emma peré-trepat 1 and romà tauler 2 *

INVESTIGATION OF MAIN CONTAMINATION SOURCES OF HEAVY METAL IONS IN FISH,

SEDIMENTS, AND WATERS FROM CATALONIA RIVERS USING DIFFERENT MULTIWAY DATA

ANALYSIS METHODS

Emma Peré-Trepat1 and Romà Tauler 2*

1 Dept. of Analytical Chemistry, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain

2 IIQAB-CSIC, Jordi Girona 18-26, 08034 Barcelona, Spain

* e-mail: [email protected]

Outline:

• Introduction and motivations of this work

• Environmental data tables and chemometrics models and methods

• Example of application: metal contamination sources in fish, sediment and surface water river samples.

• Conclusions

Introduction and motivations of this work

• Pollution and toxicological chemical compounds are a threat for the environment and the health which need urgent measures and actions

• Environmental monitoring studies produce huge amounts of multivariate data ordered in large data tables (data matrices)

• The bottle neck in the study of these environmental data tables is their analysis and interpretation

• There is a need for chemometrics (statistical and numerical analysis of multivariate chemical data) analysis of these data tables!

What kind of information can be obtained from chemometric analysis of environmental multivariate data tables?

1. Detection, identification, interpretation and resolution of the main sources of contamination

2. Distribution of these contamination sources in the environment: geographically, temporally, by environmental compartment (air, water, sediments, biota,...),…

3. Distinction between point and diffuse contamination sources sources

4. Quantitative apportionment of these sources .....


In this work different chemometric multiway data analysis methods are compared for the resolution of the environmental sources of 11 metal ions in 17 river samples of fish, sediment and water at the same site locations of Catalonia (NE, Spain).

• Two-way bilinear model based methods• MA-PCA Matrix Augmentation Principal Component

Analysis • MA-MCR-ALS Matrix Augmentation Multivariate Curve

Resolution Alternating Least Squares• Three-way trilinear models based methods

• PARAFAC • TUCKER3• MCR-ALS trilinear• MCR-ALS TUCKER3


Special attention will be paid to:

• Finding ways to compare results obtained using bilinear and trilinear models for three-way data: getting profiles in three modes from bilinear models of three-way data

• Adaptation of MCR-ALS to the fulfillment of PARAFAC and TUCKER3 trilinear models

•Reliability of solutions: calculation of boundaries of bands of feasible solutions

•Integration of Geostatistics and Chemometrics in the investigation of environmental data

Outline:


• Environmental data tables and chemometrics models and methods

• Example of application: metal contamination sources in fish, sediment and river surface water samples.

• Conclusions

I sa

mpl

es

J variables

0 5 10 15 20 25 30-50

0

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200

250

300

350

0 5 10 15 20 25 30 35 40 45 50-50

0

50

100

150

200

250

300

350

Data table or matrix

Plot of samples(rows)

Plot of variables(columns)

12 13 45 67 89 42 35 0 0.3 0.005 111 33 5 67 90 0.06 44 33 1 2

X

Environmental data tables (two-way data)

Conc. of chemicalsPhysical PropertiesBiological propertiesOther .....

‘m’

<LOD

Environmental three-way data sets

Measured data usually consisted on concentrations of differentchemical compounds (variables) measured in different samplesat different times/situations/conditions/compartments.

Data are ordered in a two-way or in a three-way data table accordingto their structure

time/

compartm

ent3-way data sets

variables (conc. Chemical ompounds)

sam

ples

Three measurement modes- variables mode- sample mode- times/situations/conditions/ compartments mode

Models for what?Models for:1. identification of contamination sources?2. exploration of contamination sources?3. interpretation of contamination sources?4. resolution of environmental source?5. apportionment/quantitation of environmental

source?6. ??????..............................

