Spatio-Temporal Analysis of Bare-Ice Melt Dynamics in the Western Greenland Ice Sheet (2000–2024)

Spatio-Temporal Analysis of Bare-Ice Melt Dynamics in the Western Greenland Ice Sheet (2000–2024) | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Spatio-Temporal Analysis of Bare-Ice Melt Dynamics in the Western Greenland Ice Sheet (2000–2024) Asaram Janwale, Savita Mohurle, Richa Purohit, Minal Deshmukh, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9498957/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Bare-ice zone dynamics along the western Greenland Ice Sheet (GrIS) ablation zone (60°N–80°N; 25°W–55°W) were examined over a 25-year period from 2000 to 2024. Surface ablation accounts for over half of total annual GrIS mass loss, yet the interannual drivers of bare-ice extent remain incompletely characterised. Bare-ice pixels were identified where the Normalised Difference Snow Index (NDSI) dropped below 0.4, marking full seasonal snow ablation and direct glacier ice exposure. Four open-access datasets were processed in Google Earth Engine (GEE): MODIS MOD10A1 Collection 6.1, ERA5-Land hourly 2-m air temperature, ArcticDEM V4 two-metre mosaic, and Landsat 8 OLI for supraglacial lake mapping. All calculations were confined to an ice-sheet proxy mask covering 1,524,897 km² (~ 89% of GrIS). Annual bare-ice extent ranged from 1,375 km² (2018) to 11,033 km² (2012), with a 25-year mean of 4,820 km². OLS regression and the Mann-Kendall test (α = 0.05) found no significant trend in bare-ice extent (+ 12.5 km²/yr, p = 0.878) or summer positive degree days (PDD; +0.07°C-days/yr, p = 0.728). A power analysis shows the minimum detectable trend at 80% power is roughly 216 km²/yr, meaning slower forced changes are statistically unresolvable at this record length. Despite the null trend, summer PDD and annual bare-ice extent were strongly correlated across the full record (r = 0.814, p = 7.23 × 10⁻⁷); this relationship stayed significant after removing four documented blocking years (r = 0.521, p = 0.016, n = 21), pointing to thermal forcing as the dominant control on interannual bare-ice variability. Greenland Ice Sheet bare-ice zone MODIS NDSI ERA5-Land positive degree days Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Highlights • 25-year MODIS bare-ice record reveals strong PDD control (r = 0.814) over western GrIS • No significant bare-ice trend detectable over 25 years at observed GrIS melt variance • Power analysis establishes ~216 km² a⁻¹ minimum detectable trend at 80% power • PDD–bare-ice coupling robust after excluding atmospheric blocking years (r = 0.521) • Reproducible GEE workflow integrating MODIS, ERA5-Land, ArcticDEM V4 and Landsat 8 1. Introduction 1.1. Background and Motivation Full melting of the Greenland Ice Sheet (GrIS) would raise global mean sea levels by roughly 7.2 m (Bamber et al., 2019 ). Surface melt and meltwater routing to the ocean currently drives approximately 50–60% of total GrIS mass loss, making it the dominant ablation pathway along the western margin (Mouginot et al., 2019 ). Multi-decadal satellite data reveal large year-to-year swings in melt intensity; the record ablation seasons of 2010 and 2012 have been attributed to persistent anticyclonic blocking above the ice sheet (Tedesco et al., 2011; Nghiem et al., 2012 ). Identifying what governs this variability, and whether any forced long-term signal is emerging above the background atmospheric noise, is essential for improving GrIS mass-balance projections and their sea-level implications. When the seasonal snowpack is fully gone across the western ablation zone, bare glacier ice is exposed directly to the atmosphere. Bare-ice albedo (roughly 0.2–0.4) is far lower than fresh snow albedo (roughly 0.8), triggering a positive melt-albedo feedback that accelerates surface energy absorption and drives up ablation rates (Box et al., 2012 ; Tedesco et al., 2016 ). Bare-ice zone extent — defined here as the area where NDSI falls below 0.4 — therefore gives a more direct measure of active ablation than passive-microwave total melt area, which lumps bare-ice and wet-snow signals together. MODIS NDSI-based bare-ice extents for the western GrIS typically run from a few thousand km² to roughly 15,000 km² in high-melt years (Ryan et al., 2019 ), well below the 100,000–900,000 km² values from passive-microwave products. 1.2. Review of Related Studies MODIS MOD10A1 computes NDSI from visible and shortwave-infrared reflectances, classifying surfaces as snow-free or bare ice where NDSI < 0.4 (Hall and Riggs, 2016 ). Positive degree days (PDD) — the sum of temperatures above 0°C — are a well-established thermal melt proxy (Hock, 2003 ) and anchor degree-day models with ice melt factors near 8 mm °C⁻¹ day⁻¹ (van den Broeke et al., 2011 ). ERA5-Land hourly reanalysis at ~ 9 km resolution has been independently validated for near-surface temperature over the GrIS (Muñoz-Sabater et al., 2021 ). Record GrIS melt years are closely tied to persistent high-pressure blocking identified via a positive Greenland Blocking Index (Tedesco et al., 2011; Nghiem et al., 2012 ). During such events, albedo feedbacks from bare ice, cryoconite, and biological impurities further amplify ablation (Box et al., 2012 ; Tedesco et al., 2016 ). Supraglacial lake growth, hydrofracture drainage, and the resulting ice-flow acceleration add a dynamic dimension to this melt response (Williamson et al., 2017 ). The GEE platform has greatly extended the reach of continental-scale, multi-decadal cryosphere research by providing direct access to petabyte-scale satellite archives in a cloud environment (Gorelick et al., 2017 ). 1.3. Research Gaps Four gaps in the literature shape the present study. First, most multi-decadal GrIS melt area records rely on passive-microwave data; few studies derive bare-ice zone extent from MODIS NDSI with strict ice masking to exclude ocean and tundra pixels. Second, how sensitive PDD–bare-ice correlations are to the inclusion or removal of extreme blocking years has rarely been directly tested. Third, a combined GEE workflow using MODIS, ERA5-Land, ArcticDEM, and Landsat across a full 25-year record has not been documented as a reusable analytical pipeline. Fourth, the smallest trend detectable at realistic GrIS melt variance has not been formally quantified through power analysis in this context. 1.4. Objectives To fill these gaps this study pursues five objectives: (1) quantify annual bare-ice zone extent across the western GrIS ablation zone from 2000 to 2024 using MODIS NDSI restricted to ice-sheet pixels; (2) compute summer PDD from ERA5-Land hourly data over ice-sheet pixels and test for a temporal trend; (3) measure the PDD–bare-ice correlation and assess its robustness by removing documented extreme blocking years; (4) map pixel-wise melt duration trends across the study domain; and (5) build and document a fully reproducible open-access GEE workflow combining all four datasets. 2. Study Area Our study area, which covers around 2.5 million km2 of western Greenland and nearby non-glacier terrain, is located between 600 N to 800 W. We included an icesheet proxy 1,524,897 km² within this box to make sure that all melt calculations were restricted to verified ice surface. This is roughly 89% of the entire Greenland extent according to BedMachine V3 (Morlighem et al., 2017 ) placing the total glaciated area at rough 1.71 million km2. The remaining ~ 11% are located outside the domain, primarily along the northern and eastern borders. A significant amount of inner ice is directed towards the western coastline via the (Mouginot et al., 2019 ). Climate wise, the domain changes from relatively moderate coastal sub-arctic conditions around the southwest ice edge, when summer near surface temperature frequently rises over 0 0 C to cold continental polar conditions in the deep interior. The bare-ice zone has expanded with each melted season because of the ELA’s gradual upslope migration over the past few decades (Ryan et al.). On the western flank, supraglacial lakes are primarily found between 900 1400 meters, where meltwater cannot penetrate the fin column due to underlying impermeable glacier ice (Williamson et al., 2017 ). 3. Data and Datasets 3.1. MODIS MOD10A1 Snow Cover — Bare-Ice Zone Definition Daily snow cover data came from MODIS MOD10A1 Collection 6.1 (GEE asset: MODIS/061/MOD10A1), which stores NDSI at 500 m resolution as integers from 0 to 100; multiplying by 0.01 gives the fractional NDSI (Hall and Riggs, 2016 ). Cloud-contaminated pixels were removed by keeping only those with NDSI_Snow_Cover_Basic_QA = 0 or 1. Annual seasonal median composites were built from all cloud-cleared June–September images. Bare-ice pixels were flagged at NDSI < 0.4 (Hall and Riggs, 2016 ), marking surfaces where the seasonal snowpack has fully ablated and bare glacier ice is exposed. It is worth stressing that this threshold captures a much smaller and more ablation-specific area than passive-microwave total melt extents (e.g. Tedesco et al., 2011; Nghiem et al., 2012 ), which blend bare-ice and wet-snow signals and typically yield 100,000–900,000 km². The bare-ice areas in this study (1,375–11,033 km² annually; mean 4,820 km²) are consistent with published MODIS-based estimates for the western GrIS (Ryan et al., 2019 ). 3.2. ERA5-Land Hourly Temperature — Positive Degree Days Summer PDD were derived from ERA5-Land hourly 2-m air temperature (GEE asset: ECMWF/ERA5_LAND/HOURLY), using the formulation of Hock ( 2003 ) validated over the GrIS by Muñoz-Sabater et al. ( 2021 ). Temperatures were converted from Kelvin to Celsius; PDD was then calculated as the sum of positive hourly temperatures divided by 24, giving units of °C-days. Spatial averaging was confined to ice-sheet proxy mask pixels only, avoiding dilution from ocean surface temperatures (typically 5–10°C along the western coast in summer) or snow-free tundra, either of which would pull the computed PDD below the true thermal forcing at the ice surface. 