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  <front>
    <journal-meta><journal-id journal-id-type="publisher">TC</journal-id><journal-title-group>
    <journal-title>The Cryosphere</journal-title>
    <abbrev-journal-title abbrev-type="publisher">TC</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">The Cryosphere</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1994-0424</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/tc-13-2597-2019</article-id><title-group><article-title>The surface albedo of the Greenland Ice Sheet between 1982 and 2015 from the
CLARA-A2 dataset and its relationship to the <?xmltex \hack{\break}?>ice sheet's surface mass
balance</article-title><alt-title>The surface albedo of the Greenland Ice Sheet</alt-title>
      </title-group><?xmltex \runningtitle{The surface albedo of the Greenland Ice Sheet}?><?xmltex \runningauthor{A. Riihel\"{a} et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Riihelä</surname><given-names>Aku</given-names></name>
          <email>aku.riihela@fmi.fi</email>
        <ext-link>https://orcid.org/0000-0001-6581-8792</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2 aff3">
          <name><surname>King</surname><given-names>Michalea D.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-8138-4362</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Anttila</surname><given-names>Kati</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Finnish Meteorological Institute, Meteorological Research, Helsinki, 00560, Finland</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Byrd Polar and Climate Research Center, Columbus, USA</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>School of Earth Sciences, The Ohio State University, Columbus, USA</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Aku Riihelä (aku.riihela@fmi.fi)</corresp></author-notes><pub-date><day>7</day><month>October</month><year>2019</year></pub-date>
      
      <volume>13</volume>
      <issue>10</issue>
      <fpage>2597</fpage><lpage>2614</lpage>
      <history>
        <date date-type="received"><day>29</day><month>March</month><year>2019</year></date>
           <date date-type="rev-request"><day>10</day><month>April</month><year>2019</year></date>
           <date date-type="rev-recd"><day>4</day><month>September</month><year>2019</year></date>
           <date date-type="accepted"><day>5</day><month>September</month><year>2019</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2019 </copyright-statement>
        <copyright-year>2019</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://tc.copernicus.org/articles/.html">This article is available from https://tc.copernicus.org/articles/.html</self-uri><self-uri xlink:href="https://tc.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://tc.copernicus.org/articles/.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e113">The Greenland Ice Sheet is losing mass at a significant rate,
driven in part by increasing surface-melt-induced runoff. Because the ice
sheet's surface melt is closely connected to changes in the surface albedo,
studying multidecadal changes in the ice sheet's albedo offers insight into
surface melt and associated changes in its surface mass balance. Here, we
first analyse the CM SAF Cloud, Albedo and
Surface Radiation dataset from AVHRR data second edition (CLARA-A2) Surface Albedo (SAL),
covering 1982–2015, to obtain decadal albedo trends for each summer month.
We also examine the rates of albedo change during the early summer,
supported with atmospheric reanalysis data from MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, version 2), to discern changes
in the intensity of early summer melt, and their likely drivers. We find
that rates of albedo decrease during summer melt have accelerated during the
2000s relative to the early 1980s and that the surface albedos now often
decrease to values typical of bare ice at elevations 50–100 m higher on
the ice sheet. The southern margins exhibit the opposite behaviour, though,
and we suggest this is due to increasing snowfall over the area.</p>
    <p id="d1e116">We then subtract ice discharge from the mass balance estimates observed by
the Gravity Recovery and
Climate Experiment (GRACE) satellite mission to estimate surface mass balance. The CLARA-A2 albedo changes are regressed with these data to obtain a summer-aggregated
proxy surface mass balance time series for the summer periods 1982–2015. This
proxy time series is compared with latest regional climate model estimates
from the MAR model to perform an observation-based test on the dominance of
surface runoff in the magnitude and variability of the summer surface mass
balance. We show that the proxy time series agrees with MAR through the
analysed period within the associated uncertainties of the data and methods,
demonstrating and confirming that surface runoff has dominated the rapid
surface mass loss period between the 1990s and 2010s.</p>
    <p id="d1e119">Finally, we extend the analysis to the drainage basin scale to examine
discharge–albedo relationships. We find little evidence of surface-melt-induced ice flow acceleration at annual timescales.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e131">The surface albedo of the Greenland Ice Sheet's ablation area has been shown
to play a crucial role in determining melt variability through the snow/ice
albedo feedback effect (Box et al., 2012). The study of these albedo changes
over the last decade and a half from modern satellite sensors such as MODIS
has drawn considerable research attention (Tedesco et al., 2011; Stroeve et
al., 2013; Alexander et al., 2014; Tedstone et al., 2017). The observed
albedo decreases are closely tied to the increasing mass loss of the ice
sheet through the enhancement of its surface melt (Enderlin et al., 2014;
van den Broeke et al., 2016). The ice sheet also loses mass through the ice
calving at outlet glaciers, or discharge, the magnitude of which has
recently been shown to demonstrate significant spatial and seasonal
variability (King et al., 2018). The mass loss of the Greenland Ice Sheet
has been<?pagebreak page2598?> shown to currently be among the leading contributors to sea level
rise (Box et al., 2017a).</p>
      <p id="d1e134">Legacy satellite sensors such as the Advanced Very High Resolution Radiometer (AVHRR) offer us the possibility to study
the Greenland Ice Sheet's albedo changes of over a period of more than 3 decades, doubling the temporal coverage of MODIS. The drawback is lower
spectral precision and coverage. Yet, considerable efforts have recently
been paid to the intercalibration of the AVHRR sensor family (Heidinger et
al., 2010), greatly improving the sensors' capabilities to detect long-term
trends in surface albedo. Here, we use the sensor-intercalibrated 34-year
(1982–2015) surface albedo data record from the CLARA-A2 dataset family
(Karlsson et al., 2017a) to study the albedo changes of the ice sheet at
decadal scales.</p>
      <p id="d1e137">Our analyses focus on the summer months between May and August (MJJA),
comprising four topics. First, we calculate and present the trends in
surface albedo (defined here as the directional–hemispherical reflectance of
the surface, i.e. black-sky albedo or “inherent” albedo) over the ice sheet
for each respective month. In addition to the trends for the full 1982–2015