Chemometric models to describe environmental measurements

E XY D T

N

1nijjninij eyxd

dij is the concentration of chemical contaminant j in sample in=1,...,N are a reduced number of independent environmental sourcesxin is the amount of source n in sample i;ynj is the amount of contaminant j in source n

Bilinear models for two way data:

D

J

Idij


N

D XYT

E+

J J J

I I

N

N << I or J

PCA X orthogonal, YT orthonormal

YT in the direction of maximum variance

Unique solutions

but without physical meaningIdentification and Intereprtation!

MCR-ALSX and YT non-negativeX or YT normalization

other constraints (unimodality, local rank,… )

Non-unique solutions but with physical meaning

Resolution and apportionment!

I

Bilinear models for two way data:


YT

Dk Xk

(I x J) (I,n)

YT

(n,J)

Dk

Dk Xk

(I x J) (I,n)

YT

(n,J)

PCA: orthogonality; max. variance

MCR: non-negativity, nat. constraints

Xk

Daug

Xaug

Extension of Bilinear models for simultaneous analysis of multiple two way data sets


Matrix augmentation

strategy

Environmental data sets

dijk is the concentration of chemical contaminant j in sample I at time (condition) kn=1,...,N are a reduced number of independent environmental sourcesxin is the amount of source n in sample i;ynj is the amount of contaminant j in source nznk is the contribution of source n to compartment k

Tk kD =XZ Y E

z

N

ijk in jn kn ijkn=1

d = x y +e


Trilinear models for three-way data:

k=1,...,Ki=1,

...,I

j=1,...,J

Dk

Three Way data models

X-mode D

Y-mode

Z-mode

(I , J , K)

X YZ

Ni Nj Nk

I J

K

variables

sam

ples

cond

itions

D= X

YT

Z

PARAFAC (trilinear model)

The same number of components In the three modes: Ni = Nj = Nk = N

No interactions between components

Different slices Xk are decomposed In bilinear profiles having the same shape!

Tk kD =XZ Y E

z

N

ijk in jn kn ijkn=1

d = x y +e

ji k

i j k i j k

i j k

NN N

ijk n n n in jn kn ijkn =1 n =1 n =1

d = x y z +eg

D

X

YTG

Z

=•Different number of componentsin the different modes Ni Nj Nk

•Interaction between components in different modes is possible

In PARAFAC Ni = Nj = Nk = N andcore array G is a superdiagonal identity cube

Tucker3 models

Deviations from trilinearity Mild Medium Strong Array size

PARAFAC

Small PARAFAC2

Medium TUCKER

Large MCR, PCA, SVD,..

Guidelines for method selection(resolution purposes)

Journal of Chemometrics, 2001, 15, 749-771

METHODOLOGYMETHODOLOGY

INTEGRATION OF CHEMOMETRICS

—GEOSTATISTICS

(GeographicalInformation

Systems, GIS)

Outline:


• Environmental data tables

• Chemometrics bilinear and trilinear models and methods


• Conclusions

141516

17

13

1211

10

9

8

7

45 6

2

3

1

1. RIU MUGA Castelló d´Empúries J0522. RIU FLUVIÀ Besalú J0223. RIU FLUVIÀ L´Armentera J0114. RIU TER Manlleu J0345. RIU TERRI Sant Julià de Ramis J0286. RIU TER Clomers J1127. RIU TORDERA Fogars de Tordera J0628. RIU CONGOST La Garriga J0379. RIU LLOBREGAT El Pont de Vilomara J03110. RIU CARDENER Castellgali J00211. RIU LLOBREGAT Abrera J08412. RIU LLOBREGAT Martorell J00513. RIU LLOBREGAT Sant Joan Despí J04914. RIU FOIX Castellet J00815. RIU FRANCOLÍ La Masó J05916. RIU EBRE Flix J05617. RIU SEGRE Térmens J207

