Determining the occurrence and severity of low-likelihood high-impact weather events is difficult due to the relatively few recorded events. Instead of making inference on the probability of the weather event directly, we shift our focus to the drivers of the climatology surrounding weather events. We represent the climate system in terms of climatological forcing, external forcing, and internal variability and specify a statistical model for each component. The forcing terms are modeled using a set of physical drivers and account for, among other things, anthropogenic induced climate change. The internal variability represents the variation in the system due to its natural chaotic cycle, which we model using Bayesian singular value decomposition. Importantly, we are able to estimate internal variability from a single realization (e.g., observation or reanalysis product) and isolate the impact of each component of the climate signal. By decomposing the climate system in terms of its drivers, we can determine which combination of drivers result in high-impact weather events and the probability of these events occurring. We apply our statistical framework to two-meter air temperature data from ERA5 over the Pacific Northwest. Our analysis provides additional insight into the 2021 heatwave regarding the contribution of climatological forcing and internal variability to the low-likelihood high-impact event and how the impact of each change over time.