assessment of sampling and analytical uncertainty

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Assessment of sampling and analytical uncertainty

of trace element contents in arable field soilsUwe Buczko &Rolf O. Kuchenbuch &Walter belhr &Ludwig Ntscher

Received: 16 December 2010 / Accepted: 27 July 2011 /Published online: 11 August 2011# Springer Science+Business Media B.V. 2011

Abstract Assessment of trace element contents insoils is required in Germany (and other countries)before sewage sludge application on arable soils. Thereliability of measured element contents is affected bymeasurement uncertainty, which consists of compo-nents due to (1) sampling, (2) laboratory repeatability(intra-lab) and (3) reproducibility (between-lab). Acomplete characterization of average trace elementcontents in field soils should encompass the uncertain-ty of all these components. The objectives of this study

were to elucidate the magnitude and relative propor-tions of uncertainty components for the metals As, B,Cd, Co, Cr, Mo, Ni, Pb, Tl and Zn in three arable fieldsof different field-scale heterogeneity, based on a

collaborative trial (CT) (standardized procedure) andtwo sampling proficiency tests (PT) (individual sam-pling procedure). To obtain reference values andestimates of field-scale heterogeneity, a detailed refer-ence sampling was conducted. Components of uncer-tainty (sampling person, sampling repetition,laboratory) were estimated by variance componentanalysis, whereas reproducibility uncertainty was esti-mated using results from numerous laboratory profi-ciency tests. Sampling uncertainty in general increased

with field-scale heterogeneity; however, total uncer-tainty was mostly dominated by (total) laboratoryuncertainty. Reproducibility analytical uncertainty wason average by a factor of about 3 higher thanrepeatability uncertainty. Therefore, analysis withinone single laboratory and, for heterogeneous fields, areduction of sampling uncertainty (for instance bylarger numbers of sample increments and/or a densercoverage of the field area) would be most effective toreduce total uncertainty. On the other hand, when onlyintra-laboratory analytical uncertainty was considered,

total sampling uncertainty on average prevailed overanalytical uncertainty by a factor of 2. Both samplingand laboratory repeatability uncertainty were highlyvariable depending not only on the analyte but also onthe field and the sampling trial. Comparison of PT withCT sampling suggests that standardization of samplingprotocols reduces sampling uncertainty, especially forfields of low heterogeneity.

Environ Monit Assess (2012) 184:45174538

DOI 10.1007/s10661-011-2282-5

U. Buczko (*) :R. O. KuchenbuchInstitute for Land UseApplied Plant Nutrition,University of Rostock,Justus-von-Liebig-Weg 6,18059 Rostock, Germanye-mail: [email protected]

W. belhrLandwirtschaftliches Technologiezentrum Augustenberg,

Nelerstrae 23-31,76227 Karlsruhe, Germany

L. NtscherBioanalytik im Zentralinstitut fr Ernhrungs- undLebensmittelforschung der TU Mnchen,Alte Akademie 1,85350 Freising-Weihenstephan, Germany


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contaminations often requires more sophisticated sam-pling schemes (e.g. Taylor et al. 2005). Even thoughsampling schemes such as stratified random sampling(Brus et al.1999) or grid sampling (Lauzon et al.2005)may reduce sampling error, simplified samplingschemes are still often being used, since in many

situations the increased effort of more elaboratedsampling schemes is not commensurate with thepurpose of the sampling (i.e. fitness for purpose,Ramsey and Thompson2007).

The term uncertainty encompasses both preci-sion and bias (trueness), and it is commonly quanti-fied by means of standard deviations (ISO 2005;Ramsey and Ellison 2007). Whereas precision refersto the variability and repeatability of sampling results(i.e. random effects), bias refers to the trueness of theresults, i.e. systematic effects. Sampling uncertainty in

soils can be determined by a modelling, bottom-upapproach, in which the separate components ofuncertainty are summed up (in form of the respectivevariances) to obtain the overall uncertainty, or by anempirical, top-down method, in which uncertaintyis estimated based on sampling results from differentsampling trials and/or samplers (i.e. sampling partic-ipants or persons; the term sampler is used in thissense throughout this paper), often by collaborativetrials (CT), i.e. several samplers using identicalsampling protocols (Ramsey and Argyraki 1997;

Ramsey and Thompson 2007), or by samplingproficiency tests (PT), i.e. several samplers usingdifferent sampling protocols (Argyraki et al. 1995;Lischer et al. 2001; ISO2005; de Zorzi et al. 2008;Ramsey and Ellison2007; Ramsey et al.2011).

It has been claimed that soil sampling in the field isin most cases the main source of uncertainty anddominates sampling preparation and other laboratorysources (Ramsey1998). This has been demonstratedfor trace metals (Taylor et al. 2005; van der Perk et al.2008; Rawlins et al. 2009), for organic contaminants

(Lam and Defize1993) and for nutrient elements onarable soils (Jacob and Klute1956; Kerschberger andRichter 1992) and grassland (Cameron et al. 1994).However, there are also examples of analyticaluncertainty prevailing over sampling uncertainty(e.g. Lischer et al. 2001). Consequently, one cannota priori assume that sampling uncertainty alwaysdominates over laboratory uncertainty.

Total laboratory (analytical) uncertainty consists ofrepeatability (within one laboratory) and reproducibil-

4518 Environ Monit Assess (2012) 184:45174538

Keywords Soil sampling . Sampling uncertainty.

Trace elements . Heterogeneity. Sewage sludgeapplication . Heavy metals

Introduction

Soil sampling is the first step when measuring traceelement contents of soils, among other reasons forassessing the toxic heavy metal content (i.e. Cd, Cr,Cu, Hg, Ni, Pb, Zn) of arable soils before applicationof sewage sludge, which is required by the GermanFederal Soil Protection and Contaminated SitesOrdinance (BBodSchV1999; see also Lewandowskiet al.1997; Nestler2007) and similarly also in manyother countries (e.g. Nagajyoti et al. 2010). However,both chemical analysis and soil sampling are fraught

with uncertainty, which can seriously impair thequality of measurement results and the conclusionsdrawn from the measurements. Thus, in order to makea judgement about the reliability of measurements ofelement contents in soils, it is necessary to assess thetotal uncertainty of measurement and its contributionsarising from sampling, sample preparation, andchemical analysis. Moreover, it is often desirable toreduce total measurement uncertainty, and in order todirect the corresponding efforts most efficiently,knowledge about the relative proportions of uncer-

tainty is necessary (Ramsey and Thompson2007).The accuracy of field sampling has been of concern

worldwide for decades, for instance in soil tests forplant-available nutrient contents (e.g. Cline 1944;Cameron et al. 1971; Kerschberger and Richter1992; Mallarino et al. 2006), for contaminated sites(Lam and Defize1993; Correll2001), for geochem-ical exploration of ore deposits (Garrett1969; Ramseyet al. 1992), or in the context of sewage sludgeapplications (Lewandowski et al.1997; Nestler2007).