17 rivers, 11 metals (As, Ba, Cd, Co, Cu, Cr, Fe, Mn, Ni, Pb, Zn),

3 environmental conpartments: Fish (barb’, ‘bagra comuna’, bleak, carp and

trout), Sediment and Water samples

METAL CONTAMINATION SOURCES IN SEDIMENTS, FISH AND WATERS FROM CATALONIA RIVERS USING MULTIWAY DATA ANALYSIS METHODS

Emma Peré-Trepat (UB), Mónica Flo, Montserrat Muñoz, Antoni Ginebreda (ACA), Marta Terrado, Romà Tauler (CSIC)

Mediterranean Sea

Pyrinees

Barcelona

France

Ara

gó

n

Missing data (‘m’)

• Unknown values produce empty holes in data matrices•When they are few and they are evenly distributed, theymay be estimated by PCA imputation (or other method)

Below LOD values (<LOD)

• This a common problem in environmental data tables• If most of the values are below LOD, data matrices are sparse • For calculations, it is better, either to use the experimental values or set them to LOD/2 instead of to zero or to LOD

Preliminary data description: Use of descriptive statisticsIndividual sample plots1) Individual variable plots 2) Descriptive statistics (Excel Statistics)3) Histograms/Box plots4) Binary correlation between variables5) .............................................................

**

*

**

1 2 3 4 5 6 7 8 91011121314151617181920212223242526272829303132333435363738394041424344454647484950

0

50

100

150

200

250

300

Column Number

lower quartile

median

upper quartile

upper whisker

lower whisker

outliers

outliers

0 2 4 6 8 10 120

1

2

3x 10

4

1 2 3 4 5 6 7 8 9 10 11-2

0

2x 10

4

1 2 3 4 5 6 7 8 9 10 11-2

0

2

4

1 2 3 4 5 6 7 8 9 10 110

2

4

6

Effect of different data pre-treatments: Sediment samples

raw

mean-centred

auto-scaled

scaled

As Ba Cd Co Cu Cr Fe Mn Ni Pb Zn

Mo is eliminated

Data Pretreatment– No mean-centering was applied to allow an improved physical

interpretation of factors (application of non-negativity constraints instead of orthogonality constraints) and the comparison of results using MCR-ALS methods

– Two scaling possibilities:• First, data matrix augmentation and then column scaling to equal variance (each

column element divided by its standard deviation)• First, column scaling each data matrix separately and then data matrix

augmentation

– Variables with nearly no-changes and equal or close to their limit of detection were removed from scaling and divided by 20 (to avoid their miss-overweighting)

As Ba Cd Co Cu Cr Fe Mn Ni Pb Zn-1

0

1

2

3

4

5mean -+ std of scaled concentrations of 11 metals

water

sedimentsfish

metals (variables)

Description of scaled dataMetal distribution in the three compartments

Cd, Co and Ld in waterwere not scaled; only downweigthed

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170.5

1

1.5

2

2.5

3

water

sediment

fish

sample sites

Foix

Ter

Ebre

Llobregat

Terri

Segre

Tordera

Francolí

Llobregat

Llobregat

MugaFluvià

FluviàTer

Congost

Llobregat

Cardener

Description of scaled data:different sites in the three compartments


1 2 3 4 5 6 7 8 9 10 110

2

4

Unit variance scaled concentrations boxplot

Va

lues

1 2 3 4 5 6 7 8 9 10 110

2

4

Va

lues

1 2 3 4 5 6 7 8 9 10 110

2

4

6

Va

lues

Fish

Sediment

Water

Water

Sediment

Fish

Fish Sediment Water

0 1 2 3 4 5 6 7 8 9 10

0

5

10

15

20

25

30

35

40

45SVD odf augmented data matrices in the three-directions

svd column-wise (variables)

svd row-wise (samples)

svd trube-wise (type)

AUGMENTATION direction

column row tube

s1 40.2619 43.2553 41.3302

s2 16.7504 9.2823 19.4850

s3 9.4963 8.5312 14.3739

2nd component

How many componentsare needed to explain each mode?