period, we present temporally subsetted trends consistent with the MODIS
observation era (2000–2015) and the pre-MODIS era (1982–1999), in part to
compare our results with the trends identified from the latest editions of
MODIS data (Casey et al., 2017) and also to offer a rare, if somewhat more
uncertain, look into the ice sheet's surface changes in the 1980s and 1990s.
Treating each month individually additionally allows us to delineate between
albedo changes in the early and late melting season.</p>
      <p id="d1e140">Second, we examine changes in melt intensity and speed through changes in
the rate of albedo decrease and in the spatial distribution of albedo values
indicative of bare ice and wet snow as the summer melt progresses. At this
stage we also analyse atmospheric reanalysis data to discern if the observed
changes may be explained by precipitation or air temperature anomalies.</p>
      <p id="d1e144">Third, we conduct an observation-driven test for the dominance of surface
runoff in the interannual variability of May–August surface mass balance
(SMB) of the ice sheet. We calibrate discharge-corrected, gravimetrically
observed SMB with the CLARA surface albedo to form a summer-aggregated proxy
SMB. When compared against the SMB from a state-of-the-art regional climate
model for the ice sheet (MAR, Fettweis et al., 2017), we expect to find good
covariability only if surface runoff dominates SMB variability, as that is
the sole term which can be considered well-correlated with albedo changes.</p>
      <p id="d1e147">Finally, we downscale the analysis to six major drainage basins of the ice
sheet. Again assuming that surface albedo changes are an acceptable proxy
for surface runoff production, we examine the albedo–discharge relationships
to ascertain from an observational basis if inferred surface melt anomalies
correlate with the interannual variability in ice discharge.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Data and methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>CLARA-A2 SAL surface albedo dataset</title>
      <p id="d1e165">The satellite-based surface albedo dataset used here is the Satellite
Application Facility on Climate Monitoring (CM SAF) Cloud, Albedo and
Surface Radiation data record CLARA-A2 SAL, funded by the European
Organization for the Exploitation of Meteorological Satellites (EUMETSAT). It
covers the years 1982–2015 and is based on intercalibrated AVHRR data. The
retrieved albedo is defined as directional–hemispherical albedo for the
wavelength range 0.25–2.5 <inline-formula><mml:math id="M1" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m (for snow and ice), and the
observations are provided in a 0.25<inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> latitude–longitude or a 25 km
EASE grid for the polar regions. The algorithm accounts for topography
corrections over mountainous regions as well as dynamic aerosol depth
(Jääskeläinen et al., 2017). However, over the Arctic where
dynamic aerosol loading is difficult to estimate and typically exhibits a
limited variability, a constant value of 0.1 at 550 nm is used. We do not
consider September in this analysis, as worsening illumination conditions
make retrievals more uncertain and prevent full coverage over the ice sheet.</p>
      <p id="d1e185">The albedo of snow- and ice-covered areas is derived by averaging the
broadband bidirectional reflectance values of the AVHRR overpasses into
5 d or monthly means, relying on wide AVHRR swaths and temporal
aggregation to provide dense sampling of the viewing hemisphere, which forms
the albedo estimate (Riihelä et al., 2013). The sampling rate has been
further improved by the expansion of the AVHRR constellation from the
mid-1990s onward. The CLARA dataset uses data from NOAA-7 to NOAA-19, as
well as MetOp-A and B (Karlsson et al., 2017a). A critical feature of the
CLARA dataset family is that it is based on an intercalibrated Fundamental
Climate Data Record (FCDR) of observed AVHRR radiances, where the
calibration differences between satellites have been removed by use of a
variety of techniques (Heidinger et al., 2010).</p>
      <p id="d1e188">The data record has been validated against in situ data (Anttila et al.,
2016) and compared to the MODIS black-sky albedo product MCD43 (Schaaf et
al., 2002). Comparisons between CLARA-A2 SAL and in situ measurements on the
ice sheet have yielded RMSE between 0.04 and 0.07 over the more stable
accumulation zone with no obvious systematic over- or underestimation
tendencies and a RMSE of <inline-formula><mml:math id="M3" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.11</mml:mn></mml:mrow></mml:math></inline-formula> over a site (JAR2) in the
ablation zone. It should be noted that it has recently been shown that
point-to-pixel evaluation of surface albedo retrievals over the
heterogeneous surfaces of the ablation zone, particularly in the southwest,
cannot be expected to yield true estimates of retrieval quality when the
spatial resolution of the estimate is in the kilometre range (Moustafa et
al., 2017), as is certainly the case for CLARA-A2 SAL.</p>
      <p id="d1e201">A critical attribute for the surface albedo time series from the viewpoint of
trend determination is its stability. Here, we demonstrate the stability of
CLARA-A2 SAL by examining<?pagebreak page2599?> the monthly mean albedo over a small region in the
central part of the ice sheet between 73 and 75<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N latitude, and
38 and 42<inline-formula><mml:math id="M5" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W longitude. The ice sheet's uppermost parts have a
naturally stable surface albedo, and therefore variations in the albedo
estimates may be considered to primarily result from algorithm uncertainty.
The mean surface albedo for this area is shown as a time series in
Fig. 1 for the months between May and August
(MJJA). As can be seen, the variability about the 34-year interannual mean
largely falls within the reported 5 % (relative) accuracy, although
individual grid-cell-scale albedo retrievals may display larger uncertainty
as a function of cloud masking efficiency, surface sampling rate, and
uncertainty in the atmospheric correction of the satellite imagery. Still,
we observe no obvious trends in the albedo of this region. The widespread
surface melt of 2012 was relatively short-lived over this area (Bennartz et
al., 2013) and thus did not appreciably impact the albedo, as also shown
from MODIS data (Box et al., 2017b).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><?xmltex \currentcnt{1}?><label>Figure 1</label><caption><p id="d1e225">Stability of CLARA-A2 SAL over 73–75<inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 38–42<inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W, on the central part of the Greenland Ice Sheet. Spatially
averaged monthly mean albedo retrievals between May and August shown. The
black line shows the 34-year mean albedo of the area. Light blue shading shows
<inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.02</mml:mn></mml:mrow></mml:math></inline-formula> albedo variability about the interannual mean, corresponding to
the reported upper accuracy estimate of 5 % relative for CLARA-A2 SAL over
snow and ice.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://tc.copernicus.org/articles/13/2597/2019/tc-13-2597-2019-f01.png"/>

