The atmosphere is known to episodically transport dust, aerosols, and gaseous pollutants from industrialized east Asia, the Gobi desert, and Siberian wild fires to western North America. We give a novel characterization of the climatological springtime transport from these regions and of the probability of transport events, that is, long-range transport of high concentrations with minimal dispersion. Our primary transport diagnostic is the transit-time probability density function (pdf), ${cal G}$, which is a tracer-independent measure of the flow that allows us to isolate the role of transport from other factors such as source variability and chemistry. The pdf approach, unlike typical back-trajectory analyses, captures transport due to all possible paths and accounts for both resolved advection and subgrid processes. We use a numerical model of the global atmosphere (Model of Atmospheric Transport and Chemistry (MATCH)) driven by National Centers for Environmental Prediction reananlysis data to establish the springtime statistics of daily averages of ${cal G}$. A suitably defined average of ${cal G}$ quantifies the climatological mass fraction of air from the source region per interval of transit times, or ages. Over the North American west coast, this fraction peaks at transit times of ~8 days in the upper troposphere (~6 days later at the surface) for the dust and pollution regions and at 12--14 days for the Siberian region. An analysis of the variability of ${cal G}$ at fixed transit time allows us to identify transport events and to estimate their probability of occurrence. This is illustrated for transport events to the Pacific Northwest (PNW) region of North America, defined as (43.8¿--53.3¿N) ¿ (115.3¿--124.7¿W). Correlations between ${cal G}$ averaged over the PNW and the winds at any point in the atmosphere identify large-scale anomaly structures of the flow that correspond to favorable transport to the PNW.