For agricultural fields, simplified schemes to obtain

representative composite samples for sub-plots oftypically 35 ha are often applied, for instance,consisting of 2030 auger cores (increments) whichare extracted from 0 to 20 cm soil depth, using patternssuch as a double diagonal or zigzag lines (Nor Wpattern) (Lewandowski et al.1997; ISO2002). Similarsimple sampling schemes are often used for determi-nation of heavy metal contents at artificially contam-inated sites (e.g. Argyraki et al. 1995), although thelarger heterogeneity and spot-like nature of the
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ity (between different laboratories) uncertainty com-ponents. The uncertainty arising from sample prepa-ration mostly cannot be determined unambiguously.Whereas sample preparation steps involving theprimary sample (i.e. mixing of composite samples,comminution, splitting) pertain to sampling uncer-

tainty, sample preparation steps occurring in thelaboratory (i.e. drying, sieving, milling, splitting,homogenization) contribute to analytical uncertainty(Lam and Defize1993; Gerlach et al.2002; Ramseyand Ellison2007). Consequently, both sampling andanalytical uncertainty contain some variable butlargely unknown proportion of uncertainty due tosample preparation.

The objective of this study is to evaluate themagnitude and relative proportions of samplinguncertainty and intra- and between-laboratory uncer-

tainty when applying simple sampling schemes toobtain representative average trace metal contents ofagricultural fields. Whereas this topic has been ingeneral investigated in previous studies (as cited inthe introductory section above), the present studycontains several aspects the combination of which isnovel in comparison with previous studies:

1. Both intra-laboratory and between-laboratory un-certainty components are evaluated; intra-laboratory uncertainty is evaluated exhaustivelyby duplicate analyses of all samples

2. Several different simple sampling paths areevaluated here by incorporation of a large number(18) of samplers

3. Comparison of the effect of sampling person andsampling repetition by applying two repetitions ofa sampling proficiency test

4. Evaluation of the effect of standardizing thesampling protocol by comparing proficiency testsand collaborative trials

5. Inclusion of several analytes differing in theirgeological origin and environmental impact

Material and methods

Study sites

Sampling trials were performed on three fields (F1,F2, F3) located in Vhl near Korbach, about 40 kmsouthwest of Kassel (Federal state Hesse, Germany)

(5112 N, 855 E). The geological underground iscomposed of a lower Triassic sandstone-shale se-quence and upper Permian dolomites and salt clays.The fields are located approximately 400 m above sealevel. The soil texture of the fields is loamy sand (F1),sandy loam (F2) and clay loam (F3). The outline of

the fields along with schematics of the referencesampling, the CT sampling and the PT samplings isdepicted in Fig. 1. Normal background ranges andthreshold values (according to BBodSchV 1999) ofthe analytes are summarized in Table 2. Since theparent material of F1 consists of a large variety ofbedrocks from Permian limestone and dolomites toTriassic sandstones and shales and because soiltexture exhibits the largest variety on this field, itwas assumed before the sampling trial that the F1field is the most heterogeneous among the three

fields. Based on similar criteria, F2 was considered tobe the most homogeneous of the fields.

Whereas F1 and F2 were managed during the lastfew years using reduced tillage practices (cultivator),F3 was tilled in a conventional manner by mould-board ploughing. The crop rotations during thepreceding years show a great variety among fieldsand years. At the time of sampling, F2 and F3 wereprepared for maize cultivation, and at F1 was astanding grass crop intended for seed production.Climatic conditions in the area (station Kassel, 231 m

above msl) are characterized by an average annualtemperature of 8.9C and mean annual precipitationof 686 mm (average over the years 19712000).

Soil sampling

Prior to the main sampling trials, a reference samplingwas performed, in order to obtain reference averageanalyte contents and an estimate of the spatialheterogeneity of the fields. The plots were subdividedinto seven (F1) and nine (F2 and F3) sub-plots of

approximately equal area. From each sub-plot, 20sample increments were taken by auger cores (diam-eter of 14 mm) from 0 to 20 cm soil depth. Thelocations of core extraction were equally distributedalong the perimeter of a circle located centrally withinthe sub-plot (Fig.1). The perimeter of this circle wasapproximately equal to the diagonal of the respectivesub-plot (MLUV2009). This circle sampling patternhas the advantage that an area can be covered equallywithout much effort, and no spatial direction is

Environ Monit Assess (2012) 184:45174538 4519
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favoured. Since the sub-plots of each field were ofapproximately equal area, the circles used for collect-ing the increments of the reference samples were alsoof approximately equal size for each field (Fig. 1).The increments of each sub-plot were combined into acomposite sample for the respective sub-plot. Theanalysis of these samples resulted in element concen-trations for each sub-plot, which were (arithmetically)averaged to yield reference values for the whole field.For estimating sampling uncertainty using the top-

down (or empirical) approach, a collaborative trial insampling (i.e. multiple samplers using a singleprotocol) and a sampling proficiency test (i.e.multiple samplers using multiple protocols) wereapplied. In both the collaborative sampling trial andsampling proficiency test, 18 professional soil sam-plers from institutions of ten German Federal statesparticipated. Each of the three fields was sampledthree times by each of the 18 participants. Twosampling repetitions were performed by the partic-

3F2F1FgnilpmaS

reference

sampling

(RS)

53

6

2

7

4

1

123

45 6

78

9

23

5

6

7

8

1

4

9

collaborative

trial (CT)

sampling

proficiency

test (PT)

Fig. 1 Schematic of the three investigated fields; upper rowreference sampling numbers within the fields denote sub-plots;middle row sampling pattern of CT sampling; bottom row

examples of frequently used sampling patterns of the samplingproficiency test. The double-headed arrow scale baris 100 m

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ipants procedure of choice (sampling proficiencytest, PT samples; the two repetitions are termed PT1and PT2 in the following), and one samplingrepetition was a standardized procedure (samplingCT). The aim of all sampling was to obtain arepresentative average element concentration of the

whole field.For the standardized procedure (CT), the sample

increments were taken from 0 to 20 cm depth. Twentycores were extracted using an X-shaped (doublediagonal) sampling pattern (Fig. 1) with augers of14 mm diameter. For the PT sampling, varioussampling patterns were used by the participants. Thefields were covered using W and N (zigzag)shapes, double diagonals (X), circles and simple linesfor sample collection (Fig.1). The number of sampleincrements varied between 15 and 40, but the

majority (more than 50%) of the participants took20 cores. The diameter of the auger varied between 12and 18 mm, with 50% of the participants using 14 mmdiameter augers. Fifty percent of the participants chosethe same sampling depth as in the collaborative trial(20 cm), whereas six sampled 025 cm and threesampled 030 cm. As a consequence, the resulting totalmasses of the composite samples varied widelybetween 266 and 1,177 g, with a mean of 590 g (totaldry mass before sieving).

All samples of the collaborative trial and the

sampling proficiency test were taken on April 17,2007. Prior to this date, there had been no precipita-tion for 2 weeks. At the sampling day, the weatherconditions were dry with temperatures of 12C in themorning and 20C in the afternoon.

