasfitted with the range estimated as approximately 52 nm. The resulting interpolated eoncentrationvalues are mapped in Fig. M.1a and the kriging errors (0"1;(8)) in Fig. E.1a.

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With the possible exception of cells along the boundary, the differenees between Fig. M.1 andM.1a are ineonsequential. The kriging errors appear very stable over the region, but increasesomewhat along the boundary. They are also a shade greater in that part of the region with thelarger mesh size for the grid of data loeations. It might be thought that, since the regression onlatitude and longitude has aeeounted for 35% of the original varianee and the residual variogramhas a sill, whereas that of the data per se appears unbounded, the kriging errors based on theformer should be less than those of the latter. This, however, turns out to be not always the ease.

2. U.K. - Zine (normalized to aluminium).

The variogram construeted from the data per se is indieative of a drift in E[Z(8)]. Accordingly,the coneentrations were regressed on latitude and longitude (R2 = 0.26) and a variogrameonstructed from the regression residuals (Fig. 3). The estimated regression parameters indieate adecrease in (normalized) coneentration from south to north and from east to west which is reflectedin the interpolated values (Fig. 1\1.2). The estimated nugget of the fitted spherieal variogram (Fig.2) is relatively large with respect to the estimated sill (56.5%) although the first point of theempirical variogram is considerably less than this. However only 14 distances go into thecalculation of this point (cf. the minimum of 30 reeommended by Journel and I1uijbregts, 1978) soit reeeives little weight in the least squares estimation of ,(h). The variogram suggests thatstructure comes principally from the drift and what is left is not far removed from random noise.

The kriging errors (Fig. E.2) show essentially the same pattern as for aluminium; this isexpected since their pattern, but not their magnitude, depends primarily on the spatialdistribution of the data locations No comparison with estimates based on the variogram of the rawdata was attempted.

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3. U.K. - Chromium (normalized to aluminium).

The variogram eonstructed from the aetual eoneentration suggests that the spherieal modelwould be appropriate (range 58 nm), (Fig. 3); unlike aluminium and zine, there is no evidenee ofdrift. The interpolated eoneentrations are given in Fig. 1\1.3.

The kriging errors (Fig. E.3) show a pattern similar to that of aluminium and zine, althoughthe patterns for aluminium and zine are, if anything, more similar to eaeh other. This likely stemsfrom there being fewer data loeations for ehromium (253) than for zine and aluminium, for whiehthe sampie loeations were exaetly the same (275).

In this ease, interpolated eoneentrations were also obtained through use of a krigingneighbourhood with d = 1.0° of latitude (60 nm), i.e. approximately the range of the variogram.The eoneentrations are given in Fig. 1\1.3a and the kriging errors in Fig. E.3a. With the exeeptionof the easternmost boundary of the region, the interpolated eoneentrations are virtually unaffeetedby the use of the kriging neighbourhoo.d, while the kriging errors are inereased almostimpereeptibly.

4. U.K. - Lead (normalized to aluminium).

This is a ease where the variogram based on the aetual eoneentrations (not presented) appearsto be adversely affected by, in partieular, one seemingly outlying·eoneentration. The variogrambased on the logarithms of the eoneentrations turns out to have a well-defined spherieal form(range 68 nm), (Fig. 4).

The proeedure deseribed in the previous seetion was employed and resulted in the interpolatedvalues of Fig. :\1..t. For the reason given above, kriging errors were not ealculated.

5. U.K. - Iron (normalized to aluminium).

As with lead, the distribution of eoneentrations appeared strongly positively skewed.Aeeordingly the same proeedure was followedj the variogram based on the logarithm of theeonecntrations is given in Fig. 5. Thc form of the variogram is not weil definedj this is likely aeonsequenee of there being eonsiderably fewer data loeations (118) for iron than for the othermetals. Nevertheless, there is no evidence of a sill; thus a linear variogram was fitted .

The interpolated eoneentrations are given in Fig. :\1.5. The drift that produeed the linearvariogram is very dear, eoncentrations deereasing from south to north and from west to east. Theemployment of residuals from a regression of coneentration on latitude and longitude was not hereattempted.

6. Norway - Aluminium.

As with the U.K. aluminium data, the variogram based on the raw data appears to inereaselinearly with the distanee, evcn at distanees greater than 192 nm. (Fig.6) however there isevidenee of a sill in the variogram eonstructed from the residuals of the regression on latitude andlongitude (R2 = 0.49, Fig. i.), here supported by residual variogram estimates at distanees greaterthan 192 nm, although the range is estimated as elose to 200 nm.

The interpolated eoncentrations are given in Figs. M.6 and M.6a based on the raw data andregression residual variograms, respeetively, with the kriging errors in Figs. E.6 and E.6a. For themost part the differences beween J\1.6 and M.6a would be regarded as ineonsequental; there are,however, some subregions where the interpolated values differ more markedly than in othersubregions. Also, the kriging errors in E.6 are universally, and sometimes substantially, greater

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than those of E.6a.

7. Norway - Zine (normalized to aluminium).

A linear variogram is indieated by the raw data (Fig. 7) and is here used to obtain theinterpolated concentrations (Fig. :M.7) and the kriging errors (Fig. E.i). The north-south andeast-west drifts are apparent (Fig. 1\1.7). Indeed, a variogram eonstrueted from the regressionresiduals (not presented) seems not far removed from pure nugget, i.e. ICh) = co. In other words,excluding random noise, virtuaBy aB the spatial strueture is embodied in the drift. Theinterpolated concentrations would then be given simply by the estimated regression on latitudeand longitude.

8. Norway - Chromium (normalized to aluminium).

The variogram is not weB defined; it is possible, however, for a spherical modd to be fitted(Fig. 8) to the raw data. The first point of the empirical variogram appears to be on outlier but isbased on only 6 pairs of data loeations and, thus, reeeives little weight in the fitting of the model. •The range is estimated as e. 77 nm. The interpolated concentrations and kriging errors are givenin Figs. M.8 anti E.8, respectively.

This is the other case where interpolated concentrations and kriging errors were also obtainedby using a kriging neighbourhood with, here, d = 1.250 of latitude (or 75 nm), againapproximately equal to the range of the variogram. The resulting eoncentrations are given in Figs.1\1.8a and E.8a. Unlike the situation with U.K. chromium, although the general pattern is similar,the are subregions where the concentration differences are noticeably greater than in othersubregions. It is noted that the kriging errors are always greater, although sometimes not muchgreater, when the neighbourhood is used.

9. Norway - Lead (normalized to aluminium).

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Again the variogram is not weil defined but a spherical model can be fitted to the raw data(Fig. 9) (range 100 nm). (Definition of the variogram was not improved by taking logarithms).The interpolated concentrations and kriging errors are given in Figs. M.9 and E.9, respectively.

10. Norway - Copper (normalized to aluminium).

The raw-data variogram is not weB defined but (including data from distances greater than192 nm) a linear model was judged preferable to a spherical model (Fig 10). The interpolatedconcentrations and kriging errors are given in Figs. ;\1.10 and E.10, respeetively. North-south andeast-west drifts are clearly indicated. The variogram based on the regression residuals (R2 = 0.35)was constructed and is also not wel! defined and could, possibly, be interpreted as pure nugget(-y(h) = co); nevertheless a spherieal model (range 25 nm) was fitted (Fig. 10a). The interpolatedconcentrations and kriging errors are given in Figs. 1\I.10a and E.I0a, respectively. Although thepatterns of concentration are similar there are some substantial differences in the estimated values.The kriging errors are sometimes less, sometimes greater.

