Comparing Simple Albedo Scaling Methods for Estimating Arctic Glacier Mass T Balance ⁎ Scott N

Remote Sensing of Environment 246 (2020) 111858

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Remote Sensing of Environment

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Comparing simple albedo scaling methods for estimating Arctic glacier mass T balance ⁎ Scott N. Williamsona, , Luke Coplanda, Laura Thomsonb, David Burgessc a Department of Geography, Environment and Geomatics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada b Department of Geography and Planning, Queen's University, Kingston, Ontario K7L 3N6, Canada c Cryosphere Geoscience Section, Natural Resources Canada, Ottawa, Ontario K1A 0E8, Canada

ARTICLE INFO ABSTRACT

Keywords: Mass balance measurements in the Canadian Arctic are limited, particularly for smaller glaciers, which in- Albedo troduces significant uncertainties in regional mass balance assessment. Here we report on the correlations be- Glacier mass balance tween Moderate Resolution Imaging Spectroradiometer (MODIS) Terra albedo measurements (Version 6) and MODIS net annual mass balance for five glaciers in the Canadian Arctic over the period 2002–2016. Three glacier albedo Canadian Arctic aggregation methods are tested for the melt season (June, July and August): minimum, raw average, and interpolated average. These are evaluated in terms of a 53–71% reduction in observations due to cloud cover in the raw albedo time series. For the minimum method, the whole glacier albedo is calculated from the average of the minimum melt season albedo of each grid cell, irrespective of the day on which they occurred, resulting in R2 values between 0.20 and 0.87. In the raw average method, averaging all albedo values within a glacier outline over the melt season improves the correlation to mass balance to a range of 0.61–0.95. In the interpolated average method, linear interpolation of the raw average albedo values to fill cloud gaps, then averaging them, improves the raw average correlations for all ice masses by ~5% (R2 range 0.68–0.97). Overall, the interpolated average albedo method performs substantially better for the smallest glacier than the minimum or the raw average methods. The most negative net mass balance occurs at Grise Fiord Glacier, which is the smallest (< 4.0 km2), but not the lowest elevation, glacier analysed. For this glacier, the interpolated average albedo improves the correlation with mass balance to an R2 = 0.68 (p-value < .05), compared to an R2 = 0.17 for the minimum albedo method (p-value > .05). When the five glaciers' interpolated average albedo is correlated to their ensemble mass balance, an R2 = 0.82 is achieved. These results show that interpolated MODIS Terra melt season albedo measurements can realistically approximate net annual glacier mass balance for Arctic glaciers and ice caps, without additional information about precipitation or temperature, and in the absence of a melt model.

1. Introduction Experiment (GRACE) gravimetry (Harig and Simons, 2016) and regional climate model simulations (Noël et al., 2018). However, glacier- The recent mass balance of Canadian Arctic glaciers is strongly specific estimates of mass balance are limited (e.g., Koerner, 2005), negative (Koerner, 2005; Gardner et al., 2010; Harig and Simons, 2016; especially for small and low-elevation ice caps and glaciers that con- Noël et al., 2018) and melt rates have accelerated since 2005 (Sharp tribute disproportionately to current sea-level rise. Small glaciers (i.e., et al., 2011). Glaciers outside of the ice sheets total 3% of the Earth's ice ≤1 km2) represent a large area and volume of ice when added together volume and contribute approximately 1/3 of contemporary sea level and could represent up to 10% error in global volume calculated from rise (Jacob et al., 2012; Church et al., 2013; Gardner et al., 2013), of standard glacier inventories (Bahr and Radic, 2012). However, small ice which Canadian Arctic glaciers are the biggest contributor (Harig and masses are poorly monitored and have the potential to provide large Simons, 2016) and modelling suggests will provide a significant con- contributions to sea level rise in the near future (Bahr and Radic, 2012). tribution through 2100 (Radić et al., 2014). The general patterns of In addition, the mass balance of small glaciers is difficult to measure glacier change in the Canadian Arctic (e.g., Box et al., 2018) are rea- with coarse resolution observations, such as GRACE. Modelling of sonably well understood from Gravity Recovery and Climate Arctic glacier mass balance is also difficult for small glaciers, where

