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\begin{document}

\title{Assimilation of Satellite Albedo to Improve Simulations of Glacier
Hydrology}



\author[1]{André Bertoncini}%
\author[1]{John Pomeroy}%
\affil[1]{University of Saskatchewan}%


\vspace{-1em}



  
  \date{May 26, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
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.%
\end{abstract}%



\sloppy


\textbf{Assimilation of Satellite Albedo to Improve Simulations of
Glacier Hydrology}

Andr\selectlanguage{ngerman}é Bertoncini\textsuperscript{a} and John W.
Pomeroy\textsuperscript{a}

\textsuperscript{a}\emph{Centre for Hydrology, University of
Saskatchewan, Canmore, Alberta, Canada}

\emph{Corresponding author} : André Bertoncini,
andre.bertoncini@usask.ca

\emph{Co-author e-mail} : John W. Pomeroy, john.pomeroy@usask.ca

\textbf{Data Availability Statement}

MODIS, Sentinel-2, and ERA5-Land data can all be found in the GEE
platform. Forcing and evaluation data, as well as the Python codes for
computing the remotely sensed albedos and R codes to perform the EnKF DA
can be found
at:\emph{https://github.com/andrebertoncini/albedo\_data\_assimilation}.

\textbf{Funding Statement}

This work was supported by the Canada Research Chairs programme, the
Natural Sciences and Engineering Research Council of Canada (NSERC),
Alberta Innovates, and the Canada First Research Excellence Fund's
(CFREF) Global Water Futures programme.

\textbf{Conflict of Interest Disclosure}

We have no conflict of interest to disclose.

\textbf{Abstract}

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.

\textbf{Keywords:} Albedo, Data Assimilation, Wildfires, Heatwaves, Cold
Regions Hydrological Model (CRHM), Streamflow Prediction, Glacier
Hydrology, Sentinel-2.

\textbf{1. Introduction}

In an era of global environmental change, hydrological models need to
account for processes resulting from unprecedented combinations of
forcing meteorology, state variables, and parameters. Although the
hydrological community has made advances in creating physically based
process hydrology models, many process representations are based on
historical behaviour. Recent wildfires and heatwaves worldwide,
especially in Canada (Baars \emph{et al.} , 2019; Parisien \emph{et al.}
, 2023), challenge the calculation of net shortwave radiation using snow
and ice albedo algorithms based on historical representations. Snow and
ice surfaces can be darkened by wildfire soot deposition. Likewise, snow
surfaces can be darkened by accelerated snowmelt caused by rapid
above-average temperature changes from heatwaves. These two conditions
strongly impact melt energy for the seasonal snowpack, perennial
snowfields and mountain glaciers, resulting in faster melt than might be
estimated without consideration of rapid surface darkening.

Shortwave (SW) radiation input into glacierized basins is often the most
important source of available energy for melt and runoff generation.
Albedo, therefore, controls the amount of SW radiation entering snow and
ice surfaces and the availability of melt energy. The mechanism
controlling snow and ice albedo decrease due to wildfire soot deposition
is straightforward. It depends on the amount of soot deposited over a
surface and whether or not that soot would be washout by melt or be
further developed by algae growth (Aubry-Wake \emph{et al.} , 2022a;
Bertoncini \emph{et al.} , 2022; Esser et al., accepted manuscript).
Heatwaves, in contrast, have a more intricate effect on snow and ice
albedo. Rapid above-temperature changes can cause accelerated snowmelt
(Koboltschnig \emph{et al.} , 2009; Box \emph{et al.} , 2022) and
consequently earlier exposure of firn and ice; however, these same high
temperatures will most likely not further decrease the albedo of firn
and ice in nature. It is unknown whether or not current hydrological
model albedo algorithms are able to account for such different interplay
of environmental conditions in a nonstationary changing climate, given
they were developed and parameterised based on historical observations.
Up-to-date albedo observations are, therefore, necessary to update
hydrological model albedo algorithms. The availability of near
real-time, high-resolution satellite data with shorter revisit times
combined with the advancement of albedo retrieval algorithms has
provided superior quality albedo data for effective assimilation into
hydrological models.

Glacio-hydrological models are a set of numerical representations of
hydrological processes that together culminate in the ability to predict
surface water and energy budget terms, the states of soil moisture,
groundwater storage, snowpacks, and glacier mass balance and fluxes of
evaporation, sublimation, and streamflow. These models are forced with
meteorological variables and parameterized with environmental
information, and they can be used to simulate hydrologically-relevant
variables such as snow water equivalent (SWE) (Wrzesien \emph{et al.} ,
2017; Marsh \emph{et al.} , 2020) to unobserved locations or to diagnose
previous flood (Hamlet and Lettenmaier, 2007; Pomeroy \emph{et al.} ,
2016) and drought (Fang and Pomeroy, 2007; Mishra and Singh, 2011)
events. Numerical weather precipitation models can force hydrological
models for short-term flood forecasting to prepare riverine communities
for flooding (Alfieri \emph{et al.} , 2013; Thieken \emph{et al.} ,
2023). Finally, climate projections coupled with hydrological models can
guide governments and environmental planners regarding a region's future
state of water resources (Milly \emph{et al.} , 2002; Blöschl \emph{et
al.} , 2019). All these applications make hydrological modelling a
crucial tool to learn from the past and prepare for short- and long-term
changes in the hydrological cycle to avoid the large cost of floods and
droughts. The global costs of floods and drought-related (plus heatwaves
and wildfires) extreme events attributed to climate change amounts to
US\$ 127 billion per year between 2000 and 2019 (Newman and Noy, 2023).

There are three main types of hydrological models depending on the
manner in which how hydrological processes are represented. These range
from empirical, semi-empirical, to physically based hydrological models
(Beven, 2012). Ideally models should represent hydrological processes as
physically-based as possible (Paniconi and Putti, 2015); however, often
inefficiencies in model physical processes development are masked by
heavy calibration (Menard \emph{et al.} , 2021). The physically based
effort is a pledge to make hydrological models more robust to
unprecedented environmental conditions (Kreibich \emph{et al.} , 2022).
Models that heavily rely on empiricism to represent hydrological
processes are more likely to be deemed unsuccessful under conditions
that have not been observed in the past. For instance, the uncertainty
in end-of-century mean flows can be over 40\% due to the choice of
hydrological models of various degrees of physical process
representation (Krysanova \emph{et al.} , 2017). Moreover, these
unprecedented environmental conditions will likely be more common under
climate change-induced modifications in the overall hydrological system
(Blöschl \emph{et al.} , 2019; Queen \emph{et al.} , 2021). Therefore,
it is crucial that process representation in hydrological models be as
physically based as possible for riverine communities to be prepared for
upcoming extreme hydrological events. However, developing robust
physical process representation is time-consuming. In the meantime,
other techniques should be explored to account for inherent process
representation inefficiencies that are still represented
semi-empirically in physically based models (Beven, 2012).