contaminants

compartments

site

s

THREE-WAY DATA ARRAY MATRICIZING

or MATRIX AUGMENTATION

FishSediment

Water

Daug

Y

metals

compartments

site

s

F

S

W

F

S

W

contaminants

site

ssi

tes

site

s

1

2

3

4

5

6

MA-PCAMA-MCR-ALS

Bilinear modelling of three-way data(Matrix Augmentation or matricizing, stretching, unfolding )

Xaug

Augmenteddata matrix

Augmentedscores matrix

Loadings

I

1i

J

1j

2j,i

d

I

1i

J

1j

2j,i

e

12R

j,ij,ij,i dde

where di,j is the experimental value in the augmented data matrix for metal j and sample i

and j,id

is the corresponding calculated value using PCA or MCR-ALS bilinear models

and number of components

Explained variances using bilinear models (profiles in two modes)

N

1n j,ien,jyn,ixj,id

1 2 3 4 5 6 7 8 9 10 110

0.1

0.2

0.3

0.4

0.5

1 2 3 4 5 6 7 8 9 10 11-0.5

0

0.5

MA-PCA of scaled data without scores refolding

As Ba Cd Co Cu Cr Fe Mn Ni Pb Znmetals

%R2 (2-WAY)

1rst Compone

nt

2nd Compone

ntTotal

67.3 13.2 80.5

0

2

4

6

8

10

water samples

sediment and fishsamples

0 5 10 15 20 25 30 35 40 45 50

0 5 10 15 20 25 30 35 40 45 50-5

0

5

MA-PCA

As Ba Cu Zn

water soluble

metal ions


1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

MA-MCR-ALS of scaled data with nn and without scores refolding

%R2 (2-WAY)

1rst Compone

nt

2nd Compone

ntTotal

48.2 42.8 80.5

67.3 13.2 80.5

MA-MCR-ALSMA-PCA

0 5 10 15 20 25 30 35 40 45 500

2

4

6

8

10

0 5 10 15 20 25 30 35 40 45 500

2

4

6

8

10



water samples

sediment and fishsamples

As

BaCu Zn

More easilyInterpretable!!!

0 10 20 30 40 500

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

0.8

0 10 20 30 40 500

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

Calculation of the boundaries of feasible band solutions(Journal of Chemometrics, 2001, 15, 627-646)

Nearly no rotation ambiguities are present in non-negative environmental profiles calculated by MCR-ALS

(very different to spectroscopy!!!!!)

max

min

Xaug

D

X Y

Y

contaminants

compartments

site

s

SVD

Z

FS

W

F

S

W

contaminants

site

ssi

tes

site

s

1

2

3

1 2 3 x

i

site

s

contaminants

compartments (F,S,W)

SVD4 5 6

4

5

6

xii

z

i

z

ii

x

i

xii

PCAMCR-ALS

z

iz

ii

Bilinear modelling of three-way data(Matrix Augmentation or matricizing, stretching, unfolding )

Scores refolding

strategy!!!(applied only

to final augmented

Scores)

Loadings recalculationin two modes

from augmentedscores

I

1i

J

1j

K

1k

2k,j,i

d

I

1i

J

1j

K

1k

2k,j,i

e

12R

k,j,id

k.j,id

k,j,ie

where di,j,k is the experimental value in the data cube for metal j.

sample i environmental compartment k

and k,j,id

is the corresponding calculated value using PARAFAC , Tucker3 or for PCA or MCR-ALS of augmented data matrices after recovery ogf loadings in three modes (either from scores refolding or from constraints application,

d̂ zN

i,j,k i,n j,n k,nn=1

= x yji k

i j k i j k

i j k

NN N

i,j,k n ,n ,n i,n j,n k,nn =1 n =1 n =1

d = x y zg

Explained variances using trlinear models (profiles in three modes)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