⁎ Corresponding author. E-mail address: [email protected] (S.N. Williamson). https://doi.org/10.1016/j.rse.2020.111858 Received 4 November 2019; Received in revised form 29 April 2020; Accepted 29 April 2020 0034-4257/ Crown Copyright © 2020 Published by Elsevier Inc. All rights reserved. S.N. Williamson, et al. Remote Sensing of Environment 246 (2020) 111858 models often don't adequately capture the magnitude of melt (e.g., Noël ratio (AAR) also scales to annual glacier net mass balance (Dyurgerov et al., 2018). et al., 2009; Bahr et al., 2009) in a similar way to that of ELA. The AAR The Canadian Arctic typically has low annual snowfall, so annual and ELA can be represented by albedo, providing that albedo values are glacier mass balance fluctuations are primarily a function of summer measured in sufficient density across an entire glacier, meaning thata balance (Sharp et al., 2011), which is typically driven by the melting of glacier's mass balance can be estimated with satellite remote sensing. snow and ice. Inter-annual variability of melt-period onset and duration This technique integrates many aspects of glacier mass balance that are in the Queen Elizabeth Islands (QEI) is primarily dependent on glacier difficult to measure, such as summer snowfall events that restrict melt surface elevation and distance from Baffin Bay (Wang et al., 2005). Melt (Oerlemans and Klok, 2004). The use of albedo to determine glacier onset typically occurs between late May and mid-July, with melt ces- mass balance directly integrates shortwave solar radiation in a way that sation occurring between mid-July and early September. Over the other measures of glacier mass balance do not. In general, satellite- period 2000–2004, melt duration ranged from 100 days in areas facing measured albedo for an entire glacier is aggregated into a single value Baffin Bay in the southeast QEI at low elevations, to one dayathigh using one of two albedo aggregation methods: melt season minimum or elevations (Wang et al., 2005). Glacier surface elevation over the QEI melt season average, which are then correlated to net annual mass ranges from sea level to 2616 m a.s.l. at the summit of Mt. Barbeau balance. (81.927°N, 74.987°W) on northern Ellesmere Island. The average an- Using the glacier minimum albedo and MODIS data, statistically nual melt duration for the QEI was 37.7 ± 4.9 days between 1979 and significant correlations between mass balance and minimum albedo 2011, with melt onset occurring ~2–3 days earlier at the end of this have been found for glaciers in the European Alps (Dumont et al., 2012; period than at the start (Wang et al., 2013). In addition to melt dura- Davaze et al., 2018), New Zealand (Sirguey et al., 2016), Himalayas tion, the length of the snow free period in the Arctic has also increased (Brun et al., 2015) and the Tibetan Plateau (Zhang et al., 2018). The by ~3–5 days decade−1 over the last several decades (Bokhorst et al., minimum melt season albedo of a whole glacier as proposed by Dumont 2016). Mortimer and Sharp (2018) used 16 day MODIS MCD43A3 et al. (2012) describes the smallest whole glacier average albedo shortwave broadband black sky albedo to identify Canadian High Arctic measured on a single day over the course of a melt season when there is June, July and August glacier albedo changes between 2001 and 2016. no partial or total cloud obstruction (i.e., clear sky conditions). The Over this period the average summer albedo decreased by most comprehensive analysis of whole glacier albedo correlation to 0.029 ± 0.025 decade−1, with most of the reductions recorded in mass balance was conducted for 30 mountain glaciers in the European July. The majority of the albedo decreases occurred between 2007 and Alps that had net annual mass balance records, of which 6 also had 2012 at the margins of lower elevation ice masses. summer mass balance (Davaze et al., 2018). Near-daily MODIS white Long-term field-based mass balance monitoring is limited tofive sky albedo data, produced at 250 m resolution using the MODImLab locations in the Canadian Arctic (e.g., Koerner, 2005; Thomson et al., software following Sirguey et al. (2009, 2016), indicated large varia- 2017; Burgess, 2017), which are insufficient to derive regional esti- bility in correlation between minimum (spatially averaged) albedo and mates of mass balance by extrapolation alone (Marzeion et al., 2017). mass balance. The average melt season albedo correlated better with This lack of detail in mass balance monitoring limits our understanding summer mass balance than did the minimum albedo with net annual of melt patterns, and thus the ability to constrain predictions of future mass balance, suggesting that glacier wide minimum albedo might not sea level rise. Studies suggest a strong climate-driven component in be the optimal aggregation method for glacier mass balance estimation. glacial mass losses (Gardner et al., 2011; Noël et al., 2018), but large Inter-annual climate variability might, for example, produce the same scale, high resolution, measurements of energy balance in relation to annual minimum albedo, but change the shape of the seasonal albedo melt are currently lacking, even though solar radiation provides the curve if a warm spring results in an earlier decline in albedo and as- majority of energy required to melt glaciers (Van As, 2011). Longwave sociated increase in total summer melt. Furthermore, cloud cover might radiation has recently been shown to be important in glacier melt obscure the true minimum albedo value, which could be hidden within (Bennartz et al., 2013) and in limiting refreezing (Van Tricht et al., a cloud cover gap in the seasonal albedo curve. 2016). Thus, a complete energy balance, not just air temperature, is Average albedo, measured with AVHRR (Advanced Very High needed to explain the mass wasting of ice caps. Resolution Radiometer), has been correlated against the surface mass The processes that control a glacier's surface mass balance (i.e., balance of six Svalbard glaciers (De Ruyter de Wildt et al., 2002; Calluy discounting substantial dynamic contributions) also dictate the seasonal et al., 2005) with a large range of variances (R2 = 0 to 0.87) for up to variation of a glacier's albedo, or the ratio of reflected to incident five years of mass balance records. The average albedo of various shortwave (solar) radiation. Glacier broadband albedo is on Greenland glaciers was correlated to surface mass balance using average ~ 0.85 across the whole of a snow covered glacier in the spring AVHRR by Greuell and Oerlemans (2004) for 13 years and with MODIS prior to the onset of melt (Cuffey and Paterson, 2010). Snow cover is MOD10A1 by Colgan et al. (2014) for 10 years. The correlation coef- typically retained at the highest elevations of a glacier throughout the ficients for these studies were 0.84 and 0.90, respectively. MODIS Terra summer melt period, in the accumulation zone, where weathering and albedo modified to produce an average melt season total energy fluxfor snow grain metamorphosis decrease the accumulation area albedo to two glaciers in Svalbard was found to be highly correlated to annual ~0.5 (Wiscombe and Warren, 1980). At a glacier's lower elevations, in glacier net mass balance by Greuell et al. (2007) for six years of data. the ablation zone, bare clean glacier ice is typically present in the In this study we first determine if glacier minimum average MODIS summer, which reduces the albedo to ~0.34–0.51 for areas of exposed albedo for the melt season, calculated on a grid cell by grid cell basis, ice (Paterson, 1994), although values between 0.5 and 0.6 have been correlates to net annual mass balance for two valley glaciers and three reported for clean bare ice on the Greenland Ice Sheet (Bøggild et al., small ice caps (hereafter, collectively referred to as glaciers) in the 2010). Surface albedo values for bare ice can be much lower (as low as Canadian Arctic for which in situ mass balance measurements are ~0.06) if dust, liquid water or rock debris accumulates in sufficient available. We then assess if correlation to mass balance is improved by quantities on the surface (Cuffey and Paterson, 2010). using glacier average albedo from the whole melt season (raw average). The Equilibrium Line Altitude (ELA) marks the boundary between Lastly, we investigate if correlation between mass balance and albedo is the ablation and accumulation zones, and has been shown to scale ef- further improved by using melt season glacier average albedo with gaps fectively to annual glacier net mass balance (Braithwaite, 1984; Rabatel caused by cloud cover filled by linear interpolation (interpolated et al., 2005) for glaciers where the surface mass balance dominates (i.e., average). No such assessment between albedo and glacier mass balance little or no dynamic discharge). Alternatively, the accumulation–area has been previously made for the Canadian Arctic.