One way to correct for the lack of physical representation in
hydrological modelling is through DA. In simple terms, DA tries to
create an optimal estimate (\(\hat{x}\)) of a true real-world
state (\(x\)) by combining a modelled state
(\(m\)) and a corresponding observation
(\(o\)). The optimal state \(\hat{x}\) is a weighted
sum of\(m\) and \(o\). The weights are defined
by the uncertainty in \(m\) and\(o\),
favouring the less uncertain estimate of \(\hat{x}\). The
observation uncertainty, or measurement error, is usually defined a
priori based on the literature or ground-truthing. On the other hand,
the modelling error can be determined using many available techniques,
which are usually based on some sort of Monte Carlo simulations that can
capture the spread in multiple model trajectories (Reichle, 2008). The
most commonly used technique in hydrology and snow modelling is the
Ensemble Kalman Filter (EnKF) (Andreadis and Lettenmaier, 2006;
Clark\emph{et al.} , 2006, 2008; Slater and Clark, 2006; Huang \emph{et
al.} , 2017; Lv and Pomeroy, 2020), which is a less computationally
expensive version of the previously developed Extended Kalman Filter
(EKF) (Reichle \emph{et al.} , 2002). The EnKF method calculates the
modelling error based on an ensemble of simulated model states forced by
perturbed variables. The simulations are carried out until the most
recent available observation. Then, the Kalman gain is calculated,
allowing the optimal state estimate to be calculated and replaced in the
model for future simulations (Evensen, 1994). The EnKF is advantageous
against other smoothing DA techniques because it can be implemented in a
forecasting mode by calculating modelling error using only one available
observation (Reichle, 2008). This EnKF characteristic is suitable for
improving streamflow forecasting systems (Huang \emph{et al.} , 2017).
Among many snow and hydrology variables, remotely sensed albedo DA has
been utilized in large-scale land surface models (LSMs) to estimate SWE
(Dumont \emph{et al.} , 2012; Malik \emph{et al.} , 2012; Wang \emph{et
al.} , 2015), but not yet in a full hydrological model capable of
predicting streamflow.

Some hydrological models, especially those dedicated to the simulation
of snow and ice processes important to cold regions, have a dynamic
albedo simulation algorithm. Accurate simulation of albedo is critical
to define the net shortwave radiation of snowpacks and glaciers, as
shortwave radiation is the primary source of available energy for melt.
Albedo algorithms intend to simulate temporal changes in surface albedo
within a spatial modelling unit arising from soil moisture variations,
vegetation phenology, addition of fresh snow cover, snow depletion, and
firn and glacier ice exposure. In the case of partially or completely
covered snowpacks, the albedo varies due to solar angle diurnal and
seasonal variations, snow grain size (Marks and Dozier, 1992), the
amount of snow-free surfaces (Pomeroy \emph{et al.} , 1998), and the
amount of light-absorbing particles (LAPs) in snow (Warren and Wiscombe,
1980). Empirical snow albedo estimation algorithms have been developed
and applied satisfactorily in the past (Gray and Landine, 1987;
Verseghy, 2012); however, the conditions to which they were developed
have changed drastically with climate change. In the case of bare ground
and short vegetation, these algorithms usually apply a constant known
albedo for fresh snow and a decay function until it reaches a depth in
which the snow-free albedo starts to contribute, and ultimately, a
constant snow-free albedo is used. The albedo is reset when fresh snow
accumulates on the ground, and the decay function starts again.
Physically based radiative transfer algorithms have been developed to
simulate snow and ice albedo (Wiscombe and Warren, 1980; Gardner and
Sharp, 2010). Some of these physically based algorithms can also account
for the introduction of LAPs into the snowpack (Zhang \emph{et al.} ,
2017; McKenzie Skiles \emph{et al.} , 2018). Although these physically
based algorithms should be more robust in their ability to estimate
albedo in a changing climate with more wildfires and heatwaves, they are
usually complex and, therefore, rarely implemented in hydrological
models (Pietroniro \emph{et al.} , 2007; Bergström and Lindström, 2015;
Hamman \emph{et al.} , 2018; Pomeroy \emph{et al.} , 2022), especially
algorithms capable of accounting for LAPs deposition. Studies usually
determine the LAPs radiate forcing and its respective melt, but are
unable to directly couple them into a hydrological model
(Flanner\emph{et al.} , 2007; Zhang \emph{et al.} , 2017; McKenzie
Skiles \emph{et al.} , 2018; Magalhães \emph{et al.} , 2019), unless the
model is directly forced by albedo observations (Aubry-Wake \emph{et
al.} , 2022a).

Albedo can also be estimated using remotely sensed imagery. Spectral
albedo can be simply calculated by dividing the reflected spectral
radiance by the incoming solar radiation at the surface for a given
region of the solar electromagnetic spectrum. Besides hyperspectral
sensors, most remote sensing systems only have a few narrow spectral
bands, and a conversion to the full broadband solar spectrum is
necessary to calculate albedo. This conversion is usually done using
narrow-to-broadband equations developed for the most common sensors
using field spectroscopy libraries or radiative transfer simulations
(Liang, 2000; Greuell \emph{et al.} , 2002; Li \emph{et al.} , 2018). In
addition, because most high-resolution multi-spectral remote sensing
systems operate at nadir viewing angles, they cannot observe albedo
variations due to different sensor-solar geometries. One way to overcome
that is to use coarse resolution systems with off-nadir capabilities,
such as the Visible Infrared Imaging Radiometer Suite (VIIRS) or the
Moderate Resolution Imaging Spectroradiometer (MODIS), to calculate a
Bidirectional Reflectance Distribution Function (BRDF) (Roujean \emph{et
al.} , 1992; Wanner \emph{et al.} , 1995; Li \emph{et al.} , 2001). This
BRDF information can be downscaled to Landsat-era (30-m) and Sentinel-2
(20-m) resolutions in soil and vegetation surfaces (Shuai \emph{et al.}
, 2011). These methodologies have been successfully applied for soil and
vegetation surfaces, but they were suboptimal on snow and ice surfaces
due to sensor saturation prior to the launch of Landsat-8. With the
advancement in sensor radiometric technology onboard Landsat-8 and
Sentinel-2 platforms, surface reflectance can be estimated over snow and
ice at high-resolution and, in conjunction with BRDFs, calculate albedo
over snow and ice (Wang \emph{et al.} , 2016; Li \emph{et al.} , 2018;
Bertoncini \emph{et al.} , 2022). The high revisit time of Sentinel-2
platforms has allowed such technologies to capture rapid snow and ice
albedo changes caused by wildfire soot deposition and its associated SW
radiative forcing (Bertoncini \emph{et al.} , 2022).