2

4

6

8

10

12

sample sites

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

2

4

6

8

10

12

sample sites

F S W0

0.4

0.8

compartments

F S W-0.8

-0.4

0

0.4

0.8

compartments

As Ba Cd Co Cu Cr Fe Mn Ni Pb Zn0

0.1

0.2

0.3

0.4

0.5

metals

As Ba Cd Co Cu Cr Fe Mn Ni Pb Zn-0.5

0

0.5

metals

%R2 (3-WAY)

1rst Component

2nd Component Total

64.7 11.7 76.4

67.3 13.2 80.5

MA-PCA + refolding MA-PCA

MA-PCA of scaled data with nn and scores refolding

Little differences in samples mode!!!


0.2

0.4

0.6

0.8

metals


0.2

0.4

0.6

0.8

metals1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0

5

10

15

sample sites

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

5

10

15

sample sites

F S W0

0.5

1

compartments

F S W0

0.5

1

compartments

MA-MCR-ALS of scaled data with scores refolding

47.0 40.7 76.9

%R2 (3-WAY)

1rst Componen

t

2nd Component Total

MA-MCR-ALS + refoldingMA-MCR-ALS

48.2 42.8 80.5

D PARAFAC

Zcontaminants

compartments

site

s

X

YF

S

W

metals

site

scom

partm

ents

(F,S

,W)

site

s

metals

com

partm

ents

(F,S

,W)

Trilinear modelling of three-way data


0.2

0.4

0.6

0.8

metals


0.2

0.4

0.6

0.8

metals

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

5

10

15

samples sites

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

5

10

15

sample sites

F S W0

0.5

1

compartments

F S W0

0.5

1

compartments

PARAFAC of scaled data

%R2 (3-WAY)

1rst Component

2nd Component Total

43.4 36.2 77.4

67.3 13.2 80.5

PARAFACMA-PCA (bilinear)

1 2 3 4 5 6 7 8

-0.2

0

0.2

0.4

0.6

0.8

1

1.2Core consistency 99.9395% (yellow target)

Core elements (green should be zero/red non-zero)

Cor

e S

ize

D

Xaug

Y

contaminants

compartments

site

s

X Y

Z

TRILINEARITY CONSTRAINT(ALS iteration step)

Selection of species profile

Folding SVDRebuilding augmented scores

Substitution ofspecies profile

F

S

W

F

S

W

contaminants

site

ssi

tes

site

s

site

s

contaminants


1

2

3

1

2

3

1’

2’

3’

MCR-ALS

every augmentedscored wnated tofollow the trilinearmodel is refolded



MA-MCR-ALSTrilinear constraint

This constraintis applied at each stepof the ALS optimization

and independently for each component

individually

MA-MCR-ALS of scaled data with nn, trilinearity (without scores refolding)

1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

0 5 10 15 20 25 30 35 40 45 500

2

4

6

8

10

0 5 10 15 20 25 30 35 40 45 500

2

4

6

8

10



%R2 (2-WAY)

1rst Component

2nd Compon

entTotal

44.3 42.9 76.8

48.2 42.8 80.5

MA-MCR-ALS nn + trilinearMA-MCR-ALS nn

0 10 20 30 40 500

2

4

6

8

10

0 10 20 30 40 500

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

0.8

1 2 3 4 5 6 7 8 9 10 110

0.1

0.2

0.3

0.4

0.5

Calculation of the boundaries of feasible band solutions(Journal of Chemometrics, 2001, 15, 627-646)

No rotation ambiguities are present in trilinear non-negative environmental profiles calculated by MCR-ALS

(very different to spectroscopy!!!!!)