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2. Study area Axel Heiberg Island; 5 - Grise Fiord Glacier, located on southern Ellesmere Island. The 1999–2003 outlines for these ice masses were Five glaciers in the Canadian Arctic with net annual mass balance extracted from the most current Randolph Glacier Inventory version 6.0 records between 2002 and 2016 are examined in this study: 1 - Melville (Pfeffer et al., 2014), retrieved from the Global Land Ice Measurements South Ice Cap, located on Melville Island; 2 - Sverdrup Glacier Basin, an from Space database (https://www.glims.org/RGI/). Further de- outlet of the northwest portion of Devon Island Ice Cap; 3 - Meighen Ice scriptive information regarding these ice masses can be found in Table 1 Cap, located on Meighen Island; 4 - White Glacier, located on western and Fig. 1. The elevation values for glaciers is provided by the Canadian

Table 1 Glacier location, area and elevation information. Area information extracted from Randolph Glacier Inventory version 6.0, and originates from the 1999 to 2003 period.

Glacier Location Latitude °N Area (km2) Average elevation (m) ± standard deviation Longitude °W

1. Melville South Ice Cap Melville Island 75.40 53.26 646.59 ± 42.25 115.00 2. Sverdrup Glacier Basin Devon Island 75.42 746.94 1247.93 ± 385.93 83.25 3. Meighen Ice Cap Meighen Island 79.95 92.93 144.67 ± 47.24 99.13 4. White Glacier Axel Heiberg Island 79.45 38.54 1094.29 ± 325.07 90.70 5. Grise Fiord Glacier Ellesmere Island 76.42 4.07 599.69 ± 19.06 82.69

Fig. 1. Study area showing Canadian Arctic glaciers used in this study: 1. Melville South Ice Cap; 2. Sverdrup Glacier Basin; 3. Meighen Ice Cap; 4. White Glacier; 5. Grise Fiord Glacier. See Table 1 for location details. The blue areas indicate glacier ice extent. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Digital Elevation Model (CDEM) produced at 3 arc sec (approximately 90 m) by Natural Resources Canada and acquired from https://open. canada.ca/data/en/dataset. These data were resampled to 500 m grids that correspond to the MODIS snow albedo grid.