The degree to which streamflow predictions during melt of snow and ice
can be improved by high-resolution remotely sensed albedo DA into
hydrological models has not been assessed yet. Given the importance of
simulating accurate current and future streamflows and the increasing
trends of unprecedented wildfire and heatwaves (Jolly \emph{et al.} ,
2015; Kirchmeier-Young \emph{et al.} , 2019; Al-Yaari \emph{et al.} ,
2023; Parisien \emph{et al.} , 2023), accounting for these unrepresented
processes in glacio-hydrological models can be crucial. Because current
hydrological model's albedo algorithms are not able to account for rapid
and unseasonal snow and ice albedo changes (Pietroniro \emph{et al.} ,
2007; Bergström and Lindström, 2015; Hamman \emph{et al.} , 2018;
Pomeroy\emph{et al.} , 2022; Wheater \emph{et al.} , 2022), albedo DA
provides a path forward in improving this process's representation.
Modular physically based models such as CRHM (Pomeroy \emph{et al.} ,
2022) provide a suitable platform to test albedo DA in cold regions.
Although coarse-resolution remotely sensed snow and ice albedo DA into
LSMs has been performed to estimate SWE in the past (Dumont \emph{et
al.} , 2012; Malik \emph{et al.} , 2012; Wang \emph{et al.} , 2015), not
until recently that high-resolution remotely sensed snow and ice albedo
estimates became reliable and frequent enough (Li \emph{et al.} , 2018;
Bertoncini\emph{et al.} , 2022) to have an impact on hydrological model
streamflow predictions. Therefore, no studies have assessed the impact
of remotely sensed high-resolution albedo DA into a cold regions
hydrological model on streamflow predictions during extreme wildfire and
heatwave conditions, especially in glacierized mountain headwater
basins.

The purpose of this chapter is to diagnose the effects of remotely
sensed high-resolution snow and ice albedo data assimilation on the
prediction of streamflow of high mountain glacierized basins during
wildfires and heatwaves. The specific objectives are (i) to develop and
evaluate a cloud-computing remotely sensed snow and ice albedo retrieval
framework, (ii) to develop a framework for remotely sensed albedo DA
into a physically-based cold regions hydrological model, and (iii) to
assess the impact of albedo DA on streamflow prediction of glacierized
basins during wildfire and heatwave conditions. The albedo DA framework
was developed and tested in the Athabasca Glacier and Peyto Glacier
research basins in the Canadian Rockies during contrasting environmental
conditions that included wildfires and heatwaves between the 2018 and
2021 water years (WYs). The framework was developed based on 20-m
Sentinel-2 imagery albedo estimates that were assimilated into CRHM to
assess the impact of wildfires and heatwaves on streamflow predictions.

\textbf{2. Material and Methods}

2.1. Study Area

Two glacierized basins in the Canadian Rockies, Alberta, were used as
study areas for this research: Athabasca Glacier and Peyto Glacier
research basins (Figure 1). AGRB is in Jasper National Park and is part
of the Global Water Futures Observatory (GWFO) and operated by the
Centre for Hydrology, University of Saskatchewan. AGBR is a glacier
outlet of the Columbia Icefield, the largest icefield in the Canadian
Rockies and a triple continental drainage divide between the Mackenzie,
Nelson, and Columbia river basins which flow into the Arctic, Atlantic,
and Pacific oceans, respectively. AGBR has an area of 29.3
km\textsuperscript{2} and sits between 1926 and 3459 m of elevation (as
of 2011), with 58\% of its area covered by glacier ice (as of 2016)
(Pradhananga and Pomeroy, 2022). AGBR is equipped with two automatic
weather stations (AWS), Athabasca Ice and Athabasca Moraine, and one
streamflow gauge. PGRB drains into the Nelson river basin. PGRB has an
area of 22.4 km\textsuperscript{2} and sits between 1907 and 3152 m (as
of 2014), with 44\% of its area covered by glacier ice (as of 2016)
(Pradhananga and Pomeroy, 2022). PGRB has one AWS (Peyto Main) and a
streamflow gauge and has been the subject of intense scientific studies
since the 1960s. For more information about these research basins and
their instruments the readers are referred to Pradhananga \emph{et
al.}(2021) and Pradhananga and Pomeroy (2022).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1: Athabasca Glacier Research Basin (AGRB, left) and Peyto
Glacier Research Basin (PGRB, right) study areas in the Canadian
Rockies, Alberta. Glacier ice and snow Hydrological Response Units
(HRUs) used as examples for result discussions are highlighted in red.

2.2. Study Period and Environmental Conditions

The study was conducted between July 2017 and September 2021, and
streamflow evaluation was performed for the four complete WYs inside
this period (2018, 2019, 2020, and 2021). The 2018 year was the worst
interior British Columbia wildfire season to date (Parisien \emph{et
al.} , 2023) -- as these fires were generally upwind of the study basins
they impacted the sites with smoke and soot deposition
(Aubrey-Wake\emph{et al.} , 2022). The 2019 year did not have any major
wildfires; however, field inspections revealed that albedo remained low
in the Athabasca Glacier from soot and algae growth feeding off soot
deposited in 2017 and 2018 (Aubry-Wake \emph{et al.} , 2022a; Bertoncini
\emph{et al.} , 2022; Esser \emph{et al.} , accepted manuscript). The
2020 year had no major wildfires and can be considered a control year
with greatly reduced soot and algae. The 2021 year was characterized by
intense heat and an unprecedented heat dome that dominated the region
for many days in late June and early July (Lin \emph{et al.} , 2022).
Although there was also a considerable Western Canada wildfire season in
2021, only light smoke was observed in the study basins; therefore, this
year was not considered a high-activity wildfire season. The 2017 year
was also a high-activity wildfire season. However, DA evaluation was not
performed in that year because Sentinel-2B satellite images were only
available from July 2017 onwards and thus not spanning the whole glacier
ablation period. The Sentinel-2B satellite launch conferred high revisit
rates every 2 to 5 days in the region.