11. Norway - Nickel (normalized to aluminium).

llecause of the presence of outliers, or perhaps a highly skew distribution of concentrations,the data werc logarithmically transformed for construction of the variogram. The same proeedureas for U.K. iron was used, the variogram appearing to the linear. (Fig. 11). The interpolatedconcentratons are given in Fig. M.12.

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Comparisons in the Common Subregion.

There is a small overlap in the U.K. and ;'{orwegian regions over which interpolation has beenperformed, namely the area from 55.25°~ to 56°N and from ODE to 3.5°E. Accordingly, it is ofinterest to see how well the estimates agree within this area for each of the four metals in common.\Vithin the area, the estimates are not very well correlated, however averaged over the area thedifferences in the concentrations of chromium and lead are about 5% and 3%, respectiveIy, theNorewgian values being lower. For aluminium, the estimates from the Norwegian data averageabout 14% more than those from the U.K. data. For zinc the difference is about 34% but thissomewhat inflated since in each case the values are amongst the lowest obtained for the region andthe absolute difference is relatively small. Given that these differences are small in relation to therange of concentrations throughout the whole of the two regions, and that that the area is in thecorner of each region, so that the estimation is, perhaps, more like extrapolation thaninterpolation, the level of agreement ill, perhaps, reasonable. On the other hand, the possibility ofinterlaboratory differences cannot be completely discounted.

Discussion

1. General.

The concentration maps speak for themselves. In most cases one sees concentrations decliningas one moves further from the coast. For the Norwegian data the higher concentrations are, ingeneral, along the coast from Bergen to Stavanger and in the Skagerrak and Kattegat. For theU.K. data the higher concentrations tend to be along the coast from the IIumber to the Tyne andin the Thames Estuary.

As noted above, the key to geostatistical analysis is the construction of the variogram (giventhat the underlying stochastic-process model is reasonable). The variograms are, in general,considerably better defined for the U.K. than the Norwegian data. This is due in part to theregular rather than random disposition of the data, but also to there being far more data locationswith the U.K. data (with the exception of iron, in excess of 250, whereas for the Norwegian data,the number of distinct locations is of the order of 60). It has been suggested (R. Webster, pers.comm.) that a minimum of 150 locations is necessary for kriging to be viable. The estimates areconditional on the choice of variogram. With the possible exception of iron, for which there wereonly 118 data locations, it would appear that reasonable confidence can be placed in the variogramsconstructed from the U.K. data, particularly in the the more critical lower end. The same cannotbe said of those constructed from the Norwegian data. This is not to denigrate the Norwegian database; it does have the merit of replicated measurements at most locations, thus permitting directestimation of the measurement error. Nevertheless, in relation to the concentrations, the krigingerrors are substantially greater than those obtained from the U.K. data, and, given the cost ofchemical analysis, from a geostatistical viewpont it would seem preferable to have increased,perhaps doubled, the number of data locations. To obtain information on the measur'ement error,replicate analyses of a small subset of locations could still have been undertaken.

2. Allowing for Drift.

The effect of attempting to remove the drift by basing the variogram on the residuals of theregression of concentration on latitude and longHude was examined for aluminium with both theU.K. and Norwegian data, and for copper with solely the Norwegian data. When compared withestimates obtained using the variogram based on the data per se, the effect on the estimatedaluminium concentrations was inconsequential for the U.K. data but for only subregions of theNorwegian data. To account for this, it is noted that at any interpolation location which is at adistance more than the range of the variogram from all data Iocations, the interpolated value isthe same weighted average of the measured concentrations. As noted above, because of the

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seemingly random selection of Norwegian sampie locations, there are relatively large subregionsthat are void of data locations; this does not happen within the U.K. region because the datalocations occur at the nodes of a regular grid. When the regression residuals are used, the weightedaverage of the concentrations is replaced by the weighted average of the residuals (which, ingeneral should be not far removed from zero) added to the concentration predicted by theregression on latitude and longitude. Thus, at Norwegian locations weIl removed from datalocations, when the raw data are used the estimated value will tcnd towards the common weightedaverage of the concentrations, but towards the concentration predicted by the regression when theregression residuals are used. These two estimates will, in general, differ especially as one movestowards the boundary of the region. On the other hand, the estimates at sites nearer to datalocations will be dominated by the concentrations (or residuals) at those locations, so that itshould make little difference whether the raw data or regression residuals were used.

The difTerences between the two set of estimates appear more pronounced for the Norwegiancopper data. This may retate, in part, to the variograms being rather poor~y defined, but it shouldalso be noted that, if the variogram were pure nugget (-y(h) = co), the estimate would be theaverage of the concentrations or, in the case of regression residuals, exactly the regression-predicted •value. Since the variogram based on the residuals is elose to being pure nugget, one might expectsomething akin to this to occur, and the differences to be more exaggerated.

The kriging errors based on the rcsiduals are not always less than those based on the raw data;indeed, in these examples, there is a tendency for them to be greater. This sterns, at least in part,from the fact that, although for the larger h the fitted ,(h) based on the raw data is greater thanthat based on the residuals, this is not necessarily the case for the smaller values of h, i.e. for themore critical part of the variogram. [Also, O'f(so) is of the form Li >'n(h;) + m, and, while,(hi ) ::::: 0 there is no restrietion that all Ai and m have to be positive]. Whether the kriging errorbased on the residuals is greater or less than that based on the raw data depends on the variogramand how the point for interpolation is placed in relation to the data locations. In the examples,even for the Norwegian copper, the differences do not appear to be of great importance.

3. Use of Kriging Neighbourhood.

The effect of using a kriging neighbourhood rather than all data locations was examined forthe U.K. and i'J'orwegian chromium data In both cases the kriging neighbourhood was taken as arectangle with length of each side equal, approximately, to the range of the variogram (60 and 75nm, respectively). However, because of the disparity in the density of data locations, the number •of data locations in the kriging neighbourhoods ranged from 16 to 135 for the U.K. data but from

. only 3 to 20 for the Norwegian data. Because of this and the fact that the U.K. data locations fallessentially at the nodes of a rectangular grid, the diffences between the two sets of estimatedconcentrations are here, with the possible expection of some locations near the boundary of theregion, negligible. For the same reason, the kriging variances are almost imperceptibly increased.\Vith the Norwegian data, however, there are again subregions where the differences are noticeable.Recall that at sites more distant from the data locations the estimate will tend towards a weightedaverage of all data or, if a kriging neighbourhhod is used, to a weighted average of theconcentrations of those locations in the neighbourhood. At some locations the latter weightedaverage will coincide (or be elose to) the former, at other locations it may differ substantially. Inother words, where data is sparse, under one strategy, the estimate will tend towards somethinglike the overall mean, under the other, to something like the mean of the values at the nearer datalocations. \Vhere data is not sparse, there will be little if any difference. The increase in thekriging errors due to the use of these neighbourhoods is, naturally, greater than for the U.K. databut, from a practical viewpont, of little consequence.

