Glacier mass balance models are needed at sites with
scarce long-term observations to reconstruct past glacier mass balance and
assess its sensitivity to future climate change. In this study, North
American Regional Reanalysis (NARR) data were used to force a
physically based, distributed glacier mass balance model of Saskatchewan
Glacier for the historical period 1979–2016 and assess its sensitivity to
climate change. A 2-year record (2014–2016) from an on-glacier automatic
weather station (AWS) and historical precipitation records from nearby
permanent weather stations were used to downscale air temperature, relative
humidity, wind speed, incoming solar radiation and precipitation from the NARR
to the station sites. The model was run with fixed (1979, 2010) and
time-varying (dynamic) geometry using a multitemporal digital elevation
model dataset. The model showed a good performance against recent
(2012–2016) direct glaciological mass balance observations as well as with
cumulative geodetic mass balance estimates. The simulated mass balance was
not very sensitive to the NARR spatial interpolation method, as long as
station data were used for bias correction. The simulated mass balance was
however sensitive to the biases in NARR precipitation and air temperature,
as well as to the prescribed precipitation lapse rate and ice aerodynamic
roughness lengths, showing the importance of constraining these two
parameters with ancillary data. The glacier-wide simulated energy balance
regime showed a large contribution (57 %) of turbulent (sensible and
latent) heat fluxes to melting in summer, higher than typical mid-latitude
glaciers in continental climates, which reflects the local humid “icefield
weather” of the Columbia Icefield. The static mass balance sensitivity to
climate was assessed for prescribed changes in regional mean air temperature
between 0 and 7 ∘C and precipitation between -20 % and +20 %,
which comprise the spread of ensemble Representative Concentration Pathway (RCP) climate scenarios for the mid
(2041–2070) and late (2071–2100) 21st century. The climate sensitivity
experiments showed that future changes in precipitation would have a small
impact on glacier mass balance, while the temperature sensitivity increases
with warming, from -0.65 to -0.93 m w.e. a-1∘C-1.
The mass balance response to warming was driven by a positive albedo
feedback (44 %), followed by direct atmospheric warming impacts (24 %),
a positive air humidity feedback (22 %) and a positive precipitation phase
feedback (10 %). Our study underlines the key role of albedo and air
humidity in modulating the response of winter-accumulation type mountain
glaciers and upland icefield-outlet glacier settings to climate.
Introduction
Global warming is expected to cause reduced precipitation as snowfall in
cold regions, earlier snowmelt in spring and a longer ice melt period in
summer (e.g. Barnett et al., 2005; Aygün et al., 2020a). Even if
precipitation remains unchanged, warming alone will reduce snow and ice
storage in catchments, affecting the seasonality of river streamflow regimes
and accelerating water losses to the ocean (Escanilla-Minchel et al.,
2020; Huss et al., 2017; Huss and Hock, 2018). The transition from a
nivo-glacial to a more pluvial river regime in response to warming will
change the timing and magnitude of floods, leading to altered patterns of
erosion and sediment deposition and impacting biodiversity and water quality
downstream (Déry et al., 2009; Huss et al., 2017). The impacts of the
progressive loss of ice and snow surfaces and resulting alterations of the
hydrological cycle can reach well beyond the glacierised catchments,
affecting agriculture (Barnett et al., 2005; Comeau et al., 2009; Milner
et al., 2017; Schindler and Donahue, 2006), fisheries (Dittmer, 2013;
Grah and Beaulieu, 2013; Huss et al., 2017), hydropower and general
ecological integrity (Huss et al., 2017).
The surface mass balance is the prime variable of interest to monitor and
project the state of glaciers and their hydrological contribution under
global warming scenarios (Hock and Huss, 2021). However, only a
few glaciers around the world have long-term direct mass balance
observations because these measurements are time consuming and logistically
complicated. For example, only 30 glaciers have uninterrupted mass balance
records since 1976 (Zemp et al., 2009). Geodetic estimates provide
a complementary picture of cumulative mass changes for a greater number of
glaciers worldwide, but their coarser sampling interval (typically >5 years) makes their link with climate less direct (Cogley,
2009; Cogley and Adams, 1998; Menounos et al., 2019). For this reason,
models are often used to extrapolate scarce measurements, estimate unsampled
glaciers and assess glacier mass balance sensitivity to climate.
Temperature-index models, which use air temperature as the sole predictor of
ablation (Hock, 2003), have been extensively used to project regional and
global glacier mass balance under climate change scenarios, due to their
simple implementation and readily available global precipitation and
temperature forcing data (Hock et al., 2019; Huss and Hock, 2015;
Marzeion et al., 2012; Radić et al., 2014). Enhanced temperature-index
models, which include additional predictors such as potential (Hock,
1999) or net (Pellicciotti et al., 2005) solar radiation, have also been
shown to improve glacier melt simulation and to be more transferable outside
their calibration interval (Gabbi et al., 2014; Réveillet et al.,
2017). These empirical models contain few parameters, which simplifies their
application, but they must be calibrated on observations, which makes model
extrapolation in a different climate questionable (Carenzo et al., 2009;
Gabbi et al., 2014; Hock et al., 2007; Wheler, 2009). Hence,
spatially distributed, energy balance models that better represent the
physical processes driving glacier ablation are more suited to simulate
glacier mass balance outside of present-day climate conditions (Hock et
al., 2007; MacDougall and Flowers, 2011), given that accurate forcing data
were available (Réveillet et al., 2018).
Energy balance glacier models require several input observations and contain
multiple parameters that are sometimes difficult to measure or estimate (e.g. Anderson et al., 2010; Anslow et al., 2008; Arnold et al., 1996;
Ayala et al., 2017; Gerbaux et al., 2005; Hock and Holmgren, 2005; Klok and
Oerlemans, 2002; Marshall, 2014; Mölg et al., 2008). Glacier mass
balance models have been mostly forced with observations from automatic
weather stations (AWSs) on or near glaciers. However, the management of
weather stations networks in mountainous areas poses financial and
logistical challenges. At sites with scarce or missing data, outputs from
meteorological forecasting models (Bonekamp et al., 2019; Mölg et
al., 2012; Radić et al., 2018), regional climate models (Machguth et al.,
2009; Paul and Kotlarski, 2010) and reanalysis data (Clarke et al., 2015;
Hofer et al., 2010; Østby et al., 2017; Radić and
Hock, 2006) have been used to force glacier models. In particular, climate
reanalyses provide consistent and readily available gridded estimates of
past atmospheric states at sub-daily intervals, which constitute a useful
alternative to drive glaciological and hydrological models in data-scarce
regions (Hofer et al., 2010). Reanalyses are produced by retrospective
numerical weather model simulations that assimilate long-term and
quality-controlled observations. Regional products like the North American
Regional Reanalysis (NARR) have been developed to enhance the spatial and
temporal resolution of reanalyses at the continental scale (Mesinger et
al., 2006). Statistical downscaling of reanalysis data using on- or
near-glacier meteorological observations is necessary to reduce biases
resulting from this temporal- and spatial-scale mismatch as well as from
structural and parameterisations errors in the reanalysis model (Hofer
et al., 2010). Several methods can be used to correct those errors, such as
a simple bias shift toward observations (scaling or delta method) or the
matching of two probability distributions (e.g. quantile mapping) (Radić and Hock, 2006; Rye et al., 2010; Teutschbein and Seibert,
2012). This step is crucial, as uncertainties in climate forcing can be the
main source of error in mass balance modelling (Østby et al., 2017).
Forcing physically based glacier models with global or regional gridded
climate data introduces additional uncertainties which add up to the
structural and parameter uncertainties in the glacier model. In a context of
sparse in situ observations, the combination of poorly constrained model
parameters, biases in meteorological forcings and limited validation data
can result in biased long-term mass balance reconstructions and an incorrect
appraisal of glacier–climate relationships (Anslow et al., 2008; Machguth
et al., 2008; Zolles et al., 2019). A careful application, validation and
sensitivity analysis of the model becomes crucial in these situations.
Paradoxically, glaciers with sparse or no observations are typically those
where longer-term model reconstructions of mass balance are often most
sought (e.g. Kinnard et al., 2020; Kronenberg et al., 2016; Sunako et
al., 2019). Saskatchewan Glacier (52.15∘ N, 117.29∘ W), one of the main outlet glaciers of the Columbia Icefield in the Canadian
Rocky Mountains, is such a glacier with sparse mass balance observations,
which challenges the application of physically based mass balance models.
The Canadian Rocky Mountains support many glaciers which provide several
ecosystem services, such as water provision for hydropower production and
agriculture, and constitute iconic features highly valorised for tourism (Anderson and Radić, 2020; Comeau et al., 2009; Moore et al., 2009;
Petts et al., 2006; Schindler and Donahue, 2006). However, only a few
glaciers have been directly and continuously monitored for mass balance.
Peyto Glacier (51.67∘ N, 116.53∘ W) is the only
reference site with a long mass balance record (since 1966) and, with the
exception of 1996 and 2000, exhibits a consistent trend of negative annual
balance beginning in the mid 1970s (Demuth, 2018; Demuth et al.,
2006; Demuth and Pietroniro, 2002). Menounos et al. (2019) recently used
multisensor digital elevation models from spaceborne optical imagery to
calculate a mean mass balance of -0.410± 0.213 m w.e. a-1 for
the 2000–2018 period in the Canadian Rocky Mountains, with accelerated mass
loss between 2000–2009 and 2009–2018. A large-scale modelling study by
Clarke et al. (2015) showed that the volume of western Canada's glaciers
could decrease by more than 90 % from 2005 to 2100 in the Canadian
Rockies. Clarke et al. (2015) concluded that the main source of
uncertainty in their simulations of glacier evolution at the mountain range
scale was not the parameterisation of glacier flow but rather the simulation
of surface mass balance. Thus, accurate models of surface mass balance are
still needed at the scale of individual glaciers to extend and give
context to sparse mass balance observations as well as to characterise the
mass balance sensitivity to climate change.
Well-validated glacier models are an ideal tool to estimate glacier climate
sensitivity, i.e. the mass balance response to a change in climate
conditions (Braithwaite and Raper, 2002; Che et al., 2019; Ebrahimi and
Marshall, 2016; Engelhardt et al., 2015; Gerbaux et al., 2005; Hock et al.,
2007; Klok and Oerlemans, 2004; Mölg et al., 2008; Oerlemans et al.,
1998; Yang et al., 2013). These and other studies have reported on the
varying sensitivity of mass balance to warming air temperatures, however
often without unravelling the respective contributions of atmospheric
warming, surface feedbacks and precipitation phase feedbacks on the
temperature sensitivity. Distributed energy balance models offer the ability
to resolve the changes in energy fluxes that underpin the sensitivity of
mass balance to warming air temperatures, shedding light on the driving
forces of ablation under a changing climate (e.g. Anderson et al., 2010; Rupper and Roe, 2008).
This study uses a physically based, distributed mass balance model in the
context of sparse observations to reconstruct long-term glacier mass changes
and spatiotemporal patterns of energy and mass fluxes and to investigate
the glacier mass balance sensitivity to climate change. The main issues
addressed in this study are (i) how to constrain a physically based mass
balance model forced by reanalysis data in a context of sparse observations
and (ii) to quantify the respective contributions of energy balance,
precipitation phase and air humidity feedbacks to the mass balance climate
sensitivity under various warming scenarios.
Study area
The Columbia Icefield is located in the Canadian Rocky Mountains and
straddles the border between Alberta and British Columbia
(Fig. 1a). The Columbia Icefield is accessible via
the Icefields Parkway which is surrounded by two national parks (Jasper and
Banff), which makes the Columbia Icefield a highly valued cultural and
touristic site (Sandford, 2016).
Study area map. (a) Location of the Columbia Icefield in the
Canadian Rockies; the red rectangle shows the area of (b). (b) Weather
stations from the permanent network used to calculate temperature and
precipitation lapse rate. The nine NARR grid cells closest to Saskatchewan
Glacier are shown as red squares. (c) Map of Saskatchewan Glacier showing
the location of ablation stakes and additional snow survey points, as well as air
temperature sensors used to determine the diurnal lapse rate over the
glacier. The mean end of summer snow line position (1986–2013) is shown
with a red line. A Landsat 8 scene from 22 August 2013 is used for the map
background.