2.3. Cloud-computing Remotely Sensed Albedo Framework Implementation

High-resolution remotely sensed albedo was estimated using a framework
developed by Shuai \emph{et al.} (2011) for Landsat images, updated by
Li \emph{et al.} (2018) for Sentinel-2 images, and applied by
Bertoncini\emph{et al.} (2022) in the Columbia Icefield to assess the
impacts of wildfires on albedo and net SW radiation. To extend the
application for use in hydrological models, Bertoncini \emph{et al.}
(2022)'s framework was implemented in the Google Earth Engine (GEE)
cloud-computing platform. The algorithm was slightly modified to run in
GEE. The main differences from Bertoncini \emph{et al.} (2022) include
the following: the use of both MODIS Aqua and Terra platforms to
retrieve BRDF, which was made to simplify the quality control (QC) steps
with more observations; the BRDF inversion method allowed negative
coefficients, but the inversion was run once more without the negative
coefficient to alleviate the issue since there is no non-negative least
squares option in GEE; and also in order to make the framework
widespread applicable instead of using station-measured incoming SW
radiation, ERA5-Land 9-km incoming SW radiation was utilized. In
addition, Sentinel-2 reflectance atmospheric correction was performed
using the 6S model (Vermote\emph{et al.} , 1997) through its Python
implementation (Py6S) instead of Sen2Cor.

In summary, the framework utilizes BRDF information from MODIS to
account for differences in spectral albedo due to sensor-solar angular
variability. This BRDF information is then downscaled to Sentinel-2 20-m
resolution, and the high spatial resolution spectral albedo is converted
to a broadband albedo using Li \emph{et al.} (2018) conversion equations
for Sentinel-2. The algorithm can be applied worldwide because it was
implemented in GEE. The algorithm was run for both study area basins,
and the mean snow and ice 20-m albedo within each HRU was extracted for
DA. The station-measured albedo at Athabasca Ice AWS was utilized to
evaluate the remotely sensed albedo estimates. This evaluation standard
error was used as the satellite albedo measurement error for DA in both
basins since the pixel that Peyto Main AWS falls within is not
representative of snow and ice albedo due to infrastructure and bare
soil contamination.

2.4. CRHM Hydrological Modelling

CRHM was used to predict streamflow in both basins without (CTRL) and
with albedo data assimilation (DA). The CRHM configuration employed was
similar to that of Pradhananga \emph{et al.} (2022), with an updated
firn and ice HRU designation from the two 2021-08-12 Sentinel-2 images
in Figure 1. CRHM is a modular physically based hydrological model with
a glacier energy and mass balance and routing modelling modules
(Pomeroy\emph{et al.} , 2022). The models were set up with 90 and 65
HRUs for AGRB and PGRB, respectively. The CTRL run used off-the-shelf
constant albedos for ice (0.30) and firn (0.55). For spin-up purposes,
the model was run from 2015-10-01 to 2021-09-30. Both models were forced
with hourly station-measured air temperature, relative humidity, wind
speed, incoming short- and long-wave radiation, and precipitation using
the Athabasca Moraine and Peyto Main AWSs (Figure 1). These forcing
variables were quality-controlled using the Fang \emph{et al.} (2019)
methodology. No calibration was performed in the CTRL or DA runs.
Another difference in model configuration from Pradhananga and Pomeroy
(2022) is that this study used a glacier and firn melt module employing
a katabatic calculation of turbulent energy fluxes based on Grisogono
and Oerlemans (2001) and tested in Peyto Glacier by Munro (2004) and
Aubry-Wake \emph{et al.} (2022b). This katabatic module represents the
contribution of sub-daily glacier katabatic winds to the overall melt of
ice and firn, advancing upon the less physically based configuration
utilized by Pradhananga and Pomeroy (2022).

Snow albedo was simulated using the same algorithm employed in the
Canadian Land Surface Scheme (CLASS) (Verseghy, 2012). The CRHM version
used in this study has four other albedo algorithms capable of
simulating snow albedo, including from observations and simply using a
constant albedo. The model can calculate albedo using Gray and Landine
(1987)'s method, which accounts for snow-covered area depletion in
shallow snowpacks. The model can also simulate albedo utilizing
Baker\emph{et al.} (1990)'s method, which is based on a decay function
that refreshes when snowfall occurs. Verseghy's algorithm evolves upon
Barker's by accounting for differences between dry and wet snow and also
taking into consideration daily mean temperatures, which is crucial in
the context of heatwaves. Verseghy's algorithm was chosen to be used in
this study given the widespread use of CLASS inside land surface and
hydrology prediction systems in cold regions, e.g., in the Mod\selectlanguage{ngerman}élisation
Environmentale Communautaire (MEC) - Surface and Hydrology (MESH) model
(Pietroniro \emph{et al.} , 2007; Wheater \emph{et al.} , 2022). The
chosen albedo algorithm feeds albedo information to the utilized energy
balance snowmelt model SNOBAL (Marks \emph{et al.} , 1998); therefore,
it is expected that albedo assimilation will also have a large impact on
snow depth and SWE.

2.5. Ensemble Kalman Filter Assimilation Framework

The DA period started in July 2017 when Sentinel-2 images became
available at a higher revisit frequency, with the addition of
Sentinel-2B. One individual Sentinel-2 scene was sufficient to cover
each basin. Sentinel-2 images with less than 30\% cloud cover were
selected for albedo generation and as a DA date. If clouds or shadows
completely covered an HRU, DA was not performed, but assimilation was
executed for the other HRUs on the same date. DA was conducted using an
EnKF method, following Clark \emph{et al.} (2006) and Lv and Pomeroy
(2020). EnKF was run with 20 ensemble members. Station-measured
variables were perturbed with standard deviations displayed in Table 1.
The standard deviation for less uncertain forcings (air temperature,
relative humidity, incoming short- and long-wave radiation) was reduced
to half of that used by Lv and Pomeroy (2020) since there is evidence
that previously employed perturbation standard deviations were
disproportionately large for these variables. For instance, Tang\emph{et
al.} (2023) have shown that hydrological modelling uncertainty due to
temperature forcing is closer to 2 ºC instead of the commonly used 5 ºC.
Wind speed and precipitation remain highly uncertain variables, and
their standard deviations were kept the same as Lv and Pomeroy (2020).