0.2

0.4

0.6

metals


0.2

0.4

0.6

metals

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

5

10

15

sample sites

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

5

10

15

sample sites

F S W0

0.5

1

compartments

F S W0

0.5

1

compartments

MA-MCR-ALS of scaled data with nn, trilinearity and with scores refolding

%R2 (3-WAY)

1rst Componen

t

2nd Component Total

44.3 42.9 76.8

43.4 36.2 77.4

MA-MCR-ALS nn + trilinearPARAFAC nn


0.2

0.4

0.6

0.8

metals


0.2

0.4

0.6

0.8

metals

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

5

10

15

samples sites

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

5

10

15

sample sites

F S W0

0.5

1

compartments

F S W0

0.5

1

compartments


0.2

0.4

0.6

metals


0.2

0.4

0.6

metals

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

5

10

15

sample sites

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

5

10

15

sample sites

F S W0

0.5

1

compartments

F S W0

0.5

1

compartments

Comparison PARAFAC vs MCR-ALS (trilinearity)

TUCKER3

GModel (1,2,2)

D =

metals

compartments

site

s

X

Y

Z

F

S

W

site

s

metalsmetals

site

scom

partm

ents

(F,S

,W)

12

21

22

com

partm

ents

(F,S

,W)

Tucker3 modelling of three-way data

Tucker Models with non-negativityconstraints

0 5 10 15 20 25 3064

66

68

70

72

74

76

78

80

82

84

[1 2 2] [1 2 3]

[1 3 3]

[2 2 2] [2 2 3]

[2 3 3] [3 3 3]

Explained variances (%) for each

TUCKER3 mstudied odel studied.

TUCKER3 model

Sum of Squares (%)

[1,1,1] 64.7

[1,1,2] 64.7

[1,1,3] 64.7

[1,2,1] 64.7

[1,2,2] 76.1

[1,2,3] 76.1

[1,3,1] 64.7

[1,3,2] 76.1

[1,3,3] 80.3

[2,1,1] 64.7

[2,1,2] 66.3

[2,1,3] 66.3

[2,2,1] 66.9

[2,2,2] 77.3

[2,2,3] 78.1

[2,3,1] 66.9

[2,3,2] 78.4

[2,3,3] 82.4

[3,1,1] 64.7

[3,1,2] 66.3

[3,1,3] 67.3

[3,2,1] 66.9

[3,2,2] 77.9

[3,2,3] 79.3

[3,3,1] 68.4

[3,3,2] 79.8

[3,3,3] 83.6

[3 2 3]

parsimonious model[1 2 2]

0 5 10 150

0.2

0.4

1 2 3 4 5 6 7 8 9 10110

0.5

1

1 2 30

0.5

1

1 2 3 4 5 6 7 8 9 10110

0.5

1

1 2 30

0.5

1

Tucker3 of scaled data

%R2 (3-WAY)

1rst Componen

t

2nd Component Total

50.7 35.3 76.1

43.4 36.2 77.4

TUCKER3PARAFAC

model [1 2 2]model [2 2 2]

Folding

D

=

XY

Xaug

Y

contaminants

compartments

site

s

Z

=

F

S

W

F

S

W

metals

site

ssi

tes

site

s

1

2

3

4

5

6

1 2 3 4 5 6


1’

2’

3’

4’

5’

6’

=

MCR-ALS

Tucker3 CONSTRAINT(ALS iteration step)

SVD

interacting augmented scores are folded

together



MA-MCR-ALSTucker3

constraint

This constraint is applied at each step of the ALS optimizationand independently and individually for each component i

1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

MA-MCR-ALS of scaled data with nn, tucker3 (without scores refolding)

0 5 10 15 20 25 30 35 40 45 500

2

4

6

8

10

0 5 10 15 20 25 30 35 40 45 500

2

4

6

8

10

%R2 (2-WAY)

1rst Component

2nd Compon

entTotal

45.2 41.4 75.8

44.3 42.9 76.8

MA-MCR-ALS nn + Tucker3MA-MCR-ALS nn + PARAFAC

model [1 2 2]model [2 2 2]