3. Methods & data

3.1. Methods

We calculate the correlation between net annual mass balance and glacier averages of melt season (June, July, August) albedo, using the

0.71 ± 0.09 0.53 ± 0.08 0.67 ± 0.08 0.65 ± 0.09 0.63 ± 0.10 MOD10A1 MODIS/Terra Snow Cover Daily L3 Global 500 m SIN Grid, Version 6 albedo data downloaded from the National Snow and Ice Data Center (https://nsidc.org/data). These data were processed using the MODIS Reprojection Tool to produce daily albedo images in Lambert Conformal Conic projection with the WGS84 datum between June 1 and August 31 for the years 2002 to 2016. Large gaps in the albedo time series in 2000 and 2001 precluded their use. Outlines for the five ice masses (Table 1) were used to subset the daily MOD10A1 albedo images. Many QEI glaciated regions are mountainous, with glaciers in deeply incised valleys, so shadowed areas were excluded to avoid the inclusion of unrealistically low albedo values. Furthermore, bright dry snow and cloud could have similar albedo but are notoriously difficult to distinguish in satellite reflectance 0.58 ± 0.09 0.61 ± 0.07 0.48 ± 0.08 0.69 ± 0.04 0.56 ± 0.09 (Stillinger et al., 2019). To reduce bias due to possible misclassified snow, we use expected ranges for glacier snow and ice albedo (Cuffey and Paterson, 2010) to filter the MODIS gridded daily albedo product. Albedo values > 0.99 were considered physically unrealistic for snow or glacier ice and were excluded; albedo values < 0.05 were considered to be influenced by shadow and were also excluded. In addition, data gaps of ~1 to 10 days due to cloud cover occur in the melt season daily albedo time series. These gaps do not present a strong seasonal pattern and can apply to some or all of a glacier's extent. Using these MODIS MOD10A1 daily snow albedo data, three dif- 0.60 ± 0.09 0.61 ± 0.06 0.53 ± 0.07 0.69 ± 0.04 0.58 ± 0.09 ferent aggregation methods were used to determine a single average albedo value for each glacier and for each melt season:

1. Minimum: the minimum albedo value from June, July or August for each grid cell contained within each glacier outline was individually identified. This step produced a map of melt season minimum albedo for each glacier, which was averaged using equal weighting to produce a minimum average value for each of the five ice masses for each melt season between 2002 and 2016. This differs from the minimum method of Dumont et al. (2012), which uses the average 0.29 ± 0.08 0.32 ± 0.07 0.22 ± 0.05 0.42 ± 0.05 0.27 ± 0.07 minimum melt season albedo for an entire glacier on a single cloud- free day. This modification was necessary due to the prevalence of

) Minimum albedo ± s.d. Raw average albedo ± s.d. Interpolated average albedo ± s.d. Proportion of daytime cloud cover ± s.d. cloud cover over our Arctic study area, which severely limited the

−1 number of clear sky images of a glacier's full extent over the course of a melt season. 2. Raw average: June, July and August average albedo was produced by averaging all available albedo values for each grid cell within a glacier outline (i.e., cells with cloud cover were excluded). This step produced a map of average melt season albedo for all cloud-free cells, which was then averaged into a single value for each glacier for each year using an equally weighted mean. 3. Interpolated average: the daily June, July and August albedo maps −0.449 ± 0.483 −0.439 ± 0.383 −1.281 ± 0.572 Mass balance ± s.d. (m w.e. a were gap-filled for periods when cloud cover was present byusing linear interpolation of the daily time series for each grid cell. Spatial interpolation was not employed. For each grid cell, an equally weighted mean was used to produce maps of interpolated average melt season albedo, which were then averaged into a single albedo value for each glacier for each year using equal weighting.

The minimum, raw average and interpolated average glacier melt season albedo values were regressed against net annual mass balance Sverdrup Glacier BasinMeighen Ice Cap White Glacier Grise Fiord Glacier −0.314 ± 0.224 Melville South Ice Cap −0.582 ± 0.578 Glacier

Table 2 Average net annual mass balance andeach melt ice season mass (June, is July, August) also minimum, included. raw average and interpolated average albedo for the period 2002 to 2016. The proportion of daytime cloud cover for the melt season for using standard least-squares linear regression. Lastly, a representative

4 S.N. Williamson, et al. Remote Sensing of Environment 246 (2020) 111858 cloud cover value for each glacier was calculated as the proportion of 9 times each day because MODIS Terra is in a near-polar sun-syn- grid cells in the raw images that were classified as cloud-covered by the chronous orbit. As a result of the frequent MODIS Terra coverage, and MODIS algorithm, relative to the total number of grid cells. Cloud cover to avoid any potential sensor calibration differences, data from MODIS is also explored through its relation to glacier elevation. Aqua was not used. The MODIS Basic Quality Assessment (QA) for each albedo grid cell 3.2. Data used in this study was analysed in relation to known issues with solar zenith angle (SZA). When SZA is greater than 70° the MODIS snow 3.2.1. MODIS Terra albedo MOD10A1 Version 6 albedo product includes additional uncertainty (Stroeve et al., 2006). The snow albedo data used in this study originated from the MODIS The possible QA values were defined as best quality, good quality, OK sensor on the Terra satellite platform. Terra is in a near-polar sun quality, night, ocean and no data. The night classification is for in- synchronous descending orbit and collects data with the MODIS sensor stances when the SZA is greater than 85°. When the range of SZA is over a spectral range of 0.459 to 14.385 μm in 36 spectral bands. Daily 70° ≤ SZA ≤ 85° the QA is set to OK quality. The OK quality in these MOD10A1 snow albedo is produced in 500 m grid cells for cloud-free instances indicates an increased uncertainty in the albedo quality be- conditions from the best single daily observation, which is determined cause of low illumination (National Snow and Ice Data Center (NSIDC), by an algorithm that ingests illumination and satellite view angles, in 2020). addition to cloud mask and fractional snow cover (Hall et al., 2002). The MODIS snow albedo data was not explicitly filtered for quality The glaciers in the high latitude study area are observed approximately flags related to SZA for several reasons:

