Climate models are critical tools for developing strategies to manage the risks posed by sea-level rise to coastal communities. While these models are necessary for understanding climate risks, there is a level of uncertainty inherent in each parameter in the models. This model parametric uncertainty leads to uncertainty in future climate risks. Consequently, there is a need to understand how those parameter uncertainties impact our assessment of future climate risks and the efficacy of strategies to manage them. Here, we use random forests to examine the parametric drivers of future climate risk and how the relative importances of those drivers change over time. We find that the equilibrium climate sensitivity and a factor that scales the effect of aerosols on radiative forcing are consistently the most important climate model parametric uncertainties throughout the 2020 to 2150 interval for both low and high radiative forcing scenarios. The near-term hazards of high-end sea-level rise are driven primarily by thermal expansion, while the longer-term hazards are associated with mass loss from the Antarctic and Greenland ice sheets. Our results highlight the practical importance of considering time-evolving parametric uncertainties when developing strategies to manage future climate risks.