We propose a framework to classify precipitation events accompanied by snow accumulation/ablation process (precipitation-and-snow, or PAS events) into five regimes, based on the relative contributions of snowpack change and precipitation amount to the runoff response. This framework is applied to a regional climate simulation over the western U.S. to reveal the regions where snowpack process plays important roles. Over the western U.S., PAS events account for 50-90% of all the precipitation events. About 60-80% of PAS events feature snow accumulation, while snow melting type PAS events frequently happen in high-elevation areas. Compared with snow accumulation PAS events, snow melting PAS events have a more limited spatial distribution. Different regimes peak in different months between early winter and late spring. Lastly, the impact of atmospheric rivers is investigated. Although accounting for only 2% of the grid-scale precipitation events, atmospheric rivers trigger significant snowmelt and account for 20% and 11% of light and heavy snow melting event occurrences, respectively.