There can be considerable difference between the computational effort of the two strategies.When all data locations are used, only one matrix inversion is needed, although the matrix is

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generally of large dimension so that the inversion may take several minutes of C.P. U. time, even onthe most modern computers. On the other hand, the use of a kriging neighbourhood requires amatrix inversion for each interpolation location. [The case where each interpolation location issimilarly placed in relation to its neighbours is exeluded]. Since the time required for matrixinversion increases exponentially with dimension, if the kriging neighbourhood is sufficiently smalI,it is possible for the C.P.U. time required by the latter strategy to be less than that required bythe former. IIowever, as the kriging neighbourhood increases in size, the C.P.U. time increasesrapidly and will quickly exceed that needed by the single large inversion.

4. Transformations.

Variograms using the logarithmically transformed data were used for U.K. lead, U.K. iron andNorwegian nickel. In these cases the variograms constructed from the raw data were distorted bywhat at first appeared to be atypically large concentrations. A eloser examination suggested thatthese large values resulted frorü the distributions of concentrations being positively skew and, inthis sense, they were not outliers (or a~ypical). Logarithmic transformation resulted in betterdefined variograrns. (Logarithmic transformation of the Norwegian lead data did not, however,give any notable improvement - the analysis was, therefore, based on the raw data). Estirnates soobtained would have to be backtransformed. To avoid this, the variogram on the logarithmic scalewas backtransformed. Estimation is then simpler but kriging errors cannot be obtained withoutadditional work.

Conclusions

To sum up: kriging is but one method of spatial interpolationj unlikeO most other methods itcomes with a measure of precision, the kriging error. Application to sets of trace metalconcentrations in North Sea sediment appears to yield meaningful maps. Kriging works best whenthe data are located on a regular grid. There should also be a sufficient number of data locationsjat least 150 has been recommended. The U.K. data (apart) from iron, meet this criterion, theNorwegian data do not, and this is reflected in the lack of definition of the constructed variograms.

Ineluded in the assumptions is the one that the expected value of the concentration is thesame throughout the region. For most metals this assumption is elearly violated, with, forexample, concentrations decreasing and one moves outwards from the coastline. Nevertheless,simple kriging seems fairly robust against the viol~tion of this assumption. Attempting to allow fordrift in the mean by using the residuals from the regression of concentration on latitude andlongitude, for the most part gives estimates that differ inconsequentially from those of simplekriging. Some differences do occur where data locations are sparsej if one believes that theregression on latitude and longitude is viable then, perhaps, the estimates based on the regressionresiduals should be prefered.

Likewise, the use of a kriging neighbourhood for the most part yields estimates that differinconsequentially from those based on the complete data set. In terms of computing time, thelatter would usually be preferable (at least with the type of data encountered in this study). Againdifferences again occur where data locations are sparse. It is then a matter of whether one feelsthat something approaching the overall mean is more realistic for at such a site than somethingapproaching the mean of the concentrations of the nearer sampie locations, although these may betoo distant to have much bearing, at least theoretically, on the value at the point of interest.

The is no doubt that transforming the data can sometimes result in better definition of thevariogram. There is, however, "no free lunch". There is a price to be paid in either the compexityof back transformation or the sacrificing of the estimation of the kriging error.

Kriging, therefore, is not, nor should be, a "black box". Subjective decisions have to be made;

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fortunately, the results are often little affected. But there are exceptions, and the user should becognizant or the reasons for these, and choose his/her options and make his/her inferencesaccordingly.

In conclusion, it should be noted that we have here chosen to illustate point kriging, i.e.interpolate values at the centres of rectangles covering the region of interest. It is also possible toestimate the average concentrations over these (or other) rectangles, this is known as block kriging.

Acknowledgements

I wish to express my thanks to, initially. Simon Wilson and, subsequently, Marilynn S~rensen

for extracting the appropriate data from the ICES records.

References

Cressie, N.A.C. 1991. Statistics for Spc;tial Data. J. Wiley, New York, NY.

Hawkins, D.M. and Cressie, N.A.C. 1984. Robust kriging- a proposal. J. Int. Assoc. Math. Geol.16:3-18.

Journel, A.G. and Huijbregts, C.J. 1978. Mining Geostatistics. Academic Press, New York, NY.

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APPENDIX

Estimated parameters of variograms and, when applicable, the regression of concentration oflatitude and longitude.

1. U.K. - Aluminium.Linear variogram: Co = 0.0014452, bl = 0.0018419.Regression: ao = -0.65343, al = 0.159121, a2 = -0.027847.Spherical variogram: Co = 0.0012681, Cl = 0.0020156, a = 0.8625.

2. U.K. - Zinc.Regression: ao = 20.82436, al = -0.35929, a2 = -0.23872.Spherical variogram: Co = 0.14450, Cl = 0.11113, a = 1.81606.

3. U.K. - Chromium.Spherical variogram: Co = 0.06436, Cl = 0.13006, a = 0.96406 .

4. U.K. - Lead (logarithmically transformed).Spherical variogram: Co = 0.07533, Cl = 0.11022, a = 1.12969.

5. U.K. - Iron (logarithmically transformed).Linear variogram: Co = 0.14883, bl = 0.10396.

6. Norway - Aluminium.Linear variogram: Co = 0.0024465, b1 = 0.012430.Regression: ao =-1.92887, al = 0.036424, a2 = 0.035201.Spherical variogram: Co = 0.0057392, Cl = 0.024682, a = 3.38125.

7. Norway - Zinc.Linear variogram: Co = 0.17916, bl = 0.21051.

8. Norway - Chromium.Spherical variogram: Co = 0.08644, Cl = 0.12284, == 1.2875.

9. Norway - Lead .Spherical variogram: Co = 0.02731, Cl = 0.033358, a = 1.64609.

10. Norway - Copper.Linear variogram: Co = 0.009534, bl = 0.005153.Regression: ao = -2.78957, al = 0.051472, a2 = 0.023074.Spherical variogram: Co = 0.006395, Cl = 0.090822, a = 0.41562.

11. Norway - Nickel (logarithmically transformed).Linear variogram: Co = 0.10981, b1 = 0.11393.

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_{E:

- .

-1---fL- -.L

.L

---v:1{

r---

1- -

I-r=l

Fig. 10atopper Concentrations

Spherical Variogram(Regression Residuals)

-l-L

-~ -.I.- -

-I- ...

J

.,t.... -t-t-t-t-t

i7 ~__--I--

I-

- - ... - -t-II-t--H

+-If-+-t-t-t-t- - - - -f­

-f- -

-~ ...- - - - -1-1-- ... I- ...- -I-- - - -I- - -I-- -I-- ... ... -I- - -1--1-1-- -1--1-- - - -I-- -1--

•

ANNEX 14

An exploratory graphieal display for the analysis of covariance

Jaap van der Meer

Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, The Netherlands

Introduction

The linear relationship between a variable ofinterest and a covariate may differ among the levels

of some factor. For example, the relationship between copper coneentration in eod muscle and the

length of the fish may differ from year to year. That is, the model

Yjt = at + bt Xjt + e,

cannot, generally, be simplified to either

Yjt = at + b Xjt + e,

nor to .

Yjt = a + b Xjt + e,

where j indieates an individual observation, t the level of some factor, and e is IIND(0,s2). The

• F-tests for testing these models against eaeh other are usually referred to as the analysis of

covariance (ANCOVA). Generally, therefore, differences among the levels cannot be expressed

by differences in a single figure, such as, for example, the trend over years in length adjusted

copper concentration. At eaeh level two figures, i. e. the intercept and the slope of the regression

line, are needed to summarize what is going on.