Sample preparation and analysis

The composite samples were filled, after mixing andhomogenization, into plastic bags, immediately trans-ported to the laboratory and oven-dried at 50C

overnight. The following day, after drying andbreaking up agglomerates by a jaw crushing machine,the samples were weighed and passed through a 2-mm sieve (mechanical sieving machine). Particleswith diameters >2 mm were discarded. From thefraction


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coefficient of variation has been used in many studiesof field-scale variability as an indicator for heteroge-neity (e.g. Cameron et al. 1971; Lauzon et al. 2005;Taylor et al.2005; Mallarino et al.2006). However, inmost cases, measured data based on point-like support(i.e. area or volume that is represented by a single

sample or measurement) were used. In this study, thesupport of separate data (i.e. composite samples) wasan appreciable percentage of the field area. Thisshould result in lower standard deviations comparedwith data based on point measurements.

Components of variance

The proportions of total measurement variance ofthe sampling trials contributed by the sampler, thesampling repetition and laboratory analysis were

estimated with variance component analysis (VCA)(Cox and Solomon 2002). It was assumed that theeffects of sampler, sampling repetitions of theproficiency test and analytical repeatability errors(chemical analyses in duplicate) are random. Theeffects of different fields and the sampling of thecollaborative trial cannot be viewed as random andtherefore were not included in the VCA.

Since the design of the sampling trials is structuredin a hierarchical way (each of 18 samplers took twoPT samples, each of which was analysed in duplicate,

Fig.2), the following statistical model was used:

Yijk m ai bj ai "ijk 1

with the dependent variable Yijk representing oneindividual result of one chemical analysis of a givenanalyte on a given field (ofi-th sampler,j-th samplingrepetition, k-th chemical duplicate analysis), is theoverall mean value (for a given analyte and samplingtarget, i.e. field), i is the effect of the i-th sampler(i=1 18) and j(i) the effect of the j-th sampling

repetition of i-th sampler (j=1, 2) and ijk is theresidual effect (corresponding to the analyticalrepeatability error, the index kdenotes the analyticalrepetition, k=1, 2).

It is assumed that the mean values of the variablesi, j(i) and ijk are zero and that they havecorresponding variances sp

2, sr2, ak

2, respectively.Further, it is assumed that both the random variablesi,j(i) and ijkand the corresponding variances aredistributed normally, in accordance with assumptions

generally made in chemical analyses (e.g. Thompsonand Howarth 1976). Tests for normal distributionusing the KolmogorovSmirnov test revealed that thevariables were not significantly different from anormal distribution. The VCA was conducted using

the restricted maximum likelihood (REML) method(Corbeil and Searle1976), in which negative variancecomponents are set to zero.

Estimates of variance components using ANOVAare often biased and can be negative (variances, bydefinition, must be either zero or positive). Maximumlikelihood estimation methods of variance compo-nents such as REML provide less biased estimates ofvariance components, since fixed effects are filteredout so that the variance component estimates do notdepend on them. This reduces bias in the variance

estimates (e.g. Webster et al.2006). The equivalencesand interconversion of variables are summarized inFig.2.

The analytical (laboratory) uncertainty resultingfrom different laboratories could not be analysed herewith VCA because all chemical analyses wereconducted in the same laboratory. Therefore, theresidual component ijk contains only the randomerror of one laboratory and thus corresponds to theintra-laboratory (repeatability) uncertainty uak. Thestatistical calculations were performed using the

software SAS 9.1.

Laboratory uncertainty

Total analytical uncertainty (uat) consists of repeat-ability uncertainty within one laboratory (uak) andreproducibility uncertainty between different labora-tories (uab) (Thompson and Lowthian1995; Lischer etal.2001; Munzert et al. 2007; Nestler2007). uakwasestimated from duplicate determinations of all sam-

Fig. 2 Sketch (similar as in Ramsey and Thompson2007) ofthe sampling design and data used for estimating uncertaintycomponents with VCA. Note that only the uppermost branch isdepicted completely. Consecutive branches below have ananalogous structure and are not shown due to space constraints.The compilation beneath the graph shows equivalences andconversion equations of variables for (1) effect on separate data(Eq. 1), (2) corresponding variances (absolute values), (3)variance components (percent) and (4) standard uncertaintyvalues (percent). Sampling targets (i.e. fields) and analytes areanalysed only separately; consequently, refers to a givenanalyte and field

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ples, using the root-mean-square (RMS) precisionestimator(Hyslop and White2009):

uak

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffi1

n

Xni1

ci;1 ci;2

=ffiffiffi

2p

ci

!2vuut 100 2with ci,1andci,2the measured concentration (of the i-thsample) of the first and second analytical replication,respectively, and ci the mean concentration of bothanalytical repetitions. Compared with other estimatorsof analytical precision (for instance, mean absolutevalue or percentile spread), the RMS precision estima-tor is somewhat sensitive to extreme values and tendsto yield larger precision uncertainty estimates (Hyslopand White2009). Thus, this estimator provides a largersafety margin, which seems advantageous whenestimating overall sampling uncertainty of toxic metals.

Values ofuakcalculated with Eq.2proved to be nearlyidentical withuakvalues obtained by the VCA (for thePT samplings); uak values were calculated for eachanalyte, field, and sampling trial.

The between-laboratory (reproducibility) analyticaluncertainty uab was not captured by the data of thepresent study (because analyses were conducted withina single laboratory). It was estimated instead (for Cd,Cr, Pb, Zn) using linear regression equations which arebased on analytical proficiency tests conducted inseveral laboratories throughout Germany (Table 1).

The calculation procedure of these regressions and theresults for macro- and micronutrient elements are givenin Munzert et al. (2007). In a similar manner, for totalcontents of the heavy metals Cd, Cr, Ni, Pb and Znfrom the same type of data, linear regression equationswere developed for estimation of the between-laboratory uncertainty uab a b c =c 100,

Table 1 Values of regression parameters and characteristics of the regression (all analyte concentrations are in milligrams perkilogram) for estimation ofuabvalues based on laboratory proficiency tests

Analyte Number of data a b r2

n cmin cavrg cmax

Cd 20 0.01 0.188 0.50 20 0.12 0.25 0.35

Cr 22 0.791 0.076 0.65 22 14.5 37.9 58.6

Ni 22 0.24 0.074 0.87 22 7.6 25.8 42.1

Pb 20 0.8 0.057 0.79 20 12.2 26.8 59.3

Zn 21 1.5 0.042 0.66 21 29.9 69.7 122.9

For the regression equationuab a b c =c 100, withcthe mean concentration of one specific of the ndatasets andaandbthe intercept and slope parameters; cminand cmaxdenote the minimum and maximum concentration values on which the regression is

based, whereascavrg is the overall mean concentration of all n datasets (i.e. proficiency tests)


with c the mean concentration of one out of nlaboratory proficiency tests and a and b the interceptand slope parameters, respectively).

Regression parameters and characteristics of theregression are compiled in Table 1. Because theregressions are based on mean values for each

laboratory, we assumed that the uncertainty derivedfrom these regressions comprises only inter-laboratoryuncertainty, but not uncertainty within one specificlaboratory.

