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.