The plateau lying at ∼2800 m above sea level (m a.s.l)
intercepts moist air masses originating from the Pacific Ocean, which
results in large snow accumulation and the formation of glacial ice flowing
downward through several outlet glaciers (Demuth and Horne, 2018). The
Columbia Icefield is of crucial importance to the region's water budget, as
it feeds three different continental-scale watersheds flowing towards the
Arctic, Pacific and Atlantic oceans (Fig. 1a). The
main and largest outlet glaciers are located east of the icefield
(Saskatchewan and Athabasca Glacier), draining ∼60 % of the
eastern Columbia Icefield to the North Saskatchewan River (Hudson and Atlantic)
and the Sunwapta–Athabasca River (Arctic) (Marshall et al., 2011). Tennant and Menounos (2013) used historical aerial photographs and
satellite images to reconstruct the extent and volume changes in the
Columbia Icefield. The area of the Columbia Icefield was estimated to be
265.1 ± 12.3 km2 in 1919. By 2009 the icefield had
declined by 59.6 ± 1.2 km2 (-22± 0.5 %).
Saskatchewan Glacier is the largest outlet glacier of the icefield and the
source of the North Saskatchewan River; its area was 23 km2
in 2017 with elevations ranging from 1784 to 3322 m, the summit of Mount
Snow Dome – the hydrological apex of western Canada (Ednie et al.,
2017). Saskatchewan Glacier experienced the greatest absolute area loss
among the icefield glaciers, at -10.1± 0.6 km2 since
1919 (Tennant and Menounos, 2013). At the catchment scale, Demuth et al. (2008) reported glacier-area-wise losses of -22 % for the North
Saskatchewan River headwater basin between 1975 and 1998.
Data and methodsTopographic data
The main topographic data used in this study are a 1 m resolution digital
elevation model (DEM) derived from two WorldView-2 (WV2) satellite stereo
images acquired on 31 July 2010, covering the lower glacier, and 18
September 2010, covering the upper glacier. The DEM was mosaicked with tiles
from the Canadian Digital Surface Model (CDSM) (20 m resolution) to
include all adjacent topography that could cast shadows on the glacier. The
merged DEM was resampled to 100 m resolution to allow for faster
calculation with the mass balance model. The firn area was delimited by a
mean snowline delineated from Landsat satellite images from the year 1986 to
2013 (Fig. 1c). A total of 18 cloud-free images were
chosen near the end of the hydrological season (30 September) and used to
map the mean transient snowline position at the end of summer, which was
used as a proxy for the equilibrium line altitude (ELA). Image dates ranged
between 22 August and 2 October, necessary to find cloud-free images
capturing the transient snow line near the end of the ablation period.
To take into account historical glacier contraction in mass balance
simulations, multitemporal DEMs and glacier boundaries from Tennant and
Menounos (2013) (hereafter “TM2013”) were used to update the glacier
geometry over time in the mass balance model. TM2013 derived DEMs and
glacier extents from aerial stereo photographs from 1979, 1986 and 1993. For
1999, they used the Shuttle Radar Topography Mission (SRTM) DEM of February
2000, which they attributed to best represent the glacier surface at the end
of the 1999 summer ablation season, due to the penetration of the radar wave
in the following year's winter snowpack. The glacier extent in 1999 was
derived from the closest cloud-free, 30 m resolution Landsat 5 Thematic
Mapper (TM) image in September 2001. The 2009 DEM and glacier extent from
TM2013 were derived from Satellite Pour l'Observation de la Terre 5 (SPOT 5)
stereo images with a resolution of 2.5 m. Points matched on stereoscopic
image pairs were gridded to a 100 m resolution in the ablation area and to
200 m in the accumulation area, where low contrasts resulted in a smaller
number of elevation points and varying amounts of data gaps. We
re-interpolated all TM2013 DEMs to continuous 100 m resolution using
shape-preserving linear interpolation. The 2010 WV2 DEM was used instead of
the 2009 DEM from TM2013, which particularly suffered from extensive gaps in
the accumulation zone, but the glacier extent of August 2009 was conserved
as a boundary for the 2010 WV2 DEM. The slope, aspect and sky-view factors
were derived from all DEMs to be used as inputs for the mass balance model.
A more recent, 2 m resolution DEM was built from a stereo pair of Pléiades
satellite panchromatic images acquired in September 2016 and using the NASA
Ames Stereo Pipeline (ASP) (Shean et al., 2016). This DEM was used to
update the geodetic mass balance from TM2013 (in the Supplement). Since
the 2010 WV2 DEM has the highest resolution and few gaps, it was considered
the most reliable and used for model calibration and climate sensitivity
experiments.
Two static balance simulations were performed, one using the 1979 DEM as
the initial boundary condition and the other with the 2010 DEM. These were
compared with a dynamical simulation in which the glacier geometry was
adjusted with the multitemporal DEMs to consider the impact of glacier
recession on mass balance. The TM2013 glacier boundaries were used, but two
ice masses, disconnected from Saskatchewan Glacier since 1979, were excluded
from the original TM2013 outlines (see Fig. 1c).
The lateral, debris-covered moraines were also excluded from the glacier
outlines (see Fig. 1c). The term “reference mass
balance” (Bar) is used hereafter to refer to
glacier-wide mass balance simulated with a fixed reference geometry, while
the term “conventional mass balance” (Bac) is used for
the simulation with adjusted glacier geometries (Huss et al., 2012).
The effect of dynamical adjustment on Bar was
obtained by subtracting the reference balance using the 1979 geometry
(Bar1979) from Bac.
Meteorological dataOn-glacier automatic weather station
An automatic weather station (AWS) was deployed in August 2014 on the medial
moraine of Saskatchewan Glacier at an elevation of 2193 m a.s.l., collecting
near-continuous hourly data for a 2-year period, until June 2016
(Fig. 1c). Recorded variables include air
temperature (Ta), relative humidity (RH), incoming global (G) and reflected
(SW↑) shortwave solar radiation, wind speed (WS) and direction (WD), and snow
depths from an ultrasonic sensor. HOBO air temperature sensors were
installed by the Geological Survey of Canada (GSC) on five ablation stakes
(Fig. 1c) and operated between May and August 2015.
The HOBO sensors were shielded from solar radiation using naturally ventilated
gill shields.
Meteorological data from permanent weather monitoring network
Seven weather stations were chosen from the permanent weather monitoring
network maintained by Environment and Climate Change Canada in order to
calculate temperature and precipitation lapse rates. The stations ranged in
elevation from 1050 to 2025 m a.s.l. (Fig. 1b). As
precipitation was not measured at the AWS site, a historical precipitation
record was produced using data from the two weather stations closest to
Saskatchewan Glacier and highest in elevation (Parker Ridge, 2023 m a.s.l.,
and Columbia Icefield, 1981 m a.s.l.; see Fig. 1b). The Columbia Icefield station was only operated between May and
November, while Parker Ridge was operated mostly in winter and sometimes all
year-round depending on road accessibility. Both discontinuous records were
merged by averaging them.
Reanalysis data
While the precision of the on-glacier AWS data is useful to characterise the
glacier microclimate, the short and discontinuous record is not adequate to
drive a physically based, distributed glacier mass balance model for periods
of a decade or more. Meteorological reanalysis data were thus used to force
the mass balance model over the period 1979–2016, and the AWS data were
used to apply a first-order bias correction to the reanalysis data. Data
from the North American Regional Reanalysis (NARR) (Mesinger et al.,
2006) were chosen for this study because of its higher temporal (3 h) and
spatial (32 km) resolution compared to other commonly used products, such as
the ERA-Interim (6-hourly, ∼80 km resolution) and NCEP (National Center for Environmental Prediction; 6-hourly,
∼600 km resolution) reanalyses. NARR precipitation data have been
found to be superior to other global reanalysis products in the US (Bukovsky and Karoly, 2007) and to represent well air temperature
and humidity at high-elevation sites in southern British Columbia, Canada (Trubilowicz et al., 2016). Chen and Brissette (2017)
also showed that the NARR reproduced well the seasonality of precipitation and
temperature for 12 catchments across the US and Canada.
NARR data were acquired from the National Center for Environmental
Prediction (NCEP) at the National Center for Atmospheric Research (NCAR)
for the nine grid cells closest to the on-glacier AWS (see
Fig. 1b). The NARR cell whose center point is
closest to the on-glacier AWS has an elevation of 2430 m a.s.l., i.e. 237 m
higher than the AWS. The following NARR variables were used: (i) instantaneous values of air temperature and relative humidity at 2 m a.s.l. (TMP2m-ANL, RH2m-ANL), (ii) wind speed vectors at 10 m above the
model surface (U and V wind components of UGRD10m-ANL and VGRD10m-ANL), (iii) surface 3-hourly accumulated precipitation (APCPsfc-ACC), and (iv) 3-hourly
averaged surface downward shortwave radiation fluxes (DSWRFsfc-AVE).
The 3-hourly NARR variables were interpolated to the center of the hourly
averaging interval used by the AWS data logger. For instantaneous variables
(ANL) the concurrent time tag was used for the interpolation, while for
averages (AVE) the time at the center of the averaging interval was used.
Linear interpolation was used for relative humidity and wind speed. However,
both incoming solar radiation and air temperature have strong diurnal cycles
at the AWS site. Over the year, solar noon varies between 12:41 and 12:56,
and sunshine duration varies between 7.75 and 16.75 h. The 3-hourly NARR
data could thus underestimate the daily peaks in solar radiation and air
temperature, especially since the midday NARR 3-hourly average value spreads
between 11:00 and 14:00. However, given that solar noon occurs near the
middle of this interval, the NARR midday solar radiation average may in fact
well approximate the peak midday value, while the 14:00 instantaneous
temperature value is close to the time of maximum daily temperature.
Nevertheless, to reduce the probability of the diurnal cycle being
attenuated in the interpolated NARR data, a shape-preserving piecewise cubic
interpolation was used to interpolate air temperature and solar radiation to
an hourly interval. The 3-hourly accumulated (ACC) precipitation totals were
disaggregated to hourly values by dividing the 3 h totals into three
exact quantities.
Downscaling the NARR to weather stations
Downscaling the NARR variables to the glacier model grid involved two steps:
(1) interpolation of the NARR gridded data to the reference weather
stations and (2) bias correction of the interpolated NARR data. Two
interpolation methods were used and compared to extract NARR time series.
The first one is a simple nearest-neighbour interpolation; i.e. the NARR
grid point whose center point is closest to the reference stations (the
on-glacier AWS and the merged Parker Ridge–Columbia precipitation station;
see Fig. 1 for locations) was used. The second method used bilinear
interpolation from the nine NARR grid points closest to the weather
stations.
A simple bias correction procedure (Teutschbein and Seibert,
2012) was used to correct NARR biases. Air temperature, relative humidity,
wind speed and solar radiation from the interpolated NARR time series were
corrected relative to the on-glacier AWS. Since precipitation was not
measured at the glacier AWS, the NARR precipitation data were corrected with the
merged historical precipitation record from the Parker Ridge and Columbia
stations. Several data gaps remained in the merged record, and no
observations were available after 2008. Hence only days with observations
were used for bias correction over the period when the NARR overlapped the
merged precipitation record (1980–2008). Two simple bias correction methods
were tested and compared, namely scaling and empirical quantile mapping
(EQM) (e.g. Teutschbein and Seibert, 2012; Wetterhall et al., 2012). The
scaling method is the simplest, in which the NARR outputs are scaled with
the difference (additive correction) or quotient (multiplicative correction)
between the mean NARR and mean of observations. An additive correction was
used for unbounded variables (Ta,NARR) and a multiplicative correction
for strictly positive variables (RHNARR, WSNARR, GNARR and
PNARR; P for precipitation), as it also preserves the frequency. Because errors in incoming
solar radiation can originate from improper representation of the
atmospheric transmissivity and cloud cover in the NARR and/or shading
differences between the NARR smoothed topography and the real topography
surrounding the AWS, a time-varying scaling method was used to correct the
NARR global shortwave radiation data (GNARR). A mean diurnal
multiplicative correction factor was calculated by scaling the mean observed
diurnal G cycle with that of the hourly interpolated NARR. A separate diurnal
correction factor was calculated for each month of the year to account for
the seasonality in sun angle and related errors between the NARR and
observations.