        </fig>

      <p id="d1e262">A notable deviation from the interannual mean albedo occurs over the years
1992 and 1993. The cause of this is known. The eruption of Mt Pinatubo, on
15 June 1991, injected vast quantities of aerosols and dust into the
atmosphere. This altered the atmospheric composition on a global scale for
the next 2–3 years. Stroeve (2001) attributed a concurrent increase in
observed Greenland Ice Sheet albedo to the cooling effect of the additional
stratospheric aerosols. While we see a similar effect in the CLARA data, it
should be noted that the atmospheric correction necessary to derive surface
reflectances from AVHRR observations in CLARA depends on the aerosol loading
being correct. Larger aerosol loading conditions over bright snow are
challenging for the atmospheric correction algorithms. It is difficult to
deconvolve cooling-induced albedo increase from potential artefacts
resulting from an incomplete characterization of the atmosphere. We
therefore exclude these years from the analysis but otherwise conclude that
the time series appears stable enough for trend analysis. The observed
variability envelope shall form the first, but not only, boundary condition
for evaluating the significance for any obtained trends, as explained in
detail in Sect. 2.7.2.</p>
      <p id="d1e265">To exclude the non-glaciated surfaces of Greenland from the analysis, the
PROMICE ice mask (Citterio and Ahlstrøm, 2013) was resampled into the
CLARA grid and all grid cells with a fractional ice cover of less than
50 % were discarded. We also attached surface elevation data into the
CLARA dataset from CLARA grid-resampled digital elevation model by Helm et al. (2014).</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>MAR regional climate model</title>
      <p id="d1e276">The regional climate model data comes from the Modèle Atmosphérique
Régional (MAR) model (version 3.5.2) (Fettweis et al., 2017). Here, we
use the model run data forced with the ERA-Interim atmospheric reanalysis
for the period 1979–2014. To obtain the MJJA surface mass balance from MAR,
we first extract the monthly surface mass balance fields, correct for the
variation in grid cell areas in the model domain, mask out all grid cells
with fractional ice cover less than 50 % for consistency with the CLARA
data, and sum the MJJA output.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Ice discharge estimates</title>
      <p id="d1e287">Here we use continuous estimates of ice discharge from all large Greenland
outlet glaciers over the 2000–2015 period, taken from King et al. (2018).
These glacier-scale time series are derived by incorporating changes in
glacier velocity, from both radar and optical imagery, and changes in
glacier thickness calculated from time-varying surface elevation data. With
high temporal and spatial resolution, these records allow for ice-sheet-wide
and basin-scale sub-monthly changes in ice discharge, hereafter referred to
as <inline-formula><mml:math id="M9" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>, to be compared with albedo-based meltwater proxies.</p>
</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>MERRA-2 atmospheric reanalysis and the Greenland Blocking Index (GBI)</title>
      <p id="d1e305">The Modern-Era Retrospective analysis for Research and Applications, version
2 (MERRA-2), is a global atmospheric reanalysis of the modern satellite era,
covering the period from 1980 to the present day (Gelaro et al., 2017).
Operating at 72 atmospheric levels with a spatial resolution of 0.5 by 0.625<inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, MERRA-2 ingests a wide variety of satellite observations and
features for example observation-based corrections of the model precipitation field
and a sophisticated treatment for atmospheric aerosols.</p>
      <p id="d1e317">The representation of glaciated surfaces has also received substantial
attention in the development of MERRA-2 (Cullather et al., 2014). It was
also recently shown that the surface air temperatures (SATs) in MERRA-2 are
well aligned with station observations across the ice sheet (Reeves Eyre and
Zeng, 2017). For these reasons, we selected MERRA-2 to provide (winter)
precipitation and SAT data for our analysis.</p>
      <p id="d1e320">The Greenland Blocking Index (GBI) used here is defined<?pagebreak page2600?> as the weighted mean
500 hPa geopotential height over a region bounded by 60–80<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N
and 20–80<inline-formula><mml:math id="M12" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W. The dataset is obtained from the NOAA Earth System
Research Laboratory (ESRL) and based on Hanna et al. (2013).</p>
</sec>
<sec id="Ch1.S2.SS5">
  <label>2.5</label><title>Mass balance estimates from GRACE satellite observations</title>
      <p id="d1e350">The gravimetric mass balance data used here are from the Greenland Ice Sheet
Climate Change Initiative (CCI) project, based on Gravity Recovery and
Climate Experiment (GRACE) satellite pair measurements and the GRACE
ITSG-Grace2016 gravity field model (Mayer-Gürr et al., 2016). The data
cover 2003–2015, as prepared by the Technical University of Dresden (Groh
and Horwath, 2016).</p>
      <p id="d1e353">The CCI mass balance estimates are based on a point mass inversion method
following Forsberg and Reeh (2006), Sørensen and Forsberg (2010), and
Barletta et al. (2013). A notable feature in the use of GRACE for the mass
loss estimation is that the gravimetric signals from outer ice caps and
small glaciers are not distinguishable from the ice sheet gravity changes.
However, on the scale of the whole ice sheet, the optimal mass balance
solution needs to contain this contribution. As the ice sheet extent defined
for CLARA also contains any outer glacier or ice cap grid cells if their ice
coverage is sufficiently large, there is no major discrepancy in the
combined use of GRACE and CLARA data.</p>
</sec>
<sec id="Ch1.S2.SS6">
  <label>2.6</label><title>Surface albedo dataset from MODIS (MOD10A1)</title>
      <p id="d1e364">We obtained the latest (Collection 6) MODIS-based ice sheet surface albedo
data from the MOD10A1 time series (Hall et al., 1995) for comparison with the
CLARA-A2 SAL. These data are provided in 5 km spatial resolution as daily
means between 2000 and 2017, as well as feature denoising, gap filling, and bias
correction procedures as described in Box et al. (2017b). For the comparison,
these data are reprojected to the 25 km CLARA grid with radial weight
resampling, and grid cells with ice cover less than 50 % were discarded.</p>
</sec>
<sec id="Ch1.S2.SS7">
  <label>2.7</label><title>Methods</title>
<sec id="Ch1.S2.SS7.SSS1">
  <label>2.7.1</label><title>Study area definitions</title>
      <p id="d1e382">As mentioned, here we define the ice sheet extent through the use of the
PROMICE ice mask (Citterio and Ahlstrøm, 2013) using a threshold of
50 % for fractional ice cover as the inclusion condition. Basin-scale
analyses were done using the six basin boundaries based on Sasgen et al. (2012), with the modification that we combine their basins D and E into our
basin 4. The basin delineation and ice sheet extent are illustrated in
Fig. 2.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><label>Figure 2</label><caption><p id="d1e387">Ice sheet drainage basins as used in this study. Basin boundaries
overlaid on an example of CLARA-A2 SAL monthly mean surface albedo from June 2010.</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://tc.copernicus.org/articles/13/2597/2019/tc-13-2597-2019-f02.png"/>

