Wildfires and heatwaves have recently affected the hydrological system in unprecedented ways due to climate change. In cold regions, these extremes cause rapid reductions in snow and ice albedo due to soot deposition and unseasonal melt. Snow and ice albedo dynamics control net shortwave radiation and the available energy for melt and runoff generation. Many albedo algorithms in hydrological models cannot accurately simulate albedo dynamics because they were developed or parameterised based on historical observations. Remotely sensed albedo data assimilation (DA) can potentially improve model performance by updating modelled albedo with observations. This study seeks to diagnose the effects of remotely sensed snow and ice albedo DA on the prediction of streamflow from glacierized basins during wildfires and heatwaves. Sentinel-2 20-m albedo estimates were assimilated into a glacio-hydrological model created using the Cold Regions Hydrological Modelling Platform (CRHM) in two Canadian Rockies glacierized basins, Athabasca Glacier Research Basin (AGRB) and Peyto Glacier Research Basin (PGRB). The study was conducted in 2018 (wildfires), 2019 (soot/algae), 2020 (normal), and 2021 (heatwaves). DA was employed to assimilate albedo into CRHM to simulate streamflow and was compared to a control run (CTRL) using off-the-shelf albedo parameters. Albedo DA benefited streamflow predictions during wildfires for both basins, with a KGE coefficient improvement of 0.18 and 0.20 in AGRB and PGRB, respectively. Four-year DA streamflow predictions were superior to CTRL in PGRB, but DA was slightly better in AGRB. DA was not beneficial to streamflow predictions during heatwaves. These results show that albedo DA can reveal otherwise unknown albedo and snowpack dynamics occurring in remote glacier accumulation zones that are not well simulated by model predictions alone. These findings corroborate the power of observational tools to incorporate near real-time information into hydrological models to better inform water managers of the streamflow response to wildfires and heatwaves.