This note provides a simple exploratory graphical tool to present differences (in time) among

linear regression lines.

141

Graphical Methods for Exploring Changes in Slopes

Hitherto two methods have been used. The first method plots all regression lines in a single plot

(Fig. 1). The second one plots both at and bt (or at+bt and at-bt) versus t (Fig. 2). Here it is

proposed to plot at against bt, where at and bt are now the estimated parameters from

(Yjt - }jt) = at + bt (Xjt - Xjt) + e,

where italics indicate the overall mean (Fig. 3). Note that for each point on the x-axis, it holds that

at = O. In other words the x-axis represents all regression lines far which an observation at the

average level ofthe covariate, x = x (a fish ofaverage length), has an average value ofthe variable

ofinterest (average concentration), that is Y = Y. •

Similarly, lines of average concentration level can be drawn for large fish, e.g. fish of

length x + 2 Sx, and for small fish of length x - 2 Sx, where Sx is the sampie standard deviation of

fish length. These lines follow

at + bt 2 Sx = 0,

and

at - bt 2 Sx = 0,

respectively.

The scaling ofboth axis is a point of concern, and will be considered in the next future.

Table 1. Hypothetical data, estimated regression coefficients

•

1·:J 2

number

at

bt

oo

2

o-1

3

2

4

o1

5

-2

1

•

•Figure 2

1 II I

! ! I: I I! I I

(lihi) I

I I!II

Figure I

I I !

I I

IUl1

+-hH+tnmT-~I II I I

I I I I

I I I I I I II I I~ I I jI !! ,

143

Figure 3

•

•

I ,

'JJ I_~=' ..~_. .1::- - _ .I I

I - 1 I 11-- I -li!. I 1 I 'I -i. I . I !

I-LJLW~~~-t-17zr--ltrt!jI ~~;--°

1

\1 ! \I i : iI 1 ! I

, I , I j, 1

! I -

I II I I

j I I iI I 1 i ! II I I I i I

1

I MI1 1

11 i I

I

11

I Ii Ii

•

•

ANNEX 15

Same notes of the intercalibration of two methods, measuringch1orobiphenyls (PCBs).

Anders Bignert, Swedish Museum of Natural History

IntroductionIn the end of the 1980s the determination of organochlorineschanged from gas chromatography analysis based on packedcolurms tO,analyses based on capillary colurms. Hence theconcentrat~ons of PCBs analysed by the two methods are notdirectly corrparable. The packed colurm was used up to 1988when the analysis using the capillary colurm started. Inorder to intercalibrate the two methods, both methods wereused on 12 herring sarrples, corrprising 10-20 individualanalyses each, and one serie of guillemot eggs comprising 11individual analyses, also coo, dab and flounder have beenanalysed with both methods but only for one year, sofar.

When the packed colurm method is used, the concentration ofthe total sum of the PCBs is estimated through the sum offorteen peaks each contaning one to several PCB-congenerswhere as the capillary method estimates the concentration ofseven selected congeners(CE-28, CE-52, CE-lOl, CB-118, CB­138, CB-153 , CB-180), according to an lCES recommendation.

The chemical analysis of organochlorines follows the methoddescribed by Jensen, Reutergardh and Jansson, 1983 forpacked colurm. and (REF) for capillary colurm and wasperformed at the Laboratory for Analytical EnvironmentalChemistry at the Institute for Applied EnvironmentalResearch, Stockholm University and at the Special AnalyticalLaboratory at the Swedish Museum of Natural History.

Resul t and discussionThe sPCB from packed column and the sum of the sevenselected congeners showed a strong relation (r2>.90 in mostcases) within-year but the slopes differed between years(Fig .1a, lb). Furthermore, the proportion of variouscongeners varied depending on the S1.lffi (Fig 2). It could alsobe expected that small peaks, using the packed column, wouldfall below the detection limit and hence lead to an underestimation of the total sum of PCB, when it becomes low.

To overcome this problem, one of the major peaks (PCB-10)from the packed colurm and the major congener in that peak,CB-138 were selected in the subsequent intercalibration.

It soon turned out that the peak that was thought to containonly CB-138 was not pure but contained also CB-163. It wasalso shown that PCB-10 contained not only CB-138 and CB-163but also an unknown component. The amount of that

145

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

constituent was fairly stable between years but varied tosome extent between the investigated regions. Figure 3 givessome examples of regression lines (forced through origo)indicating the proportion of the unknown constituent forherring samples from various years and sites, see also table1 for a sunmery. The variation between years were consideredsmall in comparison with the ordinary between-yearvariation. Hence, by estimating the proportion of theunknown constituent (the deviation of the slope from 1) forthe various regions and adjusting for this, the timeseriesof the new method could be added to the old ones.

i4~

ConclusionsIt is important to deposit resources for intercalibrationex.ercises when new methods are' introduced. Not only for oneyear at one site. •

•

Table 1. The correlation between determination of p~s using packed collumn andcapillary collumn. The coefficient of determination (r ) and % deviation between the twomethods are given.

Species/locality..,

% deviationseason year n r-

HerringHarufjärden autumn 1987 10 0.998 30

1989 9 0.991 231991 7 0.998 25

Ängskärsklubb autumQ 1989 20 0.991 161991 6 0.999 32

spring 1989 25 0.971 21

• Landsor! autumn 1987 10 0.996 381991 6 0.997 29

UtIängan autumn 1991 15 0.993 29spring 1987 10 0.998 33

1990 6 0.995 33

Fladen autumn 1991 5 0.995 26

GuillemotStora Karlsä spring 1989 11 0.994 25

•

147

Fig 1b sPCB (mg/kg l.w.) packad kolonn. regression mot summan av Sju ca kapillar kolonn.

•

+

t.ll + +

StrOmming.Ängsk .• B94.0 r2- .91 lt

l) - 1.9

20~----:"--:'-----~2-----3~---

6

StrOmming. Ängsk •• B88 r2-.91 lt

l) - 1.9

3.11

t.O L..-.----...-;:------:;-:------:r-::---.8 1.2 1.6

2.11

3.0

2.0

+

Stromming.Harufj •• B9r2-.61 11

b - 1.0

t.ll

+

I +++.5 ~.O::----"'i-.•::----"'i-=.8:----'Ti..-=2:----1'T'.-=6-

t.O

2.0

.32

.20

2 II StrOmming. Haruf j .• 88. r2-.89 lt +

b - 2.4

.16 '----..<:..,...-----..------,..- --,,.--.24

.2.

.29

Fig 1<tsPCB (mg/kg 1.M.) packad kolonn. regression mot summan av Sju CB kaoillar kolonn.

StrOmm1ng. Ängsk •• B9 Str •• Lands .. 8B Str., Kar lSk •• 88 Torsk. Gatl., 8Br2-.9<4 11 3.0 r2-.98 11 r2-.91 lt r2-.97 ,.l) - 2.3 b - 3.1

/3.0 l) - 2.9 5 b - 2.<4

2.5 •2.542.5

2.02.0 3 +

I2.0

t.llt.ll 2

t.O t.llt.O

.ll .ll t.O 0.. .5 . 8 1.0 t.2 t •• .0 .2 .. .6 .8 .. .5 .8 1.0 .0 .ll 1.0 t.ll 2.0

+8

Skrutltla. vaderO.8Br2-.97 ,.tl - 1.5

/2/1812

5andsk •• Fladen. 88r2-.96 lt

tl - 1.3

t5+

TarSk.Flaoen.88r2-.96 ,.b - 2.1

2

1&11

Sill. Flaoen. 88r2-.99 11b - 2.4

t.O

t.ll

2.0

.0 L--o-:---'r-:---:---:--:, 0 L..-._....... __...--.0 .2 .4 .8 .8 1.0 0 2:1

.j.-~.ß.24

p..l-

~-ri~ ~.PCB-10 from packed co lumn (NSL/RSL) vs CB-13B from cap i llary co lumn (NSL).Regression line forced through origo.