3.3. ArcticDEM V4 and Ice-Sheet Proxy Mask Terrain data came from the ArcticDEM V4 two-metre mosaic (GEE asset: UMN/PGC/ArcticDEM/V4/2m_mosaic; Noh and Howat, 2015 ). The ice-sheet proxy mask was defined by two spatial filters: (1) elevation above 200 m a.s.l., removing open ocean and most coastal tundra; and (2) median NDSI > 0.1 from a summer 2010 MODIS composite, removing snow-free high-elevation features such as nunataks and bedrock outcrops. Cross-checking against the formal BedMachine V3 ice-sheet boundary (Morlighem et al., 2017 ) confirmed that this mask captures roughly 89% of total GrIS area, amounting to 1,524,897 km². We subsequently derived surface slope and aspect from the ArcticDEM V4 mosaic using the Horn ( 1981 ) finite-difference algorithm, then exported both terrain layers as GeoTIFFs at 500 m resolution in the EPSG:3413 Polar Stereographic North projection. 3.4. Landsat 8 OLI — Supraglacial Lake Detection Landsat 8 Collection 2 Tier 1 Level-2 surface reflectance (GEE asset: LANDSAT/LC08/C02/T1_L2) was used for qualitative supraglacial lake mapping. Scenes with cloud cover above 20% were discarded; cloud and shadow pixels were masked using QA_PIXEL bits 3 and 4. The Normalised Difference Water Index (NDWI) was computed from scaled green (Band 3) and near-infrared (Band 5) reflectances, with NDWI > 0.2 taken as open water. Continental-scale vectorisation of lake polygons at 30 m was not feasible within standard GEE memory limits; NDWI composites for 2015 and 2024 were instead exported to Google Drive as qualitative spatial indicators of lake distribution. Table 1 Satellite datasets used in this study, all processed within Google Earth Engine. Dataset GEE Asset Resolution Variable Extracted Period MODIS MOD10A1 C6.1 MODIS/061/MOD10A1 500 m daily NDSI, bare-ice extent 2000–2024 ERA5-Land Hourly ECMWF/ERA5_LAND/HOURLY ~ 9 km hourly 2-m air temperature → PDD 2000–2024 ArcticDEM V4 UMN/PGC/ArcticDEM/V4/2m_mosaic 2 m (mosaic) Elevation, slope, aspect Reference Landsat 8 OLI C2 LANDSAT/LC08/C02/T1_L2 30 m NDWI, supraglacial lakes 2015, 2024 4. Methodology 4.1. Bare-Ice Zone Extent For each year, all cloud-cleared MODIS MOD10A1 images from June to September were combined into a seasonal median NDSI composite. Pixels with NDSI < 0.4 inside the ice-sheet proxy mask were classified as bare ice. Annual bare-ice extent was then calculated by summing pixel areas via the GEE pixelArea() function at 500 m resolution, with outputs converted from square metres to km². 4.2. Melt Duration Melt duration was tracked at the pixel level by classifying every cloud-cleared daily MODIS image during the melt season as bare-ice (NDSI < 0.4, within the ice mask) or snow-covered. Summing the binary daily flags through each season gave annual melt duration in days per pixel. Basin-mean melt duration was obtained by averaging over all ice-sheet proxy mask pixels. A pixel-wise OLS linear trend was then fitted across the 25 annual melt duration images using the GEE linearFit() reducer, returning slopes in days per year. 4.3. Positive Degree Days and Potential Melt PDD was computed from ERA5-Land hourly temperatures restricted to ice-sheet mask pixels, following Hock ( 2003 ). Potential melt was estimated as: potential melt (m w.e.) = PDD × DDF / 1000, with a degree-day factor (DDF) of 8 mm °C⁻¹ day⁻¹ for glacier ice (van den Broeke et al., 2011 ). Applying a single uniform DDF is a recognised simplification; site-specific measurements across the western GrIS ablation zone span roughly 6 to 10 mm °C⁻¹ day⁻¹, with the spread attributable to differences in elevation, surface type, and varying degrees of debris and biological impurities on the ice. 4.4. Terrain Analysis Slope and aspect grids were generated from the ArcticDEM V4 mosaic within the GEE environment by calling ee.Terrain.slope() and ee.Terrain.aspect(), both of which apply the Horn ( 1981 ) finite-difference algorithm internally. The resulting terrain layers were then exported to Google Drive as GeoTIFF files, resampled to 500 m spatial resolution and referenced to the EPSG:3413 Polar Stereographic North coordinate system. 4.5. Statistical Analysis and Power Assessment Temporal trends in annual bare-ice extent, basin-mean PDD, and melt duration were examined with two complementary methods: (1) OLS linear regression, reporting slope, R², and two-tailed p-value; and (2) the Mann-Kendall non-parametric trend test (Mann, 1945 ; Kendall, 1975 ), reporting Kendall’s τ and p-value via the pymannkendall library (Hussain and Mahmud, 2019 ). A significance level of α = 0.05 was used throughout. Pearson correlation coefficients between summer PDD and annual bare-ice extent were computed for two subsets: (i) the full 25-year record (n = 25) and (ii) a 21-year record excluding four extreme blocking years — 2010, 2012, 2016, and 2019 — to test whether the PDD–melt coupling is a genuine physical signal or an outlier effect. A power analysis was then run to contextualise the null trend results. With n = 25, residual standard deviation σ = 2,778 km², and OLS slope standard error of 77.0 km²/yr, the minimum detectable trend at 80% power (α = 0.05, two-tailed) is roughly 216 km²/yr. Any real forced trend below this cannot be statistically identified within a 25-year record at the observed interannual variance, whether or not it is present. 5. Results 5.1. Bare-Ice Zone Extent (2000–2024) Annual bare-ice extent ranged from 1,375 km² (2018) to 11,033 km² (2012), with a 25-year mean of 4,820 km² (Table 2 ). These figures match MODIS-based bare-ice estimates from Ryan et al. ( 2019 ) and should not be compared with passive-microwave total melt areas, which are typically 50–100 times larger because they include wet-snow zones. OLS regression returned a trend of + 12.5 km²/yr (p = 0.878, R² = 0.001); the Mann-Kendall test likewise found no significant monotonic change (τ = 0.020, p = 0.907). As noted in Section 4.5 , the 25-year record can detect only trends exceeding ~ 216 km²/yr at 80% power, so the null result does not rule out a real but smaller forced trend. Pronounced interannual variability dominates the series: the four highest bare-ice years — 2012 (11,033 km²), 2016 (10,361 km²), 2010 (9,620 km²), and 2019 (9,419 km²) — all correspond to documented blocking events (Tedesco et al., 2011; Nghiem et al., 2012 ). The two lowest years were 2018 (1,375 km²) and 2015 (1,746 km²), both cool and cloud-heavy summers. 5.2. Melt Duration (2000–2024) With a 25-year mean of 0.307 days, the basin mean melt duration varied from 0.195 days (2018) to 0.469 days (2012) (Table 2 ). These do not equal melt-day totals at any one pixel; rather, they are spatially averaged fractional melt days across all ice – sheet pixels, including core region where bare – ice classification is unknown. The pixel-wise OLS trend was − 0.001 days/yr (p = 0.612), with no significant basin-wide directional change. Spatial heterogeneity is nonetheless present: coastal south-western pixels below ~ 1,000 m show positive trends reflecting lengthening bare-ice seasons at the ice margin, while interior pixels above ~ 1,500 m show near-zero or slightly negative trends consistent with persistent dry-snow or percolation-zone conditions. This spatial contrast is broadly consistent with the upward ELA shift documented by Ryan et al. ( 2019 ), whereby the retreating snowline progressively uncovers low-albedo glacier ice at elevations that were previously snow-covered through much of the summer. 5.3. Positive Degree Days (2000–2024) Basin-mean summer PDD ranged from 38.5°C-days (2018) to 65.8°C-days (2012), with a 25-year mean of 47.8°C-days. OLS regression yielded a near-zero trend of + 0.07°C-days/yr (p = 0.728), and the Mann-Kendall test equally showed no significant monotonic shift (τ = 0.020, p = 0.728). Not surprisingly, the two warmest summers — 2012 at 65.8°C-days and 2010 at 60.5°C-days — align with the well-documented anticyclonic blocking episodes described by Nghiem et al. ( 2012 ) and Tedesco et al. (2011). Potential melt estimated through the degree-day model spanned 0.308 m w.e. in 2018 to 0.527 m w.e. in 2012, with a 25-year mean of 0.383 m w.e. These estimates fall comfortably within the range of field-based ablation stake records collected at comparable elevations across the western ablation zone (van den Broeke et al., 2016 ), lending confidence to ERA5-Land PDD as a credible thermal forcing proxy. 5.4. PDD–Melt Extent Correlation and Sensitivity Analysis Over the course of 25-year period, there was a substantial correlation between summer PDD and annual bear ice extent (r = 0.814, p = 7.23 × 10⁻⁷), with the thermal forcing explaining around 66% of the interannual bear – ice variance. The association remained significant (r = 0.521, p = 0.016) when the four severe blocking years (2010, 2012, 2016, 2019; n = 21) were eliminated from the analysis. The indicates that the PDD – bare – ice coupling is a true physical signal throughout the whole melt intensity and is not a result of outlier years. Anticyclonic blocking drives both PDD and bare – ice extent upward concurrently, so eliminating these co-elevated pairings weakness but does not break the connection, which explain the physical decline from r = 0.814 to r = 0.521. PDD still accounts for around 27% of bare – ice variance in the absence of blocking years; the residual considers energy- balance considerations beyond the degree – day method, albedo feedback, incoming shortwave radiation, and aerosol loading (Box et al. 2012 ). 