The bias correction methods were evaluated against the glacier AWS data
using split sample cross-validation and compared with the baseline
performance, i.e. without corrections to the NARR variables. The AWS data
were split into two 1-year sub-periods on which downscaling methods were,
respectively, calibrated and validated; then both sub-periods were inverted,
and the mean validation statistics were calculated. For precipitation the entire
historical record was used, so validation sub-periods are longer than for
other variables. The cross-validated Pearson correlation coefficient (r),
mean error (bias) and root mean square error (RMSE) were used for
performance assessment. The performance of bias correction was evaluated at
both hourly and daily time intervals.
Extrapolation of NARR data to the glacier DEM
The downscaled NARR data were extrapolated from the reference stations to the
glacier DEM. Because data gaps remained in the merged Parker Ridge–Columbia
precipitation record, the downscaled NARR precipitation record was used to
force the mass balance model. As the glacier mass balance model only
considers a constant precipitation lapse rate, a mean lapse rate of 15.6 % per 100 m was calculated from the weather station network for the months
of November to March, when snow precipitation is most abundant on the
glacier and the relation between precipitation and elevation is strongest
(in the Supplement). The extrapolated total precipitation was split
between rain and snowfall according to a threshold temperature (T) of
1.5 ∘C, at which 50 % of the precipitation falls as snow and
50 % as rain. This value corresponds to a typical rain–snow temperature
threshold for continental mountain ranges and was inferred from the relative
humidity at the AWS site (83 %) following Jennings et al. (2018). A
linear interpolation of the rain–snow fraction is performed between
T-1∘C (100 % snow) and T+1 ∘C (100 % rain).
A mean monthly air temperature lapse rate was calculated from the permanent
weather station network. Lapse rates were calculated by linear regression of
mean temperature against elevation, using a minimum of five stations for
each month, depending on available data. Since variations in the diurnal lapse rate
can affect glacier melt simulations (Petersen and Pellicciotti,
2011), the on-glacier HOBO sensors were used to calculate a mean diurnal air
temperature lapse rate cycle on the glacier. Diurnal anomalies were produced
by subtracting the mean on-glacier lapse rates from this diurnal cycle and
were then added to the mean monthly lapse rates estimated from the permanent
weather station network. Hence, the lapse prescribed to the model varied on
a diurnal as well as on a seasonal (monthly) scale and was used to
extrapolate air temperature to the glacier DEM.
In the absence of constraining data, wind speed and relative humidity were
assumed spatially invariant, as was done in earlier modelling studies of
mountain glaciers (e.g. Anderson et al., 2010; Anslow et al., 2008;
Arnold et al., 1996, 2006; Hock and Holmgren, 2005; Mölg
et al., 2008). Wind speed can be expected to be relatively constant
downglacier due to the presence of a katabatic wind or an “icefield
breeze” wind, as found on the neighbouring Athabasca outlet glacier (Conway et al., 2021); however, it is possible that the
more open accumulation zone of Saskatchewan Glacier could have higher winds
than measured at the mid-glacier AWS (Fig. 1). Global solar radiation from
the downscaled NARR (GNARR) was separated into direct (I) and diffuse
(D) components, which were then extrapolated individually to each grid cell
considering terrain effects of the multitemporal DEMs. Further details are
given in the model description in Sect. 3.3.
Mass balance model
The physically based, distributed glacier mass balance model DEBAM (Hock and Holmgren, 2005) was used to simulate the mass balance of
Saskatchewan Glacier over the period 1979–2016. The surface mass balance is
expressed as
bt=Pst-Mt-S(t),
where b(t) is the point surface mass balance at time t, Ps is snow
precipitation, M is melt and S is sublimation. The model calculates the
distributed mass and energy balance on each 100 m × 100 m grid cell from the
hourly downscaled NARR meteorological forcing data including air
temperature, relative humidity, precipitation, wind speed and incoming
shortwave global radiation. The energy at the surface available for melt on
the glacier QM (W m-2) was calculated according to Eq. (2) and
converted into meltwater equivalent M (m w.e. h-1) using the latent
heat of fusion:
QM+QG+QR+QL+QS+LWS↓+LWT↓+LW↑+1-αI+DS+DT=0,
where I is the direct (beam) incoming shortwave solar radiation;
DS and DT are the diffuse sky and terrain shortwave
radiation, respectively; α is the albedo;
LWS↓ and LWT↓ are the
longwave sky and terrain irradiance, respectively; LW↑ is
longwave outgoing radiation; QS is the sensible-heat flux; QL is
the latent-heat flux; and QR is the energy supplied by rain (Hock
and Holmgren, 2005). The ground heat flux in the ice or snow QG is
often small for temperate glaciers and was neglected (e.g. Hock, 2005;
Yang et al., 2021). Fluxes are positive towards the glacier surface and
measured or calculated in watts per square meter. The model allows for different
parameterisations for calculating energy balance components, depending on
the availability of forcing data. The parameterisations used in this work
are detailed in the next sections.
Shortwave incoming radiation
Following Hock and Holmgren (2005), the separation of the downscaled
NARR global radiation (GNARR) into direct (I) and diffuse (D) radiation
is based on an empirical relationship between the ratio of measured global
radiation to top-of-atmosphere radiation GNARR/ITOA and the ratio
of diffuse to global radiation D/GNARR. Total diffuse radiation D
calculated at the AWS is then subtracted from the global radiation to yield
the direct solar radiation at the AWS site IS. Topographic shading is
calculated at each hour and for each grid cell from the path of the sun and
the effective horizon. If the AWS is shaded by surrounding topography, any
measured global radiation is assumed diffuse. Direct radiation I is
obtained at each grid cell following Hock and Holmgren (2005) as
I=ISISCIC,
where the subscript S refers to the location of the climate station and C
denotes clear-sky conditions. IC is the potential clear-sky direct
solar radiation which accounts for the effects of slope and aspect of each
grid cell, as well as shading from surrounding topography. The ratio IS/ISC measured at the AWS accounts for deviations from clear-sky
conditions, expressing the reduction in potential clear-sky direct solar
radiation mainly due to clouds. The ratio is assumed to be spatially
constant, which is reasonable given the large (∼400 km)
correlation length scale of cloud cover (Jones, 1992). Equation (3)
can not be applied when the AWS is shaded, since IC=0. In this case
and for glacier grid cells that remain illuminated, the last ratio that
could be obtained before the AWS grid cell became shaded is applied, which
assumes that cloud conditions remain constant until the climate station is
illuminated again (usually the next morning). The constant ratio was applied
to 57 % of the glacier surface, which was sunlit while the AWS was shaded,
for a mean and maximum duration of 0.73 and 2.16 h, respectively. The
impact on the radiative balance is thus considered to be small because this
situation occurs in the mornings and evenings at low sun illumination
angles and also because the temporal correlation length scale of cloud
cover is a few hours (Jones, 1992).
The total diffuse radiation (D) is calculated as
D=D0F+αmGNARR1-F,
where the first right-hand term represents sky radiation (DS) and the
second term is terrain radiation (DT). D0 is diffuse radiation from
an unobstructed sky calculated at the AWS and is considered spatially
constant. F is the grid cell sky-view factor defined by Oke (1987), and
GNARR is the downscaled NARR global radiation at the AWS. The mean
albedo (αm) of the surrounding terrain obtained for every hour is
the arithmetic mean of the modelled albedo of all grid cells for the entire
glacier (Hock and Holmgren, 2005).
Albedo
The albedo parameterisation of Oerlemans and Knap (1998) was used to
simulate the albedo (α):
5αsnow(t)=αfirn+αfrsnow-αfirnexps-tt∗,6α(t)=αsnow(t)+αice-αsnow(t)expdd∗,
where αsnow(t) is snow albedo, αt is the
final glacier albedo at time t, αfirn is the characteristic albedo
of firn, αfrsnow is the characteristic albedo of fresh snow and
αice is the characteristic albedo of ice, the timescale
(t∗) determines how fast the snow albedo decays over time (days)
and approaches the firn albedo after a fresh snowfall, d∗ is a
characteristic snow depth scale (cm) controlling the transition from snow
albedo to ice albedo, s is the day of the last snowfall, and d is snow depth
(cm). The constant, characteristic albedo values were set to αfrsnow=0.9 for fresh snow based on observations at the AWS. Ice
albedo was mapped using 17 of the 18 cloud-free, end-of-summer Landsat
images used to delineate the mean snowline position. Atmospherically
corrected surface reflectance from the Landsat 5 TM and Landsat 7 ETM+ (Enhanced Thematic Mapper Plus) sensors were converted to broadband albedo following Knap et al. (1999). A
median albedo map was produced, from which the distribution of ice albedo
values was extracted in a region of interest extending below the mean
snowline and excluding the glacier margins where shade effects were noticed
(in the Supplement). The median of the distribution (0.24) was used as
the representative ice albedo (αice). The characteristic timescale
(t∗) and depth scale (d∗) were calibrated using snow depth
and albedo measurements at the AWS. Since the AWS was on a moraine the value
for αice was set instead to the measured soil albedo for
calibration purposes. The optimum values used in the model, found by
minimising the RMSE of the simulated albedo, were t∗=14 d and
d∗=3 cm.
Longwave calculation
Since no observations of incoming longwave radiation were available at the
AWS for bias correction, NARR longwave radiation was not used for model
forcing because it would carry an elevation bias and would not account for
terrain effects. Instead, the incoming sky longwave radiation
(LWS↓) was calculated based on the Stefan–Boltzmann equation,
which relies on independent variables of air temperature and atmospheric
emissivity according to Eq. (7):
LWS↓=FεNARRσTa,NARR4,
where F is the sky-view factor, εNARR is the atmospheric
emissivity from the NARR, σ is the Stefan–Boltzmann constant (5.67 ×108 m-2 K-4) and Ta,NARR is the
downscaled NARR air temperature in kelvin. We adjusted the
LWS↓ calculation in DEBAM to include the spatial
variability in air temperature, i.e. by using Ta,NARR extrapolated to the glacier DEM, since the default parameterisation only
used air temperature measured at the AWS location for the entire glacier
area. This led to an overestimation of melt in the accumulation zone and an
underestimation in the ablation zone – both corrected when including the
distributed Ta,NARR in Eq. (7). Terrain longwave irradiance LWT↓ was calculated using the parameterisation by Plüss
and Ohmura (1997) for snow-covered alpine terrains:
LWT↓=(1-F)π(Lb+aTa,NARR+bTs),
where F is the sky-view factor, Lb=100.2 W m-2 sr-1 is
the emitted radiance of a 0∘ black body, Ts is the temperature
of the emitting surface, and a=0.77 W m-2 sr-1 and b=0.54 W m-2 sr-1 are coefficients calibrated for snow-covered alpine
environments (Plüss and Ohmura, 1997).
Outgoing longwave radiation (LW↑) is calculated from the Stefan–Boltzmann equation and the simulated surface temperature (Ts). Ts is
obtained in an iterative process by lowering surface temperatures in case of
negative energy balances until the energy balance equals zero (Hock
and Holmgren, 2005).
Turbulent heat fluxes
The turbulent sensible- (QS) and latent-heat (QL) fluxes
were calculated from the bulk aerodynamic method (Hock and Holmgren,
2005) based on air temperature (Ta,NARR), wind speed (WSNARR)
and vapour pressure (e) at height z=2 m a.s.l.:
QS=ρCpk2Inzz0w-ψMzLInzz0T-ψHzLWSNARR(Ta,NARR-Ts),QL=Lv0.623ρ0P0k2Inzz0w-ψMzLInzz0e-ψEzLWSNARR(e-es),
where ρ is air density at sea level (1.29 kg m-3); P0 is the
mean atmospheric pressure at sea level (101 325 Pa); Cp is the specific
heat capacity of air (1005 J kg-1 K-1); k is the von
Kármán constant (0.4); Ts is the surface temperature in
kelvin; e is the air vapour pressure as defined before; es is the
surface vapour pressure in pascals; z0w, z0T and z0e are the
roughness lengths for the logarithmic profiles of wind speed, temperature
and water vapour, respectively; ψM, ψH and ψE are
the stability functions for momentum, heat and water vapour, respectively; L is the Monin–Obukhov length; and
Lv is the latent heat of evaporation (2.514×106 J kg-1) or sublimation (2.849×106 J kg-1), depending on surface temperature and the direction of the latent-heat flux. If QL is positive, condensation occurs if the surface is
melting or deposition if the surface is frozen. Sublimation occurs when
QL is negative. The aerodynamic roughness length (z0) for snow and
ice influences the intensity of turbulent fluxes at the glacier surface.
