64
R. Bruggemann et al.
locations, their values are derived following a procedure described by Nimis and
Bargagli (1999).
Lichens are perennial, slow-growing organisms, highly dependent on the atmosphere for nutrients. The lack of a waxy cuticle and stomata allows many contaminants, which are deposited on lichens by precipitation, fog and dew, dry
sedimentation and gaseous absorption, to be absorbed over the whole lichen thallus
surface, indicating levels of these contaminants in the surrounding environment
(Loppi et al. 1999). By biomonitoring at specifically selected sites, for example
near roads (Frati et al. 2006) or more pristine areas (Loppi and Pirintsos 2003),
information is obtained about the transport and origins of pollution.
In Pirintsos et al. (2014) 11 metals/metalloids are investigated in 20 sites of an
urban and industrial area based on the lichen biomonitoring data set of Demiray
et al. (2012), where Xanthoria parietina lichen specimen have been used as a
biomonitoring organism. The evaluation of the corresponding data matrix is based
on the conception that the Hasse diagram technique (see below) can further be
expanded and improved in the direction of (i) cumulative risk, (ii) the up-to-date
formal presentation and (iii) the interpretation of results in biomonitoring studies of
metal atmospheric pollution.
The analysis of biomonitoring results can be crudely characterized by two
aspects: (a) attempts to support a decision, based on order relations and (b) attempts
to present small scale spatial variations within a geostatistical approach. Here our
focus is on the order theoretical aspects.
As the metals and metalloids are measured at m different sites the concentrations
found in lichens of each site define, after transformations as recommended by Nimis
and Bargagli (1999) an indicator. Hence the MIS contains m indicators, the values
describing the pollution due to a single metal or metalloid.
The question arises how to derive a decision when confronted with m indicators.
Here we show first a Hasse diagram, which is a visualization of the partial order,
induced by the set of indicators (cf. Bruggemann and Patil 2011), then we discuss,
as to how far a single ranking (a weak order (see below)) can be obtained without
the need of a subjective weighting scheme of the indicators in order to aggregate
them by a weighted sum. As an exact solution of the problem how to get a weak
order is hardly computationally tractable, we investigate a new calculation method.
2 Material and Methods
2.1 Data Set
Eleven Metals and metalloids, i.e., Hg, Al, As, Cd, Cu, Fe, Mn, Ni, Pb, V and Zn for
which their pollution has been monitored are included in the study (Pirintsos et al.
2014). For a management it is of importance which of these metals or metalloids (in
the following we call them simply metals, although this is not a chemically correct
R. Bruggemann et al.
locations, their values are derived following a procedure described by Nimis and
Bargagli (1999).
Lichens are perennial, slow-growing organisms, highly dependent on the atmosphere for nutrients. The lack of a waxy cuticle and stomata allows many contaminants, which are deposited on lichens by precipitation, fog and dew, dry
sedimentation and gaseous absorption, to be absorbed over the whole lichen thallus
surface, indicating levels of these contaminants in the surrounding environment
(Loppi et al. 1999). By biomonitoring at specifically selected sites, for example
near roads (Frati et al. 2006) or more pristine areas (Loppi and Pirintsos 2003),
information is obtained about the transport and origins of pollution.
In Pirintsos et al. (2014) 11 metals/metalloids are investigated in 20 sites of an
urban and industrial area based on the lichen biomonitoring data set of Demiray
et al. (2012), where Xanthoria parietina lichen specimen have been used as a
biomonitoring organism. The evaluation of the corresponding data matrix is based
on the conception that the Hasse diagram technique (see below) can further be
expanded and improved in the direction of (i) cumulative risk, (ii) the up-to-date
formal presentation and (iii) the interpretation of results in biomonitoring studies of
metal atmospheric pollution.
The analysis of biomonitoring results can be crudely characterized by two
aspects: (a) attempts to support a decision, based on order relations and (b) attempts
to present small scale spatial variations within a geostatistical approach. Here our
focus is on the order theoretical aspects.
As the metals and metalloids are measured at m different sites the concentrations
found in lichens of each site define, after transformations as recommended by Nimis
and Bargagli (1999) an indicator. Hence the MIS contains m indicators, the values
describing the pollution due to a single metal or metalloid.
The question arises how to derive a decision when confronted with m indicators.
Here we show first a Hasse diagram, which is a visualization of the partial order,
induced by the set of indicators (cf. Bruggemann and Patil 2011), then we discuss,
as to how far a single ranking (a weak order (see below)) can be obtained without
the need of a subjective weighting scheme of the indicators in order to aggregate
them by a weighted sum. As an exact solution of the problem how to get a weak
order is hardly computationally tractable, we investigate a new calculation method.
2 Material and Methods
2.1 Data Set
Eleven Metals and metalloids, i.e., Hg, Al, As, Cd, Cu, Fe, Mn, Ni, Pb, V and Zn for
which their pollution has been monitored are included in the study (Pirintsos et al.
2014). For a management it is of importance which of these metals or metalloids (in
the following we call them simply metals, although this is not a chemically correct