Fig. 2. Melville South Ice Cap: (a) minimum albedo, and (b) interpolated average albedo, for 2011. Contour lines with elevations in m a.s.l. are shown in black.

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1. Analysis of the quality flag indicates that data that might suffer from period. However, these low illumination conditions did not influ- poor illumination constitutes ~1–5% of the valid albedo data for the ence the timing of the minimum melt season albedo. three southern glaciers (Sverdrup, Melville and Grise Fiord). This 2. During high northern latitude summer the full inversion, and the OK quality flag only occurred in 3 or 4 years of the 15 year time poorer quality magnitude inversion, of the bidirectional reflectance series, and when it did occur it was generally restricted to one to distribution function for MODIS albedo products are typically si- several days in the melt season. The two northern glaciers (White milar (e.g., Schaaf et al., 2011; Williamson et al., 2016). Glacier and Meighen) had the OK quality flag occur consistently for 3. At high latitudes, the number of high quality albedo retrievals de- the last ~10 days of August, which comprised ~5–15% of the total creases considerably in the shoulder seasons compared to summer melt season albedo data depending on the cloud-cover during this (Schaaf et al., 2011). In our analysis we use summer season only,

Fig. 3. Meighen Ice Cap: (a) minimum albedo, and (b) interpolated average albedo, for 2011. For White Glacier: (c) minimum albedo, and (d) interpolated average albedo, for 2011. Contour lines with elevations in m a.s.l. are shown in black.

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thereby maximising the number of high quality albedo returns. The (Polashenski et al., 2015; Casey et al., 2017) and albedo trends of 0.01 two highest latitude glaciers in the study likely violate this state- decade−1 are near the limit of sensor calibration. The Version 6 cor- ment over the last ~10 days of August, but this data was retained for rection applied to MODIS albedo largely compensates for sensor de- consistency between all glaciers in the study area and because melt gradation found in the Version 5 data (Casey et al., 2017). could still be occurring during this period. 4. The base level input data to each method analysed here is identical, 3.2.2. Field measurement of glacier mass balance and the methods employed in our analyses are concerned with cloud Glaciological (direct-method) mass balance observations in the QEI cover data reduction, not data quality reduction. Therefore, in terms are conducted each spring in April–May and involve the measurement of model evaluation, the likelihood that some data are of poorer of snow accumulation and melt along stake networks installed along the quality than others is not relevant to the comparison of models. centreline of five glaciers. The mass balance year spans September 1to August 31 of the following year, comprising the accumulation season MODIS albedo data is recorded as unsigned 8-bit, with values from 0 (generally fall and winter) and the melt season (generally summer). to 255. Albedo values are recorded as 0–100, and ancillary data, such as Ablation is dominated by surface melt (Noël et al., 2018) and is esti- cloud cover, assigned a static value between 101 and 254. mated from changes in glacier surface height relative to stakes drilled The MOD10A1 product (Hall et al., 2002) is suitable for in- into the glacier surface. Mass loss can also occur by dynamic (i.e., vestigating glacier-scale mass balance in the Canadian Arctic because of iceberg) discharge for marine terminating glaciers, but Sverdrup is the its high precision in ground positioning ( ± 50 m; Wolfe et al., 2002). only such glacier in this study and its dynamic discharge is negligible The high spatial precision of MODIS is important because the albedo (~4%) in comparison to its surface mass balance (Van Wychen et al., within a MODIS grid cell varies with land cover and snow properties. 2017). Accumulation is determined from snow pit analysis at elevations The accuracy of MOD10A1 Version 5 albedo in the glaciated St. Elias above the historical ELA, where the previous summer surface at the Mountains was found to be ± 0.06 (Williamson et al., 2016) and ± snow pit base is commonly recognizable by the presence of a dense, 0.07 on the Greenland Ice Sheet (Stroeve et al., 2006), both of which sometimes dirty, layer overlain by depth hoar. A polynomial or linear show that the product is reliable over glaciated terrain. Ryan et al. fit through the point mass balance estimates versus elevation is usedto (2017) found that surface-based albedo measurements overestimate estimate mass balance between stakes. The mass balance-elevation re- MOD10A1 (Version 6) albedo by up to 0.10 for bare ice surfaces on the lationship is then extrapolated to unsampled glacier regions using Greenland Ice Sheet during the summer melt season because meteor- known hypsometry and the profile method (Østrem and Brugman, ological station footprints do not accurately represent within grid cell 1991). albedo variability, which is primarily related to the under-sampling of To correct for systematic errors due to change in glacier hypsometry meltwater. over time, reanalysis of glaciological method mass balance estimates Error in MODIS Terra albedo due to sensor degradation has been can be conducted using geodetic (volume-change derived) mass balance reported to reduce the absolute value of surface albedo measurements estimates. Reanalysis of White Glacier's mass balance record revealed

Fig. 4. Sverdrup Glacier Basin: (a) minimum albedo, (b) interpolated average albedo, for 2011. Contour lines with elevations in m a.s.l. are shown in black.