          </fig>

</sec>
<sec id="Ch1.S2.SS7.SSS2">
  <label>2.7.2</label><title>Trend assessment</title>
      <p id="d1e404">All trends shown here have been calculated as Theil–Sen estimators, i.e. as
the median of all possible slopes between data pairs in the examined dataset
(Theil, 1950; Sen, 1968). The Theil–Sen estimator is robust against outlier
influence compared to ordinary least squares regression. This feature is
highly useful in trend analysis of CLARA-A2 SAL data over the ice sheet,
where misclassified clouds may contribute noise into the clear-sky surface
albedo estimates (Karlsson et al., 2017a).</p>
      <p id="d1e407">The trends in surface albedo were deemed significant only if both of the
following conditions were met. First, the observed trend slopes were
non-zero at the 95 % confidence interval. Second, the decadal albedo
trends were larger than 0.015 per decade. The latter condition largely
follows the analysis by Casey et al. (2017) for the MODIS Collection 6
surface albedo, who considered a decadal trend of 0.01 as the limit of MODIS
observability. We have tightened that limit to 0.015 for CLARA to account
for the less precise radiometric accuracy of AVHRR, which remains even after
the considerable intercalibration work done on the CLARA input radiances
(Heidinger et al., 2010). We finally note that while the observed trend
magnitudes were largely insensitive to the choice of CLARA input data (5 d
or monthly means), monthly means are used for the decadal trend calculations
when shown here.</p>
</sec>
<?pagebreak page2601?><sec id="Ch1.S2.SS7.SSS3">
  <label>2.7.3</label><title>Melt rate and ice exposure calculations</title>
      <p id="d1e418">In order to examine changes in the intensity of melt across the ice sheet
margins during our 1982–2015 study period, it is necessary to estimate two
parameters: the melt rate, expressed as albedo decrease per day during the
melting season; and a yes/no condition for determining if a particular area
of the ice sheet melted substantially enough to be composed primarily of
bare ice and wet snow. The detection of melt onset is challenging, as
reductions in albedo typically begin gradually and sporadic snowfall events
may reset the albedo to the pre-melt range. We tested the use of a
sophisticated Gaussian process (GP)-based change point detection algorithm
implemented following Fearnhead (2006) and Xuan and Murphy (2007), but the
gradual impact of melt onset in the albedo data proved too difficult to
capture with such a probability-based change point detection method.</p>
      <p id="d1e421">We then implemented a simpler scheme, in which the 5 d albedo record
between May and August for each grid cell and year is first smoothed with a GP
regressor algorithm with a Mátern kernel to contain 120 data points,
corresponding to a temporal resolution of <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> d. The
smoothed data series is evaluated to find the first sample after early May
for which the albedo value deviates more than 2 standard deviations from
the preceding early summer albedo mean. The melt rate estimate is then taken
to be the albedo difference between that value and the summer minimum
albedo, divided by the time between the two events. As this method may be
expected to provide reasonable melt rate estimates only for the ice sheet
margins where significant seasonal albedo dynamic exists, we present the
melt rates only for areas where the surface elevation is less than 2200 m a.s.l.</p>
      <p id="d1e434">For the detection of bare ice and wet snow surfaces, we first note that
melting bare ice surfaces around the ice sheet margins generally have
surface albedos in the range of 0.5 to 0.65 (Bøggild et al., 2010),
although significant amounts of impurities at the ice surface may of course
further reduce the albedo. This albedo range is also applicable for wet snow
areas with significant melt ponding. We therefore selected an empirically
suitable threshold albedo of 0.58 and observed the CLARA grid cells in which
the surface albedo reaches this value for each year in the study period.
Changes in the melt rate and distribution of bare ice/wet snow areas were
studied by comparing 3-year means at the beginning and end of the full
study period (1982–2015), as well as the MODIS (2000–2015) and pre-MODIS
(1982–1999) eras. For the continuous melt rate estimates, trends for these
time periods were further determined using the Theil–Sen estimator as
described in Sect. 2.7.2.</p>
</sec>
<sec id="Ch1.S2.SS7.SSS4">
  <label>2.7.4</label><title>Forming a surface mass balance proxy from surface albedo observations to
test surface runoff dominance in summer-aggregated SMB</title>
      <p id="d1e445"><?xmltex \hack{\newpage}?>The mass balance of the ice sheet may be expressed as (e.g. van den Broeke
et al., 2017)
              <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M14" display="block"><mml:mrow><mml:mi mathvariant="normal">MB</mml:mi><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mi mathvariant="normal">SMB</mml:mi><mml:mo>-</mml:mo><mml:mi>D</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where SMB is the ice sheet's surface mass balance, and <inline-formula><mml:math id="M15" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula> represents the
summed solid ice discharge from all large marine-terminating outlet
glaciers. Furthermore, the surface mass balance may be expressed as (e.g.
van den Broeke et al., 2017)
              <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M16" display="block"><mml:mrow><mml:mi mathvariant="normal">SMB</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">SU</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">ER</mml:mi><mml:mi mathvariant="normal">ds</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mi mathvariant="normal">RU</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the sum total of snowfall and rainfall, SU<inline-formula><mml:math id="M18" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">tot</mml:mi></mml:msub></mml:math></inline-formula> represents the total sublimation, ER<inline-formula><mml:math id="M19" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">ds</mml:mi></mml:msub></mml:math></inline-formula> represents surface snow mass
lost via wind-driven erosion, and RU represents meltwater runoff.</p>
      <p id="d1e554">An earlier study by Colgan et al. (2014) presented the idea that, because of
the very strong impact of surface melt on the ice sheet's surface mass
balance (e.g. van den Broeke et al., 2016), the ice sheet average surface
albedo could serve as a meaningful and stationary proxy for the melt season
mass balance (MB) dynamic when calibrated against gravimetric mass balance
observations from the Gravity Recovery and Climate Experiment (GRACE)
satellite pair. However, the full mass balance of the ice sheet includes
dynamic ice losses from glacier discharge, to which surface albedo is
insensitive. Expanding on the original idea, we correlated CLARA-observed
surface albedo and GRACE-based SMB changes in order to infer a proxy SMB
time series from the CLARA surface albedo dataset.</p>
      <p id="d1e557">To obtain the proxy, we first add the monthly MB change record from GRACE
data and the state-of-the-art discharge (<inline-formula><mml:math id="M20" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>) estimates from recent work by
King et al. (2018) to obtain a GRACE-based SMB estimate. Then, a linear
regression is sought between the new GRACE SMB estimate and CLARA monthly
mean ice sheet albedo for all MJJA months in
the overlap period 2003–2015 for which valid GRACE data exist (<inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">45</mml:mn></mml:mrow></mml:math></inline-formula>). The
regression period thus contains data from the period of rapid ice sheet mass
loss in the 2000s, as well as from the years 2013–2015 when the mass loss
had somewhat decelerated. The regression parameters are used to create
summed MJJA surface mass balance proxy data from CLARA/GRACE for 1982–2015
for comparison with corresponding MAR SMB. The variability range observed
for the central ice sheet albedo in CLARA (0.02) is taken to be the
uncertainty range of the proxy SMB. For comparison, we also calculate and
present the proxy SMB from the most recent MOD10A1 data as described
earlier, using the same methods as for CLARA.</p>
      <p id="d1e579">While surface albedo is correlated with surface runoff at the
summer-aggregated scale, the relationship with the other SMB terms in Eq. (2) is less certain. Albedo initially increases with snowfall, but saturates
at fresh snow albedo levels (&gt; 0.8) once the fresh snow layer is
optically semi-infinite,<?pagebreak page2602?> regardless of how much additional snowfall occurs
after that. Rainfall produces the opposite effect, increasing mass but
decreasing albedo, although at the summer-aggregated scale some of the
rainfall near the ice sheet margins may be quickly lost as runoff, depending
on the firn retention properties. The modelling-based finding that surface
runoff dominates the MJJA surface mass loss (e.g. van den Broeke et al.,
2017, and references therein) is therefore confirmed in this test only if
the SMB proxy exhibits a strong degree of covariability with the MAR SMB.</p>
      <p id="d1e583">It should be noted that use of this regression method is not suited for
deriving a proxy SMB for a specific month or location on the ice sheet. This
is particularly the case for the early summer (May), where surface melt is
less important than precipitation for SMB changes. In terms of the MJJA
aggregate, however, the early summer SMB variability is small compared to
the total, thus incurring no greater uncertainty in the proxy than that
already propagated from the albedo retrieval uncertainty itself.</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Greenland surface albedo trends, 1982–2015</title>
      <p id="d1e603">The Theil–Sen decadal albedo trend estimates are shown in
Fig. 3. Here, we omit the years 1992 and 1993 from
analysis as their albedo estimates are likely both externally forced and
less reliable. Over the full CLARA period, we note that ice sheet albedo has
largely remained stable during the early summer months of May and June,
though some of the outermost ice sheet margins in the north and east show
statistically significant albedo decrease in June. However, in July and
August, we observe significant and negative albedo trends along most of the
ice sheet margins. Analysing the CLARA subperiods corresponding the
pre-MODIS and MODIS eras (Fig. 3, centre and bottom
rows), we find that the majority of the albedo decrease signal originates
after 2000, with a strong albedo decrease (up to <inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula> per decade as an area
average, individual grid cells may reach <inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> per decade) along the
Kangerlussuaq sector on the west margin. The MODIS era trends are consistent
in magnitude and pattern with those presented by Casey et al. (2017) from
the latest MOD10A1/MYD10A1 time series (see also Supplement).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><label>Figure 3</label><caption><p id="d1e628">Theil–Sen decadal albedo trends over the ice sheet from CLARA-A2
SAL during 1982–2015 <bold>(a–d)</bold>, 1982–1999 <bold>(e–h)</bold>, and 2000–2015 <bold>(i–l)</bold>. Columns
correspond to the summer months May–August from left to right. The hatched
regions in the trend figures indicate areas over which the trend is
significant (i.e. non-zero slope) at the 95 % confidence level, and its
magnitude exceeds the uncertainty limit of 0.015 per decade. Years 1992 and 1993
are excluded. Colour bar is limited to highlight majority values.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/13/2597/2019/tc-13-2597-2019-f03.png"/>