For As, data of laboratory proficiency tests from 27laboratories given in Nestler (2007) were used. Fromboth repeatability and reproducibility analytical un-certainty components, total analytical uncertainty uatis calculated as (addition of variances):

uat ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2ak u

2abq 3

Sampling uncertainty

For the PT sampling, sampling uncertainty us iscalculated from VCA, the components due to thesampling person usp and that due to the samplingrepetition usr:

usffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

u2sp u2sr

q 4

The us values obtained from VCA are similar to usvalues estimated from reproducibility standard devi-ation (rsd; i.e. standard deviation of results amongdifferent samplers) and uakusing

us

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirsd2

u2ak2

r 5
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Therefore, for the CT samples, us was estimatedusing Eq. 5. Total measurement uncertainty utcomprises us and uatand is calculated by addition ofvariances as

ut ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2at u2sq 6

Results and discussion

Reference sampling

Mean values of cref and sref of the three fieldsobtained by the reference sampling are summarizedin Table 3. The mean contents of most analytes arewithin the normal background range and indicate no

contamination (Table2). However, thallium contentsare extraordinarily high on all fields, but especially onF1 and F3. Since F2 is located between F1 and F3 andno contamination sources of Tl are known in thisregion, the elevated Tl contents are presumablyconnected with the upper Permian parent material ofF1 and F3. Elevated Tl contents are known to occur in

upper Perminan sediments (e.g. Wedepohl 1964) andalso in PbZn mineralizations, which have beenmined in the area (Kulick1997). Highly elevated soilTl contents have been reported from other areas of theEuropean Variscan Orogeny, for instance in France(Tremel et al. 1997).

Averaged for all analytes of a specific field, srefvalues were the highest for F1 (average of tenanalytes 27.5%) and the lowest for F2 (12.7%)(Table 3). This was expected before the samplingtrials, since before the sampling, F1 was considered tobe the most heterogeneous and F2 the most homoge-neous of the three fields. Overall, compared with CVvalues reported in other studies, these values arerather low (see general discussion). However, srefvalues varied considerablyamong the analytes (Table 3),whereas for six of the ten analytes, the highest sref

values were observed for F1; for Co and Ni, F2exhibited the highestsrefvalues of the three fields andfor B and Cr, the highestsrefvalues were observed onF3. Averaged over the three fields, the highest srefvalues were observed for Cd (34.6%) and Tl (28.7%)and the lowest for Cr (9.7%), while average srefvaluesfor the other analytes range between 13% and 21%.

The mean concentrations cpt1, cpt2 and cctof thecomposite samples of the PT1, PT2 and CT samplingrepetitions, respectively, indicate that bias values (i.e.the mean sampling errors of the 18 samplers, related

to crefvalues) are on F1 distinctly negative for mostanalytes and sampling repetitions. In contrast, abso-lute bias values are generally lower on F2 and F3(Table 3). This is probably caused by the relativelyirregular shape and the nutrient distribution within theF1 field, combined with the sampling patternspreferred by the participants: In the two sub-plots 4and 5, in the western part of the field (Fig. 1),distinctly different analyte concentrations comparedwith the other sub-plots of this field were observed(connected with different parent materials in these

sub-plots). On the other hand, sub-plots 4 and 5 wereavoided by most of the participants, among otherreasons because the soil in these sub-plots wasrelatively hard and therefore difficult to sample.

Sampling trials: analytical uncertainty

The results of the sampling trials show distinctdifferences between analytes and sampling trials asregards the relative variation between samplers,

Table 2 Natural background and threshold concentrations ofthe analytes

Analyte Background concentrationa Threshold concentrationb

As 120 25

B 580

Co 515

Mo 0.25

Tl 0.020.4

Cd 0.10.6 0.4c, 1.0d, 1.5e

Cr 5100 30c, 60d, 100e

Ni 350 15c, 50d, 70e

Pb 260 40c, 70d, 100e

Zn 1080 60c, 150d, 200e

aNatural background concentration range (cf. Nagajyoti et al. 2010)b Threshold values given here are precautionary thresholdvalues (depending on soil texture) according to the Germansewage sludge and Federal Soil Protection Ordinance(BbodSchV 1999); the precautionary nature of these valuesentails that they are lower than threshold values reportedelsewhere and in other countries (cf. Nagajyoti et al. 2010)c For loamy sand (F1)d For sandy loam (F2)e For clay loam (F3)

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sampling trials or analytical repetitions. This isdepicted exemplarily in Fig. 3 for all 18 samplersseparately (left side) and as boxplots (right side): Coon F2 is an example for high variability betweensamplers, Pb on F1 shows high variability betweensampling repetitions and Mo on F3 shows highvariability between analytical repetitions.

Among the fields and the sampling trials, uakvalues varied considerably (Table 4), especially forCd, Ni, Tl and Pb. Mean uakvalues (averaged over

the three fields and the PT and CT samplings), for theanalytes, are for As 4.0%, B 3.2%, Co 4.0%, Mo

Field Analyte Reference sampling PT sampling CT sampling

crefb sref cpt1

b Bias cpt2b Bias cct

b Bias

F1 As 9.9 23.6 9.1 7.6 9.6 2.9 10.4 4.7

B 10.5 19.5 10.2 2.9 10.9 3.6 11.3 7.8

Co 6.5 14.1 6.2 4.6 6.5 0.0 6.7 3.3

Mo 0.37 16.8 0.3 12.3 0.3 13.8 0.4 3.8

Tl 4.7 44.1 3.9 15.6 3.1 32.6 2.7 41.1

Cd 0.4 49.6 0.2 53.6 0.2 35.3 0.3 29.9

Cr 23.6 7.5 21.6 8.5 23.2 2.0 22.5 5.0

Ni 19.2 17.1 17.0 11.5 13.6 29.2 13.2 31.2

Pb 23.9 24.7 21.2 11.6 18.1 24.3 17.6 26.6

Zn 65.7 27.6 56.9 13.5 45.9 30.1 40.9 37.8

Meana 27.5 14.2 16.7 15.9

F2 As 6.6 9.6 7.5 12.8 7.1 8.1 7.0 5.4

B 6.8 12.7 7.9 16.6 8.0 17.6 8.5 25.7

Co 6.3 15.5 7.0 11.7 6.8 8.6 7.2 14.7Mo 0.3 8.4 0.4 22.7 0.4 27.2 0.4 47.0

Tl 1.9 8.2 0.9 51.2 1.6 16.5 1.7 11.7

Cd 0.24 16.8 0.2 24.8 0.2 22.3 0.2 3.3

Cr 23.5 10.0 26.3 12.2 26.3 12.2 26.6 13.3

Ni 13.9 19.1 12.6 9.6 13.0 6.8 13.6 2.2

Pb 18.3 8.2 17.2 5.7 17.6 3.8 16.9 7.4

Zn 41.0 12.9 39.7 3.0 41.9 2.2 41.5 1.3

Meana 12.7 1.8 2.6 8.3

F3 As 17.8 19.2 17.0 4.7 17.8 0.2 17.6 0.9

B 14.9 21.4 15.9 6.8 16.4 9.9 16.9 13.1

Co 10.7 12.1 10.8 1.2 10.8 1.7 11.1 4.1Mo 0.5 14.3 0.6 31.8 0.5 6.5 0.5 0.2

Tl 4.3 21.2 3.0 30.0 3.0 30.7 3.2 26.9

Cd 0.4 29.0 0.5 1.7 0.5 1.9 0.5 4.5

Cr 21.8 11.3 24.3 11.4 24.9 14.1 24.8 13.6

Ni 29.8 15.0 24.2 18.8 22.0 26.0 22.4 25.0

Pb 39.2 14.0 29.7 24.2 32.2 17.9 33.7 14.1

Zn 141.1 20.3 112.8 20.0 108.0 23.5 110.8 21.5

Meana 18.5 4.5 6.4 5.3

aAll means of standarddeviation are calculated byaveraging the correspondingvariances because variancesrather than standarddeviation are additiveb Units of cref, cpt1, cpt2 andcctare milligrams perkilogram