7 S.N. Williamson, et al. Remote Sensing of Environment 246 (2020) 111858 no statistically significant difference between the average annual gla- Fluctuations of Glaciers Database provides access to annual glaciolo- ciological balance (−213 ± 28 mm w.e. a−1) and geodetic balance gical mass balance results in the form of a single, glacier-wide annual (−178 ± 16 mm w.e. a−1) over the 1960–2014 time period (Thomson mass balance, as well as individual point mass balance values and the et al., 2017). Random errors in the glaciological method are related to average mass balance conditions across elevation bands. In this study both field measurements and spatial interpolation and extrapolation we use glaciological mass balance data (glacier-wide) from this data- across the glacier basin, and have been approximated to average ± base; geodetic mass balance data is not used. 200 mm w.e. a−1 (Cogley and Adams, 1998). This error is typically several times smaller than the annual mass balance for Arctic glaciers, 4. Results especially in years of large mass loss. Furthermore, the error in the glaciological method has not acted as an impediment to other studies Net annual mass balance, together with melt season minimum al- comparing albedo to mass balance (e.g., Dumont et al., 2012). bedo, raw average albedo and interpolated average albedo, are pre- The World Glacier Monitoring Service (https://wgms.ch/) sented for each glacier in Table 2 for the period 2002 to 2016, together

Fig. 5. Grise Fiord Glacier: (a) minimum albedo, and (b) interpolated average albedo, for 2011. Contour lines with elevations in m a.s.l. are shown in black.

8 S.N. Williamson, et al. Remote Sensing of Environment 246 (2020) 111858 with average cloud cover. The annual mass balance was predominately Figs. 2 to 5 reveal that the interpolated average method produces a negative during the study period, with only a few years of positive mass stronger albedo – elevation gradient than the minimum method. The balance. Grise Fiord Glacier is the exception to this pattern, as its mass minimum method albedo maps often display a speckled surface which balance was consistently negative. is consistent with the appearance of dirty ice, bedrock or melt ponds The albedo for the minimum albedo aggregation method is ap- over the course of a melt season. proximately 30% smaller than the albedo from the raw and interpolated The net annual mass balance time series and the time series for the averages, when averaged over the study period. The minimum method three melt season albedo aggregation methods for the five glaciers are produced a range of albedo values of 0.22–0.42. The raw average shown in Fig. 6. Grise Fiord Glacier, the smallest glacier studied, had method produced an albedo value range of 0.53–0.69 over the five the largest net mass loss. This glacier also showed the lowest values for glaciers, whereas the interpolated average method produced a similar albedo irrespective of albedo aggregation method. Sverdrup Glacier range of 0.53–0.71. Figs. 2 through 5 illustrate the spatial distribution Basin, which is part of Devon Ice Cap, is the highest elevation and of minimum albedo and interpolated average albedo for 2011 over the largest glacier considered in this study and showed the smallest net five glaciers analysed in this study. The year 2011 was chosen because annual mass loss. it was a particularly negative mass balance year, resulting in larger The proportion of grid cells that are masked as cloud-covered in the differences in albedo values between the methods and spatial location. raw daily MODIS albedo images ranged between 53% and 71%

Fig. 6. Net annual glacier mass balance (left axis), and whole glacier melt season (June to August) minimum albedo, raw average albedo and interpolated average albedo (right axis) for the five ice masses for the period 2002 to 2016.

