Temporally compounding atmospheric river (AR) events cause severe flooding and damage in California. However, the contribution of temporal compounding to AR-induced loss has yet to be systematically quantified. We show that the strongest ARs are more likely to be part of sequences, which are periods of elevated hydrologic hazard associated with temporally clustered ARs. Sequences increase the likelihood of flood-related impacts by 8.3% on AR days and 5.4% on non-AR days, and across two independent loss datasets, we find that ARs within sequences have over three times higher expected losses compared to ARs outside of sequences. Expected losses also increase when the preceding AR is higher intensity, when time since the preceding AR is shorter, and when an AR is the second or later event within a sequence. We conclude that temporal compounding is a critical source of information for predicting an AR's potential consequences.