        </fig>

      <p id="d1e646">For the pre-MODIS era of 1982–1999, we note that while the ice sheet's
albedo was mostly stable according to CLARA, significant negative decadal
trends in late-summer albedo (Fig. 3g and h) manifest over the northeast
ice sheet. The cause of this albedo decrease remains unclear at present.
Based on in situ energy balance measurements over this area during summer of
1994, Konzelmann and Braithwaite (1995) argued that surface melt in the
region was primarily driven by net radiative fluxes during a relatively
cloudless summer. They also note that the relatively high downslope wind
speeds increase the importance of turbulent fluxes, possibly making the area
more sensitive to near-surface air temperature anomalies. Mouginot et al. (2015) also reported an increase in modelled runoff in this area from the
late 1980s onward, which is consistent with the negative albedo trend seen
here. Some significant negative albedo trends are also apparent on the
eastern margin, particularly along the Blosseville Coast. Box et al. (2006)
noted similar trends (in blue-sky albedo) based on an early version of the
Polar Pathfinder extended (APP-x) dataset in the same area for the 1988–1999
period for the region. In contrast, though, they found no negative albedo
trends in the northeast.</p>
      <p id="d1e650">Because the Theil–Sen trend estimator is defined as the median of all
possible slopes between data points in a time series, the subperiod trends
shown in Fig. 3 do not necessarily sum up to the
trends over the full 1982–2015 period. However, because the albedo trends
from MODIS time series data have been extensively studied, we felt that
presentation of the subperiod trends is important to compare results.</p>
      <p id="d1e653">The subperiod division used here is also useful in that the clear change in
late-summer albedo trends between 1982–1999 and 2000–2015 is fully
consistent with a documented change in atmospheric regime over the ice sheet
which began to favour high-pressure blocking patterns, as well as northward
transport of warm and moist air, increasing near-surface air temperatures
and enhancing downward longwave energy fluxes, all of which are features
which promote surface melt (e.g. Box et al., 2012; Hanna et al., 2013;
Mioduszewski et al., 2016; Välisuo et al., 2018). Some of the other
potential causes of the recent darkening of the western margin include
increasing biological activity (algae growth; Ryan et al., 2018) and
previously deposited impurities emerging from the ice with each melting
season, although recent field measurements have not detected evidence of
this (Polashenski et al., 2015).</p>
      <p id="d1e656">Stroeve (2001) analysed the Pathfinder surface albedo record, also from
AVHRR observations, obtaining negative blue-sky albedo trends over a set of
in situ measurement sites across the ice sheet during 1981–1998. The study
noted, however, that the trends were not statistically significant and were
largely driven by the anomalously low albedos observed during the summer of
1998, a feature present in CLARA as well. Yet our 1982–1999 subperiod sees
few substantial albedo decreases apart from the northeastern and eastern
margins. The difference to the earlier study is likely attributable to three
factors. First, the CLARA record is based on a more sophisticated AVHRR
intercalibration and comprises of more satellites carrying the instrument
relative to Pathfinder. Second, the Theil–Sen trend estimator used here is
resistant against outlier influence in trends, such as that from the
low-albedo summer of 1998. And, thirdly, the Pathfinder albedo record
quantified the blue-sky albedo of the ice sheet, thus containing an
influence of variable cloud cover, whereas the CLARA record describes the
black-sky albedo, which is an inherent property of the surface itself under
unidirectional illumination.</p>
      <?pagebreak page2603?><p id="d1e659">We finally observe that some of the outermost grid cells of for example the western
edge of the ice sheet display very small negative or even positive trends
for all studied months. This finding, while somewhat surprising, is
consistent with earlier field observations stating that the outermost zone
of the ice sheet margin consists of clean ice, effectively drained of meltwater by ubiquitous crevasses and moulins (Knap and Oerlemans, 1996) and
containing fewer biotic or abiotic impurities, and thus resistant to albedo
decreases caused by enhanced melting. However, we note that with the
relatively coarse spatial resolution of CLARA, the outermost grid cells are
mixed pixels even after the exclusion of grid cells with &lt; 50 %
ice cover. The albedo of these pixels includes relatively constant values of
the bare soil surrounding the ice, which could also explain the observed
stability. In any event, the impact of these areas on the overall ice sheet
albedo trends is negligible.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><label>Figure 4</label><caption><p id="d1e664"><bold>(a)</bold> Changes in time required (days) to reach bare-ice-typical
albedos between averaged periods 2013–2015 and 1982–1984. Green-yellow
pentagons indicate areas where bare ice albedo is reached during the last
but not the first years of the period. Crosses indicate areas where bare ice albedo is reached during the first but not the last years of the period. <bold>(b)</bold> MERRA-2 mean winter precipitation anomaly (m w.e.) of 1982–2015 vs.
1982–1992 mean. <bold>(c)</bold> MERRA-2 mean May–August SAT anomaly of 1982–2015 vs.
1982–1992 mean.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://tc.copernicus.org/articles/13/2597/2019/tc-13-2597-2019-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Melt intensity and bare ice exposure</title>
      <p id="d1e689">Figures 4a, 5a, and 6a show the change in the time required from
early May for the grid cell to reach an albedo typical of bare ice, taken as
a proxy for melt season intensity, between the last and first 3 years of
each period. Here, the decrease rates are shown only for elevations below
2200 m a.s.l., where the trend signal originates. The overlaid pentagons
(and crosses) indicate areas where albedos typical of bare ice and wet snow
have been reached at the end but not the beginning of each period (and vice
versa). The patterns correlate well spatially, as expected. We see increases
in melt intensity along the western margin (basin 5) for the full<?pagebreak page2604?> CLARA
period and both subperiods. The MODIS era has seen systematically more bare
ice exposure also over basin 6, which is further north. To assess the consistency and
robustness of the changes in melt intensity, we also calculated the
Theil–Sen decadal trend estimates for the melt rates during each period,
shown in Fig. 7. The acceleration in melt rate
between 1982 and 2015 is significant over large areas in the western,
northern, and northeastern margins, largely as a consequence of changes
seen during 2000–2012.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><label>Figure 5</label><caption><p id="d1e694"><bold>(a)</bold> Changes in time required (days) to reach bare-ice-typical
albedos between averaged periods 1997–1999 and 1982–1984. Green-yellow
pentagons indicate areas where bare ice albedo is reached during the last
but not the first years of the period. Crosses indicate areas where bare ice albedo is reached during the first but not the last years of the period. <bold>(b)</bold> MERRA-2 mean winter precipitation anomaly (m w.e.) of 1982–1999 vs.
1982–1992 mean. <bold>(c)</bold> MERRA-2 mean May–August SAT anomaly of 1982–1999 vs.
1982–1992 mean.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://tc.copernicus.org/articles/13/2597/2019/tc-13-2597-2019-f05.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><label>Figure 6</label><caption><p id="d1e713"><bold>(a)</bold> Changes in time required (days) to reach bare-ice-typical
albedos between averaged periods 2013–2015 and 2000–2002. Green-yellow
pentagons indicate areas where bare ice albedo is reached during the last
but not the first years of the period. Crosses indicate areas where bare ice albedo is reached during the first but not the last years of the period. <bold>(b)</bold> MERRA-2 mean winter precipitation anomaly (m w.e.) of 2000–2015 vs.
1982–1992 mean. <bold>(c)</bold> MERRA-2 mean May–August SAT anomaly of 2000–2015 vs.
1982–1992 mean.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://tc.copernicus.org/articles/13/2597/2019/tc-13-2597-2019-f06.png"/>