Table 1: Station-measured forcings perturbed by prescribed standard
deviations. The type of perturbation is also displayed.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\textbf{Forcing} & \textbf{Perturbation type} & \textbf{Standard
deviation}\tabularnewline
\midrule
\endhead
Air temperature {[}\selectlanguage{ngerman}ºC{]} & Additive & 2.50\tabularnewline
Relative humidity {[}\%{]} & Additive & 5\tabularnewline
Wind speed {[}m/s{]} & Additive & 2\tabularnewline
Incoming short-wave {[}W/m\selectlanguage{ngerman}²{]} & Multiplicative & 0.15\tabularnewline
Incoming long-wave {[}W/m\selectlanguage{ngerman}²{]} & Additive & 25\tabularnewline
Precipitation {[}mm{]} & Multiplicative & 0.50\tabularnewline
\bottomrule
\end{longtable}

The implemented EnKF framework generates an optimal albedo estimate
(\(\hat{\alpha}\)) between the CRHM modelled (\(\alpha_{m}\)) and
Sentinel-2 observed (\(\alpha_{o}\)) albedo by weighing the
modelling (\(\sigma_{m}^{2}\)) and measurement error variance
(\(\sigma_{o}^{2}\)) using the Kalman gain (\(K\)),\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\hat{\alpha}=\left(1-K\right)\alpha_{m}+K\alpha_{o}\) & (1)\tabularnewline
\midrule
\endhead
\(K=\ \sigma_{m}^{2}/(\sigma_{m}^{2}+\sigma_{o}^{2}\)) & (2)\tabularnewline
\bottomrule
\end{longtable}

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 (Gupta\emph{et
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.).

\textbf{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 \selectlanguage{greek}σ \selectlanguage{english}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 \emph{et al.} , 2011;
Bertoncini\emph{et al.} , 2022), -0.029 and 0.019, and 0.025 and 0.043
(Shuai\emph{et al.} , 2011; Wang \emph{et al.} , 2016; Li \emph{et al.}
, 2018; Bertoncini \emph{et al.} , 2022), respectively.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure 2: Remotely sensed albedo evaluation for Athabasca Ice AWS.

Figure 3 shows both basins' mid-summer remotely sensed snow and ice
albedo maps. These maps demonstrate the vast spatial variability of
intra-HRU and -basin snow and ice albedos. Such spatial variabilities
cannot be captured by modelling in scales smaller than its HRU units.
Although the intra-HRU albedo variability was averaged out before DA was
performed, the collective variations caused by wildfires and heatwaves
can generate different integrated responses. This heterogeneity suggests
that the remotely sensed albedos can contribute new information to a
cold regions DA framework. Intra-basin snow and ice albedo variability
is also observed in both basins. For example, in AGRB, there is a clear
distinction between lower glacier ice albedos and the higher albedos
from the Columbia Icefield. The transition from snow to firn albedos is
also evident in PGRB. This date also exhibits an area in which albedo
was not retrieved for the most terminal glacier HRU in PGRB. Masked
albedo values in Figure 3 can occur if clouds and shadows obstruct the
area or if the coarse resolution BRDF retrieval is unable to generate
enough observations for a particular landcover class. DA was not
performed when there were no snow and ice 20-m albedo pixels inside an
HRU, and the modelling continued with its old state variables. Note that
there were 68 and 33 dates with available remotely sensed albedo
estimates for assimilation in AGRB and PGRB, respectively.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Figure 3: Remotely sensed snow and ice albedos for both basins during
mid-summer conditions. Light grey corresponds to masked areas due to
snow- and ice-free pixels, obstruction by clouds and shadows, or if the
BRDF retrieval was not possible for that landcover class.

3.2. Albedo DA Streamflow Evaluation

DA and CTRL streamflow evaluation metrics had accurate results for most
analyzed years. In the heavily wildfire-impacted year of 2018, DA
outperformed CTRL for both basins. The KGE difference between DA and
CTRL was 0.18 and 0.20 for AGRB and PGRB, respectively. In 2019 (soot
algae growth) and 2020 (normal year), DA was only beneficial for PGRB.
In 2021, the year affected by heatwaves and a few light late summer
wildfires, DA did not improve streamflow predictions for either basins,
indicating that other mechanisms might have influenced streamflow
predictions during heatwave conditions or that the operation of the
albedo algorithm in CRHM could not be improved upon by assimilating
observations. The four-year overall evaluation revealed that albedo DA
substantially benefited streamflow predictions in PGRB (KGE improvement
of 0.12), but only a slight advantage was found for streamflow
predictions in AGRB (KGE improvement of 0.02) (Table 2). The four-year
overall evaluation NSEs for AGRB (0.74) and PGRB (0.78) were above the
mean of maximum values (0.64) found in 20 studies that predicted
streamflow with the CRHM model (Pomeroy \emph{et al.} , 2022).

Table 2: Streamflow evaluation metrics for AGRB and PGRB. Metrics were
calculated for the combined four melt seasons and each melt season
individually (May 1 to Sept. 30), since streamflow rarely occurs outside
that period.

