Modelling error (\(\sigma_{m}^{2}\)) was determined by the departure from the mean of the 20 modelled albedos, and measurement error (\(\sigma_{o}^{2}\)) was defined by utilizing the standard error from Sentinel-2 albedo evaluation with Athabasca Ice AWS. Snow depth, SWE, snowpack cold content, water in the snowpack, firn and ice total water equivalents were also updated proportionally to \(K\). Other related variables were updated to maintain physical coherence when updating the latter state variables. For example, snow density was updated based on the new snow depth and SWE states. The above DA process was repeated the same number of times as of available Sentinel-2 albedo estimates for each basin until the whole period was covered. CRHM streamflow simulations were continued for an extra two days with old model states into the new assimilation interval. This procedure was performed to cover the first two days in which streamflow calculated with the new states was still being routed through the basin. The period of two days was chosen because it covers the time of concentration for both basins.
2.6. Streamflow Evaluation
Model performance with and without DA was only assessed in the last four WYs because they had a complete Sentinel-2 albedo time series. These years also encompassed very contrasting environmental conditions: a heavily wildfire soot-impacted WY (2018); a mildly soot-impacted WY (2019) from algae feeding from 2017 and 2018 soot; a normal WY (2020); and a WY impacted by heatwaves (2021). Streamflow prediction performance was estimated by the Nash-Sutcliffe Efficiency (NSE) coefficient (Nash and Sutcliffe, 1970), bias, RMSE, and the KGE coefficient (Guptaet al. , 2009). The evaluation was made considering the entire four WY periods and on a WY basis. It is worth noting that streamflow in these two glacierized basins is limited to the spring and summer seasons (May to Sept.).
3. Results
3.1. Remotely Sensed Albedo Evaluation
Remotely sensed albedo presented satisfactory results for the Athabasca Ice AWS evaluation. Twenty-eight matching observations were available for evaluation. Albedo correlation was 0.96, bias was 0.026, RMSE was 0.060, and the regression model standard error (\(\sigma_{o}\)) was 0.046 (Figure 2). It was important to calculate σ as this metric determines the remote sensing measurement error necessary for DA. In summary, snow albedos were less accurate than ice albedos. Snow albedos had a higher spread and positive bias, whereas ice albedo errors were more evenly distributed around the 1:1 line. These results were similar to those previously found in the literature with r, bias, and RMSE values between 0.82 and 0.88 (Shuai et al. , 2011; Bertonciniet al. , 2022), -0.029 and 0.019, and 0.025 and 0.043 (Shuaiet al. , 2011; Wang et al. , 2016; Li et al. , 2018; Bertoncini et al. , 2022), respectively.