        </fig>

      <p id="d1e731">Also, while some areas saw new bare ice exposure in the late 1990s (relative
to the early 1980s), there has been a widespread increase in areas experiencing
bare ice exposure (or very wet snow cover) during the 2000s, so that these
areas now routinely reach elevations 50–100 m higher up the ice sheet
compared to 1982–1984 (Fig. 8). These changes are
consistent with corresponding positive anomalies in MERRA-2 mean SAT during
the summer months, as shown in Figs. 4c, 5c, and 6c.</p>
      <p id="d1e734">A notable and interesting deviation from this trend towards faster melt and
expanding bare ice/very wet snow cover has occurred along the southeastern
margin, roughly between Tasiilaq and Paamiut (basin 4). Here, we observe no
increase in melt rate during the MODIS era, and areas which reached bare ice
albedos during the melting season at the turn of the century no longer do so
in 2013–2015. We suggest that both of these effects are explained by
substantial increases in winter snowfall over this region, as shown by the
MERRA-2 winter precipitation anomalies (Fig. 6b). The increasing snow deposition, also reported by Box (2013),
creates a buffer against melt rate acceleration, inhibiting bare ice
exposure at the same time. The summer SAT anomalies during the MODIS era
over this region are also less significant than those over the western
margin, consistent with prior analysis suggesting that the presently
dominant atmospheric circulation patterns particularly favour northward warm
air transport along the western margin of the ice sheet (Fettweis et al.,
2013), likely enhanced at times by atmospheric river events
(Neff et al., 2014; Mattingly et al., 2018).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><label>Figure 7</label><caption><p id="d1e739">Theil–Sen decadal trend estimates in albedo decrease rate (units
per 30 d) serving as a proxy for melt intensity. Hatched pattern
indicates areas where the trend is statistically significant (non-zero
slope) at the 95 % confidence level. Estimates shown only for elevations
lower than 2200 m a.s.l.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://tc.copernicus.org/articles/13/2597/2019/tc-13-2597-2019-f07.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8"><?xmltex \currentcnt{8}?><label>Figure 8</label><caption><p id="d1e750">Change in the median elevation (a.s.l.) of the parts of the ice
sheet reaching albedo typical of bare ice between 1982 and 2015. Years 1992
and 1993 are excluded from analysis.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://tc.copernicus.org/articles/13/2597/2019/tc-13-2597-2019-f08.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Runoff contribution in the variability of the ice sheet's surface mass balance (SMB) in summer during 1982–2015</title>
      <p id="d1e767">Figure 9a shows the Theil–Sen regression fit between
the monthly means of the CLARA albedo time series and the ice sheet SMB,
obtained by correcting the GRACE mass balance observations with the
state-of-the-art monthly ice discharge estimates (King et al., 2018) following
Eq. (1). The obtained fit shows no temporal dependency (years marked by
colours) and is fairly robust (<inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.77</mml:mn></mml:mrow></mml:math></inline-formula>). For
completeness, the regression parameters for both CLARA and MOD10A1 are
provided in the Supplement and discuss considerations and
limitations to their use in Sect. 2.7.4.</p>
      <p id="d1e785">We then calculate the summer-summed proxy SMB for both CLARA and MOD10A1,
shown in Fig. 9b. The original GRACE SMB estimates
and MAR SMB are shown for comparison. Both proxy SMB time series overestimate
MAR SMB, largely because the original GRACE SMB estimates do so as well.
However, it is notable that the GRACE proxy SMB largely does agree with MAR
SMB between 1982 and 2014 within its uncertainty envelope, apart from the<?pagebreak page2605?> a
priori known period of 1992–1993 and 1999–2000 to a smaller extent. The
1999–2000 disagreement may be traceable to a change in the NOAA AVHRR
constellation which occurred at the time. Both CLARA and MOD10A1 proxy SMB
exhibit a significant Pearson correlation coefficient against MAR (CLARA:
0.79, MOD10A1: 0.95), confirming, on an observational basis, the modelling-based
finding that surface melt and subsequent runoff dominate the interannual
summer SMB variability of the ice sheet.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><label>Figure 9</label><caption><p id="d1e790"><bold>(a)</bold> Linear regression fit between CLARA-A2 SAL monthly mean ice
sheet surface albedo (<inline-formula><mml:math id="M25" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> axis) and the TU Dresden GRACE RL06 monthly SMB,
obtained by correcting the GRACE mass balance data with ice discharge
estimates by King et al. (2018). <bold>(b)</bold> May–August (MJJA) surface mass balance
sums between 1982 and 2017. Blue line and markers show the CLARA-proxy SMB
as calibrated against GRACE observations, with an uncertainty envelope (blue
shading) based on the best estimate for the mean snow/ice albedo stability of
0.02 in CLARA. Green line shows the corresponding SMB estimates from the MAR
regional climate model. The magenta line and markers show the
discharge-corrected GRACE SMB estimate, shown only for years with full GRACE
MJJA availability. The red dashed line and markers show the MOD10A1-based
SMB estimate for comparison.</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://tc.copernicus.org/articles/13/2597/2019/tc-13-2597-2019-f09.png"/>