Typical z0 values for glacier snow (z0_snow) range
between 0.5 and 6 mm (Brock et al., 2006; Fitzpatrick et al., 2019;
Munro, 1989), while z0 for smooth glacier ice surfaces
(z0_ice) typically ranges between 0.1 and 6 mm (Brock
et al., 2006). Munro (1989) measured z0 values between 0.67 and 2.48 mm
along and across the grain of the ice, respectively, and 5–6 mm for snow on
nearby Peyto Glacier, which has a similar ice facies morphology as the
Saskatchewan Glacier, based on our field observations. A mean
z0_ice of 1.58 mm and z0_snow of 5.5 mm was thus used in the model. The roughness length for temperature and
water vapour were both considered to be 2 orders of magnitude less than
roughness lengths for wind (Hock and Holmgren, 2005).
Model validation and uncertainty analyses
The simulated mass balance has been validated at the point scale against
available seasonal and annual glaciological mass balance observations since
2012 and was at the glacier scale using the reconstructed geodetic mass balance
from 1979 to 2016. These data are described in detail in the Supplement. The sensitivity of the reconstructed mass balance was tested with
respect to (i) the NARR interpolation method, (ii) the NARR bias correction
method, (iii) replacing NARR forcings with their AWS counterpart and (iv) uncertain model parameters. For (i), the model was run with NARR forcings,
respectively, interpolated with the nearest-neighbour and bilinear methods.
For (ii), the model forced with the bias-corrected NARR forcings was
compared with a model forced with the raw NARR but correcting for the elevation
difference between the NARR and the reference stations using the mean measured
temperature and precipitation lapse rates (e.g. Fiddes and Gruber,
2014). For (iii), the NARR forcings (GNARR,Ta,NARR,WSNARR,RHNARR) were replaced one at a time by the AWS observations and the
simulated point mass balances compared with stake observations for 2015, the
only year with continuous AWS data and concurrent glaciological
observations. For (iv), while the physical nature of the model did not
require formal calibration, four uncertain model parameters were subjected
to a sensitivity analysis to characterise their impact on the modelled mass
balance. The precipitation lapse rate was varied within ± 4 % per 100 m, which corresponds to the standard deviation of the precipitation
lapse rate calculated from the permanent weather network (see Sect. 3.2.5
and the Supplement). The ice albedo (αice) was varied
within ± 0.03, which corresponds to the spatial standard deviation of
ice albedo observed from satellite images (see Sect. 3.3.2). The aerodynamic
roughness lengths for ice (z0_ice) and snow
(z0_snow) were varied within ± 1 mm, which covers
the range of values by Munro (1989) on nearby Peyto Glacier (see Sect. 3.3.4). The sensitivity to roughness lengths was also extended to ±1 order of magnitude, as an extreme case.
Climate sensitivity
The validated DEBAM model was used to perform a climate sensitivity analysis
of the reference mass balance (with respect to the 2010 glacier hypsometry:
Br2010) to potential changes in air temperature (ΔTa)
ranging between 0 and 7 ∘C (1 ∘C interval) and
precipitation (ΔP) ranging between -20 % and +20 % (5 % interval).
These warming and precipitation change scenarios encompass mean annual
changes projected by ensemble general circulation model (GCM) simulations
for the mid (2041–2070) and late (2071–2100) 21st century relative to the
most recent 30-year climatological period (1981–2010) and under different
Representative Concentration Pathway (RCP) scenarios (IPCC, 2013). The ensemble climate projections from
the Coupled Model Intercomparison Project Phase 5 (CMIP5) were obtained from
the KNMI (Koninklijk Nederlands Meteorologisch Instituut, Royal Netherlands Meteorological Institute) Climate Change Atlas (Trouet and Van Oldenborgh, 2013) for RCP2.6 (n=32), RCP4.5 (n=42), RCP6.0 (n=25) and RCP8.5 (n=39) for the grid point
closest to the ELA of Saskatchewan Glacier (Fig. 1). The number of simulations (n) depended on the availability of the CMIP5
models for each scenario (IPCC, 2013). The IPCC AR5 Atlas (Intergovernmental Panel on Climate Change Fifth Assessment Report) subset
was used, which uses only a single realisation of each model and weights all
models equally, where model realisations differing only in model parameter
settings are treated as different models (IPCC,
2013). The DEBAM model was run 63 times for every combination of ΔTa and ΔP perturbation imposed on the Ta,NARR and
PNARR records over the 30-year reference period 1981–2010. Changes in
mass balance for each sensitivity run were plotted as response surfaces,
which provides a simple way to assess climate sensitivity across a range of
possible climate change scenarios (e.g. Aygün et al.,
2020b; Prudhomme et al., 2010). Mean temperature and precipitation changes
along with their 95 % confidence intervals were overlaid onto the
response surfaces to show the most likely future climate trajectories given
by the GCM projections.
ResultsMeteorological observations
Daily and monthly averages of air temperature (Ta), relative humidity
(RH), incoming solar radiation (G) and wind speed (WS) measured at the glacier
AWS show notable differences between the 2 years of observation
(Fig. 2). The winter of 2014–2015 was, overall,
colder than 2015–2016, with frequent cold excursions below -15∘C
and a winter absolute minimum of -27∘C vs. -17∘C in
2015–2016, although conditions were warmer in December. Relative humidity was
generally high throughout the year (mean = 79 %), illustrating the
predominantly humid climate of the Columbia Icefield but decreases
noticeably in summer. The variability in daily RH is similar between the 2 years of measurements. The incoming solar radiation shows pronounced
seasonality, varying between ∼50 W m-2 in winter and
∼300 W m-2 in summer, with daily variations between 50 W m-2 in winter and 150 W m-2 in summer caused by variable cloud
cover. A gentle breeze blows on average on the glacier (mean wind speed = 4.46 m s-1), but wind speed shows significant day-to-day variations as
well as higher values in winter. A gradual increase in wind speed is notably
observed from the lowest monthly mean value in May 2015 (1.76 m s-1) to
a maximum in February (7.13 m s-1). The historical precipitation
records from the Columbia Icefield and Parker Ridge stations contain several
gaps but still portray the seasonal and interannual variability in
precipitation near the glacier (Fig. 2e). The mean
annual accumulated precipitation throughout the historical period with
complete data was 874 mm a-1 but varied between 276 and
1704 mm a-1. Precipitation data are more abundant in winter, with 58 % of
precipitation falling between October to March, mostly as snow, and 42 %
falling during April–September, mostly as rain.
A 2-year record from the Saskatchewan Glacier AWS (2014–2016). (a) Air temperature (Ta); (b) relative humidity (RH); (c) incoming global
solar radiation (G); (d) wind speed (WS). Pink shades delineate the data gap
caused by the fall of the AWS (11 to 30 June 2015). (e) Daily precipitation
records from the Parker Ridge and Columbia Icefield permanent stations. Note the
several gaps after 1995 when the Columbia Icefield station was interrupted.
NARR downscaling
The NARR meteorological variables used to drive the glacier mass balance
model were compared with data from the glacier AWS (2014–2016) and the
29-year-long merged daily precipitation record
(Fig. 3). Even prior to applying bias correction,
Ta,NARR, RHNARR and GNARR show a good correlation with AWS
observations on a daily scale, for both NARR spatial interpolation methods.
As expected, the correlation is poorer for WSNARR, likely because the
local glacier katabatic wind recorded by the AWS is not well represented in
the NARR due to its coarse grid resolution. The NARR precipitation is also
rather poorly correlated with observations (r=0.30). Biases in raw NARR
variables are relatively small compared to the mean and range of values
recorded (blue dots in Fig. 3), except for
GNARR (30.4 W m-2) and PNARR (0.55 mm d-1), which
represent 15 % and 25 % of their mean measured values over their period
of observation, respectively. The cold bias (-1.26∘C) observed
for Ta,NARR from the closest grid cell is consistent with the elevation
difference between the AWS (2193 m) and the NARR grid cell (2430 m) (ΔZ= 237 m), which results in an expected temperature difference of -1.19∘C using the mean observed lapse rate of -0.5∘C per 100 m (see Sect. 4.3). Neither the scaling nor the EQM correction
methods improved the Pearson correlation coefficient (r) – primarily since
it is a relative measure of the synchronicity between two time series and is
unaffected by the mean values. The EQM method was found to improve
Ta,NARR best, closely followed by the scaling method, while
the scaling method was slightly superior for RHNARR, WSNARR and
PNARR. However, scaling only slightly reduced the errors for
WSNARR and PNARR and had no effect on RHNARR, which had an initial
low error. The diurnal scaling correction applied to GNARR also reduced
its errors. Overall, the scaling bias correction method was the
more efficient approach across all variables and both NARR spatial
interpolation methods and was thus applied to all variables for consistency
except for relative humidity, which was left uncorrected. Similar results,
although with expectedly higher errors, were found for the interpolated NARR
hourly data (Table S3 in the Supplement).
Comparison between NARR reanalyses and automated weather station
(AWS) meteorological variables (2014–2016). Each panel shows the
cross-validated root mean square error (RMSE) between daily NARR and AWS
variables, before (blue) and after bias correction (red: scaling method;
yellow: EQM method), for the two NARR spatial interpolation methods
(Nearest: nearest grid cell; Interp: bilinear interpolation). The cross-validated
correlation coefficient (r), which changes little after bias correction, is
shown on top of the bars for each NARR interpolation method. Quivers on the
left-hand side of the panels show the cross-validated bias before (blue dot) and
after (red triangle) applying the scaling bias correction method. (a) Air
temperature; (b) relative humidity; (c) wind speed; (d) incoming global
solar radiation; (e) precipitation.
The bilinear NARR interpolation method resulted in slightly lower RMSE and
bias values for the raw variables, i.e. before bias correction (blue bars
and dots in Fig. 3), except for the slightly higher bias for RH. However,
after applying the station-based bias correction, the bias and RMSE values
were very similar among the two methods. As such, the NARR forcings
downscaled from the nearest NARR grid cell were used as primary model
forcings for the mass balance reconstruction and climate sensitivity
experiments, and the sensitivity of the reconstructed mass balance to the NARR
spatial interpolation method was further investigated in Sect. 4.6.
Monthly and annual averages of the downscaled NARR variables from the
nearest NARR grid cell are displayed in Fig. 4.
There is no visible trend in mean annual Ta,NARR over the 30-year
period except since 2010, but there is a noticeable increase in minimum
temperatures, with e.g. only 2 years with a monthly mean colder than
-15∘C in 2000–2015 compared to 7 years prior to 2000. The
positive trend seen in mean annual RHNARR is driven by increasing
annual minima, while annual maxima show no trend, and so the seasonal
amplitude decreases over time. The monthly RHNARR averages decrease
in July and August (mean = 72 %), while winter months have higher values
(mean = 80 %–82 %) (Fig. 4b). No noticeable
trends occur in atmospheric emissivity (εNARR) and GNARR, despite
the observed trend in RHNARR (Fig. 4d, f).
A progressive decline in WSNARR occurs from 1984 onward, reaching the
lowest annual value of the period in 1995 (∼4.3 m s-1)
(Fig. 4c). A more subdued increase in
WSNARR occurs afterward until 2010, followed by a decline. Finally,
mean monthly precipitation shows no long-term trend but significant seasonal
and interannual variability (Fig. 4e). A slight
increasing trend in PNARR is noted in the last part of the record,
since ∼2000.
Downscaled NARR variables from the nearest NARR grid cell used
to drive the DEBAM model. Grey solid lines represent monthly means, and black
solid lines represent annual averages. (a) Air temperature; (b) relative
humidity; (c) wind speed; (d) incoming global solar radiation; (e) total
precipitation; (f) atmospheric emissivity.