\textbf{Athabasca Glacier Research Basin (AGRB)}\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
\textbf{Period} & \textbf{NSE} & \textbf{NSE} & \textbf{KGE} &
\textbf{KGE} & \textbf{Bias {[}m\textsuperscript{-3}
s\textsuperscript{-1}{]}} & \textbf{Bias {[}m\textsuperscript{-3}
s\textsuperscript{-1}{]}} & \textbf{RMSE {[}m\textsuperscript{-3}
s\textsuperscript{-1}{]}} & \textbf{RMSE {[}m\textsuperscript{-3}
s\textsuperscript{-1}{]}}\tabularnewline
& \textbf{DA} & \textbf{CTRL} & \textbf{DA} & \textbf{CTRL} &
\textbf{DA} & \textbf{CTRL} & \textbf{DA} & \textbf{CTRL}\tabularnewline
\textbf{2018} & 0.63 & 0.43 & 0.72 & 0.54 & 0.61 & 1.01 & 1.28 &
1.57\tabularnewline
\textbf{2019} & 0.54 & 0.67 & 0.58 & 0.65 & 0.66 & 0.48 & 1.23 &
1.05\tabularnewline
\textbf{2020} & 0.83 & 0.82 & 0.83 & 0.85 & 0.25 & 0.18 & 0.85 &
0.87\tabularnewline
\textbf{2021} & 0.83 & 0.86 & 0.90 & 0.90 & -0.15 & -0.23 & 1.07 &
0.98\tabularnewline
\textbf{4-year} & 0.74 & 0.73 & 0.81 & 0.79 & 0.33 & 0.33 & 1.11 &
1.13\tabularnewline
\textbf{Peyto Glacier Research Basin (PGRB)} & \textbf{Peyto Glacier
Research Basin (PGRB)} & \textbf{Peyto Glacier Research Basin (PGRB)} &
\textbf{Peyto Glacier Research Basin (PGRB)} & \textbf{Peyto Glacier
Research Basin (PGRB)} & \textbf{Peyto Glacier Research Basin (PGRB)} &
\textbf{Peyto Glacier Research Basin (PGRB)} & \textbf{Peyto Glacier
Research Basin (PGRB)} & \textbf{Peyto Glacier Research Basin
(PGRB)}\tabularnewline
\textbf{Period} & \textbf{NSE} & \textbf{NSE} & \textbf{KGE} &
\textbf{KGE} & \textbf{Bias {[}m\textsuperscript{-3}
s\textsuperscript{-1}{]}} & \textbf{Bias {[}m\textsuperscript{-3}
s\textsuperscript{-1}{]}} & \textbf{RMSE {[}m\textsuperscript{-3}
s\textsuperscript{-1}{]}} & \textbf{RMSE {[}m\textsuperscript{-3}
s\textsuperscript{-1}{]}}\tabularnewline
& \textbf{DA} & \textbf{CTRL} & \textbf{DA} & \textbf{CTRL} &
\textbf{DA} & \textbf{CTRL} & \textbf{DA} & \textbf{CTRL}\tabularnewline
\textbf{2018} & 0.82 & 0.64 & 0.83 & 0.63 & 0.44 & 0.77 & 0.93 &
1.33\tabularnewline
\textbf{2019} & 0.68 & 0.22 & 0.83 & 0.50 & 0.26 & 0.98 & 0.86 &
1.33\tabularnewline
\textbf{2020} & 0.85 & 0.56 & 0.90 & 0.61 & 0.17 & 0.71 & 0.62 &
1.05\tabularnewline
\textbf{2021} & 0.71 & 0.77 & 0.65 & 0.78 & -0.78 & -0.30 & 1.47 &
1.32\tabularnewline
\textbf{4-year} & 0.78 & 0.63 & 0.85 & 0.73 & 0.10 & 0.61 & 0.98 &
1.27\tabularnewline
\bottomrule
\end{longtable}

Improvements in streamflow predictions occurred because DA decreased
streamflow compared to the CTRL run, reducing its positive bias. This
situation was observed particularly during the wildfires of 2018 for
both basins, but also in 2019, 2020, and the four-year period for PGRB.
The overall decrease in positive bias by DA is noticeable in Figure 4,
in which the CRTL streamflow (red) appears distinctly larger than the DA
streamflow (blue) in years that improvement was observed, except for
2021 in PGRB when CTRL streamflow was higher than DA. The reason for the
overall DA decrease in streamflow predictions will be further discussed
in section 5.4.3.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 4: AGRB (top) and PGRB (bottom) observed and simulated DA and
CTRL streamflows for the four analyzed WYs.

3.3. Albedo and SWE Updating with DA

As stated in section 5.4.2, satellite albedo DA improvements were
observed in years when DA streamflow predictions were lower than CTRL
and bias was positive. The benefit of satellite DA was caused by a
decrease in modelled glacier albedo combined with an increase in
snowcover in spring and summer (Figures 5, 6, and Table 2). This
mechanism occurs because the associated melt decreases considerably
while snowcover covers glacier ice, considering the relatively high
albedo snow generates less meltwater than relatively low albedo ice for
the same shortwave insolation fluxes. The DA streamflow used for
evaluation was the mean of all 20 ensembles. This mean is lower if more
ensembles have prolonged spring and summer snowcover over ice. Since the
benefits of DA stem from a decrease in streamflow, snowcover over ice
has a larger influence on melt than the decrease in albedo introduced by
DA. In AGRB, the ice albedo decrease introduced by DA was larger than in
PGRB. At the same time, the DA snowcover over ice was smaller in AGRB
(Figures 5 and 6). The integrated response was that AGRB streamflow was
less sensitive to DA than in PGRB. These results indicate that the
benefit of satellite albedo DA stems not only from the albedo itself,
but also from associated changes in other model states and glacier
configuration.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Figure 5: AGRB SWE and albedo DA mean, control, and ensembles for the
four melt seasons at the highlighted glacier ice HRU in Figure 1.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

Figure 6: PGRB SWE and albedo DA mean, control, and ensembles for the
four melt seasons at the highlighted glacier ice HRU in Figure 1.

3.4. Albedo DA Differences Between Snow and Ice HRUs

A prolonged spring and summer snowcover over glacier ice is not the only
cause of decreased streamflow in these basins. Because streamflow at the
outlet of glacierized basins is an integrated response of mainly snow,
firn, and ice melt, the melt at higher elevation snow and firn HRUs is
also relevant to the overall streamflow contribution. Figures 7 and 8
show the modelled albedo during wildfire (2018) and heatwave (2021)
conditions for snow and glacier ice HRUs in AGRB and PGRB, respectively.
Figure 7 illustrates that although AGRB DA albedo is lower for glacier
ice during wildfires and heatwaves, it is higher in snow-dominated
regions. The larger albedo in AGRB snow compensates for the smaller
albedo in glacier ice in years (e.g., 2018) when DA improved streamflow
predictions. Figure 8 shows that albedos were commonly smaller with DA
in PGRB snow, but in ice, they were only persistently lower than CTRL
during heatwaves. A larger DA PGRB ice albedo explains why streamflow
prediction improvements are better for this basin since the positive
bias in CTRL is decreased even further. During the 2021 heatwaves, DA
could not substantially improve streamflow predictions in either basin.
However, AGRB DA was closer to observed streamflows when compared to
PGRB. This difference can be explained by the longer persistence of DA
snowcover over ice in PGRB than AGRB. DA snow albedo in PGRB was closer
to CTRL, thus contributing to an even smaller streamflow for that year
(Figure 8). The results suggest that the albedo decay algorithm was
capable of simulating albedo in a heatwave, but could not predict the
lower albedos due to soot from wildfires.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

Figure 7: AGRB spring and summer DA and CTRL albedos at the snow and
glacier ice HRUs highlighted in Figure 1. The 2018 and 2021 years are
shown to represent wildfire and heatwave conditions, respectively.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

Figure 8: PGRB spring and summer DA and CTRL albedos at the snow and
glacier ice HRUs highlighted in Figure 1. The 2018 and 2021 years are
shown to represent wildfire and heatwave conditions, respectively.

