Introduction

The residence time probability analysis of Ashbaugh et al. (1985), also known as the `potential source contribution function' (PSCF) method, has been extensively used in the identification of source locations and preferred transport pathways of atmospheric trace elements and particulate species, e.g., sulphate, nitrate, ozone, black carbon, and mercury (Stohl and Kromp-Kolb, 1994; Lin et al., 2001; Poirot and Wishinski, 1986; Polissar et al., 2001a; Polissar et al., 1999; Cheng et al., 1993; Zeng and Hopke, 1988). The method has also been applied to locate the sources or source categories identified by multivariate receptor models, e.g. principal component analysis, positive matrix factorization of Paatero and Tapper (1994) or Henry's (1997) UNMIX (Xie et al., 1999; Polissar et al., 2001b; Poirot et al., 2001).

In a nutshell, PSCF is defined as the probability that an air parcel with concentration higher than a specified threshold arrives at the receptor site after having resided in a certain grid cell of the spatial domain of interest. It is calculated as the ratio between the grid cell number of backward trajectory segment endpoints associated with concentrations above the threshold and the total number of trajectory segment endpoints for the specified cell.

A modified version of this method, called `concentration field' (CF) or 'trajectory statistics' (TS) method, has been developed by Seibert et al. (1994) and refined by Stohl (1996) into the redistributed CF method. The CF method consists of assigning concentration values measured at the receptor site to corresponding air parcel backward trajectories. A mean or logarithmic mean concentration is calculated for each grid cell of the spatial domain, by using as a weighting factor the time spent by the air parcel over the cell. This approach has been employed by Wotawa et al. (2000) to investigate the transport of ozone in the Alps, and applied by Virkkula et al. (1995) and Virkkula et al. (1998) to identify the sources of non-sea-salt sulphate, ammonium, sodium, and sulphur dioxide at a site in the Finnish Lapland.

It is apparent that in both cases, a problem arises because of grid cells crossed by a small number of trajectories. Having poor counting statistics often results in false positives if trajectories travelling over true source areas extend beyond these sources. The problem is `fixed' (Cheng et al., 1993), in the case of the PSCF method, by multiplying the PSCF values with an arbitrary weighting function which reduces the contribution of the grid cells with low number of counts, and, in the case of the CF method, either by simply discarding the mean concentrations corresponding to grid cells that have a number of trajectory segment endpoints less than an arbitrary-set threshold, or by smoothing the concentration field with a nine-point filter, while imposing the constraint that the concentration values should be kept within their confidence interval (Seibert et al., 1994). An objective method for dealing with these `tailing effects' (Cheng and Lin, 2001) has been advocated by Hopke et al. (1995), who have used a bootstrap technique to examine the statistical significance of the PSCF values. To the same purpose, Vasconcelos et al. (1996b); Vasconcelos et al. (1996a) have employed two statistical tests, one based on a bootstrap method, the other, on the binomial distribution.

The performance of both methods has not been fully discussed in the literature. Vasconcelos et al. (1996a) have shown that the angular resolution of the PSCF method is good, but that the radial resolution is poor, since all trajectories converge towards the receptor site. Wotawa and Kröger (1999) have tested the ability of the CF method of Seibert et al. (1994) and the redistributed CF method of Stohl (1996) to reproduce emission inventories in cases of negligible measurement and transport errors, by applying them to a simulated concentration data set generated with a Lagrangian air quality model. They have concluded that the main features of the emission inventory are successfully replicated. Finally, Cheng and Lin (2001) have evaluated the performance of the PSCF model using data observed from the 1998 Central America smoke events. Their findings indicate that the model is able to accurately determine the smoke source locations and pollutant transport pathways.

In what follows, we will apply versions of the two methods described to four multi-species multi-annual concentration time series measured at sites in Finland, Norway and Israel, compare and discuss the results obtained. A nonparametric bootstrap method will be used for estimating the statistical significance of the calculated PSCF values.