Fig. 3 Results of the sampling trials for all 18 samplersseparately (left side) and as boxplots (right side), exemplarilyfor Co on F2 (top, high variability between samplers), for Pb onF1 (centre, high variability between sampling repetitions) andfor Mo on F3 (bottom, high variability between analyticalrepetitions). The dashed horizontal linesin the left side graphsand in the boxplots indicate mean values of the referencesampling (RS)


Table 3 Summary of results:mean (cref) and srefvalues ofthe reference sampling andmean (cpt1,cpt2, cct) and biasvalues from the PT and CTsampling trials for the threefields F1F3; units ofcref,cpt1, cpt2and cctare

milligrams per kilogram
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PT1 PT2 CT RS

0.4

0.5

0.6

0.7

0.8

0.9

PT1 PT2 CT RS

14

16

18

20

22

24

PT1 PT2 CT RS

5.5

6.0

6.5

7.0

7.5

8.0

8.5F2 Co

5.5

6.0

6.5

7.0

7.5

8.0

8.5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

sampler

Coconc.(m

g/kg)

PT1

PT2

CT

F1 Pb

13

15

17

19

21

23

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

sampler

Pbconc.

(mg/kg)

PT1

PT2

CT

F3 Mo

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

sampler

Moconc.(mg/kg)

PT1

PT2

CT



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8.6%, Tl 5.2%, Cd 10.6%, Cr 4.0%, Ni 5.0%, Pb3.3% and Zn 4.7%. Although one would expect that

uak is more or less constant for a given analyte (andconcentration), the results show that uak values are

Field Analyte uak uab

PT1 PT2 CT Meana PT1 PT2 CT Mean

F1 As 2.2 2.6 4.6 3.3 17.5 17.5 17.0 17.3

B 2.8 3.6 4.6 3.7

Co 3.8 3.9 3.6 3.8

Mo 8.4 6.7 9.0 8.1

Tl 3.4 2.7 2.5 2.9

Cd 24.5 10.0 4.8 15.5 24.4 22.9 22.5 23.3

Cr 4.0 4.4 3.6 4.0 11.3 11.0 11.1 11.1

Ni 5.9 2.3 6.5 5.2 8.8 9.1 9.2 9.0

Pb 3.0 3.8 3.8 3.5 9.5 10.2 10.3 10.0

Zn 3.0 6.9 7.0 5.9 6.8 7.4 7.8 7.4

F2 As 3.7 3.8 2.9 3.5 18.0 18.0 18.0 18.0

B 1.9 3.1 3.2 2.8

Co 5.0 4.2 5.4 4.9

Mo 5.9 7.0 8.4 7.2Tl 10.6 6.3 6.1 7.9

Cd 5.7 12.7 4.6 8.5 24.4 24.1 23.1 23.9

Cr 4.1 3.1 3.3 3.5 10.6 10.6 10.6 10.6

Ni 1.8 2.8 9.6 5.9 9.2 9.2 9.1 9.2

Pb 2.1 1.7 1.6 1.8 10.4 10.3 10.5 10.4

Zn 3.9 7.1 2.7 4.9 8.0 7.8 7.8 7.8

F3 As 5.8 3.9 5.3 5.1 12.5 12.5 12.5 12.5

B 2.7 3.3 3.0 3.0

Co 2.4 3.1 3.6 3.1

Mo 7.0 13.3 9.6 10.3

Tl 2.6 3.3 3.4 3.1Cd 6.9 4.3 3.2 5.1 21.0 21.0 21.0 21.0

Cr 3.2 5.7 4.2 4.5 10.9 10.8 10.8 10.8

Ni 3.7 2.2 8.0 5.2 8.4 8.4 8.4 8.4

Pb 2.2 1.8 6.5 4.1 8.4 8.2 8.1 8.3

Zn 3.2 1.8 3.0 2.7 5.5 5.6 5.5 5.5

All fields As 4.2 3.5 4.4 4.0 16.2 16.2 16.0 16.1

B 2.5 3.3 3.7 3.2

Co 3.9 3.7 4.3 4.0

Mo 7.2 9.5 9.0 8.6

Tl 6.6 4.4 4.3 5.2

Cd 15.1 9.7 4.3 10.6 23.3 22.7 22.2 22.8

Cr 3.8 4.5 3.7 4.0 10.9 10.8 10.8 10.9

Ni 4.2 2.4 8.1 5.5 8.8 8.9 8.9 8.9

Pb 2.5 2.6 4.4 3.3 9.5 9.6 9.7 9.6

Zn 3.4 5.8 4.7 4.7 6.8 7.0 7.1 7.0

Table 4 Repeatability andreproducibility analyticaluncertainty for all fields,analytes and sampling trials

All uncertainty (u) values

are as percentage values (i.e.relative to the concentrationof the analyte)aAll means of standarddeviation are calculated byaveraging the correspondingvariances



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all ten analytes, three fields and samplings) us/uatratio

of 0.62 (Table 6). This average ratio value is thelowest for the homogeneous F2 (0.46) and the highestfor the heterogeneous F1 (0.74). Moreover, it is onaverage lower for the CT than for the PT samplings(Table 6). This difference between CT and PTsamplings is more pronounced on the homogeneousF2 than on the heterogeneous F1. However, forparticular fields and analytes, these ratios variedwidely, between 0.14 for As on F2 with CT samplingand 1.99 for Ni on F1 with PT2 sampling.