5.5. Melt Change Maps The endpoint binary change map (2024 minus 2000) identifies spatial patterns in bare-ice occurrence between the two bounding years of the study period. South-western coastal pixels register positive values (+ 1), identifying locations classified as bare ice in 2024 but not in 2000. Interior regions record no change (0). A limited number of pixels register negative values (− 1), consistent with 2000 being a comparatively active melt year at those locations relative to 2024. This two-date comparison is an illustrative spatial indicator only; given the dependence on single-year endpoint composites, it should not be interpreted as a formal trend estimate equivalent to the pixel-wise OLS analysis. Figure 6 presents binary bare-ice classifications for the two endpoint years (2000 and 2024) and the resulting pixel-level change map (panel c). Visual contrast across all three panels is inherently limited by the sparse areal coverage of bare-ice pixels relative to the full ice-sheet proxy domain; with a 25-year mean bare-ice extent of 4,820 km² against a total domain of 1,524,897 km², bare-ice pixels constitute approximately 0.3% of the mapped area, reducing their visibility at the printed scale. Panel (c) reveals that endpoint change is spatially heterogeneous across the western ablation zone, with pixels newly classified as bare ice in 2024 (+ 1) and pixels that reverted to snow-covered conditions between endpoint years (− 1) both present. It is noted that the endpoint change map reflects conditions in two individual annual composites subject to interannual variability rather than a monotonic trend signal; formal trend analysis over the full 25-year record is presented in Section 5.1 . Table 2 Complete annual time series (2000–2024) of bare-ice zone extent, melt duration, summer PDD, and potential melt. Summary statistics and trend results are provided below the annual data. Year Bare-Ice Extent (km²) Melt Duration (days) PDD (°C-days) Potential Melt (m w.e.) 2000 1,972 0.348 44.5 0.356 2001 3,045 0.238 42.9 0.343 2002 4,203 0.269 43.0 0.344 2003 3,984 0.282 52.7 0.422 2004 3,560 0.279 44.9 0.359 2005 8,448 0.364 45.9 0.367 2006 3,125 0.274 45.7 0.365 2007 7,430 0.389 50.8 0.406 2008 3,398 0.265 46.7 0.374 2009 2,477 0.222 42.0 0.336 2010 9,620 0.447 60.5 0.484 2011 5,559 0.352 47.0 0.376 2012 11,033 0.469 65.8 0.527 2013 3,072 0.304 40.8 0.326 2014 4,151 0.320 51.7 0.414 2015 1,746 0.222 43.3 0.346 2016 10,361 0.431 52.4 0.419 2017 2,852 0.268 42.7 0.341 2018 1,375 0.195 38.5 0.308 2019 9,419 0.404 58.8 0.471 2020 4,150 0.267 44.2 0.353 2021 5,009 0.308 51.8 0.414 2022 3,221 0.253 47.8 0.382 2023 4,041 0.277 49.9 0.399 2024 3,260 0.233 41.5 0.332 Mean 4,820 0.307 47.8 0.383 Min 1,375 (2018) 0.195 (2018) 38.5 (2018) 0.308 (2018) Max 11,033 (2012) 0.469 (2012) 65.8 (2012) 0.527 (2012) OLS Slope + 12.5 km²/yr −0.001 days/yr + 0.07°C-days/yr — OLS p-value 0.878 0.612 0.728 — MK τ (p) 0.020 (0.907) — 0.020 (0.728) — Table 3 Summary of statistical results including full-record and sensitivity test (extreme years excluded) correlation analyses, and power analysis parameters. Test / Parameter Metric Value OLS Regression Bare-ice trend (km²/yr) + 12.5 OLS Regression R² 0.001 OLS Regression p-value 0.878 Mann-Kendall Kendall's τ 0.020 Mann-Kendall p-value 0.907 OLS Regression PDD trend (°C-days/yr) + 0.07 OLS Regression PDD p-value 0.728 Pearson (full, n = 25) r (PDD–melt) 0.814 Pearson (full, n = 25) p-value 7.23 × 10⁻⁷ Pearson (excl. blocking, n = 21) r (PDD–melt) 0.521 Pearson (excl. blocking, n = 21) p-value 0.016 Power Analysis Min detectable trend (80% power) ~ 216 km²/yr Power Analysis Residual SD (σ) 2,778 km² 6. Discussion 6.1. Interpreting the Absence of Statistically Significant Trends The absence of a significant trend in bare-ice extent (p = 0.878) or basin-mean summer PDD (p = 0.728) over 2000–2024 does not mean the GrIS is stable or that surface melt is unchanging. The power analysis in Section 4.5 shows that only trends exceeding ~ 216 km²/yr are detectable at the observed interannual variance with n = 25 years. A slower forced signal — for example, ELA-driven bare-ice expansion of 50–100 km²/yr — would remain invisible to both OLS and Mann-Kendall at this record length. This is consistent with the broader GrIS mass-balance literature: Mouginot et al. ( 2019 ) and Bamber et al. ( 2019 ) report accelerating total GrIS mass loss from GRACE/GRACE-FO gravity data that integrates all loss processes. GRACE-derived mass loss of ~ 200–300 Gt yr⁻¹ includes dynamic discharge and basal melt alongside surface ablation; the bare-ice NDSI metric captures only surface exposure and cannot be directly compared with gravity-based mass balance. The two findings are mutually compatible: GRACE confirms large-scale ongoing mass loss, while interannual surface bare-ice variability is governed mainly by the North Atlantic Oscillation and Greenland Blocking Index (Tedesco et al., 2016 ), both of which impose variance that dwarfs any detectable forced linear trend over 25 years. 6.2. PDD–Melt Correlation: Physical Interpretation and Robustness The full-record PDD–bare-ice correlation (r = 0.814) is the study's principal finding, and it is notably higher than values typically obtained when degree-day models are compared against total melt area inclusive of wet-snow zones (Hock, 2003 ). Physically, this is unsurprising: bare-ice exposure is controlled largely by whether enough heat has accumulated to strip away the seasonal snowpack, making it a more direct and responsive thermal indicator than passive-microwave melt extent, which also integrates radiative and turbulent fluxes over wet-snow surfaces. What we consider particularly noteworthy is that a statistically significant relationship persists even after excluding the four most anomalous blocking years (r = 0.521, p = 0.016), ruling out the possibility that the correlation is simply an artefact of the 2010 and 2012 extremes. The decline from r = 0.814 to r = 0.521 upon removing those years is physically explicable: anticyclonic blocking simultaneously drives both PDD and bare-ice extent sharply upward, so discarding these co-elevated pairs reduces the apparent correlation without eliminating it. In non-blocking years, PDD still accounts for around 27% of bare-ice variance, reflecting a steady background thermal control that operates independently of large-scale circulation anomalies. The remaining variance is almost certainly driven by incoming shortwave radiation variability, surface albedo feedbacks, aerosol loading, and additional energy-balance processes that fall outside the degree-day framework (Box et al., 2012 ; Tedesco et al., 2016 ). 6.3. Comparison with Published Bare-Ice and Melt Studies The bare-ice extents in this study (1,375–11,033 km²; mean 4,820 km²) are in close agreement with Ryan et al. ( 2019 ), who found similar bare-ice magnitudes and spatial patterns in the western GrIS from combined MODIS and Landsat data and noted a northward shift of bare-ice zones over time. The high bare-ice years of 2012 and 2010 match directly with the findings of Nghiem et al. ( 2012 ) and Tedesco et al. (2011), independently validating the MODIS time series at the event level. The non-significant PDD trend is consistent with Muñoz-Sabater et al. ( 2021 ), who found strong interannual temperature variability in ERA5-Land over Arctic regions. Potential melt estimates (mean 0.383 m w.e.; range 0.308–0.527 m w.e.) are broadly in line with ablation stake records at similar elevations in the western ablation zone (van den Broeke et al., 2011 , 2016 ). 6.4. Uncertainties and Limitations Several limitations apply. First, the 500 m MODIS pixel size prevents detection of sub-pixel bare-ice patches, and seasonal median compositing may miss short-duration melt events in cloud-heavy years. Second, our elevation-plus-NDSI proxy mask, while covering ~ 89% of the GrIS per BedMachine V3, is not a rigorously defined ice boundary; in practice it likely incorporates a small proportion of high-elevation tundra and nunatak surfaces while leaving out parts of the coastal ice margin. Third, applying a spatially uniform DDF of 8 mm °C⁻¹ day⁻¹ smooths over real melt efficiency variation; published DDF values across the western ablation zone range from 6 to 10 mm °C⁻¹ day⁻¹ (van den Broeke et al., 2011 ). Fourth, ERA5-Land at ~ 9 km resolution cannot capture sharp temperature gradients near outlet glacier termini. Fifth, continental-scale Landsat lake vectorisation was not feasible within standard GEE compute limits; NDWI rasters for 2015 and 2024 are qualitative spatial indicators only. Sixth, the 25-year record restricts trend detection to signals above ~ 216 km²/yr, capping conclusions about gradual but real changes in bare-ice zone extent. 6.5. Future Research Directions Several avenues warrant further investigation. Incorporating the NSIDC passive-microwave total melt area dataset alongside the MODIS bare-ice time series would enable a direct side-by-side evaluation of these methodologically distinct melt metrics, situating our results more clearly within the broader GrIS melt literature. Adding the MODIS MCD43A3 broadband shortwave albedo product to the GEE pipeline would allow the albedo–melt feedback loop — widely recognised as central to GrIS energy balance (Box et al., 2012 ; Tedesco et al., 2016 ) — to be monitored explicitly rather than inferred indirectly from NDSI data. Substituting our elevation-based proxy mask with the formal BedMachine V3 ice-sheet boundary (Morlighem et al., 2017 ) would improve the spatial integrity of the analysis and make comparisons with GRACE/GRACE-FO gravity-derived mass-balance estimates more straightforward (Mouginot et al., 2019 ). Finally, pushing the time series back to 1979 using either passive-microwave melt reconstructions or downscaled climate model fields would embed the 2000–2024 results within the longer centennial warming trajectory described in IPCC ( 2021 ), offering a more complete perspective on how the observed interannual variability relates to the broader multi-decadal warming signal. 7. Conclusions This study measured bare-ice zone extent, melt duration, and positive degree days across the western GrIS ablation zone from 2000 to 2024 using four open-access satellite datasets processed entirely in Google Earth Engine. Six main conclusions emerge. First, bare-ice extent (NDSI < 0.4, ice-sheet pixels only) ranged from 1,375 km² (2018) to 11,033 km² (2012), mean 4,820 km²; these figures reflect bare-ice exposure only and are not comparable to passive-microwave total melt area, which includes wet-snow zones and is typically one to two orders of magnitude larger. Second, no significant linear trend in bare-ice extent was found over 2000–2024 (+ 12.5 km²/yr, p = 0.878, R² = 0.001; Mann-Kendall: τ = 0.020, p = 0.907); power analysis shows trends below ~ 216 km²/yr are unresolvable at the observed interannual variance with n = 25, so this is a detection limit, not evidence of physical stasis. Third, basin-mean summer PDD showed no significant trend (+ 0.07°C-days/yr, p = 0.728), consistent with interannual atmospheric circulation variability dominating any forced temperature signal over 2000–2024. Fourth — the principal result — summer PDD and annual bare-ice extent were strongly correlated over the full record (r = 0.814, p = 7.23 × 10⁻⁷); this relationship held after removing four extreme blocking years (r = 0.521, p = 0.016, n = 21), confirming a real PDD–melt coupling across the full melt intensity range, not an outlier artefact. Thermal forcing accounts for ~ 66% of interannual bare-ice variance, supporting ERA5-Land PDD as a robust near-real-time monitoring proxy. Fifth, pixel-level melt duration mapping exposed spatial structure that is masked by