.0 I'.----,-----r----..--_.8 1.0.6.4.2.0

Karlskrona 88 (NSL)b=1.86(+-46%) *

.4

.0 1'.---,---,.----,..--..,.-----..-

.6

.B

.2

1.0/

.3.2. 1

Utlängan 88 (NSL)b=1.50(+33%) *

.0

. 1

.2

.3

.0 1'.-----,-----.-----,---.3.2. 1.0

Landsort 88 (NSL)b=1.57 (+36%) *

. 1

.2

.3

.05 I'.---,.----r---.----r---.6.4.2

Kar 1skrona 90 (RSL)b=l. -48 (+33%) *

.0

.2

.0 1'.----,----,.-----.----

.4

.6

.00 .05 . 10 . 15 .20 .25 .30

Ut 1ängan 91 (RSL).30 b = 1 . -4 1 (+ 2 9%) *

. 00 I'.---r--~--,--_.----,r___.

.25

.20

.15

.10

.05

•.25.20.15.10

Landsort 91 (RSL)b= 1 .41 (+29%) *

.20

.10

.25

.15

Dia - 93.12.20 12:06

ANNEX 16

Wcricing Paper WGSAEM St John's 1994

A Note on Bias in the EMS from the 3-Point Running Mean Smoother

Mike Nieholson and Rob Fryer

Introduction

The 3-point nmning mean smoother was adopted for the JMG/OSPARCOM 1993

assessment of eontaminant trends in fish and shellfish. As noted by Nieholson cl al (1994),

this smoother eould be recommended in being easy to eompute, easy to understand. and

for short time series typical of the JMG assessments, in giving similar results 10 those from

other smoothers and methods of analysis.

• However, as noted by Agge (pers. eomm.), estimates of the errar mean square from this

smoother will tend to be inflated when there is a trend. Here we assess the extent of this

inflation, and examine the implieations for tests of significanee and their power.

Inflation of the EMS

Figure la shows the mean EMS as a funetion of the annual trend increment on a log seale

when the number of years, T, is 5 or 10. The true underlying between-year variation was

estimated at 0.52 on a log seale. This value was taken from the 1993 JMG assessment of

mereury in musseIs for data submitted by Norway. The EMS becomes progressively more

inflated as the trend inerement increases, and more so when T is smaller. Figure Ib shows

• a similar pieture when the annual increment follows a triangular pattern, increasing for the

first half of the series and then decreasing by the same amount for the second half.

Although the estimate of the residual varianee is biased using this smoother, the bias is

smaII for trends of 10% per year.

For eomparison, Figures le and d show the eorresponding estimates obtained when the

systematic between-year signal is estimated by a quadratic. We see that. as would be

expected, with an underlying linear trend the EMS is unbiased. With the triangular pattern

151

152

however, there is a bias in the EMS whieh incrcases with the annual signal, OOt is similar

for T=5 and T=lO.

Power of the Statistical Test of the Smoother.

Figures 2a-d show the power of the two procedures with the two between-year patterns

for T=5 and 10. The test is whether the smoother explains signifieantly more than the

mean in Figures 2a,b, and whether the quadratie explains more than the mean in Figures 2c

and d. Generally, the power of the smoother is slightly less than that of the quadratie with

the exception of the curves for T=5 in Figures 2a and 2c. This is because with T=5, there

is aetually only 1 degree of freedom for the smoother, and hence the sum of squares due

to the linear trend is divided by 1 instead of 2 in the case of the quadratie. We also see that

the size of the tests is slightly greater than 5% with the smoother, and that with a

triangular between-year pattern, with T=5, the inflation in EMS is greater than any

increase in the effect, and the power decreases with inereasing annual increment

For the tests of the two sub-hypotheses (where the smoother is partitioned into a linear

and non-linear component) it is easy to see what the effect on the test of linearity will 00.

Tho choice of smoother will not affect the estimate of the sum of squares due to a linear

trend. However, with increasing annual increment, tho test will 00 affccted by the bias in

the estimate of the error mean square if this is used as the denominator in the test. Hence

the tcst will tend to be conservative, and the power reduced. This decrease in power will

00 moderate if there is a linear trend with annual increments in the range 0 - 0.1.

The cffect on the test of the non-linear component will be more complex.

References

Nieholson M.D., Fryer RJ. and LarscnJ.R. (1994) A robust method for analysing

contaminant trend monitoring data. Draft TIMES document submitted to WGSAEM.

•

•

Figure 1a Figure 1b0.34

0.34

0.320.32

0.3CI) 0.3:E CI)

w :::!:0.28 w

0.28 •••.-11 ••11

026.... •••••••• 0.26 • ••••11· .. ••• w·

0.24 0.240 0.1 0.2 0.3 0.4 0.5 0 0.1 02 0.3 0.4 0.5

Annuallncrement • UnearT-.5 Annual Increment • Triangular T,...... ·UnearT,.10 ......Triangular T,.

Figure 1c Figure 1d0.34 0.34

0.32 0.32

0.3 0.3CI) CI)

:::!: ::::Ew w

0.28 028

0.26 0.26

024 0.24

0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5

Annuallncrement --+-Unear T=5 Annuallncrement --+-Triangular T-.5• __UnearT,.10 _TriangularT,.10

153

Figure 2a Figure 2b1 ......... 1

0.9 .' 0.9, ,0.8 • 0.8 .-,.0.7

.0.7 .'.

Ja .,

!0.6 ... 0.6 ,.

G>0.5 ~ 0.5 ..'

Q.0.4 Q.

0.4,,.

0.3 0.3 ,.'0.2 0.2

..'

0.1 0.1.....' •0 0

0 0.1 02 0.3 0.4 0.5 0 0.1 02 0.3 0.4 0.5

Annual Increment • UnearTe5 Annuallncrement • TrianguJar T-S......UnearT=10 ..... 'TriangularT-10

Figure 2c Figura 2d

1 ............ 1. 0.90.9 ,.• .80.8 . 0.8 .'.• 0.7 .' ,0.7 .. 0.6 .0.6 . I

,.~ . 0.5 ,•~ 0.5 JII .

Q. 0.4 •Q.0.4

,. .'0.3. 0.3. ..

0.2 • 0.2 JIII. ....0.1

,.0.1

0 0

0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 •Annual Increment • UnearT=5 Annual Increment • Triangular T=5- - ... 'UnearT=10 ......TrianguJar T-10

i~4

•

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

ANNEX 17

Working paper tor WGSAEM 1994

Analysis of variance tahles fOl' the new I'obust method of assessing contaminant trendmonitoring data

Rob Fryer and Mike Nicholson

IntroductiOll

A new, robust method has been proposed for assessing temporal trends in contaminantmonitoring data (Nicholson ef al., 1994) and was used in the 1993 11\10 assessments oftemporal trends in contaminant levels in biota.