When only intra-laboratory analytical uncertainty

is considered, us/uak ratios are by a factor of 3.4higher on average than the correspondingus/uatratios,and sampling uncertainty in general prevailed overanalytical uncertainty. However, also for the casewhen only uakis considered, the ranking of the ratiovalues among fields (F1 > F3 > F2) and samplingtrials (PT > CT) is the same as for the case ofus/uatratios. Also here, large variations among analytes areobserved. However, in contrast to the case when totalanalytical uncertainty is considered, total uncertainty

Field Analyte rsd(PT1) rsd(PT2) rsd(CT) us(PT1) us(PT2) us(CT) us(avrg)

F1 As 5.8 6.8 12.5 5.6 6.5 12.1 8.6

B 5.1 9.8 13.5 4.7 9.5 13.1 9.7

Co 6.2 5.9 5.6 5.6 5.2 5.0 5.2

Mo 15.0 14.1 10.4 13.8 13.3 8.3 12.0

Tl 14.5 34.2 13.1 14.3 34.1 13.0 22.6Cd 21.3 19.9 7.6 12.3 18.6 6.8 13.4

Cr 5.3 11.8 7.1 4.5 11.4 6.6 8.0

Ni 7.5 18.8 8.9 6.2 18.7 7.6 12.2

Pb 5.3 13.7 10.0 4.8 13.4 9.6 10.0

Zn 7.5 16.5 5.5 7.2 15.8 2.4 10.1

Mean 10.7 17.0 9.8 8.7 16.6 9.1 12.0

F2 As 5.6 5.2 3.3 4.9 4.4 2.6 4.1

B 3.1 5.0 3.2 2.8 4.5 2.3 3.3

Co 6.9 8.5 5.6 5.9 8.0 4.1 6.2

Mo 21.3 9.7 13.8 20.9 8.3 12.5 14.9

Tl 45.2 10.1 8.8 44.6 9.0 7.7 26.6Cd 7.4 19.9 4.9 6.2 17.7 3.7 11.0

Cr 5.7 6.4 3.4 4.9 6.0 2.5 4.7

Ni 17.6 11.1 9.0 17.6 10.9 5.9 12.4

Pb 3.1 3.0 3.0 2.7 2.8 2.8 2.8

Zn 4.9 7.9 2.4 4.1 6.1 1.5 4.3

Mean 17.4 9.7 6.7 17.0 8.8 5.5 11.5

F3 As 8.8 10.8 5.7 7.8 10.4 4.3 7.9

B 12.7 12.0 11.1 12.6 11.8 10.9 11.8

Co 5.0 5.0 3.5 4.7 4.5 2.5 4.0

Mo 9.8 11.0 8.2 8.4 5.8 4.7 6.5

Tl 5.7 5.4 3.5 5.4 4.9 2.5 4.4

Cd 8.7 9.2 16.9 7.1 8.7 16.8 11.7

Cr 5.5 6.9 4.2 5.0 5.5 3.0 4.7

Ni 7.1 12.2 6.5 6.6 12.1 3.2 8.2

Pb 5.2 5.1 4.4 5.0 4.9 4.0

Zn 6.8 7.4 6.2 6.4 7.3 5.9 6.5

Mean 7.9 8.9 8.1 7.3 8.1 7.5 7.5

Table 5 Repeatabilitystandard deviation (rsd) andsampling uncertainty (us),for all fields, analytes andsampling trials(PT1, PT2, CT)

All uncertainty (u) valuesare as percentage values (i.e.relative to the concentrationof the analyte)

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is dominated by sampling uncertainty for mostanalytefieldsampling combinations. Thus, in termsof the relative proportions of uncertainty componentswhich constitute the total measurement uncertainty, itmakes a large difference whether samples are ana-

lysed in a single laboratory or in several differentlaboratories.

Summarizing, comparison of the us/ua ratiossuggests that (1) sampling uncertainty plays a smallerrole on more homogeneous fields (F2) compared with

Field Analyte us/uak us/uat

PT1 PT2 CT PT1 PT2 CT

F1 As 2.51 2.56 2.62 0.32 0.37 0.69

B 1.65 2.66 2.86

Co 1.47 1.34 1.37

Mo 1.65 1.98 0.92

Tl 4.16 12.46 5.24

Cd 0.50 1.86 1.42 0.36 0.74 0.30

Cr 1.12 2.60 1.86 0.38 0.96 0.57

Ni 1.04 7.99 1.18 0.58 1.99 0.68

Pb 1.60 3.58 2.53 0.48 1.24 0.88

Zn 2.42 2.30 0.34 0.96 1.56 0.22

Mean 1.81 3.93 0.51 1.14

2.87 2.03 2.59a 0.83 0.55 0.74a

F2 As 1.33 1.17 0.90 0.27 0.24 0.14

B 1.43 1.45 0.74Co 1.19 1.90 0.76

Mo 3.56 1.19 1.48

Tl 4.22 1.43 1.25

Cd 1.09 1.39 0.80 0.25 0.65 0.16

Cr 1.20 1.91 0.75 0.43 0.54 0.22

Ni 9.67 3.95 0.61 1.88 1.14 0.44

Pb 1.29 1.63 1.74 0.25 0.27 0.26

Zn 1.04 0.86 0.54 0.46 0.58 0.18

Mean 2.60 1.69 0.59 0.57

2.15 0.96 1.75 a 0.58 0.23 0.46a

F3 As 1.34 2.65 0.82 0.57 0.79 0.32B 4.63 3.56 3.63

Co 1.96 1.47 0.68

Mo 1.19 0.44 0.49

Tl 2.05 1.49 0.74

Cd 1.03 2.02 5.28 0.32 0.41 0.79

Cr 1.59 0.97 0.71 0.45 0.45 0.26

Ni 1.76 5.61 0.40 0.72 1.39 0.28

Pb 2.29 2.69 0.57 0.58

Zn 2.01 3.95 1.96 1.00 1.24 0.93

Mean 1.99 2.48 0.60 0.81

2.23 1.64 2.05a 0.71 0.52 0.65a

All fields Mean 2.42 1.54 2.13b 0.71 0.43 0.62b

Table 6 us/uak and us/uatratios for all fields, analytesand sampling trials

All uncertainty (u) valuesare as percentage values (i.e.relative to the concentrationof the analyte)aAveraged for ten analytesand three sampling trialsb Averaged for ten analytes,three sampling trials andthree fields



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more heterogeneous fields (F1) and (2) the proportionof sampling uncertainty is lower when samplingpatterns are prescribed or standardized (CT sampling),compared with the case of free (individual) sam-pling patterns (PT samplings). This difference in themean us/uat ratio between CT and PT is especially

pronounced at the homogeneous field F2. This isaccording to the theoretical considerations: Since thesampling procedure was standardized among thesamplers in the CT sampling, it was expected thatsampling uncertainty would be smaller compared withthe PT samplings and correspondingly also the us/uatratios.

Variance components

The proportion of components of the total variance

based on the hierarchical statistical model (Eq.1) forthe results of the PT sampling trials is compiled inTable 7. The components vcsp and vcsr combinedcorrespond to the proportion of sampling uncertainty,and the residual component vcak represents theanalytical repeatability (within-laboratory) uncertain-

Table 7 Variance components (percent) based on the hierar-chical variance model (Eq. 1) for proficiency test samples

Analyte F1 F2 F3

vcsp vcsr vcak vcsp vcsr vcak vcsp vcsr vcak

As 3.2 84.9 11.9 15.2 49.4 35.4 14.4 54.6 31.0

B 0.0 86.3 13.7 8.2 59.0 32.9 31.8 61.8 6.3

Co 0.0 66.8 33.2 48.6 20.6 30.9 3.2 66.4 30.4

Mo 43.3 32.5 24.2 0.0 83.8 16.2 0.0 49.7 50.3

Tl 5.2 93.3 1.4 0.0 93.8 6.2 7.2 67.0 25.8

Cd 0.0 63.0 37.0 29.2 37.3 33.5 21.2 40.1 38.7

Cr 8.3 73.4 18.3 42.9 23.7 33.3 8.9 40.8 50.3

Ni 0.0 89.5 10.5 47.7 45.7 6.7 0.0 90.4 9.6

Pb 0.0 92.3 7.7 42.6 26.1 31.3 0.0 89.1 10.9

Zn 0.0 90.7 9.3 14.2 31.2 54.6 0.0 84.9 15.1Mean 6.0 77.3 16.7 24.9 47.1 28.1 8.7 64.5 26.8

Note that no variance components for the differences betweenthe fields are calculated because the fields cannot be viewed asrandom repetitions; note also that the values of vc(sp), vc(sr)and vc(sr) do not add up exactly to 100% in all cases due torounding errors

vcsp between samplers (i.e. sampling persons, n=18) withinfield, vcsr between duplicate samples within fields andsamplers,vcakresidual component, corresponding to analyticalvariance (within samples, samplers, fields)


ty. Note that the percentage values in Table7 refer tothe proportion of total measurement variance(=100%) captured by the PT sampling trial (i.e.without uab), whereas percentage values of uak andusrefer to the mean analyte content (cf. Fig.2).