\textbf{4. Discussions}

4.1. Albedo DA During Wildfire and Heatwave Conditions

The results presented in the previous sections have demonstrated that
albedo DA can improve streamflow simulations during wildfires but not
during heatwaves. The streamflow improvement response to albedo DA in
the soot-feeding algae year was only considerable in PGRB. These results
reveal somewhat contrasting processes happening in different zones of
these basins. Over glacier ice, DA decreased albedo considerably for
AGRB due to wildfire soot deposition, a process that was expected and
confirmed in previous studies (Aubry-Wake \emph{et al.} , 2022a;
Bertoncini \emph{et al.} , 2022). In PGRB, the decrease in ice albedo
due to DA was not as pronounced because of prolonged spring and summer
snowcover over ice. SWE is another state that is updated proportionally
to albedo. Because these states are the mean of 20 ensembles, the
likelihood of all ensembles converging in the absence of a snowpack
becomes lower when several ensembles present elevated SWE values.
Figures 5 and 6 show that the SWE ensemble spread in PGRB was wider than
in AGRB, contributing to a shorter period of exposed ice in PGRB. This
mechanism could have been caused by deeper snowpacks observed in
terminal sections of PGRB and more frequent spring and summer snowfall
events. The effect of prolonged snowcover when compared to control
simulations in snow DA has been reported before, usually leading to snow
depletion simulations closer to observations (Smyth \emph{et al.} ,
2020; Alonso-Gonz\selectlanguage{ngerman}ález \emph{et al.} , 2022). It is worth noting that
once the snow is depleted and firn and ice are exposed,
temperature-driven albedo decrease ceases. This mechanism should be
captured by the albedo decay algorithm that uses constant albedo values
for exposed firn and ice. The latter can potentially explain why
streamflow predictions were not sensitive to albedo DA during the
heatwave year.

Unlike ice, snow has a different response to albedo DA. Albedo DA has
shown to be larger than modelled by CTRL in AGRB high-elevation
snow-dominated regions. The introduction of remotely sensed albedo
through DA has revealed that snow was not completely melted in the AGRB
high-elevation HRU examples displayed in Figure 7, i.e., albedo did not
reach the 0.55 firn value. The low CTRL snow albedos can be a limitation
of albedo algorithms based on decay functions, such as the one used
hereby, which were developed for seasonal snowpacks at much lower
elevations. A comparison of three empirical models with a full
physically based model (closer to observations) has shown that empirical
decay albedo models, indeed, underestimate snow albedo (Gardner and
Sharp, 2010). On the other hand, DA snow albedo is often below CTRL in
PGRB, but rarely reaches the firn value of 0.55 (Figure 8). This result
suggests that snow-dominated PGRB surfaces would have a lower DA albedo
than CTRL, since they are more heterogeneous due to greater firn and ice
exposure than in AGRB. CTRL seems to miss processes well described at
lower elevations but not at glacier accumulation zones in both basins.
This finding calls for a better representation of glaciological albedo
processes capable of accounting for the peculiarities of localized
effects (Marshall and Miller, 2020).

This study tested two main assumptions by introducing remotely sensed
albedo in a cold regions DA framework. First, soot deposition would
decrease snow and ice albedo during extreme wildfire activity, such as
in 2018. This assumption was confirmed by previous studies
(Aubry-Wake\emph{et al.} , 2022a; Bertoncini \emph{et al.} , 2022) and
hereby for ice in AGRB and snow in PGRB. A greater albedo in the AGRB
snow HRU example can be explained by the larger elevation range observed
between snow and ice regions in AGRB (Pradhananga and Pomeroy, 2022).
This larger elevation range creates a scenario in which snow-covered
plateaux are at elevations more prone to new snowfall, suppressing the
effect of soot deposition over snow at a faster pace. Rapid recovery
from soot deposition over high-elevation snow in AGRB has been
previously described in Bertoncini \emph{et al.} (2022). Second,
heatwaves would accelerate melt and expose ice or firn unseasonally.
This process does not seem to substantially affect AGRB ice since
exposure in 2021 is similar to other years. However, albedo is lower for
snow during heatwaves when compared to wildfire years. Substantial
snowmelt and decreased albedo in glacier snow due to extended periods of
above-average temperature have been reported before in Greenland
(Box\emph{et al.} , 2022) and the Austrian Alps (Koboltschnig \emph{et
al.} , 2009). This mechanism suggests that heatwaves have a greater
influence on high-elevation snow-covered plateaux albedo decreases than
does wildfire soot in AGRB. On the other hand, there is a larger
sensitivity to wildfires than heatwaves for PGRB snow, perhaps because
of more firn and ice exposure than in AGRB. PGRB ice shows greater
albedo decrease during heatwaves due to longer ice exposure. In
addition, the albedo algorithm is expected to be more robust during
heatwaves than wildfires because it considers daily mean temperatures,
limiting most albedo DA benefits to wildfire years.

4.2. Implications for Streamflow Prediction in a Changing Climate

Unprecedented wildfires and heatwaves are expected to increase with
climate change (Jolly \emph{et al.} , 2015; Kirchmeier-Young \emph{et
al.} , 2019; Al-Yaari \emph{et al.} , 2023; Parisien \emph{et al.} ,
2023) and, hence, are likely to affect glacier contribution to
streamflow. Although this is a somewhat intuitive assumption, this study
has demonstrated inter- and intra-basin peculiarities in how the effects
of wildfires and heatwaves will contribute to snow and ice melt. The
findings show that wildfires and heatwaves can decrease glacier ice
albedo, but the period that ice is covered by snow is the primary
governing factor controlling ice melt. Likewise, the amount of summer
precipitation falling as snowfall is another factor governing albedo
dynamics in snow-dominated regions. This mechanism creates a scenario
where the elevation difference from the terminal glacier to
high-elevation snow plateaus dictates whether these basins would be
affected by either wildfires or heatwaves. For instance, in AGRB where
this elevation difference was higher than in PGRB, DA generated an
increase in snow albedo. This finding alone reveals something that would
not be possible using modelling alone; remotely sensed albedos were
needed in a DA modelling framework to understand this process in a
virtually inaccessible region. There lies the power of observational
tools in aiding hydrological models beyond the conditions in which they
were developed.

