A quick visual inspection of Figures 2 and 3 shows that both methods identify the same source regions. This is not unexpected, since both methods are applied to the same concentration and trajectory data. The most likely sources to affect Sevettijärvi are located in the Volga and Ural industrial regions, and, possibly, the oil and gas complex in Western Kazakhstan. Sources in Central and Eastern Europe are also producing high concentrations. These various source regions agree with emission inventories and global budgets for sulphur dioxide and with information on major industrial areas in Russia (NILU, 1984; Vinogradova, 2000; Olivier et al., 1996). The same regions as for Sevettijärvi account for high fine sulphur concentrations at the two Norwegian sites. In addition, these sites are affected to a higher degree by sources in England, Belgium, Germany and Poland. These countries are all important emitters of sulphur dioxide (Vestreng, 2001; Olivier et al., 1996). The measured concentration values for fine sulphur at the two sites, which are about 100 km apart, were well correlated, indicating that atmospheric levels of sulphur in Southern Norway are mainly due to long-range transport. This conclusion is supported by the general patterns of the calculated maps for the two sites. It can be noted that both the PSCF and the CF maps are fairly similar, except that the concentrations calculated with the CF method are systematically lower for Skreådalen, as are the measured concentrations (about 23% for the median). It is assumed that topographical differences between the sites may be responsible for this difference. A somewhat different picture is obtained for Sde Boker. For this site, the main sources are located in Eastern Europe, the Ukraine (Donetsk), and North West Turkey (Istanbul area).
The fine sulphur ``hot spot'' over Bosnia and Herzegovina on the Sevettijärvi map has to be considered with caution, as it lies at the edge of the domain. A look at the Birkenes map also reveals a possible source in the region. To test whether we have a false positive coming from the `smearing' of a real source, a further check has been performed by calculating the probability map at Birkenes for an ideal source (Vasconcelos et al., 1996a, count 1 if trajectory crosses ideal grid cell, 0 otherwise) placed in the ``Black Triangle,'' a known source of anthropogenic sulphur, which is downwind of former Yugoslavia. The map showed no correlation between the ``Black Triangle'' and the region of former Yugoslavia. Tests for various locations of the ideal source and for the receptor site at Sevettijärvi have produced the same result, except in the case when neighbouring Hungary has been chosen as source. The EMEP inventory confirms that Bosnia and Herzegovina are an important emitter of sulphur dioxide (Vestreng, 2001). However, the calculated PSCF/CF maps cannot distinguish between the sources in former Yugoslavia and Hungary for both receptor sites. It is quite probable, that the strength of the sources in the maps is overestimated due to poor counting statistics.
Figure 4 displays the fine sulphur probability maps before bootstrapping corresponding to the plots in Figure 3. It can be seen that most of the edge cells with high probability values due to poor counting statistics are removed by the bootstrapping technique.
Figure 5 shows the spatial distribution of 
with and
without bootstrapping for fine arsenic at Sevettijärvi and for fine
vanadium at Sde Boker. As can be seen, the cells with low significance
value being excluded, the bootstrapped maps are easier to interpret in
terms of known sources. High arsenic loads in samples at Sevettijärvi
are associated with air transported from the copper-nickel production
facilities at Nikel/Zapolyarnyi on the Kola Peninsula
(Reimann et al., 2000). Other possible sources are coal mining and
combustion in the Pechora basin and copper-nickel production, fossil fuel
combustion and steel and iron industry in the Ural region
(Pacyna et al., 1985). PSCF calculations performed by placing an ideal
source in the Nikel/Zapolyarnyi industrial region showed that the source
is smeared to the East and eventually reaches the Pechora basin. The map
obtained was similar to the map in Figure 5. This means that,
while it is certain that the Kola industrial region is a source of
arsenic, it is very probable that the maxima obtained from the
calculations with actual concentration data are false positives. In
other words, by examining the (bootstrapped) PSCF map only, one is
unable to tell whether the Pechora basin or the Ural region are sources of
arsenic for Sevettijärvi.
It is apparent that the bootstrap technique does not overcome the problem of source `smearing' due to the spatial distribution of the trajectories which renders emission cells and neighbouring ones indistinguishable of each other. While the methods correctly identify the direction where sources are located, they have limited spatial resolution (Vasconcelos et al., 1996a). A straightforward solution for improving the spatial resolution would be to calculate maps of concentrations/probabilities by making use of data from more than one site -- the more, the better -- as trajectories ending at different locations would cross source cells from different directions. In our case, the sites are either too close (Birkenes and Skreådalen), or too far apart (e.g., Sevettijärvi and Sde Boker) to obtain an unambiguous result. We should note, however, that the multiplication cell by cell of the non-bootstrapped fine sulphur maps calculated with the 50-th percentile as threshold for Sevettijärvi and Sde Boker (Figure 6), i.e., the joint probability of source contributions to the two receptor sites, shows that potential sources are better spatially resolved: one can identify the Saint Petersburg and Moscow areas, Middle Volga and Kama region (Eastern Russia), Donetsk (Southern Ukraine) and North West Turkey as sources affecting both receptor sites.
Stohl (1996) and Wotawa and Kröger (1999) have advocated the use of the redistribution method. This may partly remove the smearing problem. Stohl (1996) applied the method to particulate sulphate measurement data sets at 14 EMEP sites taken separately and combined, and Wotawa and Kröger (1999) applied it to a simulated concentration data set generated with a Lagrangian air quality model. They could identify potential source areas with higher resolution than with the method of Seibert et al. (1994), i.e., the method was able to reproduce the steep gradients between emission areas and no-emission areas, though it also enhanced unrealistic structures in regions with poor counting statistics (Wotawa and Kröger, 1999). We have applied the redistribution method to various combinations of the four sites and separately to each of the sites. We have also obtained higher concentration gradients when applying the redistribution to one site only. However, when combining more sites, the results have not been conclusive, as there are not, statistically speaking, many cells crossed from different directions by trajectories.