Overall, averaged for the analytes, vcak is the

lowest for F1 (16.7%) and the highest for F2(28.1%), i.e. the proportion of sampling error isthe highest for the most heterogeneous F1 (83.3%)and the lowest for the most homogeneous F2(71.9%). On all fields, the influence of samplingrepetition (vcsr) is in general higher than that of thesamplers (vcsp). This implies a low degree ofspecificity of the applied sampling patterns (and alow influence of sampling-related parameters),especially for the most heterogeneous field F1, anda relatively high influence of spatial variability

(because the variability between the samplers maybe caused, besides soil heterogeneity, by the differ-ent sampling patterns and other sampling parame-ters, whereas in the sampling repetitions, identicalsampling patterns and parameters are compared andvariability can be caused solely by soil heterogene-ity). However, for separate analytes, vc values varyover a wide range for a given field, similarly as usand uakvalues.

In summary, results of the VCA reflect the differentfield-scale heterogeneity as determined by the refer-

ence sampling, in that the proportion of samplinguncertainty increases with field-scale heterogeneity,whereas on the most heterogeneous field F1, morethan 80% of total uncertainty are due to sampling; onthe most homogeneous F2, only about 70% and onthe intermediate F3, about 73% can be attributed tosampling uncertainty. These results are largely inaccordance with estimated ratios of sampling andanalytical uncertainty (Table 6). Moreover, the lowproportions of the sampling person (vcsp) comparedwith that of sampling repetition (vcsr) indicate that

heterogeneity has a larger influence on samplinguncertainty than sampling parameters.

Total uncertainty and probability of exceedingthreshold values

In the context of the German Federal Soil Protectionand Contaminated Sites Ordinance (BBodSchV1999), it is of interest whether measured soil elementcontents exceed a prescribed maximum permissible


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threshold value. Even if the measured average valueis below the threshold, it is possible that there existsan appreciable probability that the true elementcontent nevertheless exceeds the threshold.

This is demonstrated exemplarily for the data ofthis study in Table 8. The uncertainty of measured

contents is characterized by the total expandedmeasurement uncertainty Ut (i.e. the simple uncer-tainty multiplied by a coverage factor, in this case2), which encompasses total laboratory uncertaintyand sampling uncertainty and defines the 95%probability range of measured values.

From the measured contents andUt, the probabilitythat the true value exceeds the threshold can becalculated, assuming here a normal distribution. It canbe seen from Table8that in most cases (40 out of 53),the measured contents are safely below the threshold

value and the exceedance probability is zero. Only insome cases where the measured content is only littlebelow the threshold there is an appreciable probabilitythat the true value is above the threshold. But thereare also examples where the measured value seems tobe safely below the threshold, but due to the largetotal expanded uncertainty there is a non-negligibleprobability that the true value exceeds the threshold.Consider for instance Zn on F1 in the PT2 samplingwith a measured content of 45.9 which seems to besafely below the threshold of 60. However, Utis 38%

and consequently there is an appreciable probabilityof 5.2% that the true Zn concentration is above thethreshold.

General discussion

The results of this study show that both the absolutevalues and the importance ofusrelative to total analyticaluncertainty, i.e. us/uat ratios, increase in general withfield-scale heterogeneity (Table5 and6). Although thisis largely in agreement with many previous studies (e.g.

Jacob and Klute1956; Kerschberger and Richter1992;Kurfrst et al. 2004; van der Perk et al. 2008), us/uatratios estimated here are lower than most valuesreported in earlier studies. It is often claimed thatsampling uncertainty dominates over analytical uncer-tainty, and sampling uncertainties have been reportedwhich were by a factor of up to 30 larger than analyticaluncertainty (e.g. Taylor et al.2005; Rawlins et al.2009).Other studies reported more moderate us/ua ratios butstill higher than found here. For instance, van der Perk

et al. (2008) reported mean us/ua ratios of 3.4 andKurfrst et al. (2004) mean us/ua ratios of 1.54.However, most studies also yielded highly variable usvalues andus/uaratios depending on the type of analyteand the magnitude of field-scale heterogeneity. Theresults of the present study show in general no

predominance of sampling uncertainty over total ana-lytical uncertainty, and total laboratory uncertaintyoverall prevails over sampling uncertainty. However,this preponderance of laboratory uncertainty comparedwith sampling uncertainty is clearly connected with theinclusion ofuabintouat. When onlyuakis considered aslaboratory uncertainty (and uab ignored), samplinguncertainty in general prevails over analytical uncer-tainty withus/uakratios on average of about 2. However,even in that case, the proportion of sampling uncertaintyon total uncertainty is lower than in several other

studies. This can be explained by (1) low spatialheterogeneity, (2) low concentration levels and (3) largenumber of increments constituting the compositesamples.

Overall, the spatial heterogeneity of element con-tents found in this study is relatively low, whencompared with other studies, whereas here average

srefvalues (mean of ten analytes for each of the threefields) of 1328% were found (Table3), for instanceTaylor et al. (2005) reported for a Pb contaminatedsite CV values >50%. On the other hand, variation of

trace metals on uncontaminated sites is mostly lowerand comparable to values found in the present study:for instance van der Perk et al. (2008) reported for anagricultural site CV values of 9.3% (As), 67% (Cr)and 11% (Zn). Kurfrst et al. (2004) reported for anarable plot CV values of 54% (Cd), 13.2% (Cu),12.9% (Pb) and 18.3% (Zn).

Contrary to other studies, in the present study, thesupport of samples used to calculate the relativestandard deviations of the reference samplingsencompassed an appreciable percentage of the total

field area, and therefore, the resulting standarddeviations are presumably lower than standard devia-tions calculated from point-like data. On the otherhand, point-samples are often actually compositesamples consisting of several samples taken within aradius of a few meters (e.g. Lauzon et al. 2005).

