We present {the} Arctic atmospheric river (AR) climatology based on twelve {sets of} labels derived from ERA5 and MERRA-2 reanalyses for 1980--2019. The ARs were identified and tracked in the 3-hourly reanalysis data with a multifactorial approach based on either atmospheric column-integrated water vapor ($IWV$) or integrated water vapor transport ($IVT$) exceeding one of the three climate thresholds (75th, 85th, and 95th percentiles). Time series analysis of the AR event counts from the AR labels showed overall upward trends from the mid-1990s to 2019. The 75th $IVT$- and $IWV$-based labels, as well as the 85th $IWV$-based labels, are likely more sensitive to Arctic surface warming, therefore, detected some broadening of AR-affected areas over time, while the rest of the labels did not. Spatial exploratory analysis of these labels revealed that the AR frequency of occurrence maxima shifted poleward from over-land in 1980--1999 to over the Arctic Ocean and its outlying Seas in 2000--2019. Regions across the Atlantic, the Arctic, to the Pacific Oceans trended higher AR occurrence, surface temperature, and column-integrated moisture. Meanwhile, ARs were increasingly responsible for the rising moisture transport into the Arctic. Even though the increase of Arctic AR occurrence was primarily associated with long-term Arctic surface warming and moistening, the effects of changing atmospheric circulation could stand out locally, such as on the Pacific side over the Chukchi Sea. The changing teleconnection patterns strongly modulated AR activities in time and space, with prominent anomalies in the Arctic-Pacific sector during the latest decade. Besides, the extreme events identified by the 95th-percentile labels displayed the most significant changes and were most influenced by the teleconnection patterns. The twelve Arctic AR labels and the detailed graphics in the atlas can help navigate the uncertainty of detecting and quantifying Arctic ARs and their associated effects in current and future studies.