Potential source contribution function

Calculations are performed on a longitude-latitude grid which covers the spatial domain of interest. We assume that a species emitted within a grid cell is swept into the air parcel and transported to the receptor site without loss through diffusion, chemical transformation or atmospheric scavenging (Cheng et al., 1993). Let $n_{ij}$ be the total number of trajectory segment endpoints falling in the grid cell $(i,j)$ over the period of study, and let $m_{ij}$ be the number of endpoints in $(i,j)$ corresponding to trajectories associated with concentration values at the receptor site exceeding a specified threshold. The ratio $P_{ij} = m_{ij}/n_{ij}$ (PSCF) is then the conditional probability that an air parcel passing over the cell $(i,j)$ on its way to the receptor site arrives at the site with concentration values above the threshold. Hence, high values in the spatial distribution of $P_{ij}$ will pinpoint geographical regions that are likely to produce high concentration values at the receptor site if crossed by a trajectory.

In order to identify the high PSCF values that might have arisen purely by chance, it is necessary to test these values against the null hypothesis that there is no association between concentrations and trajectories (Vasconcelos et al., 1996b). The statistical significance of the spatial distribution of the PSCF values is examined by making use of a nonparametric bootstrap method (Wehrens et al., 2000). The method assumes that the concentration values are independent and identically distributed. We draw with replacement from the original concentration data set, $C = \{c_1,$ $c_2,$ $\ldots,$ $c_N\}$, $B$ random subsamples of size equal to the length of the data set, $C^* = \{c_1^*,$ $c_2^*,$ $\ldots,$ $c_N^*\}$. We then calculate for each bootstrapped sample $k$ the corresponding PSCF spatial distribution, $P^{*}_{k;ij}$. Let $P^{*}_{(1);ij}$ $< \ldots <$ $P^{*}_{(B);ij}$ be the ordered values $\{P^{*}_{k;ij}\}$, $k=1, \ldots, B$, and let $\alpha$ be the chosen significance level. If

$$P_{ij} \geq P^{*}_{((B+1)(1-\alpha/2));ij},$$ (1)

the null hypothesis is rejected at $(1-\alpha)\cdot 100\%$ confidence level. We decide to retain for our further analysis only the PSCF values satisfying the above relation. Note that if there are more than one trajectory assigned to a concentration value, the simple bootstrap on the concentration data set is equivalent to a blocked bootstrap on the trajectory set.