0.2

0.4

0.6

metals


0.2

0.4

0.6

metals1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0

5

10

15

sample sitesF S W

0

0.5

1

compartments

F S W0

0.5

1

compartments

MA-MCR-ALS of scaled data with nn, tucker3 and with scores refolding

%R2 (3-WAY)

1rst Componen

t

2nd Component Total

45.2 41.4 75.8

50.7 35.3 76.1

MA-MCR-ALS nn + Tucker3Tucker3

model [1 2 2]model [1 2 2]

CHEMOMETRIC METHOD%R2 (3-WAY) %R2 (2-WAY)

1rst Component

2nd Component

Total1rst

Component2nd

ComponentTotal

MA-PCA (scale) 64.7 11.7 76.4 67.3 13.2 80.5

PARAFAC (non-negativity) 43.4 36.2 77.4 - - -

TUCKER3 (non-negativity) 50.7 35.3 76.1 - - -

MA-MCR-ALS (non-negativity) 47.0 40.7 76.9 48.2 42.8 80.5

MA-MCR-ALS (non-negativity and triliniarity)

44.3 42.9 76.8 - - -

MA-MCR-ALS (non-negativity and tucker restrictions)

45.2 41.4 75.8 - - -

Summary of Results

J052 Riu Muga Castelló d'Empúries

J022 Riu Fluvià Besalú

J011 Riu Fluvià Armentera, l'

J034 Riu Ter Manlleu

J028 Riu Terri Sant Julià de Ramis

J112 Riu Ter Colomers

J062 Riu Tordera Fogars de Tordera

J037 Riu Congost Garriga, la

J031 Riu Llobregat Pont de Vilomara i Rocafort, el

J002 Riu Cardener Castellgalí

J084 Riu Llobregat Abrera

J005 Riu Llobregat Martorell

J049 Riu Llobregat Sant Joan Despí

J008 Riu Foix Castellet i la Gornal

J059 Riu Francolí Masó, la

J056 Riu Ebre Flix

E207 Riu Segre Térmens

(67.3%)(13.2%)

INTEGRATION OF CHEMOMETRICS-GEOSTATISTICS (Geographical Information

Systems, GIS)

Outline:


• Environmental data tables

• Chemometrics bilinear and trilinear models and methods


• Conclusions

Conclusions

Chemometric methods allow resolution of environemtal sources of chemical contaminants

However we should we aware of how every method displays the information because the mathematical properties of the used method are different (i.e. orthogonality vs non-negativity, bilinearity vs trilinearity, nr. of components...)

This interpretation and resolution of environmental sources is not easy because the contamination sources in real world are correlated and because of experimental data limitations (environmental sources should show variation in the investigated data set).

Bilinear PCA and MCR-ALS can be used to study multiway data sets and compared with multiway methods (like PARAFAC and Tucker if appropriate scores refolding is performed)

Bilinear non-negative MCR-ALS solutions may provide good approximation of the real sources because non-negative environmental profiles have little rotation ambiguity

Conclusions

PARAFAC and Tucker3 may provide simpler models and they are special useful for trilinear data or when not the same number of components are present in the different modes.

Intermediate situations between pure bilinear and pure trilinear models can be easily implemented in MCR-ALS

Bilinear based models are more flexible than trilinear based models to resolve ‘true’ sources of data variation

Different number of components and interactions between components in different modes (constraint under development) can be considered in mixed bilinear-trilinear-Tucker MA-MCR models

For an optimal RESOLUTION, the model should be in accordance with the 'true' data structure

Integration of Chemometrics-GIS results may facilitate geographical and temporal interpretation of contamination sources and they correlation with land uses, population and industrial activities

Acknowledgements

• Water Catalan Agency is acknowledge for its financial support and for providing experimental data sets

• Research grant Project MCYT, Nr. BQU2003-00191, Spain

emma peré-trepat 1 and romà tauler 2 *

Documents

work environmental data

environmental sources

metal contamination

chemometrics models

river samples of fish

environmental compartment

surface water river

river surface water