the basin-mean statistics: south-western coastal areas at lower elevations are experiencing measurably longer bare-ice seasons, while higher-elevation interior grid cells show trends near zero or weakly negative, a pattern in keeping with the ELA-driven upslope migration of the ablation zone described by Ryan et al. ( 2019 ). Sixth, the study produced a fully reproducible, open-access GEE analytical pipeline that integrates MODIS MOD10A1, ERA5-Land, ArcticDEM V4, and Landsat 8 under a common processing framework, providing a practical template that can be updated annually or adapted for other cryosphere monitoring applications. Declarations Declaration of Competing Interest The authors declare no competing financial or personal interests that could have influenced the work reported in this paper. Funding Statement This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Author Contributions Janwale Asaram: Conceptualization, GEE coding, data processing. Savita Mohurle: Statistical analysis, writing — original draft, Richa Purohit: revision, Supervision, methodology review, writing — review and editing. Minal Deshmukh: Data Curation, Validation. Mayur Deshmukh : Visualization, Project Admiration. Acknowledgements The authors thank NASA Earthdata for MODIS MOD10A1, ECMWF/Copernicus for ERA5-Land, USGS for Landsat 8, and the Polar Geospatial Center (PGC) for ArcticDEM V4. All satellite processing used the Google Earth Engine cloud computing platform (Gorelick et al., 2017). The GEE analysis code is available from the corresponding author on reasonable request. Data Availability Statement All datasets used in this study are publicly available: MODIS MOD10A1 ( https://earthdata.nasa.gov ); ERA5-Land ( https://cds.climate.copernicus.eu ); Landsat 8 ( https://earthexplorer.usgs.gov ); ArcticDEM V4 ( https://www.pgc.umn.edu/data/arcticdem ). The GEE analysis code is available from the corresponding author on reasonable request. References Bamber, J.L., Oppenheimer, M., Kopp, R.E., Aspinall, W.P., Cooke, R.M., 2019. Ice sheet contributions to future sea-level rise from structured expert judgment. Proc. Natl. Acad. Sci. USA 116(23), 11195–11200. https://doi.org/10.1073/pnas.1817205116 Box, J.E., Fettweis, X., Stroeve, J.C., Tedesco, M., Hall, D.K., Steffen, K., 2012. Greenland ice sheet albedo feedback: thermodynamics and atmospheric drivers. Cryosphere 6(4), 821–839. https://doi.org/10.5194/tc-6-821-2012 Gorelick, N., Hancher, M., Dixon, M., Ilyushchenko, S., Thau, D., Moore, R., 2017. Google Earth Engine: planetary-scale geospatial analysis for everyone. Remote Sens. Environ. 202, 18–27. https://doi.org/10.1016/j.rse.2017.06.031 Hall, D.K., Riggs, G.A., 2016. MODIS/Terra Snow Cover Daily L3 Global 500m SIN Grid, Version 6. NASA National Snow and Ice Data Center DAAC. https://doi.org/10.5067/MODIS/MOD10A1.006 Hock, R., 2003. Temperature index melt modelling in mountain areas. J. Hydrol. 282(1–4), 104–115. https://doi.org/10.1016/S0022-1694(03)00257-9 Horn, B.K.P., 1981. Hill shading and the reflectance map. Proc. IEEE 69(1), 14–47. https://doi.org/10.1109/PROC.1981.11918 Hussain, M., Mahmud, I., 2019. pyMannKendall: a python package for non-parametric Mann Kendall family of trend tests. J. Open Source Softw. 4(39), 1556. https://doi.org/10.21105/joss.01556 IPCC, 2021. Climate Change 2021: The Physical Science Basis. Cambridge University Press, Cambridge. https://doi.org/10.1017/9781009157896 Kendall, M.G., 1975. Rank Correlation Methods, 4th ed. Charles Griffin, London. Mann, H.B., 1945. Nonparametric tests against trend. Econometrica 13(3), 245–259. https://doi.org/10.2307/1907187 Morlighem, M., et al., 2017. BedMachine v3: complete bed topography and ocean bathymetry mapping of Greenland from multibeam echo sounding combined with mass conservation. Geophys. Res. Lett. 44(21), 11051–11061. https://doi.org/10.1002/2017GL074954 Mouginot, J., et al., 2019. Forty-six years of Greenland Ice Sheet mass balance from 1972 to 2018. Proc. Natl. Acad. Sci. USA 116(19), 9239–9244. https://doi.org/10.1073/pnas.1904242116 Muñoz-Sabater, J., et al., 2021. ERA5-Land: a state-of-the-art global reanalysis dataset for land applications. Earth Syst. Sci. Data 13(9), 4349–4383. https://doi.org/10.5194/essd-13-4349-2021 Nghiem, S.V., et al., 2012. The extreme melt across the Greenland ice sheet in 2012. Geophys. Res. Lett. 39(20), L20502. https://doi.org/10.1029/2012GL053611 Noh, M.J., Howat, I.M., 2015. Automated stereo-photogrammetric DEM generation at high latitudes: SETSM validation and demonstration over glaciated regions. GIScience Remote Sens. 52(2), 198–217. https://doi.org/10.1080/15481603.2015.1008621 Ryan, J.C., Smith, L.C., van As, D., Cooley, S.W., Cooper, M.G., Pitcher, L.H., Hubbard, A., 2019. Greenland Ice Sheet surface melt amplified by snowline migration and bare ice exposure. Sci. Adv. 5(3), eaav3738. https://doi.org/10.1126/sciadv.aav3738 Tedesco, M., Fettweis, X., van den Broeke, M.R., van de Wal, R.S.W., Smeets, C.J.P.P., van de Berg, W.J., Serreze, M.C., Box, J.E., 2016. The role of albedo and accumulation in the 2010 melting record in Greenland. Environ. Res. Lett. 6(1), 014005. https://doi.org/10.1088/1748-9326/6/1/014005 van den Broeke, M.R., et al., 2011. Partitioning recent Greenland mass loss. Science 326(5955), 984\–986. https://doi.org/10.1126/science.1178176 van den Broeke, M.R., et al., 2016. On the recent contribution of the Greenland ice sheet to sea level change. Cryosphere 10(5), 1933\–1946. https://doi.org/10.5194/tc-10-1933-2016 Williamson, A.G., Arnold, N.S., Banwell, A.F., Willis, I.C., 2017. A fully automated supraglacial lake area and volume tracking algorithm (FAST): development and application using MODIS imagery of West Greenland. Remote Sens. Environ. 196, 113\–133. https://doi.org/10.1016/j.rse.2017.04.032 Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 05 May, 2026 Reviewers invited by journal 04 May, 2026 Editor invited by journal 30 Apr, 2026 Editor assigned by journal 29 Apr, 2026 First submitted to journal 26 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9498957","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":634422066,"identity":"0b5d2512-be0f-4eae-8b44-614d1c03b598","order_by":0,"name":"Asaram Janwale","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYBACxgYQWcAgx88OYhlYEKvFgMFYsucAiCFBrF0GDIkbZiSAWERoYW4/e0zih4EN4wbJ51c3/CiQYOBv707A77CevDTJHoM0ZnPpnLKbPUCHSZw5uwG/loYcsxs8BofZLGfnpAEZEkDv5BLQ0v/G7OYfg/88BjfPpAEZxGiZkWN2m8fggITBDfZjt4mzZcYb898yBskGkj05bLdlDCR4CPrFsD/H2PBNhV19P/vxZzff/LGR42/vJaClAc7kMQCTeJWDgDyCyf6AoOpRMApGwSgYmQAAN0lHJH7BC+YAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-5325-4165","institution":"Sri Balaji University Pune","correspondingAuthor":true,"prefix":"","firstName":"Asaram","middleName":"","lastName":"Janwale","suffix":""},{"id":634422067,"identity":"6d889436-b3c7-40e8-b2d1-7543f24bf3b5","order_by":1,"name":"Savita Mohurle","email":"","orcid":"","institution":"Sri Balaji University Pune","correspondingAuthor":false,"prefix":"","firstName":"Savita","middleName":"","lastName":"Mohurle","suffix":""},{"id":634422068,"identity":"ef2a9e03-a381-468f-94ca-8cc3e8b358f0","order_by":2,"name":"Richa Purohit","email":"","orcid":"","institution":"Sri Balaji University Pune","correspondingAuthor":false,"prefix":"","firstName":"Richa","middleName":"","lastName":"Purohit","suffix":""},{"id":634422069,"identity":"5638ede4-970e-4ba9-a071-519a5b8e206d","order_by":3,"name":"Minal Deshmukh","email":"","orcid":"","institution":"Sri Balaji University Pune","correspondingAuthor":false,"prefix":"","firstName":"Minal","middleName":"","lastName":"Deshmukh","suffix":""},{"id":634422070,"identity":"a0cbbaa4-aaea-4285-b531-124cf0a94bf4","order_by":4,"name":"Mayur Deshmukh","email":"","orcid":"","institution":"Vishwakarma University","correspondingAuthor":false,"prefix":"","firstName":"Mayur","middleName":"","lastName":"Deshmukh","suffix":""}],"badges":[],"createdAt":"2026-04-22 16:49:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9498957/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9498957/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109204764,"identity":"aa0861b6-7d51-46bc-a3fe-5e3ee5d0d555","added_by":"auto","created_at":"2026-05-13 15:02:04","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":45183,"visible":true,"origin":"","legend":"\u003cp\u003eWestern Greenland study area map. Red boundary denotes the bounding domain (60°N–80°N, 25°W–55°W); blue shading indicates the ice-sheet proxy mask (1,524,897 km², approximately 89% of total GrIS area). Major outlet glacier catchments (Jakobshavn, Russell, Leverett) are labelled. Background: ArcticDEM V4 hillshade. Projection: EPSG:3413 (NSIDC Polar Stereographic North).\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9498957/v1/714f1905f83ec882ddcd15c5.jpg"},{"id":109117910,"identity":"2d5d61ac-31aa-417c-bf35-e37536b4e7be","added_by":"auto","created_at":"2026-05-12 16:43:35","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":83523,"visible":true,"origin":"","legend":"\u003cp\u003eAnalytical workflow diagram showing input datasets (MODIS MOD10A1, ERA5-Land, ArcticDEM V4, Landsat 8), GEE preprocessing steps, ice-sheet proxy mask construction, annual extraction of bare-ice extent, melt duration, and PDD, statistical analysis (OLS regression and Mann-Kendall), PDD–melt Pearson correlation including sensitivity test, and GeoTIFF export to Google Drive.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9498957/v1/01c607acd074aa2948ce4c92.jpg"},{"id":109205063,"identity":"a3bf82b3-c392-4790-afe6-ab5609270328","added_by":"auto","created_at":"2026-05-13 15:03:13","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":76463,"visible":true,"origin":"","legend":"\u003cp\u003eAnnual bare-ice zone extent time series (2000–2024) derived from MODIS MOD10A1 NDSI \u0026lt; 0.4 (ice-sheet pixels only). Blue markers and connecting line show observed annual values; red dashed line shows OLS linear trend (+12.5 km²/yr, p = 0.878). Extreme atmospheric blocking years (2010, 2012, 2016, 2019) are labelled. Shaded band indicates ±1 standard deviation about the mean.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9498957/v1/70e568e14d314cb9a3aa36f2.jpg"},{"id":109117913,"identity":"70ed165b-74d7-4592-8686-0c480811dcb2","added_by":"auto","created_at":"2026-05-12 16:43:36","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":74064,"visible":true,"origin":"","legend":"\u003cp\u003ePixel-wise linear trend in annual melt duration (days/year, 2000–2024) derived from daily MODIS MOD10A1 ice-masked bare-ice classification. Warm colours (red/orange) indicate increasing melt season length; cool colours (blue) indicate stable or slightly decreasing duration. Projection: EPSG:3413.