The analysis essentially consists of the following stages:• obtain the median log-concentration each year• app1y a smoother to the median log-concentrations to summarise systematic variation incontaminant levels over time• test whether there are any systematic trends and whether they are linear.

When there is evidence of a length effect on contaminant levels:• divide the observations into SMALL and LARGE fish• obtain the median log-concentration of both SMALL and LARGE fish each year• apply a smoother to the median SMALL and LARGE log-concentrations• test for systematic trends in time• compare the SMALL and LARGE trends.

The 1MO assessments used a three-point moving average smoother, essentially for ease ofimplementation in the SAS statistica1 language. Nicholson el al. (1994) describe tests tortemporal trends and Iength effects in terms of the three-point moving average, but point outthat other smoothers, such as a lowess smoother or a smoothing spline (Hastie andTibshirani, 1990), would generally be preferred.

Here, we present analysis 01' variance tables for a general linear smoother. We first considerthe case when there is no length effecL Although this is standard - fuH details can be foundin Hastie and Tibshirani (1990, p66) - it allows us to define some notation and set the scenefor what comes later. We then consider the case when observations are divided into SMALL

and LARGE fish; this is more complicated, because we assume that SMALL and LARGE

contaminant levels are correlated within-years.

An example is presented using a lowess smoother.

i55

156

Analysis of variance - no length effect

NOlation

Consider a contaminant time series collected in years Y/l I = 1. .. T. Let c = (Cl' ••• , CT)' bethe time series of median log-concentrations.

Assume that

where• f = (fty,), ... , .10'7)' represents smooth systematic changes in contaminant levels overtime• the errors E, are independent and normally distributed with zero mean and constantvariance rJ-. eAlinear smoother applied to the median log-concentrations c can be represented by a Tx Tsmoother matrix S (Hastie and Tibshirani, 1990), in the sense that the fitted (smoothed)values are given by Sc. In a similar way, the linear regression of c on year can berepresented by a Tx T matrix L.

Let K be the Tx T matrix with elements Kif = 1fT and let I be the Tx T identity matrix.

For any square matrix A, let RA = (I - A)'(I - A), l'A = tr(2A - A' A) = T - tr(RA) andv(A) = {tr(A)}2 I tr(A2

), where tr(·) dellOtes the trace of a matrix.

The residual sum of squares from fitting the smoother to c is then given by c'Rsc. Similarly,the residual sum of squares from the linear regression of c on year is c'RLc. The sums ofsquares about the sampie mean are given by c/RKc.

•Pseudo analysis nf variance lable

TIME effect: do contaminant levels vary with time?

Linear effect: does log-concentration vary linearly with time?Non-linear effect: does log-concentration vary non-linearly with time?

Residual

Analysis 0/ variance lable

The analysis of variance table below hasslightly more information than usual:• df is the degrees of freedom for a particular effect; this is obtained from a two momentcorrection as described in Appendix A or in Hastie and Tibshirani (1990)• SSQ is the sum of squares for a particular effect• 'Y is the divisor required to obtain the mean sum 01' squares; 'Y = df in a linear model• MSQ is the mean sum of squares given by SSQ / l' (not shown below because it does notadd anything hefe)• E(MSQ) is the expected mean sums of squares, assUl11ing that the smoother gives anunbiased estimate of f.

Effect df SSQ 'Y E(MSQ)

TIME v(R" - Rs) c'(R" - Rs)c 1'5 - 1 <J1 + f'R"f/(1's - 1)

linear I c'(Rn: - RJc I er + f' (Rn: - RJfnon-linear v(RL - Rs) c'(RL - Rs)c 'Ys - 2 er + f'R1l!('Ys - 2)

residual v(Rs) c'Rsc T - 'Ys er

To test for a particular effect, we refer the statistic

•

SSQ[e;!fec/] /1'[l1!ec/]F = -::-::--=---::-:---:---:-'---=---=-

SSQ[residual] / 'Y[residual]

to an Fdf[effcctJ. df[residuill] distribution.

MSQ[effec/]MSQ[residual]

157

Analysis of variance - length effect

More noTation

Let s = (SI> ••• , 57)" I = (11) .•• , IT)' be the time series of median SMALL and LARGE log­concentrations respectively.

Assume that

5, = h(Y,) + Es, + 0,I, = J;(y) + Eil + 01

where• fs = (fs(YI), ... ,!,(Y7) , f, = (ft(Yl) , ... ,!t(YT) represent smooth systematic changes in SMALL

and LARGE contaminant levels over time,• the errors Es" Eil are independent and normally distributed with zero mean and variance cl,• the errors 0, are independent and normally distributed with zero mean and variance -r-.The 01 model correlations between SMALL and LARGE contaminant levels within-years.

Note that previously (eg Fryer and Nicholson, 1993), we have modelIed contaminant levelsin terms of random within-year variation and random between-year variation. Here, the 0,represent random between-year variation that is common to both small and large fish. TheEsp Eil represent both random within-year variation and any random between-year variationthat is specijic to Si\1ALL and LARGE fish respectively.

Let• c. = (I - s)tV2 measure the difference between SMALL and LARGE contaminant levels overtime• c+ = (I + s)tV2 measure the average effect of SMALL and LARGE contaminant levels overtime.Similarly, define f. = (f, - OtV2, f+ = (fl + fs)tV2.

158

•

•

Pseudo analysis of mriance fable

What general statements can we make if SMALL and LARGE contaminant levels vary in thesame way with time?

TIME effect: do contaminant levels vary with time?

Linear effect: does log-concentration vary linearly with time?Non-linear effect: does log-concentration vary non-linearly with time?

Residual

Are there any length effects?

LENGTH effect: are SMALL and LARGE contaminant levels the same?

TIME.LENGTH interaction: do SMALL and LARGE contaminant levels change in the same wayover time?

Residual

If SMALL and LARGE contaminant levels vary in different ways with time, what can we sayabout SMALL contaminant levels and what can we say about LARGE contaminant levels?

SMALL fish

TIME effeCl: do SMALL contaminant levels vary \Vith time?

Linear effect: do SMALL log-concentrations vary linearly with time?Non-linear effect: do SMALL log-concentrations vary non-linearly with time?

LARGE fish

TIME effect: do LARGE contaminant levels vary with time?

Linear effect: do LARGE log-concentrations vary linearly with time?Non-linear effect: do LARGE log-concentrations vary non-linearly with time?