Air temperature lapse rates
On-glacier diurnal air temperature lapse rates were found to vary from
-0.55∘C per 100 m at night and to a maximum of -0.34 ∘C per 100 m at midday following an increase during the day
(Fig. 5a). The strength of the linear relationship
between air temperature and elevation, as measured by the correlation
coefficient (r), is generally high (r>0.95) but decreases
slightly during daytime hours (r=0.92). While wind speed increased during
the day, downglacier winds prevailed, with little deviation of the wind
direction within the day (Fig. 5a). The wind blows
dominantly downglacier, with the relative wind direction showing a mixed
contribution of the main accumulation area upwind of the AWS and the
glacierised plateau north of the AWS. Stronger daytime downglacier winds,
possibly driven by a larger thermal gradient between the lower ice-free
valley and the glacier, could result in downglacier cooling and
correspondingly shallower near-surface lapse rates or even inverted lapse
rates, as shown on the neighbouring Athabasca Glacier (Conway
et al., 2021). Closer inspection of hourly lapse rates revealed that
inversions only occurred 1.7 % of the time between May and August on
Saskatchewan Glacier. On a monthly scale, the lapse rate, calculated from
seven stations from the permanent network, varied between -0.58 and -0.42∘C per 100 m without any systematic
seasonal pattern (Fig. 5b). The correlation for
the monthly lapse rates is also more variable than for the diurnal lapse
rates, varying between low values (r=0.6) in winter and higher values
(r=0.94) in summer. The mean on-glacier summer (May–August) lapse rate
(-0.46∘C per 100 m) was very close to that calculated from the
permanent weather station network for the same period (-0.49∘C per 100 m), which gives confidence in extrapolating the monthly lapse
rates from the network to the glacier surface. Superimposing the on-glacier
anomalies of diurnal lapse rates onto the mean monthly lapse rates allowed for a
better representation of the diurnal changes associated with the glacier wind.
Calculated air temperature lapse rates. The black axis represents
the air temperature lapse rate in ∘C per 100 m; the blue axis
represents the correlation (r) between air temperature and elevation; the red
axis represents wind speed; and the green axis the wind direction relative to
the main glacier axis (0∘= downglacier, 180∘= upglacier). (a) Diurnal temperature lapse rate from the five HOBO
microloggers installed on ablation stakes from May to August 2015 (see
Fig. 1). (b) Seasonal variation in the lapse rate derived from the
permanent weather stations (see Fig. 1). Wind
speeds and directions on both panels are from the glacier AWS.
Model performanceComparison with glaciological mass balance
The mass balance simulated with DEBAM was compared with point glaciological
mass balance observations available between 2012 and 2016. Overall, the
seasonal and annual mass balance components are well simulated by the model,
with most observations lying near the 1:1 line and with Nash–Sutcliffe
efficiency (NSE; Nash and Sutcliffe, 1970) coefficients of 0.84 for the
winter balance (bw, n=49), 0.83 for the summer balance (bs,
n=12) and 0.91 for the annual balance (ba, n=12)
(Fig. 6). Before the adjustment of the atmospheric
emissivity calculation in the LW↓ equation (see Sect. 3.3.3), the
model tended to overestimate melt in the accumulation zone and underestimate
it in the ablation zone. The NSE was increased by 0.04 for bw, 0.07 for
bs and 0.06 for ba after modifying the parameterisation. The
modelled bw was underestimated in 2016 in the upper part of the glacier
and overestimated in the lower part, suggesting that the precipitation
gradient for that year significantly differed from the other years. This
shows one limitation of the current model configuration, which uses a
constant, average precipitation lapse rate to distribute precipitation over
the glacier surface. The year 2016 was dry, with the ultrasonic gauge on the
glacier AWS recording a small amount of snow accumulation during winter (25 cm in 2016 vs. 135 cm in 2015). Observations from ablation stakes are more
limited, and despite the overall good model performance as seen by the
linear relationship between observed and simulated b and the high NSE values,
modelled bs and ba were slightly underestimated in 2014 and 2016 and
overestimated in 2015 compared to observations
(Fig. 6).
Simulated mass balance compared with point mass balance
observations available between 2012 and 2016. (a) Winter balance (bw);
(b) summer balance (bs, only available since 2014); (c) annual balance
(ba, since 2014). The dashed line is the 1:1 relationship. (d) Simulated vs. observed annual mass balance gradient between 2014 and 2016.
The simulated mass balance gradient compares generally well with
observations for the 3 years with available ba measurements
(Fig. 6d). Overestimation of ablation at the two
ablation stakes from 2014 is apparent, however, leading to underestimated
mass balance (ba) in the upper glacier for that year. The equilibrium
line altitude (ELA) was ∼2600 m for 2014–2016, which is near
the average ELA of 2587 m simulated for the entire 1979–2016 period. The
mean simulated mass balance gradient for the three validation years
(2014–2016) was 0.98 m w.e. per 100 m in the ablation zone, with a
steeper inflection below the ELA, and decreased to 0.32 m w.e. per 100 m
in the accumulation zone (up to 2900 m, where the model is constrained by
observations; see Fig. 6d). Long-term values were 0.96 and 0.31 m w.e. per 100 m for 1979–2016, yielding a balance ratio (BR: the ratio of ablation to accumulation area balance gradients) of 3.10. A
higher BR value implies that a smaller ablation area is needed to balance
inputs in the accumulation area (Benn and Evans, 2010). The BR value
simulated for Saskatchewan Glacier is rather high, i.e. triple that computed
by Rea (2009) for the “North America – Eastern Rockies” region (mean BR ± SD = 1.11 ± 0.1). The simulated BR is within the range, but
still on the high side, of values found for “North America – West Coast”
glaciers (mean BR ± SD = 2.09 ± 0.93) which have a more humid
climate (Rea, 2009).
Mass balance reconstruction and comparison with geodetic estimates
The simulated annual specific (glacier-wide) conventional mass balance
(Bac) was overall negative throughout the period (mean =-0.72 m w.e. a-1) with pronounced interannual variability (SD = 0.57 m w.e. a-1) (Fig. 7a). The cumulative
conventional mass balance simulated with the multitemporal DEMs agrees well
with the geodetic estimates (Fig. 7b). The
simulated and geodetic cumulative mass balance were -26.79 and -25.59± 8.44 m w.e., respectively, for 1979–2016. The cumulative error in
the geodetic estimates increases in 1999 due to the large error in the SRTM
DEM, even though it was coregistered to the high-quality WV2 2010 DEM
(in the Supplement).
Simulated mass balance compared with geodetic estimates. (a) Conventional annual glacier-wide mass balance (Bac) from
the dynamical simulation (multitemporal DEMs). The blue curve represents the
effect of dynamical adjustment on Bac. (b) Cumulative
mass balance from reference (red: 1979, blue: 2010) and conventional (black:
multitemporal DEM) simulations. Error bars represent 1σ cumulative
confidence intervals around the cumulative geodetic mass balance.
The simulation with the 1979 reference DEM (Bar1979),
when the glacier was thicker and larger, results in a larger cumulative mass
loss (∼-3 m w.e. over 37 years) than when using the 2010 DEM
(Bar2010) with the smallest historical extent
(Fig. 7b). The difference essentially arises from
the larger extent in 1979 which provides more area available for melting at
lower elevations. The conventional mass balance simulation remains between
the limits of the two endmember reference simulations, with a difference in
cumulative mass loss of ∼± 1.4 m w.e., at the end of the
period. The effect of dynamical adjustment was overall small from 1986
(first DEM update) onward (mean = 0.06 m w.e. a-1) but accelerated
over the last 15 years (Fig. 7a).
Model sensitivity to uncertainties in parameters and NARR forcingsSensitivity to NARR interpolation and bias correction method
Forcing the mass balance with the nearest NARR grid cell or with the
bilinearly interpolated NARR forcings resulted in negligible differences on
the simulated cumulative balance, when both types of NARR forcings were
bias-corrected by station observations (Fig. 8a).
However, when station data were not used for bias correction and the NARR
precipitation and air temperature were only lapsed to the station elevations
using the mean observed lapse rates, the simulated mass loss was
overestimated relative to geodetic observations. However, the lapse-rate-corrected and bilinearly interpolated NARR forcings resulted in a
closer agreement with the geodetic observations than when using the lapse-rate-corrected NARR forcings from the nearest grid cell.
Model sensitivity to NARR forcings and model parameters
uncertainty. (a) Sensitivity to NARR interpolation method (nearest grid cell:
black, bilinear interpolation: blue) and bias correction method
(continuous line: bias-corrected with AWS, stippled line: PNARR and
Ta,NARR lapse-rate-corrected to the DEM). (b) Sensitivity to NARR
forcings: measured vs. simulated point mass balance for glaciological year
2014–2015 after replacing NARR forcings (Ta,NARR, RHNARR,
GNARR, WSNARR) one at a time by AWS observations; (c) corresponding
mean error (bias, m w.e., coloured bars) and Nash–Sutcliffe efficiency
scores (labels). (d) Sensitivity to model parameter uncertainty. Coloured
envelopes represent the cumulative uncertainty; coloured error bars on the
right show the effect of parameter uncertainty on the cumulative mass
balance in 2016. Error bars for ice (green) and snow (red) roughness lengths
correspond to a ± 1 mm measurement uncertainty; the dotted error bars
extend the uncertainty to ±1 order of magnitude.
Sensitivity to NARR forcings
The model sensitivity to the type of NARR variable used for forcing was
investigated for the glaciological year 2014–2015, when both complete
on-glacier AWS data and point mass balance were available
(Fig. 8b, c). Results show that the model was most
sensitive to air temperature, whereas replacing the other NARR forcings
(RHNARR, WSNARR, GNARR) by their AWS counterparts had a
comparatively small effect on the mass balance validation against
observations. Hence, despite the good correlation between NARR and AWS air
temperatures and the low errors following bias correction
(Fig. 3), the model remains most sensitive to air
temperature, while it is less sensitive to other variables that showed
comparatively higher errors with respect to AWS observations, such as wind
speed (Fig. 3).
Sensitivity to model parameters
The model parameter sensitivity analysis shows that the simulated mass
balance was most sensitive to the uncertainty in the precipitation lapse
rate (± 4 % per 100 m) followed by the ice aerodynamic roughness
length (z0_ice: ± 1 mm)
(Fig. 8d). The sensitivity to uncertainties in ice
albedo (αice: ± 0.03) and the snow aerodynamic roughness
length (z0_snow: ± 1 mm) were smaller and of
similar magnitude. Large changes in simulated cumulative mass balance
occurred when considering change of an order of magnitude on aerodynamic
roughness lengths. While spatial variability in z0 of that order is
possible across a single glacier due to heterogeneous snow and even more so
on rougher ice surface morphology (Chambers et al., 2020),
the resulting uncertainty on the glacier-wide average z0 would be much
lower (Brock et al., 2006; Chambers et al., 2020; Munro, 1989).
Nonetheless, these results clearly show that a careful assessment of the
precipitation lapse rate and ice aerodynamic roughness length are crucial to
derive a reliable long-term mass balance reconstruction. Constraining these
two parameters as well as the ice albedo and the snow aerodynamic roughness
length against observations and ancillary information is thus pivotal to
reliably simulate the recent direct mass balance observations
(Fig. 6) and long-term geodetic estimates
(Fig. 8).
Energy and mass fluxes
Monthly energy balance shows that the sensible-heat flux (QS) dominates
energy gains throughout most of the year (Fig. 9).
The contribution of QS is fairly constant throughout the year,
increasing only slightly in July–August and decreasing slightly in spring
(March–May). The contribution of the net solar radiation flux (SW*) increases
systematically from low values in winter (November–February) when the sun
angle is low and the glacier is covered by highly reflective snow to peak
values in July–August when the sun angle is high and low-albedo ice is
exposed in the ablation area. Only in July and August does the net solar
radiation (SW*) become the dominant energy source. The latent-heat flux
(QL) is small over Saskatchewan Glacier, due to the generally high
relative humidity (see Fig. 2). QL is
positive on average and highest in summer, reflecting the predominance of
deposition and condensation processes over sublimation. QL represents a
small but non-negligible (7 %) heat gain throughout the year, which
reaches 11.5 % in July–August. Energy loss occurs mainly by radiative
cooling, i.e. through a negative net longwave radiation flux (LW*). Lower air
and surface temperature, respectively, reduce the incoming atmospheric
longwave radiation and outgoing longwave emissions from the glacier surface,
thereby reducing LW* in winter. LW* increases somewhat in summer (June–August),
mainly because the glacier surface is near its melting point, limiting
longwave radiation losses. The energy supplied by rain (QR) has a
negligible influence on the energy balance. Melting (QM) predominantly
occurs between May and October and peaks in July–August, due to the elevated
SW*, QS and QL fluxes and radiative cooling (LW↑) limited
by the melting surface.