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9498957/v1/cdff1dfde4646b093fe31a35.jpg"},{"id":109205068,"identity":"936245b3-3021-419c-a946-dd94e7cced5e","added_by":"auto","created_at":"2026-05-13 15:03:15","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":110319,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Summer PDD time series (2000–2024) from ERA5-Land hourly temperature spatially averaged over ice-sheet proxy mask pixels, with OLS trend line (p = 0.728). (b) Scatter plot of summer PDD versus annual bare-ice zone extent: solid red regression line shows full-record relationship (r = 0.814, n = 25); dashed orange line shows relationship with extreme blocking years excluded (r = 0.521, n = 21). Points are colour-coded by year; extreme years (2010, 2012, 2016, 2019) are indicated by triangular markers.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9498957/v1/bcb0330d56e447d3665102f5.jpg"},{"id":109205065,"identity":"6e0c1eda-543b-41d1-a5f9-c24401578311","added_by":"auto","created_at":"2026-05-13 15:03:14","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":69634,"visible":true,"origin":"","legend":"\u003cp\u003eThree-panel melt map. (a) Binary bare-ice classification for 2000 (NDSI \u0026lt; 0.4, ice-masked). (b) Binary bare-ice classification for 2024. (c) Endpoint change map (2024 minus 2000): +1 = pixels newly classified as bare ice in 2024; 0 = no change between endpoint years; −1 = pixels classified as bare ice in 2000 but not 2024. Projection: EPSG:3413.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9498957/v1/35e85dcc67904426acbaf895.jpg"},{"id":109206684,"identity":"a44a01b4-12d3-436c-be09-016b74381170","added_by":"auto","created_at":"2026-05-13 15:15:19","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":742256,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9498957/v1/b1f22053-995a-4ab7-a58a-efbf241793fb.pdf"}],"financialInterests":"","formattedTitle":"Spatio-Temporal Analysis of Bare-Ice Melt Dynamics in the Western Greenland Ice Sheet (2000–2024)","fulltext":[{"header":"Highlights","content":"\u003cp\u003e\u0026bull; 25-year MODIS bare-ice record reveals strong PDD control (r\u0026nbsp;=\u0026nbsp;0.814) over western GrIS\u003c/p\u003e\n\u003cp\u003e\u0026bull; No significant bare-ice trend detectable over 25 years at observed GrIS melt variance\u003c/p\u003e\n\u003cp\u003e\u0026bull; Power analysis establishes ~216\u0026nbsp;km\u0026sup2;\u0026nbsp;a⁻\u0026sup1; minimum detectable trend at 80% power\u003c/p\u003e\n\u003cp\u003e\u0026bull; PDD\u0026ndash;bare-ice coupling robust after excluding atmospheric blocking years (r\u0026nbsp;=\u0026nbsp;0.521)\u003c/p\u003e\n\u003cp\u003e\u0026bull; Reproducible GEE workflow integrating MODIS, ERA5-Land, ArcticDEM V4 and Landsat 8\u003c/p\u003e"},{"header":"1. Introduction","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.1. Background and Motivation\u003c/h2\u003e \u003cp\u003eFull melting of the Greenland Ice Sheet (GrIS) would raise global mean sea levels by roughly 7.2 m (Bamber et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Surface melt and meltwater routing to the ocean currently drives approximately 50\u0026ndash;60% of total GrIS mass loss, making it the dominant ablation pathway along the western margin (Mouginot et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Multi-decadal satellite data reveal large year-to-year swings in melt intensity; the record ablation seasons of 2010 and 2012 have been attributed to persistent anticyclonic blocking above the ice sheet (Tedesco et al., 2011; Nghiem et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Identifying what governs this variability, and whether any forced long-term signal is emerging above the background atmospheric noise, is essential for improving GrIS mass-balance projections and their sea-level implications.\u003c/p\u003e \u003cp\u003eWhen the seasonal snowpack is fully gone across the western ablation zone, bare glacier ice is exposed directly to the atmosphere. Bare-ice albedo (roughly 0.2\u0026ndash;0.4) is far lower than fresh snow albedo (roughly 0.8), triggering a positive melt-albedo feedback that accelerates surface energy absorption and drives up ablation rates (Box et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Tedesco et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Bare-ice zone extent \u0026mdash; defined here as the area where NDSI falls below 0.4 \u0026mdash; therefore gives a more direct measure of active ablation than passive-microwave total melt area, which lumps bare-ice and wet-snow signals together. MODIS NDSI-based bare-ice extents for the western GrIS typically run from a few thousand km\u0026sup2; to roughly 15,000 km\u0026sup2; in high-melt years (Ryan et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), well below the 100,000\u0026ndash;900,000 km\u0026sup2; values from passive-microwave products.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e1.2. Review of Related Studies\u003c/h2\u003e \u003cp\u003eMODIS MOD10A1 computes NDSI from visible and shortwave-infrared reflectances, classifying surfaces as snow-free or bare ice where NDSI\u0026thinsp;\u0026lt;\u0026thinsp;0.4 (Hall and Riggs, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Positive degree days (PDD) \u0026mdash; the sum of temperatures above 0\u0026deg;C \u0026mdash; are a well-established thermal melt proxy (Hock, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2003\u003c/span\u003e) and anchor degree-day models with ice melt factors near 8 mm \u0026deg;C⁻\u0026sup1; day⁻\u0026sup1; (van den Broeke et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). ERA5-Land hourly reanalysis at ~\u0026thinsp;9 km resolution has been independently validated for near-surface temperature over the GrIS (Mu\u0026ntilde;oz-Sabater et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Record GrIS melt years are closely tied to persistent high-pressure blocking identified via a positive Greenland Blocking Index (Tedesco et al., 2011; Nghiem et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). During such events, albedo feedbacks from bare ice, cryoconite, and biological impurities further amplify ablation (Box et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Tedesco et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Supraglacial lake growth, hydrofracture drainage, and the resulting ice-flow acceleration add a dynamic dimension to this melt response (Williamson et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). The GEE platform has greatly extended the reach of continental-scale, multi-decadal cryosphere research by providing direct access to petabyte-scale satellite archives in a cloud environment (Gorelick et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e1.3. Research Gaps\u003c/h2\u003e \u003cp\u003eFour gaps in the literature shape the present study. First, most multi-decadal GrIS melt area records rely on passive-microwave data; few studies derive bare-ice zone extent from MODIS NDSI with strict ice masking to exclude ocean and tundra pixels. Second, how sensitive PDD\u0026ndash;bare-ice correlations are to the inclusion or removal of extreme blocking years has rarely been directly tested. Third, a combined GEE workflow using MODIS, ERA5-Land, ArcticDEM, and Landsat across a full 25-year record has not been documented as a reusable analytical pipeline. Fourth, the smallest trend detectable at realistic GrIS melt variance has not been formally quantified through power analysis in this context.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e1.4. Objectives\u003c/h2\u003e \u003cp\u003eTo fill these gaps this study pursues five objectives: (1) quantify annual bare-ice zone extent across the western GrIS ablation zone from 2000 to 2024 using MODIS NDSI restricted to ice-sheet pixels; (2) compute summer PDD from ERA5-Land hourly data over ice-sheet pixels and test for a temporal trend; (3) measure the PDD\u0026ndash;bare-ice correlation and assess its robustness by removing documented extreme blocking years; (4) map pixel-wise melt duration trends across the study domain; and (5) build and document a fully reproducible open-access GEE workflow combining all four datasets.\u003c/p\u003e \u003c/div\u003e"},{"header":"2. Study Area","content":"\u003cp\u003eOur study area, which covers around 2.5\u0026nbsp;million km2 of western Greenland and nearby non-glacier terrain, is located between 600 N to 800 W. We included an icesheet proxy 1,524,897 km\u0026sup2; within this box to make sure that all melt calculations were restricted to verified ice surface. This is roughly 89% of the entire Greenland extent according to BedMachine V3 (Morlighem et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) placing the total glaciated area at rough 1.71\u0026nbsp;million km2. The remaining\u0026thinsp;~\u0026thinsp;11% are located outside the domain, primarily along the northern and eastern borders. A significant amount of inner ice is directed towards the western coastline via the (Mouginot et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Climate wise, the domain changes from relatively moderate coastal sub-arctic conditions around the southwest ice edge, when summer near surface temperature frequently rises over 0 0 C to cold continental polar conditions in the deep interior. The bare-ice zone has expanded with each melted season because of the ELA\u0026rsquo;s gradual upslope migration over the past few decades (Ryan et al.). On the western flank, supraglacial lakes are primarily found between 900 1400 meters, where meltwater cannot penetrate the fin column due to underlying impermeable glacier ice (Williamson et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3. Data and Datasets","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1. MODIS MOD10A1 Snow Cover \u0026mdash; Bare-Ice Zone Definition\u003c/h2\u003e \u003cp\u003eDaily snow cover data came from MODIS MOD10A1 Collection 6.1 (GEE asset: MODIS/061/MOD10A1), which stores NDSI at 500 m resolution as integers from 0 to 100; multiplying by 0.01 gives the fractional NDSI (Hall and Riggs, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Cloud-contaminated