Residual

159

Analysis 0/ variance fable

Effect df SSQ E(MSQ)

TIME v(RK - Rs) C/(RK - Rs)c+ 'Ys - I er + 272+ f/RKf+/('Ys-I)

linear 1 c+ ' (RK- R()c+ 1 er + 272 + f/(RK-RJf+non-linear v(R(. - Rs) c+' (RL - Rs)c+ 'Ys - 2 er + 272+ f/RLf+/('Ys-2)

residual 1 veRs) c+'Rsc+ T - 'Ys er + 272

LENGTH 1TIME.LENGTH v(RK- Rs)

residual 2

c.'(I - RJc.c.' (RK- Rs)c.

c.'Rsc. T - 'Ys

er + C' (I - RJf.er + f.'RKf./('Ys - 1) •

160

SMALL v(RK - Rs) s'(RK - Rs)s 'Ys - 1 er + 72 + fs'RKf/('Ys - 1)

linear 1 s/(RK- RJs 1 er + 72 + f:(RK- RJfsnon-linear v(R(. - Rs) s'(RL - Rs)s 'Ys - 2 er + r + f:RLf/('Ys - 2)

LARGE v(RK- Rs) 1/(RK- Rs)l 'Ys - I er + 72 + f(/RKfl/('Ys - 1)

linear 1 I/(RK- R,)I 1 er + 72 + f.' (RK- RI)f,

non-linear v(R(. - Rs) I/(RL - Rs)l 'Ys - 2 er + 72 + f./RLf/('Ys - 2)

residual 3 2v(Rs)/(l +lP) s/Rss + I/Rsl 2(T - 'Ys) er + 72 •The residual 3 degrees of freedom are derived in Appendix Band depend on1/;2 = 7

2 / (ci + 72). Thus, the residual 3 degrees of freedom vary between 2v(Rs) when

1/;2 = 0 (SMALL and LARGE contaminant levels are uncorrelated) and veRs) when '/;2 is doseto 1 (SMALL and LARGE contaminant levels are highly correlated). In practice, 1/;2 isunknown. However, the tests of time trends in SMALL and LARGE contaminant levels willbe conservative if we take the residual 3 degrees of freedom to be veRs).

Note timt:

• time trends in SMALL and LARGE cüntaminant levels are tested für using the residual 3sums of squares• length effects are tested tor using the residual 2 sums of squares• time trends when St\'IALL and LARGE contaminant levels vary in the same way are tested

for using the residual 1 sums of squares• correlated errors (ie r ;c 0) can be tested for by comparing the residual land residual2 sums of squares.

Example

Nicholson et ai. (1994) give an example of an 8 year contaminant time series of mercuryconcentrations in fish muscle. The data were collected in consecutive years, so thaty, = 1981 + t. Further,

s = (-2.81, -2.59, -3.00, -3.10, -3.10, -3.00, ~2.81, -2.53)'I = (-2.04, -2.16, -2.35, -2.41, -2.47, -2.30, -2.41, -2.21)'

Applying a lowess smoother using the 8 nearest neighbours (giving approximately 1 degreeof freedorn for assessing non-linear effects) gives the following analysis of variance table:

Effect df SSQ 'Y MSQ F Prob

TIME 1.94 0.268 1.79 0.150 6.19 0.044

linearnon-linear

residual 1

1 0.006 1 0.006 0.24 0.6440.96 0.262 0.79 0.332 13.74 0.014

5.36 0.126 5.21 0.024

5.36 0.049 5.21 0.010•LENGTH 1TIME.LENGTH 1.94

residual 2

1.316 10.046 1.79

1.316 138.4 <0.0010.026 2.72 0.158

SMALL 1.94 0.206 1.79 0.115 6.85 0.037

linear 1 0.005 1 0.005 0.29 0.616non-linear 0.96 0.202 0.79 0.256 15.19 0.011

LARGE 1.94 0.108 1.79 0.060 3.57 0.109

linear 1 0.031 1 0.031 1.87 0.230non-linear 0.96 0.076 0.79 0.097 5.74 0.062

residual 3 5.36 0.176 10.42 0.017

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162

Note that the residual 3 degrees of 1'reedom are taken to be veRs) to give conservative testsfor time trends in SM ALL and LARGE contal11inant levels.

• There is no evidence timt SMALL and LARGE contaminant levels vary differently over time• There is a big di1'ference between SMALL and LARGE contaminant levels (confirming thatmercury concentration depends on fish length)• Log-concentration appears to vary non-Iinearly over time.

These conclusions are in broad agreement with tllose 01' Nicholson er al. (1994).

A comparison of the residual land residual 2 sums of squares gives no evidence ofcorrelated errors (F = 2.54, P = 0.164). However, using these two residual sums ofsquares to estimate cl and -r suggests timt 1/;2 = 1"2 I (er + 1"2) :::= 0.4.

Thoughts

In the example above, the test for correlated errors was not significant. However, the testis not very powerful when there are only about 5 degrees of freedom for each residual term.Analysis of ICES CMP data (Fryer and Nicholson, 1990) suggests that non-zero 1"2 wouldgenerally be expected. Using a more powerful test, Fryer and Nicholson (1990) concludethat incorporating correlated errors within-years is necessary to 1110dell11ost contaminant timeseries. This is true regardless of whether there is a length effect. If we chose to split fishinto SMALL and LARGE when there is no length effect, the correlated error structure wouldbe preserved, giving non-zero 1"2. This implies that non-zero -r would also be expected whenthere is a length effect.

In the example above, the residual 3 degrees of freedom are taken to be veRs) to giveconservative tests for time trends in SMALL and LARGE contaminant levels. This might beunduly pessimistic if 1/;2 is not dose to I. One approach might be to use the residual landresidual 2 sums 01' squares to estimate 1/;2 and hence the residual 3 degrees of freedom.Taking 1/;2 = 0.4 gives 9.2 residual 3 degrees of freedom and p-values:

Ef1'ect Prob

SMALL 0.016

linear 0.603non-linear 0.004

LARGE 0.072

linear 0.205non-linear 0.040

•

lf ,2 is known to be zero, the residual 3 sums of squares could be used to test all the effects.However, care is needed here. For example, suppose that 1f2 = 0.4, but we incorrectlyassume from the F-test that 1f2 = °and test all the effects using the residual 3 sums ofsquares on 2v(Rs) = 10.7 degrees of freedom. Then tests of TIME and LENGTH of nominalsize 95% have actual size 90% and 98% respectively.

References

Fryer, R.J. and Nicholson, M.D., 1990. The ICES Cooperative Monitoring Programme.Part 2. Testing for trends in annua1 mean contaminant levels. Report of the Working Groupon Statistica1 Aspects 01' Trend Monitoring.

Fryer, R.J. and Nicholson, M.D., 1993. The pO\ver of a contaminant monitoringprogramme to detect linear trends and incidents. ICES Journal of Marine Scienee, 50: 161­168.

Hastie, T.J. and Tibshirani, R.J., 1990. Generalized additive models. Chapman and Hall,London.

Stuart, A. and Ord, J.K., 1987. Kendall's advaneed theory of statisties. Fifth edition,Volume 1. Charles Griffin and Company, London.

Nieholson, M.D., Fryer, R.J. and Larsen, J.R., 1994. A robust method far analysingeontaminant trend monitoring data. Warking Doeument for WGSAEM 1994.

Appendix A

Suppose c - N(O, 1:) and we are interested in the distribution of the quadratie formQ = c' Ac, where A is any symmetrie matrix.

Assuming 1: is positive definite, there exists a non-singular matrix V, such that 1: = VV ' .

Letting x = V-1c, gives x - N(O, I), a standardized normal variable.

Then Q = c'Ac = x'V' AVx so that

E[Q] = tr(V' AV) = tr(AVV') = tr(A1:)

Var[Q] = 2tr{ (V'AV)2} = 2tr{V'AVV'AV} = 2tr{(A1:)2}

(eg Stuart and Ord, 1987, p488).

Approximately, Q - tr(AE)x2Jv where v = {tr(AE)}2 / tr{(AE?} is chosen to make the firsttwo moments agree.