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Fig. 7. Relationship between elevation and average cloud covered days (2002–2016) for the five glaciers in the Canadian Arctic. Cloud cover is averaged overthe course of the study period by grid cell. Trend lines are shown in red. Sverdrup, Meighen and White Glacier show statistically significant negative correlation between cloud covered days and elevation (p < .05). Melville shows no statistically significant correlation and Grise Fiord Glacier shows a statistically significant positive correlation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) depending on location (Table 2). Fig. 7 shows the cloud count by grid 5. Discussion cell versus elevation for each glacier over the melt season. There is an obvious negative relationship between cloud cover and glacier eleva- Our results show that MODIS Terra MOD10A1 snow albedo can be tion for most glaciers, in that the lower elevation grid cells exhibit more used to estimate the net annual mass balance of Canadian Arctic gla- cloud cover. These negative relationships are statistically significant for ciers using a variety of aggregation methods. To start, the minimum Sverdrup Glacier Basin, Meighen Ice Cap, and White Glacier. Melville albedo methodology was the least successful overall, providing a sig- Ice Cap shows no statistically significant relationship between elevation nificant relationship with mass balance for four out of the five glaciers and cloud cover. Grise Fiord Glacier shows a statistically significant studied (Fig. 8) and an overall R2 of 0.62 (Fig. 9). Our minimum method increase in cloud-covered days with grid cell elevation, although this is incorporates more albedo data than is possible if the entire glacier is based on a small number of points (ten MODIS 500 m grid cells) due to required to be cloud-free on a particular day as stipulated by Dumont the small size of the glacier. Visual inspection of the daily MODIS al- et al. (2012). Our minimum method considers each grid cell in- bedo maps reveal that spatially complete albedo maps rarely exist for dependently, meaning that a grid cell can still be chosen even if sur- each glacier and do not occur in sufficient quantity to apply the rounding cells are cloud-covered. This provides an improved opportu- minimum albedo method as specified by Dumont et al. (2012). nity to record cells when they reach their annual minimum albedo The regressions between net annual mass balance and the raw value in the Arctic. If no clouds occurred throughout the melt season average and interpolated average albedo results for the five ice masses the albedo values produced by our minimum method and Dumont show statistically significant correlations at the p < .05 level (Fig. 8), et al.'s (2012) minimum method should be equivalent. Furthermore, the with the interpolated average method producing the best correlations minimum albedo methods are likely insensitive to differences in annual overall. However, this was not always true for the minimum method, as net mass balance when a glacier no longer retains snow cover and the Grise Fiord Glacier did not show a statistically significant correlation. ELA has risen above its highest elevation. The interpolated average albedo method identifies the mass balance of Davaze et al. (2018) showed little correlation between glacier area Grise Fiord Glacier with a R2 correlation of 0.68, which is a large im- and the statistical relationship between glacier daily minimum albedo provement compared to the correlation of 0.l7 produced by the (using the Dumont et al., 2012 method) versus net annual mass balance minimum method. The minimum method displays a large degree of for 30 glaciers in the Alps. However, it's difficult to compare minimum variability in the mass balance vs. albedo slopes of the correlations for results calculated in different ways, and mid-latitude Alpine glaciers are different glaciers. In comparison, the slopes of the correlations fromthe generally much smaller than those in the Canadian Arctic, have higher raw average and interpolated average methods display much less surrounding mountains, and are subjected to more intense summer variability, with Grise Fiord Glacier displaying a slope similar to the melting and more mixing of ice and rock within grid cells. Of the gla- other glaciers. Fig. 9 shows the 2002–2016 ensemble of the five Ca- ciers considered in this study, Grise Fiord Glacier compares most closely nadian Arctic glaciers correlated to net annual mass balance for the in physical dimensions with smaller alpine glaciers, but common cloud three methods considered in this analysis. All three of these correlations cover in the Arctic demands a different approach to minimum albedo are statistically significant at the 95% level. aggregation.

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Fig. 8. Regressions between albedo aggregation methods and in-situ net annual mass balance for five glaciers in the Canadian Arctic over the period 2002–2016. Melt season (June to August) minimum albedo (top row), raw average albedo (middle row) and interpolated average albedo (bottom row). Correlations for the minimum albedos are statistically significant (p < .05) with the exception of Grise Fiord Glacier. All regressions for the raw average and interpolated average albedo methods are statistically significant (p < .05).

The use of interpolated average albedo for the melt season produces five glaciers analysed here (Fig. 7). This persistent cloud cover renders a better correlation with net annual mass balance than the minimum or the application of the whole glacier minimum method proposed by raw average albedo methods. This increase in correlation suggests that Dumont et al. (2012) untenable because very few daily instances occur the averaging methods (raw and interpolated) better capture the total of a whole glacier being cloud free in the Canadian Arctic. The lack of amount of absorbed solar radiation during the melt season than the inclusion of albedo data from these low elevation areas would skew the minimum albedo method. Minimum albedo is indicative of the max- whole glacier raw average albedo to being higher than expected due to imum solar radiation that a glacier absorbs over a short period of time, the dominance of high albedo accumulation area in the calculations. but does not capture the influence of cloud cover on the total solar Support for this interpretation is found in Table 2, where the average radiation absorbed over an entire melt season. The use of average melt albedo values for the interpolated average method are always less than, season albedo (both raw and interpolated) likely captures the effects of or the same as, the raw average method. Thus, the interpolated method melt season snowfall events which can retard seasonal mass loss by weights each day equally, instead of skewing the average by using al- raising the glacier albedo (Oerlemans and Klok, 2004). bedo data obtained exclusively under clear skies. The interpolated average albedo method connects observations Although the correlations between interpolated average albedo and made during cloud-free periods to gap-fill the intervening cloudy per- net annual mass balance are highly significant (Fig. 8), there is a large iods, and might underestimate albedo during the cloudy periods, par- difference between the four larger ice masses and the small Grise Fiord ticularly during summer snowfall events. The interpolated average al- Glacier. In particular, mixed grid cells at the periphery of a glacier and bedo method likely scales better to mass balance than the minimum around nunataks are a potential cause of error in the albedo signal, with method explored here because it partially remediates observation bias smaller glaciers more susceptible to this error due to a larger proportion caused by cloud cover. The interpolated average albedo likely produces of MODIS grid cells on their periphery than larger glaciers. However, a better correlation to mass balance than the raw average because many small glaciers are too small to have perimeter grid cells buffered spatially complete daily albedo values are obtained, rather than the as a way to mitigate the mixed grid cell error. This coupled with the albedo average values being skewed to cloud-free glacier areas and positional uncertainty ( ± 50 m) of gridded MODIS products suggests dates. This consistent albedo field weights the resulting melt season that the correlation between mass balance and minimum average al- average equally. bedo should be higher, and the overall uncertainty lower, for larger ice A known bias in optical remote sensing of glaciers is the occurrence masses. The random errors in glacier mass balance determined by the of persistent clouds and low level fog in the ablation area of Arctic glaciological method average ± 200 mm w.e. a−1 (Cogley and Adams, glaciers near the ocean (Gilson et al., 2018), as found for three of the 1998), but the consistently high correlation between mass balance and