pixels were removed by keeping only those with NDSI_Snow_Cover_Basic_QA\u0026thinsp;=\u0026thinsp;0 or 1. Annual seasonal median composites were built from all cloud-cleared June\u0026ndash;September images. Bare-ice pixels were flagged at NDSI\u0026thinsp;\u0026lt;\u0026thinsp;0.4 (Hall and Riggs, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), marking surfaces where the seasonal snowpack has fully ablated and bare glacier ice is exposed. It is worth stressing that this threshold captures a much smaller and more ablation-specific area than passive-microwave total melt extents (e.g. Tedesco et al., 2011; Nghiem et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), which blend bare-ice and wet-snow signals and typically yield 100,000\u0026ndash;900,000 km\u0026sup2;. The bare-ice areas in this study (1,375\u0026ndash;11,033 km\u0026sup2; annually; mean 4,820 km\u0026sup2;) are consistent with published MODIS-based estimates for the western GrIS (Ryan et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2. ERA5-Land Hourly Temperature \u0026mdash; Positive Degree Days\u003c/h2\u003e \u003cp\u003eSummer PDD were derived from ERA5-Land hourly 2-m air temperature (GEE asset: ECMWF/ERA5_LAND/HOURLY), using the formulation of Hock (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2003\u003c/span\u003e) validated over the GrIS by Mu\u0026ntilde;oz-Sabater et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Temperatures were converted from Kelvin to Celsius; PDD was then calculated as the sum of positive hourly temperatures divided by 24, giving units of \u0026deg;C-days. Spatial averaging was confined to ice-sheet proxy mask pixels only, avoiding dilution from ocean surface temperatures (typically 5\u0026ndash;10\u0026deg;C along the western coast in summer) or snow-free tundra, either of which would pull the computed PDD below the true thermal forcing at the ice surface.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.3. ArcticDEM V4 and Ice-Sheet Proxy Mask\u003c/h2\u003e \u003cp\u003eTerrain data came from the ArcticDEM V4 two-metre mosaic (GEE asset: UMN/PGC/ArcticDEM/V4/2m_mosaic; Noh and Howat, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). The ice-sheet proxy mask was defined by two spatial filters: (1) elevation above 200 m a.s.l., removing open ocean and most coastal tundra; and (2) median NDSI\u0026thinsp;\u0026gt;\u0026thinsp;0.1 from a summer 2010 MODIS composite, removing snow-free high-elevation features such as nunataks and bedrock outcrops. Cross-checking against the formal BedMachine V3 ice-sheet boundary (Morlighem et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) confirmed that this mask captures roughly 89% of total GrIS area, amounting to 1,524,897 km\u0026sup2;. We subsequently derived surface slope and aspect from the ArcticDEM V4 mosaic using the Horn (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1981\u003c/span\u003e) finite-difference algorithm, then exported both terrain layers as GeoTIFFs at 500 m resolution in the EPSG:3413 Polar Stereographic North projection.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Landsat 8 OLI \u0026mdash; Supraglacial Lake Detection\u003c/h2\u003e \u003cp\u003eLandsat 8 Collection 2 Tier 1 Level-2 surface reflectance (GEE asset: LANDSAT/LC08/C02/T1_L2) was used for qualitative supraglacial lake mapping. Scenes with cloud cover above 20% were discarded; cloud and shadow pixels were masked using QA_PIXEL bits 3 and 4. The Normalised Difference Water Index (NDWI) was computed from scaled green (Band 3) and near-infrared (Band 5) reflectances, with NDWI\u0026thinsp;\u0026gt;\u0026thinsp;0.2 taken as open water. Continental-scale vectorisation of lake polygons at 30 m was not feasible within standard GEE memory limits; NDWI composites for 2015 and 2024 were instead exported to Google Drive as qualitative spatial indicators of lake distribution.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSatellite datasets used in this study, all processed within Google Earth Engine.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDataset\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGEE Asset\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eResolution\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eVariable Extracted\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePeriod\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMODIS MOD10A1 C6.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMODIS/061/MOD10A1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e500 m daily\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNDSI, bare-ice extent\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2000\u0026ndash;2024\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eERA5-Land Hourly\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eECMWF/ERA5_LAND/HOURLY\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e~\u0026thinsp;9 km hourly\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2-m air temperature \u0026rarr; PDD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2000\u0026ndash;2024\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eArcticDEM V4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUMN/PGC/ArcticDEM/V4/2m_mosaic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2 m (mosaic)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eElevation, slope, aspect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLandsat 8 OLI C2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLANDSAT/LC08/C02/T1_L2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e30 m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNDWI, supraglacial lakes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2015, 2024\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Methodology","content":"\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Bare-Ice Zone Extent\u003c/h2\u003e \u003cp\u003eFor each year, all cloud-cleared MODIS MOD10A1 images from June to September were combined into a seasonal median NDSI composite. Pixels with NDSI\u0026thinsp;\u0026lt;\u0026thinsp;0.4 inside the ice-sheet proxy mask were classified as bare ice. Annual bare-ice extent was then calculated by summing pixel areas via the GEE pixelArea() function at 500 m resolution, with outputs converted from square metres to km\u0026sup2;.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Melt Duration\u003c/h2\u003e \u003cp\u003eMelt duration was tracked at the pixel level by classifying every cloud-cleared daily MODIS image during the melt season as bare-ice (NDSI\u0026thinsp;\u0026lt;\u0026thinsp;0.4, within the ice mask) or snow-covered. Summing the binary daily flags through each season gave annual melt duration in days per pixel. Basin-mean melt duration was obtained by averaging over all ice-sheet proxy mask pixels. A pixel-wise OLS linear trend was then fitted across the 25 annual melt duration images using the GEE linearFit() reducer, returning slopes in days per year.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Positive Degree Days and Potential Melt\u003c/h2\u003e \u003cp\u003ePDD was computed from ERA5-Land hourly temperatures restricted to ice-sheet mask pixels, following Hock (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2003\u003c/span\u003e). Potential melt was estimated as: potential melt (m w.e.)\u0026thinsp;=\u0026thinsp;PDD \u0026times; DDF / 1000, with a degree-day factor (DDF) of 8 mm \u0026deg;C⁻\u0026sup1; day⁻\u0026sup1; for glacier ice (van den Broeke et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Applying a single uniform DDF is a recognised simplification; site-specific measurements across the western GrIS ablation zone span roughly 6 to 10 mm \u0026deg;C⁻\u0026sup1; day⁻\u0026sup1;, with the spread attributable to differences in elevation, surface type, and varying degrees of debris and biological impurities on the ice.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e4.4. Terrain Analysis\u003c/h2\u003e \u003cp\u003eSlope and aspect grids were generated from the ArcticDEM V4 mosaic within the GEE environment by calling ee.Terrain.slope() and ee.Terrain.aspect(), both of which apply the Horn (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1981\u003c/span\u003e) finite-difference algorithm internally. The resulting terrain layers were then exported to Google Drive as GeoTIFF files, resampled to 500 m spatial resolution and referenced to the EPSG:3413 Polar Stereographic North coordinate system.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e4.5. Statistical Analysis and Power Assessment\u003c/h2\u003e \u003cp\u003eTemporal trends in annual bare-ice extent, basin-mean PDD, and melt duration were examined with two complementary methods: (1) OLS linear regression, reporting slope, R\u0026sup2;, and two-tailed p-value; and (2) the Mann-Kendall non-parametric trend test (Mann, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1945\u003c/span\u003e; Kendall, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1975\u003c/span\u003e), reporting Kendall\u0026rsquo;s τ and p-value via the pymannkendall library (Hussain and Mahmud, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). A significance level of α\u0026thinsp;=\u0026thinsp;0.05 was used throughout. Pearson correlation coefficients between summer PDD and annual bare-ice extent were computed for two subsets: (i) the full 25-year record (n\u0026thinsp;=\u0026thinsp;25) and (ii) a 21-year record excluding four extreme blocking years \u0026mdash; 2010, 2012, 2016, and 2019 \u0026mdash; to test whether the PDD\u0026ndash;melt coupling is a genuine physical signal or an outlier effect. A power analysis was then run to contextualise the null trend results. With n\u0026thinsp;=\u0026thinsp;25, residual standard deviation σ\u0026thinsp;=\u0026thinsp;2,778 km\u0026sup2;, and OLS slope standard error of 77.0 km\u0026sup2;/yr, the minimum detectable trend at 80% power (α\u0026thinsp;=\u0026thinsp;0.05, two-tailed) is roughly 216 km\u0026sup2;/yr. Any real forced trend below this cannot be statistically identified within a 25-year record at the observed interannual variance, whether or not it is present.