        </fig>

      <p id="d1e812">A notable divergence between the proxies and MAR in the MODIS era occurs in
2012, when evidently the summer mass loss clearly outpaced any albedo
reductions seen by either MODIS or AVHRR. A potential explanation is that
albedo decreases are physically bounded in a way that the<?pagebreak page2606?> surface-melt-induced mass loss is not. The albedo of the ice sheet margin, where the
changes are concentrated, could be considered to have physically based local
effective minima, corresponding to conditions where the ice sheet surface is
consistently melting and saturated with melt ponds and melt rivers up to the
local effective maximum coverage. In this logic, beyond this point the mean
surface albedo of the area would have almost nowhere to go in terms of
further decreases, barring the introduction of large concentrations of
light-absorbing impurities or biomass.</p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>On the basin-scale relationships between surface albedo as a runoff proxy and ice discharge</title>
      <p id="d1e823">A comparison between detrended, normalized basin-scale D anomalies and
surface albedo (serving as a proxy for runoff) between 2000 and 2015 yielded
no statistically significant relationships for any examined summer month at
the 95 % confidence level. This negative finding implies that surface
runoff anomalies do not significantly alter the solid ice discharge rates
through the outlet glaciers at the annual level. This is in line with
previous modelling work (Schoof, 2010; Tedstone et al., 2015) which has
suggested a complex relationship between meltwater availability and glacier
flow rate, where large amounts of meltwater may serve to decelerate rather
than accelerate glacier basal flow. Also, King et al. (2018) note that the
annual variability in the ice discharge is mostly connected to cumulative
changes in the calving front positions of its outlet glaciers.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussion</title>
      <?pagebreak page2607?><p id="d1e835">The CLARA-A2 SAL surface albedo estimates represent the per-grid-cell mean
solar illumination conditions of each 5 d or monthly time period and are
not normalized to any particular solar zenith angle (SZA). We choose to use a
non-normalized SZA because various in situ measurements have shown the
symmetrical u-shape diurnal cycle assumed in common normalization
algorithms (Briegleb et al., 1986; Gardner and Sharp, 2010) is not valid for
snow during the melting period, when the u shape is often
noon-asymmetrical (Dirmhirn and Eaton, 1975; Jonsell et al., 2003; Pirazzini
et al., 2006; Meinander et al., 2013). We find, however, that albedo trends
are not highly sensitive to the selection or exclusion of SZA normalization.
Figure S1 in the Supplement reproduces Fig. 3 with the application of the SZA normalization
proposed by Gardner and Sharp (2010) with a target SZA of 60<inline-formula><mml:math id="M26" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>,
yielding consistent trends. Also, the separate treatment for each summer
month and the use of a conservative SZA cutoff (of 70<inline-formula><mml:math id="M27" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>) in the albedo
estimation will further ameliorate any impacts of excluding a normalization
procedure.</p>
      <p id="d1e856">We find very similar spatio-temporal distributions of albedo trends and
overall magnitude to those in Tedesco et al. (2016b), who performed an
analysis of Greenland surface albedo changes during the summer JJA season
from the GLASS dataset, based on coherently and consecutively processed
AVHRR and MODIS observations. The JJA albedo trend for the whole ice sheet
during 1996–2012 in CLARA-A2 is <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.020</mml:mn></mml:mrow></mml:math></inline-formula> per decade (<inline-formula><mml:math id="M29" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> &lt; 0.01), matching
the result from GLASS (based on MODIS Terra and Aqua from 2000/2002
onward). They attribute the decreasing trend to increasing air temperatures
and enhanced melting but also to exposure of older impurities resulting
from increasing snow and ice melt. While our present analysis does not
attempt to attribute changes to impurity deposition or exposure, we note
that the melting seasons 2013–2015 brought about a clear amelioration in the
overall albedo decrease. The JJA decadal albedo trend in CLARA-A2 for
1996–2015 is <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M31" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> &lt; 0.05). This suggests that, if progressing
impurity exposure indeed plays a role in the large-scale darkening of the
ice sheet margins, cloudiness and circulation changes alongside regional
precipitation increases are still the more powerful drivers.</p>
      <p id="d1e893">We suggest that the recent inhibition of surface melt along the SE margin of
the ice sheet is due to increased winter precipitation, but there are
somewhat conflicting views in recent literature. Berdahl et al. (2018)
examined observation precipitation records at Tasiilaq station, taken to be
representative of the surrounding parts of the SE ice sheet, and found no
significant December–February precipitation increases in the satellite era
up to 2012. We note, however, that Tasiilaq station appears to lie at the
no-change zone between the MERRA-2 bimodal peaks, where MERRA-2 winter
precipitation anomalies during 2000–2015 increase in the southernmost parts
of the SE margins but are reduced further east. While further analysis on
this bimodal feature in precipitation anomalies is beyond the scope of this
study, we suggest it might serve to explain the lack of observed
precipitation increases by Berdahl et al. (2018). However, Koyama and
Stroeve (2018) evaluated the Arctic System Reanalysis precipitation against
in situ observation along the ice sheet margins, finding in situ
observations indicating increasing<?pagebreak page2608?> precipitation during the 2010–2015 period
near the southern tip of Greenland. These increases agree with the
increasing winter precipitation signal we observe in MERRA-2 and are consistent
with the lack of new albedo reductions or bare ice exposure in CLARA
(Fig. 6). The suggested link between melt
inhibition and increasing precipitation depends fully on the phase of the
precipitation; recent evidence demonstrates that the proportion of rainfall
to total precipitation is increasing, suggesting that our finding may be
transient in nature (Oltmanns et al., 2019).</p>
      <p id="d1e896">Wong et al. (2015) also reported consistent although regionally variable
temperature and precipitation responses along the Greenland coastal regions
to prevailing atmospheric circulation patterns, in particular to the warm
and moist southerly airflows associated with a negative North Atlantic
Oscillation (NAO) index. Their finding of increasing winter precipitation in
the NW region of the ice sheet during 1990–2010 is consistent with the
localized lack of systematic melt acceleration seen in CLARA over the same
region (Fig. 4), even though the increasing
precipitation is not seen by MERRA-2. However, the reversal of bare ice
exposure in the NW when comparing 2013–2015 to 2000–2002
(Fig. 6) may also be related to more frequent cold
northerly airflows post-2012 (Tedesco et al., 2014).</p>
      <p id="d1e900">While our observation-based test confirms the dominance of surface melt in
the surface mass loss of the ice sheet, the general agreement between
modelled and proxy SMB shown here contains substantial (though mutually
cancelling) disagreements at the monthly level. Most notably, the
ERA-Interim-forced MAR v.3.5.2 SMB generally sees the largest annual mass
loss occurring in July, whereas the corresponding GRACE SMB estimates assign
the largest mass loss to the month of August. Such differences have
emerged in prior studies (Alexander et al., 2016), although based on
different GRACE mass balance solutions and a MAR version of different
forcing and spatial resolution, invalidating direct comparisons between
results. The reasonably good covariability between MAR SMB and albedo-based
proxy SMB is likely due, in part, to the improved agreement between GRACE
and MAR mass balance at elevations below 2000 m a.s.l. (Alexander et al.,
2016), where most of the ice sheet albedo changes occur. Also, in principle
snowfall acts to increase both SMB and albedo, although the correlation is
short-lived, diminishing once the fresh snow layer becomes optically
semi-infinite.</p>
      <p id="d1e903">The ESA Greenland Ice Sheet CCI distributes mass balance solutions from two
algorithms (TU Dresden and DTU). For completeness, we repeated the SMB
analysis also for the DTU GRACE data. The results (Fig. S2)
show a less favourable fit between CLARA and discharge-corrected GRACE SMB
with a larger slope, leading to generally much less negative surface mass
balance in the CLARA–GRACE proxy relative to MAR. The MOD10A1 is similarly
affected but to a lesser degree. It is notable that both discharge-corrected
GRACE SMB time series from ESA Greenland Ice Sheet CCI produce systematically
less negative SMB during the summers 2004–2010 relative to MAR.</p>
      <p id="d1e906">Geolocation errors have been reported as a source of difference between the
MODIS and AVHRR albedo estimates by Box et al. (2006). To further
investigate the chance that geolocation and cloud masking uncertainties have
a substantial impact on the obtained results, we compared the CLARA record
to the latest MOD10A1 (Box et al., 2017b) in terms of decadal albedo trends and grid-cell-specific mean differences per summer month during 2000–2015
(Fig. S3). The CLARA-MOD10A1 mean differences display a
substantial latitudinal dependency in May and August, in line with results
shown by Alexander et al. (2014). However, the decadal trends agree very
well between the datasets, thus reinforcing the robustness of the observed
trends in CLARA albedo. Discerning the cause of the differences would
require a rigorous study accounting for differences in spatial resolution,
diurnal sampling, and geolocation uncertainties and is as such beyond the
scope of the present work.</p>
      <p id="d1e909">A variety of drivers of the post-2000 increases in the ice sheet's surface
melt (and thus decreases in surface albedo) have been proposed. First,
atmospheric circulation pattern changes (ridging over Greenland) have led to
warm and moist air advection over the ice sheet (e.g. Fettweis et al., 2013;
Mioduszewski et al., 2016), leading to both increases in SAT (Reeves Eyre
and Zeng, 2018) and increases in clear-sky downwelling longwave radiation
(Mioduszewski et al., 2016; Välisuo et al., 2018). Changes in the
surface radiative energy budget caused by cloud coverage and composition
have also been proposed as a primary driver. Hofer et al. (2017) argued,
using the CLARA-A1 dataset, the predecessor of CLARA-A2 used here, that
decreasing cloudiness over the ablation zone in the 2000s, which increases
both downwelling shortwave and clear-sky downwelling longwave radiation in
the presence of advected warm air masses, has caused a significant increase
in insolation and surface melt. Bennartz et al. (2013) provided a different
mechanism for increased melt, arguing that, over the high-elevation centre of
the ice sheet, intrusions of optically thin, low-level, and liquid-bearing
clouds enhance the downward longwave flux while still allowing shortwave
flux penetration to the surface, promoting extensive surface melt.</p>
      <p id="d1e912">Here, we have focused on analysing the surface albedo changes using
reanalysis SAT and winter precipitation as supporting evidence. We
calculated the mean MJJA cloud fractional coverage over the ice sheet from
CLARA-A2 (1982–2015) for comparison against the corresponding MAR cloud
cover field. Figure 10 shows a recovery of cloud
cover after 2007 in CLARA, from updated algorithms and AVHRR radiance
calibration. MAR cloud cover, however, continued to decline until 2011. This
highlights the uncertainties in cloud observations from legacy AVHRR data,
even though the detection performance is improved in CLARA-A2 (Karlsson et
al., 2017a). A limited study over the central part of the accumulation zone
during 2010 showed good<?pagebreak page2609?> agreement between CLARA and MODIS cloud cover
(Riihelä et al., 2017), implying that the latest years of CLARA with the
highest number of concurrently serving AVHRR instruments should be the most
reliable.</p>
      <p id="d1e915">While the overall cloudiness decline from the mid-1990s to 2007 is still in
line with the melt mechanisms proposed by Hofer et al. (2017), the post-2007
cloudiness recovery in CLARA-A2 is then inconsistent with the continuing
large mass loss from the CLARA and MOD10A1 proxy SMB time series, as well as
MAR, up till 2012. Alongside the comparison to the results from Tedesco et al. (2016b), this suggests that the relationship between cloudiness,
atmospheric circulation patterns, and surface melt may be still more
complicated than has been shown to date. Further, cloud radiative properties
can also significantly impact bright snow surface radiative budgets, but
these parameters (e.g. cloud optical thickness (COT) and effective particle
radius, or liquid/ice water path (LWP/IWP)) are challenging to retrieve from
AVHRR (Riihelä et al., 2017).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10"><?xmltex \currentcnt{10}?><label>Figure 10</label><caption><p id="d1e921">Mean JJA fractional cloud cover over the ice sheet from CLARA-A2
and MAR v3.5.2 with ERA-Interim forcing.</p></caption>
        <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://tc.copernicus.org/articles/13/2597/2019/tc-13-2597-2019-f10.png"/>