Mean seasonal cycle of simulated surface energy balance on
Saskatchewan Glacier between 1979–2016 from the multitemporal DEM
simulation. SW*: net shortwave radiation; LW*: net longwave radiation;
QS: sensible-heat flux; QL: latent-heat flux; QR: rainfall
heat flux; QM: energy used for melting.
Four processes influence mass balance during the year
(Fig. 10a). Snowfall and snow accumulation
dominate during the accumulation season (October–April). Melt mainly occurs
from May to October and peaks in July–August in response to the positive
surface energy balance (Fig. 9).
Deposition/condensation and sublimation fluxes are small. Net deposition
predominates, while net sublimation occurs in the spring (April–June), when
there is high incoming radiation and the upper reaches of the glacier have
not yet reached the melting point (Fig. 10a).
Although the QL heat flux was found to be non-negligible during summer
(Fig. 9), the resulting mass loss is itself
negligible compared to melting because the latent heat of
sublimation/deposition is 7 times larger than that for melting.
Moreover, the latent-heat flux has a pronounced diurnal cycle, switching
from deposition at night when cooling of moist air causes the vapour
pressure to increase relative to the melting glacier surface, while daytime
heating reverses the vapour gradient between the glacier surface and the
atmosphere, causing sublimation (Fig. 10b). Hence
the two regimes tend to compensate each other, but nighttime deposition
slightly dominates daytime sublimation, leading to a net positive
deposition/condensation flux on average to the glacier surface.
Mean simulated mass fluxes on Saskatchewan Glacier between
1979–2016 using the multitemporal DEMs. (a) Mean monthly fluxes; deposition
and sublimation fluxes being much smaller, they are indicated as numbers in
cm w.e. per month. (b) Mean diurnal cycle in deposition/condensation and
sublimation.
Spatial patterns of the simulated reference mass balance
(Bar2010) (Fig. 11) show an
annual average snowfall of 1.54 m w.e., over the glacier with a minimum of
0.30 m w.e., near the toe, to ∼3 m w.e., over the upper reaches.
Annual melt can reach 7.86 m w.e. a-1 at the glacier margin and 0.54 m w.e. a-1 in the upper accumulation zone. Net deposition/condensation
predominates on average over the glacier, but fluxes are small (<0.03 m w.e. a-1), while net sublimation only occurs on the upper
reaches of the glacier, mostly in the spring (Figs. 11c, 10a), corresponding to areas with high
incoming solar radiation (Fig. S4 in the Supplement). On average, melting
losses (mean =-2.22 m w.e. a-1) exceed snow precipitation gains
(1.54 m w.e. a-1) and the small condensation gain (mean = 0.01 m w.e. a-1), yielding a mean negative reference annual balance
(Bar2010) of -0.67 m w.e. a-1.
Simulated average spatial patterns of reference annual mass
balance (Bar2010, in m w.e.) on Saskatchewan Glacier
between 1979–2016. (a) Snow accumulation; (b) melt; (c) sublimation and
deposition; (d) annual balance. The accumulation zone on (d) is delineated
by the positive blue colour scale; the ablation zone is delineated by the negative
yellow–red scale.
Climate sensitivity analysis
The static sensitivity of mean mass balance (Bar2010)
components to climate perturbations (ΔTa=0 to
+7 ∘C and ΔP=-20 % to +20 %) is shown in
Fig. 12. The reference scenario (1981–2010) yields
an average annual mass loss of -0.68 m w.e. a-1
(Fig. 12c). The response surface for
Bar2010 shows that the glacier-wide mass balance is
sensitive to changes in air temperature and much less sensitive to changes
in precipitation (Fig. 12c). The ΔBa contours also become steeper and narrower with increased warming,
which indicates a reduced sensitivity to precipitation and increased
sensitivity to temperature, respectively. The seasonal mass balance response
surfaces help to understand the Bar2010 sensitivities
(Fig. 12a, b). The Bwr2010
response surface shows that a precipitation increase of +20 % can buffer
the negative impact of warming on Bw up to +3 ∘C of
warming but only up to +0.5 ∘C for Bar2010. Moreover, a warming of more than +6 ∘C with no change
in precipitation would suppress net accumulation in winter, given the current
glacier extent (2010) (Fig. 12a). The sensitivity
of winter mass balance to temperature changes also increases markedly with
warming, as seen by the progressive tightening of the contours in
Fig. 12a. This is interpreted to result from
decreasing accumulation due to the increasing shift from snowfall to
rainfall and increased ablation during winter (October–April) due to the earlier
disappearance of the snow cover under more pronounced warming. Conversely, the
temperature sensitivity of summer mass balance (Bsr2010)
increases only slightly with the warming scenario, and the steep contours in
Fig. 12b suggest a small sensitivity to
precipitation changes. The increased temperature sensitivity of
Bar2010 with warming indicated in
Fig. 12c is therefore mainly attributed to
decreasing accumulation from reduced snowfall fraction and increased winter
ablation as the climate warms and the snow cover retreats upglacier earlier
in the spring (Fig. 12a).
Reference (2010) mass balance sensitivity to prescribed changes
in regional mean air temperature between 0 and 7 ∘C and
precipitation between -20 % and +20 %, which encompass IPCC RCP ensemble
scenarios RCP2.6, RCP4.5, RCP6.0 and RCP8.5 for the mid (2041–2070: dark blue) and late
(2071–2100: light blue) 21st century. The mean seasonal and annual mass
balance are shown for the reference period 1981–2010. (a) Winter balance
(Bwr2010); (b) summer balance (Bsr2010); (c) annual balance (Bar2010).
The IPCC RCP scenarios for the mid (2041–2070) and late (2071–2100) 21st
century were overlaid onto the response surfaces to show the most likely
future climate trajectories. The RCP projection have significant
uncertainties, as shown by their wide confidence intervals, and the annual
mass balance change can vary by as much as ± 3 m w.e. a-1 within
a single scenario. This illustrates the usefulness of scenario-free response
surfaces to assess glacier mass balance sensitivity to climate as a
background to evolving climate projections (Aygün et al.,
2020b; Prudhomme et al., 2010). Nonetheless, given the current ensemble
climate scenarios, the reference mass balance could decrease by -0.5 to -2.0 m w.e. a-1 by the mid century and by -0.5 to -4 m w.e. a-1 by the
end of the century, relative to baseline conditions (Bar2010=-0.68 m w.e. a-1) and depending on the RCP scenario
considered.
Since mass balance displays a large sensitivity to temperature and because
glacier melt is the outcome of complex glacier–atmosphere energy exchanges,
the sensitivity of energy and mass fluxes to warming alone was further
investigated in Fig. 13. The increasingly more
negative mass balance in response to warming is dominated by increased
melting (∼93 %), while increasing condensation/deposition
accounts for ∼-3 % (mass gain) of the net annual mass
changes in response to warming (Fig. 13a, b).
Warming alters the precipitation phase, with the snowfall ratio decreasing
non-linearly from 0.80 under present climate to 0.47 at ΔTa+7 ∘C (Fig. 13c). This progressive conversion of
snowfall to rainfall accounts for ∼10 % of the mass
changes in response to warming (Fig. 13b).
Reference (2010) mass and energy balance sensitivity to changes
in regional mean air temperature between 0 and 7 ∘C. (a) Annual
mass balance; (b) changes in mass balance relative to baseline (ΔTa=0); (c) changes in ratio of snowfall to total precipitation, snow
cover and albedo; (d) energy balance; (b) changes in energy balance relative
to baseline (ΔTa=0); (e) changes in energy fluxes scaled by
the changes in melt energy (Qm). All fluxes and variables represent mean
annual values averaged over the whole glacier surface and over the baseline period 1981–2010 with mean air temperature perturbed from 0 to 7 ∘C.
The total energy input to the glacier surface increases with warming
temperatures, and this energy surplus is predominantly used for melting
(QM), which shows a non-linear increase with respect to warming
(Fig. 13d, e). Interestingly, the increase in
energy supply with warming is mainly driven by an increase in net solar
radiation (SW*) and latent-heat flux (QL), with more subdued increases in
the temperature-dependent sensible heat (QS) and net longwave radiation
fluxes (LW*) (Fig. 13e). Since cloud cover remained
unchanged in the sensitivity experiments, the increase in SW* with warming is
entirely driven by the decreasing albedo, as snow cover duration on the
glacier decreases (Fig. 13c). Since the relative
humidity also remained constant in our sensitivity analyses, warming leads
to higher atmospheric vapour pressures, since the saturated vapour pressure of
the air increases with warming. Since the glacier surface is constrained to
the melting temperature (0 ∘C) during a large part of the year,
the increase in surface saturated vapour pressure in response to warming
will, on average, be less than that of the atmosphere, causing the vapour
pressure gradient to increase and boost QL fluxes
(condensation/deposition) to the surface. Similar reasoning applies to
QS; i.e. the near-surface temperature gradient will increase in
response to atmospheric warming. While the rainfall ratio increases with
warming, its influence on the energy balance is insignificant
(Fig. 13e), but the reduced snowfall greatly
impacts winter accumulation (Fig. 12a). Increasing
net solar radiation (SW*) contributes from 51 % to 42 % of the increase in
QM(ΔQM), with this contribution decreasing with warming.
The contribution of QL to ΔQM increases from 27 % to 29 %
in response to warming, while that of LW* increases from 5 % to 9 %. The
contributions of QS (∼19 %) and QR
(∼1 %) are more constant across the warming spectrum
(Fig. 13f).
The results in Fig. 13 allow for apportioning the mass balance sensitivity to
warming to four different processes (Table 1): (i) atmospheric warming, which causes an increase in the temperature-dependent
fluxes (ΔLW∗+ΔQS) and contributes on average
24.3 % to the mass balance sensitivity to warming; (ii) a precipitation
phase change feedback, which contributes 10.3 %; (iii) an albedo feedback,
which contributes 44 %; and (iv) a humidity feedback, which contributes
22.3 %. While the contributions from atmospheric warming and the humidity
feedback increase with the level of warming, the precipitation phase
feedback remains constant, while the albedo feedback decreases over time
(Table 1).
Contribution of different processes to the sensitivity of glacier
mass balance to warming from +1 to +7 ∘C.
ProcessEquationRelative contribution to ΔBa+1∘C+2∘C+3∘C+4∘C+5∘C+6∘C+7∘CMean (%)(%)(%)(%)(%)(%)(%)(%)(%)Atmospheric-ΔLW∗+ΔQS/23.022.723.324.024.925.726.524.3warmingLfΔBaPrecipitationΔPS/10.410.310.310.310.310.310.310.3phase changeΔBaAlbedo-ΔSW∗/47.147.146.144.542.841.039.244.0LfΔBaHumidity-ΔQLLf+ΔS/21.621.421.521.922.523.224.022.3ΔBa
Lf: latent heat of fusion, PS: snowfall, S: deposition/condensation.
DiscussionSuitability of the NARR for model forcing
This study focused on reconstructing the mass balance of a glacier using a
physically based model constrained by a sparse set of glacio-meteorological
data without calibration. This situation is common to many mountain glaciers
around the world where logistical and financial constrains preclude continuous
monitoring programs. In this context, the outputs of reanalysis products
represent a useful alternative for driving glaciological models. Several
previous studies have used reanalyses to force hydrological and
glaciological models in mountainous regions using statistical downscaling.
Among the downscaling strategies used, some did not rely on in situ
observations, such as such as the linear theory of orographic precipitation
used by Jarosch et al. (2012) and Clarke et al. (2015) and the
extrapolation to the glacier surface of the vertical structure of air
temperature in reanalysis products (Fiddes and Gruber, 2014;
Jarosch et al., 2012). Hofer et al. (2010, 2012, 2015), on the
other hand, used station-based downscaling and found that combining
different types of reanalysis variables and the spatial averaging of reanalyses
grid cells led to superior downscaling performance. Earlier work by Radić and
Hock (2006) used temperature and precipitation from ERA-40 reanalyses to
force a mass balance model for Storglaciären, Sweden. They used
bilinear interpolation of the nine grid cells centered on the glacier and
obtained good mass balance simulation results after correcting the ERA-40
temperature bias with a lapse rate tuned to optimise the mass balance
simulation but no correction on ERA-40 precipitation. Koppes et al. (2011) also used a simple approach by regressing temperature and
precipitation from the closest NCEP–NCAR reanalysis grid cell against station
data in Patagonia. The station-based scaling approach used in this study to
correct biases in the NARR is simple compared to station-free (e.g. Jarosch et al., 2012) or multivariate regression (Hofer et al., 2010) approaches but is similar to the station-based
methods used by Radić and Hock (2006) and Koppes et al. (2011). The
comparison between the NARR and station observations was reasonably good (r= 0.31–0.98) given the short AWS record used for comparison. Three variables
(Ta, RH, G) showed strong correlations (r= 0.85–0.98)
between the NARR and AWS observations, and the simple scaling bias correction
removed much of the bias present (Fig. 3).