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Results","content":"\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e5.1. Bare-Ice Zone Extent (2000\u0026ndash;2024)\u003c/h2\u003e \u003cp\u003eAnnual bare-ice extent ranged from 1,375 km\u0026sup2; (2018) to 11,033 km\u0026sup2; (2012), with a 25-year mean of 4,820 km\u0026sup2; (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). These figures match MODIS-based bare-ice estimates from Ryan et al. (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) and should not be compared with passive-microwave total melt areas, which are typically 50\u0026ndash;100 times larger because they include wet-snow zones. OLS regression returned a trend of +\u0026thinsp;12.5 km\u0026sup2;/yr (p\u0026thinsp;=\u0026thinsp;0.878, R\u0026sup2; = 0.001); the Mann-Kendall test likewise found no significant monotonic change (τ\u0026thinsp;=\u0026thinsp;0.020, p\u0026thinsp;=\u0026thinsp;0.907). As noted in Section \u003cspan refid=\"Sec17\" class=\"InternalRef\"\u003e4.5\u003c/span\u003e, the 25-year record can detect only trends exceeding\u0026thinsp;~\u0026thinsp;216 km\u0026sup2;/yr at 80% power, so the null result does not rule out a real but smaller forced trend. Pronounced interannual variability dominates the series: the four highest bare-ice years \u0026mdash; 2012 (11,033 km\u0026sup2;), 2016 (10,361 km\u0026sup2;), 2010 (9,620 km\u0026sup2;), and 2019 (9,419 km\u0026sup2;) \u0026mdash; all correspond to documented blocking events (Tedesco et al., 2011; Nghiem et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). The two lowest years were 2018 (1,375 km\u0026sup2;) and 2015 (1,746 km\u0026sup2;), both cool and cloud-heavy summers.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e5.2. Melt Duration (2000\u0026ndash;2024)\u003c/h2\u003e \u003cp\u003eWith a 25-year mean of 0.307 days, the basin mean melt duration varied from 0.195 days (2018) to 0.469 days (2012) (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). These do not equal melt-day totals at any one pixel; rather, they are spatially averaged fractional melt days across all ice \u0026ndash; sheet pixels, including core region where bare \u0026ndash; ice classification is unknown.\u003c/p\u003e \u003cp\u003eThe pixel-wise OLS trend was \u0026minus;\u0026thinsp;0.001 days/yr (p\u0026thinsp;=\u0026thinsp;0.612), with no significant basin-wide directional change. Spatial heterogeneity is nonetheless present: coastal south-western pixels below ~\u0026thinsp;1,000 m show positive trends reflecting lengthening bare-ice seasons at the ice margin, while interior pixels above ~\u0026thinsp;1,500 m show near-zero or slightly negative trends consistent with persistent dry-snow or percolation-zone conditions. This spatial contrast is broadly consistent with the upward ELA shift documented by Ryan et al. (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), whereby the retreating snowline progressively uncovers low-albedo glacier ice at elevations that were previously snow-covered through much of the summer.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003e5.3. Positive Degree Days (2000\u0026ndash;2024)\u003c/h2\u003e \u003cp\u003eBasin-mean summer PDD ranged from 38.5\u0026deg;C-days (2018) to 65.8\u0026deg;C-days (2012), with a 25-year mean of 47.8\u0026deg;C-days. OLS regression yielded a near-zero trend of +\u0026thinsp;0.07\u0026deg;C-days/yr (p\u0026thinsp;=\u0026thinsp;0.728), and the Mann-Kendall test equally showed no significant monotonic shift (τ\u0026thinsp;=\u0026thinsp;0.020, p\u0026thinsp;=\u0026thinsp;0.728). Not surprisingly, the two warmest summers \u0026mdash; 2012 at 65.8\u0026deg;C-days and 2010 at 60.5\u0026deg;C-days \u0026mdash; align with the well-documented anticyclonic blocking episodes described by Nghiem et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) and Tedesco et al. (2011). Potential melt estimated through the degree-day model spanned 0.308 m w.e. in 2018 to 0.527 m w.e. in 2012, with a 25-year mean of 0.383 m w.e. These estimates fall comfortably within the range of field-based ablation stake records collected at comparable elevations across the western ablation zone (van den Broeke et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), lending confidence to ERA5-Land PDD as a credible thermal forcing proxy.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e5.4. PDD\u0026ndash;Melt Extent Correlation and Sensitivity Analysis\u003c/h2\u003e \u003cp\u003eOver the course of 25-year period, there was a substantial correlation between summer PDD and annual bear ice extent (r\u0026thinsp;=\u0026thinsp;0.814, p\u0026thinsp;=\u0026thinsp;7.23 \u0026times; 10⁻⁷), with the thermal forcing explaining around 66% of the interannual bear \u0026ndash; ice variance. The association remained significant (r\u0026thinsp;=\u0026thinsp;0.521, p\u0026thinsp;=\u0026thinsp;0.016) when the four severe blocking years (2010, 2012, 2016, 2019; n\u0026thinsp;=\u0026thinsp;21) were eliminated from the analysis. The indicates that the PDD \u0026ndash; bare \u0026ndash; ice coupling is a true physical signal throughout the whole melt intensity and is not a result of outlier years. Anticyclonic blocking drives both PDD and bare \u0026ndash; ice extent upward concurrently, so eliminating these co-elevated pairings weakness but does not break the connection, which explain the physical decline from r\u0026thinsp;=\u0026thinsp;0.814 to r\u0026thinsp;=\u0026thinsp;0.521. PDD still accounts for around 27% of bare \u0026ndash; ice variance in the absence of blocking years; the residual considers energy- balance considerations beyond the degree \u0026ndash; day method, albedo feedback, incoming shortwave radiation, and aerosol loading (Box et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2012\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e5.5. Melt Change Maps\u003c/h2\u003e \u003cp\u003eThe endpoint binary change map (2024 minus 2000) identifies spatial patterns in bare-ice occurrence between the two bounding years of the study period. South-western coastal pixels register positive values (+\u0026thinsp;1), identifying locations classified as bare ice in 2024 but not in 2000. Interior regions record no change (0). A limited number of pixels register negative values (\u0026minus;\u0026thinsp;1), consistent with 2000 being a comparatively active melt year at those locations relative to 2024. This two-date comparison is an illustrative spatial indicator only; given the dependence on single-year endpoint composites, it should not be interpreted as a formal trend estimate equivalent to the pixel-wise OLS analysis. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e presents binary bare-ice classifications for the two endpoint years (2000 and 2024) and the resulting pixel-level change map (panel c). Visual contrast across all three panels is inherently limited by the sparse areal coverage of bare-ice pixels relative to the full ice-sheet proxy domain; with a 25-year mean bare-ice extent of 4,820 km\u0026sup2; against a total domain of 1,524,897 km\u0026sup2;, bare-ice pixels constitute approximately 0.3% of the mapped area, reducing their visibility at the printed scale. Panel (c) reveals that endpoint change is spatially heterogeneous across the western ablation zone, with pixels newly classified as bare ice in 2024 (+\u0026thinsp;1) and pixels that reverted to snow-covered conditions between endpoint years (\u0026minus;\u0026thinsp;1) both present. It is noted that the endpoint change map reflects conditions in two individual annual composites subject to interannual variability rather than a monotonic trend signal; formal trend analysis over the full 25-year record is presented in Section \u003cspan refid=\"Sec19\" class=\"InternalRef\"\u003e5.1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComplete annual time series (2000\u0026ndash;2024) of bare-ice zone extent, melt duration, summer PDD, and potential melt. Summary statistics and trend results are provided below the annual data.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eYear\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBare-Ice Extent (km\u0026sup2;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMelt Duration (days)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePDD (\u0026deg;C-days)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePotential Melt (m w.e.)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1,972\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.348\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e44.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.356\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3,045\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.238\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e42.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.343\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4,203\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.269\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e43.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.344\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3,984\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.282\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e52.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.422\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3,560\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.279\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e44.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.359\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8,448\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.364\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e45.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.367\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3,125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e45.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.365\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7,430\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.389\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e50.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.406\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3,398\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.265\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e46.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.374\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2,477\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.222\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e42.