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Fig. 9. Correlation between net annual mass balance and ensemble results from the five glaciers for the three different albedo aggregation methods between 2002 and 2016: a) minimum albedo; b) raw average albedo; c) interpolated average albedo. All three aggregation methods show statistically significant (p < .05) relationships to glacier mass balance. melt season interpolated albedo for different glaciers, over multiple study. We found that glacier size, except for the smallest glacier years, indicates that any error introduced by the glaciological method is (4 km2), doesn't produce a clear influence on the correlation between small compared to the absolute mass balance. albedo and mass balance, indicating that the interpolated method scales Analysis of Fig. 9 shows that, when data from the five glaciers are well across different glacier and ice cap geometries and areas inthe combined, all three albedo methods produce statistically significant Canadian Arctic, but that there could be a lower limit to the efficacy of representations of net annual mass balance. However, the interpolated the method. The decrease in correlation coefficient and slope between average albedo method represents the mass balance of the five glaciers mass balance and albedo for the small Grise Fiord Glacier compared to with the highest degree of accuracy (R2 = 0.82). In the interpolated the larger glaciers indicates that when a glacier's area is similar to the average, Sverdrup Glacier Basin systematically underestimates mass MODIS grid cell resolution a poorer correlation might be expected. The balance in the ensemble model. The small Grise Fiord Glacier displays a convergence of slopes between whole glacier interpolated average al- larger amount of variation around the trend line than White, Melville or bedo and net annual mass balance suggests that this method could be Meighen glaciers. However, for the most negative mass balance mea- used to model the mass balance for the entire Canadian high Arctic surements Grise Fiord Glacier is close to the trend line, which indicates based exclusively on albedo. The whole glacier interpolated albedo that the ensemble model is well suited for determining the mass balance method thus provides a potential technique for regional glacier mass of small glaciers in the Canadian Arctic. balance assessment that is independent of glacier melt models. Our results are based on in situ mass balance measurements on five Arctic glaciers between 2002 and 2016. An assessment of the use of 6. Conclusions and further work interpolated average albedo to improve the mass balance to albedo relationship should be confirmed with measurements in other geo- Interpolated average albedo over the melt season is highly corre- graphical areas and with other mass balance techniques. Image fusion lated with net annual mass balance for Canadian Arctic glaciers where with higher spatial resolution, but poorer temporal resolution, satellite in situ mass balance has been measured. This provides a better corre- data (e.g., Landsat, Sentinal 2) could be pursued to decrease the size of lation to glacier mass balance than the raw average method, and in turn albedo grid cells. The high degree of correlation between albedo and both of these methods provide an improvement upon the minimum glacier mass balance, at White Glacier in particular, suggests that albedo method, particularly for the smallest glacier considered in this

12 S.N. Williamson, et al. Remote Sensing of Environment 246 (2020) 111858 including a limited amount of data collected under low illumination Linking glacier annual mass balance and glacier albedo retrieved from MODIS data. conditions caused by high solar zenith angles, is not an impediment to Cryosphere 6, 1527–1539. Dyurgerov, M., Meier, M.F., Bahr, D.B., 2009. A new index of glacier area change: a tool reconstructing glacier mass balance. In light of the potential for MODIS for glacier monitoring. J. Glaciol. 55, 710–716. https://doi.org/10.3189/ sensor degradation and lifespan limitations, studies into albedo trend 002214309789471030. homogenisation for MODIS, and between MODIS and other satellite Gardner, A.S., Moholdt, G., Wouters, B., Wolken, G.J., Burgess, D.O., Sharp, M.J., Cogley, G., Braun, C., Labine, C., 2011. Sharply increased mass loss from glaciers and ice caps sensors, is required for the continuity of future albedo monitoring. in the Canadian Arctic Archipelago. 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