Moreover, the cold bias in NARR air temperature was consistent with the
elevation difference between the AWS and the NARR grid cell and the local
temperature lapse rate. The low bias and high correlation for NARR air
temperature and relative humidity, as well as solar radiation to a lesser extent
(Fig. 3), are consistent with previous findings
from Trubilowicz et al. (2016), who showed that these
variables agreed well with measured values at high-elevation stations in the
southern Coast Mountains of British Columbia, Canada. Wind speed (WS) on
Saskatchewan Glacier was however poorly represented (r= 0.37–0.38), most
probably because thermal winds (katabatic and valley winds) are not
represented at the coarse 32 km spatial resolution of the NARR. Trubilowicz
et al. (2016) also reported lower and site-dependent accuracy for NARR wind
speeds. More sophisticated wind downscaling (e.g. Vionnet et al., 2021;
Wagenbrenner et al., 2016) could help improve further modelling at this site
and other upland icefield-outlet valley glacier settings.
The positive bias in NARR precipitation was consistent with the higher
elevation of the NARR grid point relative to the merged precipitation record
(Fig. 3). However, once the effect of the
elevation difference was corrected using the calibrated precipitation lapse
rate (15.6 % per 100 m), the NARR was found to underestimate
observations by 10 %. This is consistent with the recent study by Hunter
et al. (2020), who showed that the NARR underestimates precipitation
in the mountain regions of British Columbia, Canada. The NARR precipitation
also correlated rather poorly with the off-glacier daily historical
precipitation record (r= 0.30–0.31), showing that the daily variability
in NARR precipitation is not well represented. Precipitation is notoriously
more difficult to represent in reanalysis products, especially in complex
terrain with steep orographic gradients and localised convective activity (Hofer et al., 2010; Mesinger et al., 2006). The station-free, linear
orographic model for precipitation (LOP) method used by Jarosch et al. (2012) might perhaps be better suited than station-based downscaling in
steep topography. The authors reported an improvement in the median relative
error (M=-3.1 % to -20.9 %) with respect to monthly precipitation totals
in the Canadian Rockies, compared to the raw NARR which underestimated station
precipitation (M=-9.5 % to -42.6 %). However, the median absolute error
(MAD) of the relative error did not change much and even increased in some
instances, i.e. from 13.5 %–31.3 % for the raw NARR compared with
19 %–29.5 % for LOP (see Table 3 in Jarosch et al., 2012). The station-based
scaling used in this study resulted in M= 3.8 % and MAD = 33 %,
compared to M=27 % and MAD = 41 % for the raw monthly NARR
precipitation. Hence the improvement seen is greater than that reported for
the station-free LOP model by Jarosch et al. (2012) in the Rockies.
Ebrahimi and Marshall (2016) reported that the NARR precipitation
for Haig Glacier, also in the Canadian Rocky Mountains, poorly represented
the observed winter-accumulation totals. Nevertheless, NARR precipitation
has been found to be reliable at the monthly scale and to represent a useful
input for hydrological modelling in North America generally (Chen
and Brissette, 2017). Our results suggest this finding also applies for
glaciological modelling, given that bias correction is applied. The
underestimation of precipitation in the NARR combined with the positive bias in
the raw NARR global radiation mostly explains the exaggerated mass loss
simulated by the mass balance model when forced with the lapsed NARR, i.e. when only precipitation and temperature are corrected to the elevation of
the reference stations (Fig. 8a). More elaborate
topographic corrections of solar radiation (Fiddes and Gruber, 2014)
could improve the downscaling of NARR solar radiation in the absence of
ground observations, but precipitation biases remain difficult to correct
in this situation.
The choice of the NARR spatial interpolation method for downscaling to
stations had an overall small effect on the comparison with station data
(Fig. 3). The bias and RMSE were slightly reduced
when using the bilinear interpolation of nine grid cells, compared with the
nearest-grid-cell method. However, following bias correction against station
data, both interpolation methods resulted in similar cumulative mass balance
simulation (Fig. 8a).
Despite the low correlation between the NARR and AWS wind speed, the simulated
point mass balance in 2015 was not sensitive to using either the downscaled
NARR or AWS wind speed forcings (Fig. 8b, c).
Replacing the downscaled NARR global radiation and relative humidity with
their AWS counterparts had also a small effect on the model validation.
Despite its strong correlation with AWS observations and low residual error
after bias correction, the simulated point mass balance in 2015 was most
sensitive to downscaled NARR air temperature (Fig. 8b, c). This shows that air temperature has a large influence on the
energy balance calculations and that the simple scaling correction could
probably be improved to better represent the effect of the glacier wind on
air temperature on the glacier (Shea and Moore, 2010).
The approach used in this study could be extended to other reanalysis
products, especially the new global ERA5 reanalyses (Hersbach and Dee,
2016). While its spatial resolution (0.25∘, ∼28 km)
is only slightly finer than the NARR (0.30∘, ∼32 km),
ERA5 has an hourly resolution compared to the 3-hourly NARR resolution.
Model performance and parameter sensitivity
Despite the physical nature of the model, some assumptions remain
simplistic, such as a constant precipitation lapse rate and spatially
invariant ice albedo, aerodynamic roughness and wind speeds. Despite these
limitations, the interannual variability in mass balance was relatively well
simulated by the model, with NSE values of 0.83 to 0.91 for direct point
observations (Fig. 6). Point mass balance
measurements with the glaciological method are affected by several
uncertainties related to errors in ablation stake height measurements, stake
self-drilling into the ice or firn, and snow–firn density measurements (Zemp et al., 2013). Errors are 0.14 m w.e. a-1 for
ablation measurements on ice, 0.27 m w.e. a-1 for ablation measurements
on firn and 0.21 m w.e. a-1 for snow measurements in the accumulation
area (Thibert et al., 2008). The root mean squared error (RMSE) on the
simulated bw was 0.24 m w.e. a-1 (median relative error of 15 %)
– on the same order as the typical measurement error for snow and firn.
RMSE values, however, were higher than typical measurement errors for
bs (0.87 m w.e. a-1, relative error = 22 %) and ba (0.77 m w.e. a-1, relative error = 24 %), due in part to the restricted
number of available observations for validation
(Fig. 6). The reconstructed mass balance also
compared favourably against the independent geodetic estimates (see Sect. 4.5 and Fig. 8). The
simulated cumulative mass loss (-26.79 m w.e.) was close to the geodetic
estimate (-25.59± 8.44 m w.e.), despite the large uncertainties in the
geodetic balance introduced from 2000 onward due to vertical uncertainties
in the SRTM DEM. The long-term consistency between geodetic and modelled
mass balance gives further confidence that the bias-corrected NARR forcings
do not suffer from systematic biases.
The model sensitivity to uncertain model parameters showed that the
simulated mass balance was most sensitive to uncertainties in the
precipitation lapse rate, followed by the ice aerodynamic roughness, while
the sensitivity to the snow aerodynamic roughness and ice albedo were lower.
This demonstrates that the precipitation lapse rate must be carefully
evaluated using ancillary meteorological data, which can be difficult in
regions with no permanent weather station network nearby, a conclusion also
reached for the Himalayas by Immerzeel et al. (2014). As the
model only accepted a constant lapse rate, we used a value (15.6 ± 4 %) representative of the period during which most of the snow
accumulation occurs, i.e. when the glacier toe is above the 0 ∘C
isotherm (Fig. S1 in the Supplement). Including shoulder months (April and
September) which have mixed precipitations would slightly lower this
gradient. The extrapolation of the gradient beyond the highest weather
station (2000 m) is also a common but hazardous practice, and validation
against snow courses (Avanzi et al., 2021) or winter
mass balance surveys (Carturan et al., 2012) offers a way to check
the validity of the gradient. The gradient used in this study resulted in
accurate simulations of winter mass balance (Fig. 6a), which strengthens our confidence in extrapolating the gradient to the
glacier. However, there were no observations beyond 2900 m to constrain the
gradient further. The area of the glacier above 2900 m represents only 8.8 % of the total area, so extrapolation errors in this unsampled area would
have a small impact on the glacier-wide mass balance. Further development of
the model should also consider including a time-varying precipitation lapse
rates, as it was shown for example that the lapse rate was smaller during
the dry year 2016 (Fig. 6a).
A high sensitivity to the ice aerodynamic roughness has been reported in
several studies (e.g. Brock et al., 2000; Hock and Holmgren, 1996;
MacDonell et al., 2013; Munro, 1989). It remains one of the most challenging
parameters to constrain in glacier mass balance models, and the assumption
of a spatially and temporally constant z0 value is a simplistic
representation of reality (Fitzpatrick et al., 2019). This
parameter is indeed often calibrated in the absence of direct observations (Hock, 2005). In this study, observations from the nearby Peyto
Glacier allowed using a representative value which yielded good results;
however the uncertainty range in the values reported by Munro (1989)
(± 1 mm) was sufficient to induce a ± 17% error in the
simulated cumulative balance (Fig. 8d). Advances
in deriving aerodynamic roughness from remote sensing could help in the
future to improve the calculation of turbulent fluxes in distributed glacier
models (Chambers et al., 2020; Fitzpatrick et al., 2019; Smith et al.,
2020). The use of remotely sensed albedo maps also contributed to constrain
a representative value for ice albedo (see Sect. 3.3.2), but the simulated mass balance was not very
sensitive to the uncertainty around this estimate
(Fig. 8d). Nevertheless, only an average value was
used, when in fact significant heterogeneity was found within the ablation
zone (in the Supplement). Decreasing ice albedo can occur over the
course of the melt season due to impurities of geogenic origin concentrating
at the surface (Cuffey and Paterson, 2010), cryoconite
development (Takeuchi et al., 2001) and more discrete events not taken
into account in the model, such as algal mat development (Lutz et al.,
2014) or wildfires that bring black carbon and ash onto the glacier and
decrease the albedo (Marshall and Miller, 2020). Long-term
darkening has also been observed on glaciers of the European Alps, which
questions the use of fixed albedo values in long historical and future mass
balance simulations (Oerlemans et al., 2009). Further efforts could
look to assimilate such remotely sensed albedo maps within distributed
models.
Impact of glacier recession on mass balance
The multitemporal DEMs used in the study allowed for quantifying the impact of
glacier elevation changes on long-term mass balance
(Fig. 7). The conventional mass balance simulation
with the multitemporal DEMs showed a maximum difference of ∼1.5 m w.e., or 5.6 % of the 1979 reference cumulative balance. This is a
small difference overall, which shows that glacier recession has had a minor
impact on the mass balance of Saskatchewan Glacier. This is expected for
this setting in particular, since the glacier margin is at the bottom of the
occupying valley and glacier retreat has occurred over a restricted
elevation range – thereby limiting negative feedback effects between
glacier retreat and mass balance. This study has focused on the static
climate sensitivity of mass balance, which ignores future dynamical
feedbacks. Static or reference mass balances calculated over a constant
glacier hypsometry have been proposed to be better suited for climatic
interpretation (Elsberg et al., 2001; Harrison et al., 2009). But from a
hydrological perspective, future glacier retreat towards higher elevations
would mitigate an increasing portion of the simulated mass loss, gradually
increasing the difference between the reference (2010) and conventional mass
balance and progressively decreasing the volume of meltwater released
annually (Huss and Hock, 2018; Huss et al., 2012). An increase in
dynamical adjustment effects on mass balance was already visible on
Saskatchewan Glacier from 2000 onward (Fig. 7a).