Another explanation for the low proportion ofsampling uncertainty on total uncertainty found heremay be the general low level of element contents (cf.Table8), representing largely background concentra-

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Table 8 Trace metals considered in German Federal Soil Protection Ordinance (BBodSchV1999)

Field Analyte Samplingtrial

Mean(mg/kg)

Thresholda Ut % 2 ut Probability that true valueexceeds threshold

F1 As PT1 9.1 25 37 0.0

PT2 9.6 25 38 0.0

CT 10.4 25 43 0.0F1 Cd PT1 0.17 0.4 73 0.0

PT2 0.25 0.4 62 2.4

CT 0.27 0.4 48 2.1

F1 Cr PT1 21.6 30 26 0.1

PT2 23.2 30 33 3.6

CT 22.5 30 27 0.6

F1 Ni PT1 17.0 15 25 83.0

PT2 13.6 15 42 30.8

CT 13.2 15 27 15.7

F1 Pb PT1 21.2 40 22 0.0

PT2 18.1 40 35 0.0CT 17.6 40 29 0.0

F1 Zn PT1 56.9 60 21 29.7

PT2 45.9 60 38 5.2

CT 40.9 60 22 0.0

F2 As PT1 7.5 25 38 0.0

PT2 7.1 25 38 0.0

CT 7.0 25 37 0.0

F2 Cd PT1 0.18 1 52 0.0

PT2 0.19 1 65 0.0

CT 0.23 1 48 0.0

F2 Cr PT1 26.3 60 25 0.0

PT2 26.3 60 25 0.0

CT 26.6 60 23 0.0

F2 Ni PT1 12.6 50 40 0.0

PT2 13.0 50 29 0.0

CT 13.6 50 29 0.0

F2 Pb PT1 17.2 70 22 0.0

PT2 17.6 70 22 0.0

CT 16.9 70 22 0.0

F2 Zn PT1 39.7 150 20 0.0

PT2 41.9 150 24 0.0CT 41.5 150 17 0.0

F3 As PT1 17.0 25 32 0.1

PT2 17.8 25 33 0.8

CT 17.6 25 29 0.2

F3 Cd PT1 0.46 1.5 47 0.0

PT2 0.46 1.5 46 0.0

CT 0.47 1.5 54 0.0

F3 Cr PT1 24.3 100 25 0.0

PT2 24.9 100 27 0.0

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analytical uncertainty instead of averaged values foreach analyte, as long as there is no good explanationfor this variation. Due to the uncertainty andvariability of estimated uak values (Thompson andHowarth1976; Minkkinen1986; Hyslop and White2009), it is clear that uak values themselves are

fraught with uncertainty. Therefore, it may bejustified to indicate analytical repeatability uncer-tainty using averaged uak values, even when moredetaileduakvalues have been calculated. Informationabout the variability of uncertainty estimates can beprovided as confidence intervals of the u values (Lynet al.2007).

The comparison of the PT with the CT samplingrepetitions suggests that standardization of samplingprotocols effectively reduces sampling uncertainty,especially for fields of relatively low heterogeneity.

Such a standardized sampling protocol could be forinstance the X pattern with 20 sample incrementstested here in the CT sampling and utilized in manycountries, among others, in Germany (Lewandowski etal.1997; MLUV2009). On the other hand, when usingstandardized sampling protocols (CT approach), sys-tematic sampling bias is less likely to be detected thanwith many different sampling protocols (PT approach).Consequently, sampling uncertainty estimated with aCT may be artificially low (Ramsey et al. 2011).

Conclusions

The relatively simple sampling patterns tested hereare adequate to characterize the mean contents oftrace elements in arable soils of 36 ha area and lowto moderate heterogeneity, with relative standardsampling uncertainty values of about 10%, and totaluncertainty mostly not dominated by the influence ofsampling uncertainty. Sampling uncertainty and theratio of sampling uncertainty to laboratory uncertainty

in general increase with field-scale heterogeneity;however, total analytical uncertainty, encompassingboth within- and between-laboratory components, ison average larger than sampling uncertainty, especial-ly on fields of low and moderate heterogeneity.

Laboratory repeatability uncertainty estimatedfrom duplicate chemical analyses is highly variable,depending not only on the analyte but also on thefield and the sampling trial. If duplicate analyses of allsamples are available, repeatability uncertainty could


be indicated utilizing these individual laboratoryvalues, for instance by means of ranges assigned touncertainties.

Reproducibility (between-laboratory) analyticaluncertainty is on average by a factor of 2.7 higherthan repeatability uncertainty. Consequently, total

laboratory uncertainty is dominated by reproducibilityuncertainty, and total uncertainty is dominated by totallaboratory uncertainty. Reducing the sampling uncer-tainty has little effect in that case. Thus, whenanalysing samples in a single laboratory, uncertaintyis effectively reduced. However, this analytical uncer-tainty is probably artificially low, if analytical bias isnot accounted for.

When only repeatability laboratory uncertainty isconsidered, total uncertainty is dominated by sam-pling uncertainty, especially on the most heteroge-

neous field; consequently, when samples are analysedin only one single laboratory, total uncertainty may beeffectively reduced by reducing sampling uncertainty(for instance by a larger number of sample incre-ments), at least for heterogeneous fields.

Although comparison of the PT and the CTapproach suggests that standardization of samplingprotocols leads to reduced sampling uncertainty,sampling bias is less likely to be detected by the CTthan by the PT approach (i.e. sampling uncertaintyestimated with a CT may be artificially low). For all

investigated uncertainty variables, large differencesamong the analytes are observed; these are mostlydifficult to explain and seem to a large degreeunpredictable. Consequently, conclusions drawn forone specific element are not necessarily transferableto other nutrient elements.

Based on the VCA, the effect of samplingrepetition is larger than the effect of differentsampling persons. This indicates that field heteroge-neity has a larger influence on uncertainty thansampling-related parameters, especially for the more

heterogeneous fields.When measured element contents in fields are

characterized by both mean values and total measure-ment uncertainty, there is in several cases an appre-ciable probability that prescribed maximum thresholdvalues are exceeded even in cases when the meanvalue is well below the threshold. This is importantwhen threshold element contents are of concern, forinstance in the German Sewage Sludge and FederalSoil Protection Ordinance.


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Acknowledgments We want to thank Monika Preis fromthe engineering company Schnittstelle Boden (Ober-Mrlen)for kind support in providing management and fertilizationdata of the study sites. The cooperation with the Associationof the German Agricultural Analysis and Research Institutes(VDLUFA) is greatly acknowledged. The following profes-sional soil samplers participated in the sampling trials: J.Balsing (Oldenburg), M. Bldner (Jena), T. Blumstengel

(Rostock), O. Dillmann (Mnster), H. Geyer (Jena), Goll(Karlsruhe), L. Herold (Jena), A. Hoppe (Leipzig), G. Hrig(Leipzig), W. Klein (Speyer), C. Laue (Hameln), Maul(Kassel), Paris (Bernburg), A. Pudimat (Rostock), Dr. H.Schaaf (Kassel), S. Schnersch (Karlsruhe), D. Virkus (Bernburg)and H. Wundlechner (Mnchen). We acknowledge the support ofChristian Kleimeier (Institute for Land Use, University ofRostock), Ulrich Kurfrst (University of Applied Sciences, Fulda),and Manfred Munzert (Bavarian State Research Centre forAgriculture, Freising-Weihenstephan).

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