There are many implications of remotely sensed albedo DA for streamflow
predictions under climate change. The most important one is that this
study showed that even though DA was not beneficial for streamflow
prediction during heatwaves, it was beneficial in the overall four-year
evaluation in PGRB and favourable during wildfires and similar to CTRL
in other years in AGRB. From this perspective, remotely sensed albedo DA
is recommended under unprecedented hydrological extremes imposed by
climate change; however, caution should be taken when interpreting
albedo DA results during heatwaves. The latter calls for further
investigation into other processes that might have contributed to albedo
DA degradation of streamflow predictions under heatwaves beyond what has
been discussed here. Remotely sensed albedo DA can also better inform
hydrological modelling during wildfires and heatwaves. For instance,
events of decreased albedo can happen in the future in high-elevation
snow-dominated regions but be buffered subsequently by fresh snowfall,
which can only be confirmed with certainty via remotely sensed albedos
since precipitation measurements are usually taken at much lower
rainfall-dominated elevations. Users of hydrological predictions can
then understand \emph{de facto} whether these extreme events will affect
downstream streamflows.

4.3. Uncertainty within DA Modelling Framework

The DA modelling framework has worked satisfactorily in most simulated
years; however, a few factors contributed to the uncertainty in
modelling streamflow and other model states. First, although snow and
ice remotely sensed albedo estimates were satisfactory here and
elsewhere (Wang \emph{et al.} , 2016; Li \emph{et al.} , 2018;
Bertoncini\emph{et al.} , 2022), there is still a 5\% uncertainty
(\(\sigma_{o}\) = 0.046) in albedo estimation. This 5\% uncertainty
cannot be neglected in glacier ice albedo values. Therefore, even if
modelling uncertainty is larger than 5\%, this value would be, on
average, the smallest uncertainty possible of an optimal albedo estimate
for a particular assimilation date. Second, assimilation frequency can
contribute to the influence of DA in modelling albedo and other states.
AGRB (68 estimates) had more than double the number of assimilation
dates of PGRB (33 estimates). The lower number of assimilation dates in
PGRB could have contributed to longer periods of snowcover over ice,
since albedo correction from a new remotely sensed update would take
longer to occur. Finally, uncertainty in hydrological modelling can also
affect streamflow prediction within a DA framework. This study presented
DA NSE values of 0.74 and 0.78 for AGRB and PGRB, respectively. These
NSE values are higher than the mean of maximum values (0.64) found in 20
studies that conducted uncalibrated streamflow predictions using the
CRHM model (Pomeroy \emph{et al.} , 2022). Nonetheless, these NSE values
are not perfect, i.e., equal to 1, representing that there are still
uncertainties in streamflow prediction that can be attributed to model
structure, forcing errors, parameter errors, algorithm deficiencies, and
uncertainty caused by the DA EnKF implementation.

\textbf{5. Conclusions}

This research implemented and tested a remotely sensed albedo DA
framework to predict streamflow in two highly glacierized Canadian
Rockies's basins during environmental conditions ranging from normal,
wildfire, and heatwave dominated. Glacier ice remotely sensed albedos
presented satisfactory evaluation results (r = 0.96, bias = 0.026, RMSE
= 0.060, and \(\sigma_{o}\) = 0.046) that were needed for
assimilation. Albedo DA improved streamflow predictions in the heavily
wildfire-impacted year of 2018 for both basins -- a KGE improvement of
0.18 and 0.20 for AGRB and PGRB, respectively. DA in PGRB was beneficial
for all years but 2021. In the soot-feeding algae year, streamflow
improvement due to albedo DA was only considerable in PGRB. DA
substantially enhanced overall four-year streamflow prediction in PGRB
but just slightly in AGRB. DA's streamflow prediction improvements were
caused by a balance between changes in albedo of high-elevation snow and
glacier ice. In AGRB, snow albedo was increased by DA due to frequent
summer snowfall events that buffered the streamflow generated from
decreased glacier ice albedo in lower elevations. In PGRB, snow albedo
was decreased by DA, especially during wildfires. However, glacier ice
DA albedo was only decreased during short periods of ice exposure caused
by a prolonged spring and summer snowpack. The latter mechanism results
from several ensembles generating elevated SWE values during spring and
summer in PGRB glacier ice. These findings reveal that wildfires and
heatwaves are capable of decreasing glacier ice albedo, but the
resultant melt contribution to streamflow within a DA framework will
depend on snowpack albedo and SWE dynamics.

The cloud-computing remotely sensed snow and ice albedo retrieval
framework developed in this study could generate results with comparable
accuracy to previous studies, while providing global reproducibility at
high spatial and temporal resolutions. Before this study, albedo in
snow-dominated glacier accumulation zones was based solely on albedo
modelling developed at relatively lower elevations. This albedo
representation could not account for the rapid recovery of albedo with
fresh snowfall during wildfire and heatwave seasons. This finding was
only possible utilizing high-resolution remotely sensed albedo estimates
that could reach virtually inaccessible regions. The assimilation of
these remotely sensed albedo estimates into the physically based CRHM
model improved streamflow predictions for most of the analyzed years.
Moreover, using albedo DA revealed contrasting processes happening in
poorly observed glacier zones that resulted in different streamflow
responses to wildfires and heatwaves. Considering that the environmental
conditions observed during the study are expected to increase in a
future of climate change, it can be advantageous to use remotely sensed
high-resolution snow and ice albedo DA continuously for better
streamflow predictions in glacierized basins during wildfires and
heatwaves. This study's findings also indicate that the response of
glacierized basin streamflow to wildfires and heatwaves is not always as
expected due to the interplay of different factors such as fresh
snowfall, soot deposition, and unseasonal melt with the albedo
algorithm. Using observational tools such as DA can help narrow water
managers' uncertainty when making decisions based on hydrological
predictions under a warmer and more wildfire prone future.

\textbf{Acknowledgements}

We wish to thank NASA for the MODIS data and the European Space Agency
(ESA) for the Sentinel-2 and ERA5-Land data used to estimate remotely
sensed high-resolution albedos. We also acknowledge the support of the
GEE platform for hosting the above data and providing cloud-computing
resources, and the developers of the 6S atmospheric correction model and
its Python implementation (Py6S). The help from Xing Fang to QC
meteorological forcings and to set up the CRHM model is much
appreciated. We thank Caroline Aubry-Wake and Dhiraj Pradhananga for the
discussions about glacio-hydrological modelling and the many Centre for
Hydrology field technicians who contributed to maintaining the AWS. We
also would like to acknowledge the permission of Parks Canada for
allowing our research to take place in the Banff and Jasper National
Parks and Pursuit for assistance in logistics on Athabasca Glacier.

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