      </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11" specific-use="star"><?xmltex \currentcnt{11}?><label>Figure 11</label><caption><p id="d1e932">Comparison of monthly basin-scale CLARA-A2 SAL anomalies (red
circle) against Greenland Blocking Index (GBI) anomalies (blue triangle).
All anomalies are calculated with respect to the 1982–2015 mean albedo or GBI.
Red and blue lines show 2-year running means of the respective anomalies.
Basins are ordered as in Fig. 2.
Years 1992 and 1993 are excluded from the analysis.</p></caption>
        <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://tc.copernicus.org/articles/13/2597/2019/tc-13-2597-2019-f11.png"/>

      </fig>

      <p id="d1e941">Another means of linking large-scale atmospheric circulation to the surface
albedo changes is via the Greenland Blocking Index (GBI; Hanna et al., 2013,
2016). Positive anomalies in GBI represent atmospheric conditions which
block northerly zonal airflow over the ice sheet, allow for warm southerly
airflow particularly across the west margin, and promote clear-sky
conditions over the ice sheet, enhancing surface melt (Hanna et al., 2014).
The basin-scale comparisons between surface albedo anomalies and GBI
anomalies (both calculated with respect to the 1982–2015 mean) are shown as
time series in Fig. 11. Generally, there is a
negative correlation between GBI and albedo (see Fig. S4), although with
variability between basins. For example, in agreement with Tedesco et al. (2016a), the 2015 positive GBI anomaly was linked to an atmospheric ridge
which enhanced melt in northern Greenland (basins 1 and 6) while preventing
it in the south, a feature reproduced in the corresponding albedo anomalies.
Along with the concurrent recovery in ice sheet mean cloudiness
(Fig. 10), the significant covariability between
GBI and albedo implies that the apparent post-2012 slowing in further albedo
decreases is linked to a shift in large-scale atmospheric circulation,
allowing for more cold northerly airflow (Tedesco et al., 2014) and
increasing cloudiness (during summers; Fig. 10).</p>
      <p id="d1e944">McLeod and Mote (2016) also connect increasing surface melt since the early
1990s with the increasing frequency, and partly duration, of very large GBI
(Greenland blocking episodes, GBEs), in line with results from our
observation-driven analysis. Rajewicz and Marshall (2014) report that a
substantial part of summer melt variability is directly explainable by
increasing anticyclonic circulation over Greenland, isolating that signal
from the overall near-surface air temperature increases and contesting that
any abrupt change in atmospheric regime is behind the change. They also note
that the anticyclonic circulation began to impact South Greenland
during the 1990s, with the effect spreading to other parts of the ice sheet
after 2001. Further, they note that while the NAO index is often used to
explain melt anomalies, NAO is not a causal mechanism for the melt but is
simply covariant with melt-inducing ridging conditions over the ice sheet.
This reasoning is consistent with the gradually decreasing albedo seen in
CLARA during the pre-MODIS era on the western margin but does not explain the
substantial late-summer albedo decrease in the northeast in the same era.
They are also consistent with a stronger overall correlation between CLARA
JJA albedo and GBI (<inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.64</mml:mn></mml:mrow></mml:math></inline-formula>) than between JJA albedo and NAO (<inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.47</mml:mn></mml:mrow></mml:math></inline-formula>) using data from Hurrell and Deser (2009).</p>
      <p id="d1e973">The influence of oceanic heat advection is another possible cause for some
of the observed albedo decreases. Both CLARA and MOD10A1 detect localized
negative albedo trends around Helheim and Kangerdlussuaq glaciers in the
southeast margin. Straneo et al. (2011) documented the presence of warm
subtropical waters in the Helheim Glacier fjord, Häkkinen and Rhines (2009) showed that such waters have begun to penetrate the seas around SE
Greenland with increasing intensity, and Christoffersen et al. (2011)
connected an increase in oceanic heat fluxes with subsequent Kangerdlussuaq
Glacier retreat. It could thus be postulated that the release of heat from
these warmer waters could act as a localized additional source of energy for
the surface snow and ice in the area surrounding these two glaciers served
by relatively large fjords. However, outlet glacier thinning accelerated by
oceanic heat (Murray et al., 2010) and exposure of impurities from the ice
with increasing melt (Tedesco et al., 2016b) could also produce this effect.</p>
      <p id="d1e977">Finally, we note that while the CLARA proxy does provide observation-based
confirmation on the dominance of surface melt in the variability of the
summed MJJA surface mass balance, the results show clear physical
constraints on the validity of mechanisms linking enhanced albedo reductions
as a proxy for SMB decreases. The question of increasing biological activity
as a driver of albedo reduction along the ice sheet margins remains open for
want of long-term records to compare with the present albedo estimates from
CLARA. A large-scale spread of algae colonies on the ice<?pagebreak page2610?> surface would
certainly provide a mechanism for albedo decrease unaccounted for in present
models and satellite-based retrieval algorithms.</p>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d1e989">We have investigated the decadal trends in the surface albedo of the
Greenland Ice Sheet between 1982 and 2015 and their connection to melt
rate, bare ice exposure, and surface mass balance and ice discharge
rate. The main results of this study may be summarized as follows.</p>
      <p id="d1e992">Over the 34-year investigation period, the late-summer surface albedo of the
ice sheet margins shows a statistically significant decrease at the 95 %
confidence level. The 1982–2015 decadal albedo trends reach a maximum of
approximately <inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula> over the ablation region in the Kangerlussuaq sector in
July, although some grid cells in the area display decadal trends twice as
large during 2000–2015. The trends are consistent with MODIS data for the
overlap period.</p>
      <p id="d1e1005">The albedo decrease along the west coast mainly occurred between 2000 and
2012, concurrently and consistently with a previously reported change in
atmospheric circulation favouring the advection of warm and moist southerly
air masses along the west coast. The albedo decrease of the northeastern and
eastern margins was initiated during the 1982–1999 period. While the
darkening there is statistically significant, we cannot at present identify
a clear driver for it.</p>
      <p id="d1e1008">The melt seasons along the western and northern ice sheet margins
intensified primarily after 2000, as seen by an acceleration of the albedo
decrease rate during the melting season. Also, regions where surface melt
causes the albedo to drop to values typical of bare ice were much more
widespread in 2012–2015 than in the early 1980s and expand to elevations
50–100 m higher on the ice sheet.</p>
      <p id="d1e1012">A notable exception to the widespread albedo decrease was observed along the
southern margins, consistently and concurrently with increased winter
snowfall in the MERRA-2 reanalysis. The future persistence of this effect
will undoubtedly depend on the future magnitude and phase of precipitation
along the ice sheet's southern margin.</p>
      <?pagebreak page2611?><p id="d1e1015">When calibrated against surface mass balance estimates based on GRACE
gravimetric measurements and ice discharge estimates, the CLARA surface
albedo estimates form a proxy for summer-aggregated SMB reaching back to
1982. This proxy shows reasonably good agreement and a high degree of
covariability with MAR regional climate model (v3.5.2) estimates for the
full investigation period. This confirms the dominant role of surface runoff
in the ice sheet's SMB variability during the satellite era.</p>
      <p id="d1e1018">We find no observational evidence for a connection between annual surface
albedo changes (as a proxy for runoff production anomalies) and anomalies in
annual rates of ice discharge at drainage basin scales.</p>
      <p id="d1e1021">Our 3-decade analysis of homogenized AVHRR imagery places the ice
sheet's significant albedo changes after the turn of the millennium in a
broader context. Most changes are clearly attributable to concurrently
prevailing patterns in atmospheric circulation and precipitation. The
robustness of the first half of the AVHRR record may only be assessed
indirectly for want of reliable reference data. However, we see no
significant instability in time in the CLARA surface albedo record prior to
2000. During the same period, the reasonably good covariability between MAR
and the CLARA-derived proxy provides further reinforcement to the
plausibility of the early satellite record. Our results are consistent with
a broad range of prior studies on the changing surface state of the ice
sheet.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e1028">The CLARA-A2 surface albedo data record is available from
<ext-link xlink:href="https://doi.org/10.5676/EUM_SAF_CM/CLARA_AVHRR/V002" ext-link-type="DOI">10.5676/EUM_SAF_CM/CLARA_AVHRR/V002</ext-link> (Karlsson et al., 2017b). The MAR climate model data were obtained
from <uri>ftp://ftp.climato.be/fettweis/MARv3.5/Greenland</uri> (last access: 26 October 2018). The Greenland Ice
Sheet CCI GRACE data were obtained from
<uri>http://products.esa-icesheets-cci.org/products/downloadlist/GMB/</uri> (Barletta et al., 2013; Groh and Horvath, 2016). The
Greenland Blocking Index was obtained from <uri>https://www.esrl.noaa.gov/psd/data/timeseries/daily/GBI/</uri> (Hanna et al., 2013). The MOD10A1
albedo estimates were obtained from <uri>http://promice.dk/DownloadAlbedodata.html</uri> (Box et al., 2017b).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e1046">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/tc-13-2597-2019-supplement" xlink:title="zip">https://doi.org/10.5194/tc-13-2597-2019-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e1055">AR planned the study and performed the analyses. MK was in charge of the
discharge estimate data and contributed to the manuscript text. KA was the
responsible scientist for the creation of the CLARA-A2 SAL dataset and
contributed to the manuscript text. AR prepared the manuscript with
contributions from all co-authors.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e1061">The authors declare that they have no conflict of interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e1067">The CLARA-A2 SAL data record was created by the Satellite Application
Facility on Climate Monitoring (CM SAF), a project of EUMETSAT. Colleagues
in the CM SAF project are thanked for their support in the creation of the
CLARA-A2 SAL dataset. Figures S1–S4 are available in the
Supplement of this paper.</p><p id="d1e1069">The authors would like to thank the editor, an anonymous reviewer, and
Jason Box for their insight and comments that helped improve the manuscript.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e1074">This research has been supported by the Academy of Finland, Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta (grant no. 287399), and the National Aeronautics and Space Administration (grant nos. 80NSSC18K1027 and NN13AI21A).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e1080">This paper was edited by Mark Flanner and reviewed by Jason Box and one anonymous referee.</p>
  </notes><ref-list>
    <title>References</title>

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    <!--<article-title-html>The surface albedo of the Greenland Ice Sheet between 1982 and 2015 from the CLARA-A2 dataset and its relationship to the ice sheet's surface mass balance</article-title-html>
<abstract-html><p>The Greenland Ice Sheet is losing mass at a significant rate,
driven in part by increasing surface-melt-induced runoff. Because the ice
sheet's surface melt is closely connected to changes in the surface albedo,
studying multidecadal changes in the ice sheet's albedo offers insight into
surface melt and associated changes in its surface mass balance. Here, we
first analyse the CM SAF Cloud, Albedo and
Surface Radiation dataset from AVHRR data second edition (CLARA-A2) Surface Albedo (SAL),
covering 1982–2015, to obtain decadal albedo trends for each summer month.
We also examine the rates of albedo change during the early summer,
supported with atmospheric reanalysis data from MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, version 2), to discern changes
in the intensity of early summer melt, and their likely drivers. We find
that rates of albedo decrease during summer melt have accelerated during the
2000s relative to the early 1980s and that the surface albedos now often
decrease to values typical of bare ice at elevations 50–100&thinsp;m higher on
the ice sheet. The southern margins exhibit the opposite behaviour, though,
and we suggest this is due to increasing snowfall over the area.</p><p>We then subtract ice discharge from the mass balance estimates observed by
the Gravity Recovery and
Climate Experiment (GRACE) satellite mission to estimate surface mass balance. The CLARA-A2 albedo changes are regressed with these data to obtain a summer-aggregated
proxy surface mass balance time series for the summer periods 1982–2015. This
proxy time series is compared with latest regional climate model estimates
from the MAR model to perform an observation-based test on the dominance of
surface runoff in the magnitude and variability of the summer surface mass
balance. We show that the proxy time series agrees with MAR through the
analysed period within the associated uncertainties of the data and methods,
demonstrating and confirming that surface runoff has dominated the rapid
surface mass loss period between the 1990s and 2010s.</p><p>Finally, we extend the analysis to the drainage basin scale to examine
discharge–albedo relationships. We find little evidence of surface-melt-induced ice flow acceleration at annual timescales.</p></abstract-html>
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