Energy balance regime
The simulated glacier-wide energy balance regime of Saskatchewan Glacier
showed that energy inputs are dominated by the sensible-heat flux, flowed by
net radiation and latent-heat fluxes. This is different than commonly
reported for mid-latitude glaciers in continental climates, where net
radiation dominates over turbulent fluxes (e.g. see
compilation by Smith et al., 2020). However, most studies reporting energy
flux partitioning relied on summer observations in the ablation zones of
glaciers. Hence, the often-reported high contribution of net radiation to
melting energy is biased by the season (values are commonly reported for
July–August – when net radiation is high) and to the ablation zone of
glaciers, where most micrometeorological studies have been done and where
again net radiation is higher due to the lower albedo. Year-round, glacier-wide
values are rarely published and are only available from distributed energy balance models. On Saskatchewan Glacier, the glacier-wide contribution to
melting energy was 26.1 % for net radiation, 57 % for sensible heat
(QS) and 16.9 % for the latent-heat flux (QL) during the
ablation period (July–August). The energy partitioning was quite different
when looking at the ablation zone only, with net radiation contributing
57 %, QS contributing 32 % and QL contributing 11 % of the melting energy at the AWS,
midway up the ablation zone. The lower glacier-wide contribution of net
radiation reflects the fact that much of Saskatchewan Glacier is covered in
snow and later firn in summer. This is also accordance with Klok and
Oerlemans (2002), who showed that net radiation dominates over QS in
the lower part of the glacier, while QS dominates in the higher part of
Morteratsch Glacier, Switzerland. Studies that reported
glacier-wide energy partitioning include Storglaciären, Sweden (summer
net radiation: 38 %–57 %, QS: 42 %, QL: up to 17 %) (Hock
and Holmgren, 2005); Brewster Glacier, New Zealand (annual net radiation:
45 %, QS+QL: 52 %, turbulent fluxes dominating in summer) (Anderson et al., 2010); Arolla Glacier, Switzerland (summer net
radiation: 82 %, QS: 25 %) (Arnold et al., 1996); Donjek
Range glaciers in the Yukon, Canada (summer net radiation: 60 %–83 %,
QS: 20 %–45 %, QL: -4 % to -9 %) (MacDougall and
Flowers, 2011); and Haig Glacier in Alberta, Canada (summer net radiation:
70 %, QS: 30 %) (Marshall, 2014). Point measurements in
late June–early July on nearby Peyto Glacier showed that net radiation
contributed 63 % and 42 % of the melt energy over ice and snow surfaces,
respectively, while sensible heat contributed 34 % (ice) and 50 % (snow) (Munro, 2006). Hence, the contribution of sensible- and latent-heat flux
to summer melting on Saskatchewan Glacier is higher than common values for
mid-latitude temperate glaciers with a continental climate and closer to
that encountered for glaciers in more humid climates (Anderson et al.,
2010; Smith et al., 2020). The contribution of turbulent fluxes to melting
energy was however not so different from the earlier measurements reported
by Munro (2006) at Peyto: 32 %–57 % at Saskatchewan vs. 34 %–50 % at Peyto
for QS and 11 %–17 % vs. 3 %–9 % for QL. The higher contribution
of turbulent fluxes to melting on Saskatchewan Glacier, together with a
simulated balance ratio (BR = 3.10; see Sect. 4.4.1) that is closer to
values from more humid climates (Rea, 2009), may thus reflect
the locally wetter and cloudier climate and high accumulation rates
resulting from the efficient interception of moist polar maritime air masses
from the west by the high and extensive plateau of the Columbia Icefield (Demuth and Horne, 2018; Tennant and Menounos, 2013). This “icefield
weather” frequently wraps the Columbia Icefield in clouds, while surrounding
valleys are cloud-free.
Climate sensitivity
The simulated mass balance sensitivity to a +1 ∘C warming was
-0.65 m w.e. a-1∘C-1. This value is comparable to
other mid-latitude glaciers: -0.60 m w.e. a-1∘C-1 for the Illecillewaet Glacier in the Selkirk Mountains of British Columbia (Hirose and Marshall, 2013), -0.66 m w.e. a-1∘C-1
for the Haig Glacier in the Canadian Rocky Mountains (Ebrahimi and
Marshall, 2016), -0.65± 0.05 m w.e. a-1∘C-1 for
small (<0.5 km2) glaciers in Switzerland (Huss
and Fischer, 2016), -0.60 m w.e. a-1∘C-1 for the
larger Morteratsch Glacier in Switzerland (Klok and Oerlemans, 2004), and
-0.61 m w.e. a-1∘C-1 for Storglaciären in Sweden (Hock et al., 2007). Higher sensitivities are found in more humid
climates – e.g. -0.86 m w.e. a-1∘C-1 for the South
Cascade Glacier, Washington (Anslow et al., 2008), and up to -2.0 m w.e. a-1∘C-1 on Brewster Glacier, New Zealand (Anderson
et al., 2010) – and lower sensitivities in drier climate – e.g. -0.44 m w.e. a-1∘C-1 on Urumqi Glacier No. 1 in the Chinese
Tien Shan (Che et al., 2019). Earlier work by Braithwaite (2006), Oerlemans and Fortuin (1992), and Oerlemans (2001) showed
that the mass balance sensitivity to temperature scales with mean annual
precipitation, due to larger albedo and precipitation phase feedbacks and
longer melt seasons on glaciers in wetter climates.
We found that the albedo feedback is the main contributor (mean = 44 %)
to the temperature sensitivity of mass balance on Saskatchewan Glacier
(Fig. 13). Increases in net shortwave radiation
caused by a reducing snow cover and ensuing reduced glacier albedo account
for 39 %–47 % of the increase in melt energy across the various warming
scenarios (Table 1). A similar finding was reported
on Haig Glacier by Ebrahimi and Marshall (2016), who found that introducing
albedo feedbacks doubles the net energy sensitivity to warming. This value
(44 %) is significantly high but less than the 80 % reported recently
by Johnson and Rupper (2020) for the summer-accumulation
type Chhota Shigri Glacier in High Mountain Asia. As shown by Fujita (2008), higher sensitivities are found for glaciers located in a
summer-precipitation climate, where albedo feedbacks on ablation are
stronger, than for glaciers located within a winter-precipitation climate.
Atmospheric warming itself contributed only 24.3 % to the mass balance
sensitivity to temperature across all warming scenarios, through sensible
heat and longwave radiation transfer to the glacier
(Table 1). A significant air humidity feedback was
also found, with latent-heat fluxes representing an average of 22 % of the
temperature sensitivity across all warming scenarios. Keeping the relative
humidity constant under warming scenarios may be plausible for the high-elevation Columbia Icefield. The icefield receives moist air masses from the
British Columbia interior and the Pacific Ocean uplifted onto the icefield,
as the region is subject to upslope conditions derived from convergent upper
air masses as low-pressure systems spin by the south of the region. Under a
stable atmospheric moisture regime, increasing atmospheric warming would
lead to an increasing humidity feedback on ablation (Table 1). Other
glaciers subjected to subsiding air masses could experience drier weather in
the future, which would decrease their melt sensitivity to warming (Ebrahimi and Marshall, 2016). The large contribution of latent-heat fluxes to melting under warming scenarios points to the necessity of
considering changes in specific air humidity when simulating glacier melt
under future climates. This conclusion is in line with the recent findings
by Harpold and Brooks (2018), who showed that atmospheric humidity plays
a critical role in local energy balance and snowpack ablation under warmer
climates, with latent and longwave radiant fluxes cooling the snowpack under
dry conditions and warming it under humid conditions. The precipitation
phase feedback, on the other hand, contributed the remaining 10 % of the
mass balance temperature sensitivity (Table 1).
The mass balance sensitivity of Saskatchewan Glacier to a ± 10 %
change in precipitation under the current temperature regime was 1.01
(unitless: m w.e., of mass change per m w.e., of precipitation change). A
value of 1 would occur if all precipitation were snowfall and there were no
albedo feedbacks on Ba. With the snowfall fraction being 0.81 under the
present climate (Fig. 13c), the albedo feedback on
ablation contributes 19 % to the mass balance sensitivity to
precipitation. With the mean annual precipitation on the glacier being 1880 mm for the reference period 1981–2010, the maximum +20 % precipitation
increase projected from ensemble climate scenarios for the end of the
century would add a maximum of 0.4 m w.e. a-1 if all new precipitation
falls as snow, which is small compared to the mean temperature sensitivity
of -0.65 m w.e. ∘C-1. As such, precipitation increases can
only buffer up to +0.5 ∘C-1 of warming on Saskatchewan
Glacier. As warming causes snowfall to shift to rainfall at a rate of
∼5 % ∘C-1 (Fig. 13c), the buffering effect of a +20 % increase precipitation would
decrease accordingly, i.e. from 0.29 m w.e. a-1 for a
+1 ∘C warming to 0.17 m w.e. a-1 for a
+7 ∘C warming.
Conclusions
Despite their physical basis, energy balance models often struggle to
replicate mass balance observations, due to the difficulty in constraining
their numerous parameters and obtaining reliable meteorological forcings (Gabbi et al., 2014; Réveillet et al., 2018). Our study showed that a
physically based, distributed mass balance model forced by regional
reanalysis data can adequately reproduce the recent and long-term evolution
of glacier mass balance when forcings and key model parameters are
judiciously constrained with available observations and ancillary data. This
is a key requirement for the effective application of such models, since
parameters from distributed energy balance models do not necessarily
transfer well between sites (MacDougall and Flowers, 2011).
While reanalysis data can provide realistic climate forcings for glacier
models, bias correction with in situ observations remains ideal when such
measurements are available. Adopting this approach, however, entails a
significant amount of work, which would be hard to implement at the mountain
range scale. While ancillary data were key to constraining key model
parameters, model sensitivity analyses showed that the precipitation
gradient and the aerodynamic roughness lengths were sensitive parameters
that need to be carefully prescribed.
The reconstructed mass balance of Saskatchewan Glacier shows a cumulative
loss of -26.79 m w.e., over the period 1979–2016, in good agreement with
independent geodetic estimates (-25.59± 8.44 m w.e.). Glacier retreat
has had a small impact overall on glacier mass balance, but the effect of
dynamical adjustment has been increasing in recent years. Climate
sensitivity experiments showed that future changes in precipitation would
have a small impact on glacier mass balance, while the temperature
sensitivity increases with warming, from -0.65 to -0.93 m w.e. ∘C-1. Increased melting accounted for 90 % of the temperature
sensitivity, while precipitation phase feedbacks accounted for 10 %. Close
to half (44 %) of the mass balance response to warming was driven by
reductions in glacier albedo, as the snow cover on the glacier thins and
recedes earlier in response to warming (positive albedo feedback).
Atmospheric warming directly accounted for about one-quarter (24 %) of the
mass balance sensitivity to warming. The remaining mass balance response to
warming was driven by latent-heat energy gains (positive humidity feedback)
and conversion of snowfall to rainfall (positive precipitation phase
feedback). Our study therefore underlines the key role of albedo and air
humidity in modulating the response of winter-accumulation type mountain
glaciers and upland icefield-outlet glacier settings to climate.
Code availability
The original glacier mass balance model code is available at https://github.com/regine/meltmodel (Regine/meltmodel, 2021). Modified codes can be obtained from
the corresponding author.
Data availability
Downscaled NARR forcings, geodetic mass balance estimates and reconstructed
mass balance are available from the corresponding author.
The supplement related to this article is available online at: https://doi.org/10.5194/tc-16-3071-2022-supplement.
Author contributions
CK and MND conceptualised the project. CK and OL performed the formal analysis. CK provided supervision. MND and BM curated the data. OL and CK prepared the original draft of the paper. CK, OL, MND and BM reviewed and edited the paper.
Competing interests
The contact author has declared that none of the authors has any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
CK was supported and funded by the Fonds de recherche du Québec –
Nature et technologies, the National Sciences and Engineering Research
Council of Canada, and the Canada Research Chairs Program. MND was supported
and funded by Natural Resources Canada's Climate Change Geoscience Program
and the NSERC CCAR (Natural Sciences and Engineering Research Council of Canada Climate Changes and Atmospheric Research) Changing Cold Regions Network (CCRN). The authors thank
Steve Bertollo, Eric Courtin, May Guan, Gabriel Meunier-Cardinal and Anthony
Pothier-Champagne for assisting with field data collection. Jasper National Park and Banff
National Park of Canada are thanked for supporting this work (permit no. JNP-2010-4694).
Financial support
This research has been supported by the Fonds de recherche du Québec – Nature et technologies (grant no. 2015-NC-183226), the Natural Sciences and Engineering Research Council of Canada (grant no. RGPIN-2015-03844), and the Canada Research Chairs (grant no. 231380).
Review statement
This paper was edited by Christian Haas and reviewed by Andrew MacDougall and three anonymous referees.
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