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Background to the Aerosol Particles Data (Four-way data set)

Data analysed in: Kroonenberg, P. M. (2008). Applied multiway data analysis. Hoboken NJ: Wiley.

The four-way aerosol particles data on air quality was first analysed by multiway methods by Stanimirova & Simeonov (2005). Their study can be seen as a part of the area of receptor modeling in which not only the content of aerosol samples are analyzed, but also the sources of pollution are identified. Receptor modeling has greatly benefitted from the use of multiway models as is evident from the work by Hopke and colleagues. For an introduction and relevant publications see http://people.clarkson.edu/~hopkepk/project1.html. The aim of Stanimirova and Simeonov's analysis of the air quality data from Kärnten (Carynthia), Austria was to shed light on the nature and origin of the air pollution by use of four-way methods. More in particular, they wanted to characterize air quality on the basis of particle size, seasonality, and chemical composition. To this end the airborne concentrations of the chemicals were measured between March 1999 and February 2000 in Unterloibach and Arnoldstein, both close to industrial centers. By relating the four aspects of the data, an insight was achieved into the nature of the air pollution in the Carynthian province.


Data description

The four-way profile data consisting of the concentrations of 16 chemical compounds plus dust for each of 5 particle sizes, which were measured at 2 locations in each of the 4 seasons in Kärnten (Carynthia), Austria. There are some missing data due to concentrations below the measurement threshold of the instruments. Please note that very small values may be substituted for the missing data, but not the means as the latter are completely unrepresentative for the below-threshold values and may lead to non-converging solutions.

Rows (1st mode): Fractions (Particle sizes)

No.Size Description
1..04 .1

Columns (2nd mode): Parameters (Chemical variables)

No.Chemical Description
1.Na Natrium
2.NH4 Ammonium
3.K Potassium
4.Ca Calcium
5.Mg Magnesium
6.Cl Chlorine
7.NO3 Nitrate
8.SO4 Sulfate
9.DustDust particles
10.C Carbon
11.Cd Cadmium
12.Cu Copper
13.Fe Iron
14.Mn Maganese
15.Pb Lead
16.V Vanadium
17.Zn Zinc

Slices (3rd mode): Samples

No.Abbreviation Description
1.Unterl Unterloibach, Austria
2.Arnold Arnoldstein, Austria

Pipes (4th mode): Seasons

No.Abbreviation Description
1.WinterWinter 2000
2.Fall Autumn 1999
3.SummerSummer 1999
4.SpringSpring 1999

Data arrangement

A four-way data array X = (x(i,j,k,l)) may have the following form

                      k=1                                    k=K=2

                        |-----|i=1                               |-----|i=1
                   |-----|    |i=2                          |-----|    |i=2
              |-----|    |    |..                      |-----|    |    |..
              |     |    |    |..                      |     |    |    |..
              |     |    |____|i=I=5    l=L=4          |     |    |____|i=I=5    l=L=4
              |     |____|            l=2              |     |____|            l=2
              |_____|              l=1                 |_____|              l=1

            j=1,.,J=17                               j=1,.,J=17


The actual data file has the following form:

            |     |i=2
            |     |..     k=1
            |     |..
            |_____|i=I=5              l=1
            |     |i=2
            |     |..     k=K=2
            |     |..
            |_____|i=I=5                .
          j=1,.,J=17                    .
            |     |i=2
            |     |..     k=1
            |     |..
            |-----|i=1                l=L=4
            |     |i=2
            |     |..     k=K=2
            |     |..


Thus the first mode (i) is nested in the third mode (k) which is nested in the fourth mode (l) and there are 5 (Fractions) times 2 (Locations) times 4 (Seasons) rows and 17 (Parameters) columns columns.

Data handling


Given the physical nature of the data no centring was applied. However, the data were normalised per parameter (chemical) over all fractions, samples and seasons as these parameters were measured on totally different scales. For details see Kroonenberg (2008). Applied multiway data analysis. Hoboken NJ: Wiley (Chapters 6 and 19).


These data have kindly been supplied by Dr. Ivana Stanimirova, Department of Chemometrics, Institute of Chemistry, The University of Silesia, Katowice, Poland. They were collected under the direction of Prof. Hans Puxbaum, Research Group for Atmospheric Analytical Chemistry, Vienna University of Technology, Wien, Österreich, who generously allowed their public access via this website. Please be sure to quote the papers mentioned above and this website when using these data in a publication.

[Download the zipped Aerosol Particles Data]

| Centre for Child and Family Studies | Institute of Leiden Institute of Education and Child Studies | The Three-Mode Company | Three-Mode Data Sets | TOP |
P.M. Kroonenberg
Institute of Leiden Institute of Education and Child Studies, Leiden University
Wassenaarseweg 52, 2333 AK Leiden, The Netherlands
Tel. *-31-71-5273446/5273434 (secr.); fax *-31-71-5273945
E-mail: kroonenb at fsw.leidenuniv.nl

Created: 10-7-2009
Last Updated: 10-7-2009