163

Appendix B

Let c =(s', 1')', the augmented vector of SMALL and LARGE log-concentrations. Then

[(er + 7 2)/Var(c) = 1; = r/

164

The residual 3 sums of squares are given by s'Rss + I'Rsl = c'Ac where

A = [~s 2s ]

Thus

[(0' + -r')Rs -r'R ]AB =72R «(J2 + ~)Rss

Hence,

•

ANNEX 18

Working Document for WGSAEM 1994

The power of the IICW robust mcthod of asscssing contaminant trclld Illonitoring data

Rob Fryer and Mike Nicholson

Introduction

This paper considers the power of the new robust method for assessing temporal trends incontaminant monitoring data (Nicholson el al. , 1994; Fryer and Nicholson, 1994b) andcontrasts it with the pO\ver of the more traditional method of analysis (Anon., 1985). Inparticular, we consider the effect of using sampIe medians, rather than sampIe means tosummarise contaminant levels each year. We first consider the case in which contaminantlevels are unrelated to length, and then generalize the analysis to incorporate a length effect.

Power - no Icngth cffect

A model 0/ contaminant lerels

Consider a T year contaminant time series in which R sampIes are taken at the same timeeach year, in years YP r = 1... T. Let cll" be the log-concentration of sampie r in year Y, andassurne that

where• f(') represents smooth systematic changes in contaminant levels over time• the errors E,,. are independent and nonnally distributed with zero mean and constantvariance ,;. and represent random within-year variation in contaminant levels,• the errors ö, are independent and normally distributed with zero mean and constantvariance -? and represent random between-year variation in contaminant levels.

Power

Both the traditional and new methods of analysis assess temporal trends using summarystatistics of the contaminant levels in each year. The traditional method uses the yearlysampIe means. The new method uses the yearly sampIe medians. The power of bothmethods of analysis to detect temporal trends depend on the variability of these summarystatistics (about the systematic trend).

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166

The variance of the yearly sampie means is

./,2 cl + 72'l'mran = R

whilst the variance of the yearly sampie medians is approximately

./,2 7rer ')'I'mrdian == 2R + 7-

Thus, the difference in power of the two methods depends on the relative magnitude of er,7

2 and R.

Application {o ICES CMP dota

Fryer and Nicholson (1993) give estimates of 1000" and 100t/;mean for different contaminants,species and tissues based on analyses of ICES CMP data (lCES, 1989, 1990). Table 1 givesthe median of these estimates having grouped the data into heavy metals, organics, fish andmusseI.

Taking R = 25 for fish and R = 3 for mussei, allows us to estimate 100t/;median (Table 1)from the relationship

2 2 [7r jert/;mrdian = t/;mean + :2 - 1 R

lf we standardize on a 10 year period, sampling every year, the % yearly increase inconcentration detected with 90% power by a linear regression of the yearly sampie means/ medians on time is given by

% yearly increase detected with 90% power = 100(exp(0.4087t/;) - 1)

(Fryer and Nicholson, 1994a) and is also given in Table 1.

Table 1

% yearly increase1000" 100t/;mo'l11 100t/;median mean med

heavy metals / fish 42 25 25.8 10.8 11.1heavy metals / mussei 23 33 34.5 14.4 15.1organics / fish 64 43 44.1 19.2 19.7organics / musseI 27 48 49.4 21.7 22.4

Thus, for the CMP data, the new method of analysis results in little loss of power.

•

Power - ICllgth cffcct

A model oJ cOII!amilwlI! levels

Now consider the case in which log-concentration is linearly related to length and supposethat

where llr is the length of sampIe r in year YI' For convenience, we have assumed that thelength effect is constant over years, although in practice this is often not the case.

Power

The traditional method of analysis summarises the yearly contaminant levels by the yearlysampie mean, corrected to some specific length (usually the overall mean length).

Although the new analysis would generally split the fish into' SMALL and LARGE categoriesto examine possible length effects, here we assume far simplicity that the length effect isknown apriori to be constant over years and that the yearly contaminant levels are againsllmmarised by the yearly sampie medians.

The variance of the yearly sampIe (length-corrected) means and medians now depends on thesampling design. For example, the variance would be different for a random sampie andfor a length stratified sampie..

Since the ICES CMP is based on a length stratified sampIe, lets consider what happens wheneach year we take 25 fish, one fish each at length 10 ± jA, j = 0... 12. The yearly sampIemean standardised to length 10 has variance

21/Jmt'an =

er25

independent of the value of ß. The yearly sampie median has variance

where the function g(ßt1/a) varies from approximately 7r/(2 x25) when ßt1/a = 0 to 1 whenßt1/a is large (Figure I). In particlllar, when ßt1/a is large, the median log-concentrationwill nearly always correspond to the fish of length 10 and hence will have variance er + r2•

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168

Applicatioll to ICES CMP data

Nicholson and Wilson (1987) give estimates of ß for a variety of heavy metals in fish.Estimates of IßI > 0.01 were rare.

Nicholson and Wilson (1987) also give yearly estimates of the standard deviation of length.The maximum standard deviation of length for any contaminant time series was 13 cm. Thissuggests a plausible upper bound for .1 is 2 x 13/12 = 2.2cm.

Taking a = 0.42 (from Table 1) gives an upper bound on ß!::.la of about 0.05 and on g(ß!::.la)of about 0.07, corresponding to 100,pmrdian = 26.0 and a % yearly increase detected with90% power of 11.2.

Again, for the CMP data, there is little loss in power using sampIe medians as opposed to(length-adjusted) sampIe means.

Rcfcrcllccs

Anon., 1985. Guidelines for using analysis of covariance to assess changes in the averagelevels of a single contaminant. Report of the meeting of the ad hoc group of statisticiansassisting theWGMPNA on "trend monitoring issues. ICES C1\1 1985/E: 10. Annex 4.

Fryer, R.J. and Nicholson, M.D., 1993. More on the power of the ICES CooperativeMonitoring Programme. Report of the Working Group on Statistical Aspects ofEnvironmental Monitoring. ICES CM 1993/ENV:6.

Fryer, R.J. and Nicholson, 1\1.D., 1994a. Can simple changes in sampling and analyticalstrategy improve the pO\ver of,the ICES Cooperative Monitoring Programme? Report of theSub-Group on Temporal Trend Monitoring for Contaminants in Biota. (A revised version01' which is a Working Document for WGSAEM 1994).

Fryer, R.J. and Nicholson, M.D., 1994b. Analysis of variance tables for the new robust •method of assessing contaminant trend monitoring data. Working Document for WGSAEM1994.

ICES, 1989. Statistical analysis of the ICES Cooperative Monitoring Programme data oncontaminants in fish museie tissue (1978-1985) for determination of temporal trends. ICESCooperative Research Report No. 162.

ICES, 1990. Statistical analysis of the ICES Cooperative Monitoring Programme data oncontaminants in fish liver tissue and Mytilus edulis (1978 - 1988) for determination oftemporal trends. ICES Cooperative Research Report No. 176.

Nicholson, M.D., Fryer, R.J. and Larsen, J.R., 1994. A robust method for analysingcontaminant trend monitoring data. Working Document for WGSAEM 1994.

•

..

Nicholson, M.D. and Wilson, S.l., 1987. Identification oftrends in levels ofmetals in fishmuscIe: appraisal of the statistical analysis and of data quality. Report of the Working Groupon Statistical Aspects of Trend Monitoring.

169

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1.0IiIIIi

0.8 1II

!II0.6

CJ)

I

I

l0.4

0.0o 1 2 3 4

ßLYa

170