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.336\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9,620\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.447\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e60.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.484\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5,559\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.352\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e47.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.376\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11,033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.469\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e65.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.527\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3,072\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.304\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e40.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.326\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4,151\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e51.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.414\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1,746\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.222\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e43.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.346\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10,361\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.431\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e52.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.419\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2,852\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e 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\u003cp\u003e0.404\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e58.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.471\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4,150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.267\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e44.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.353\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5,009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.308\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e51.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.414\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3,221\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.253\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e47.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.382\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4,041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.277\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e49.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.399\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3,260\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.233\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e41.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.332\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4,820\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.307\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e47.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.383\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMin\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1,375 (2018)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.195 (2018)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e38.5 (2018)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.308 (2018)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMax\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11,033 (2012)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.469 (2012)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e65.8 (2012)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.527 (2012)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOLS Slope\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e+\u0026thinsp;12.5 km\u0026sup2;/yr\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.001 days/yr\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u0026thinsp;0.07\u0026deg;C-days/yr\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOLS p-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.878\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.612\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.728\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMK τ (p)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.020 (0.907)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.020 (0.728)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of statistical results including full-record and sensitivity test (extreme years excluded) correlation analyses, and power analysis parameters.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTest / Parameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMetric\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOLS Regression\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBare-ice trend (km\u0026sup2;/yr)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;12.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOLS Regression\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOLS Regression\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.878\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMann-Kendall\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKendall's τ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.020\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMann-Kendall\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.907\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOLS Regression\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePDD trend (\u0026deg;C-days/yr)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;0.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOLS Regression\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePDD p-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.728\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePearson (full, n\u0026thinsp;=\u0026thinsp;25)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003er (PDD\u0026ndash;melt)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.814\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePearson (full, n\u0026thinsp;=\u0026thinsp;25)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.23 \u0026times; 10⁻⁷\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePearson (excl. blocking, n\u0026thinsp;=\u0026thinsp;21)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003er (PDD\u0026ndash;melt)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.521\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePearson (excl. blocking, n\u0026thinsp;=\u0026thinsp;21)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.016\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePower Analysis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMin detectable trend (80% power)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e~\u0026thinsp;216 km\u0026sup2;/yr\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePower Analysis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eResidual SD (σ)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2,778 km\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"6. Discussion","content":"\u003cdiv id=\"Sec25\" class=\"Section2\"\u003e \u003ch2\u003e6.1. Interpreting the Absence of Statistically Significant Trends\u003c/h2\u003e \u003cp\u003eThe absence of a significant trend in bare-ice extent (p\u0026thinsp;=\u0026thinsp;0.878) or basin-mean summer PDD (p\u0026thinsp;=\u0026thinsp;0.728) over 2000\u0026ndash;2024 does not mean the GrIS is stable or that surface melt is unchanging. The power analysis in Section \u003cspan refid=\"Sec17\" class=\"InternalRef\"\u003e4.5\u003c/span\u003e shows that only trends exceeding\u0026thinsp;~\u0026thinsp;216 km\u0026sup2;/yr are detectable at the observed interannual variance with n\u0026thinsp;=\u0026thinsp;25 years. A slower forced signal \u0026mdash; for example, ELA-driven bare-ice expansion of 50\u0026ndash;100 km\u0026sup2;/yr \u0026mdash; would remain invisible to both OLS and Mann-Kendall at this record length. This is consistent with the broader GrIS mass-balance literature: Mouginot et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) and Bamber et al. (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) report accelerating total GrIS mass loss from GRACE/GRACE-FO gravity data that integrates all loss processes. GRACE-derived mass loss of ~\u0026thinsp;200\u0026ndash;300 Gt yr⁻\u0026sup1; includes dynamic discharge and basal melt alongside surface ablation; the bare-ice NDSI metric captures only surface exposure and cannot be directly compared with gravity-based mass balance. The two findings are mutually compatible: GRACE confirms large-scale ongoing mass loss, while interannual surface bare-ice variability is governed mainly by the North Atlantic Oscillation and Greenland Blocking Index (Tedesco et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), both of which impose variance that dwarfs any detectable forced linear trend over 25 years.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec26\" class=\"Section2\"\u003e \u003ch2\u003e6.2. PDD\u0026ndash;Melt Correlation: Physical Interpretation and Robustness\u003c/h2\u003e \u003cp\u003eThe full-record PDD\u0026ndash;bare-ice correlation (r\u0026thinsp;=\u0026thinsp;0.814) is the study's principal finding, and it is notably higher than values typically obtained when degree-day models are compared against total melt area inclusive of wet-snow zones (Hock, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2003\u003c/span\u003e). Physically, this is unsurprising: bare-ice exposure is controlled largely by whether enough heat has accumulated to strip away the seasonal snowpack, making it a more direct and responsive thermal indicator than passive-microwave melt extent, which also integrates radiative and turbulent fluxes over wet-snow surfaces. What we consider particularly noteworthy is that a statistically significant relationship persists even after excluding the four most anomalous blocking years (r\u0026thinsp;=\u0026thinsp;0.521, p\u0026thinsp;=\u0026thinsp;0.016), ruling out the possibility that the correlation is simply an artefact of the 2010 and 2012 extremes. The decline from r\u0026thinsp;=\u0026thinsp;0.814 to r\u0026thinsp;=\u0026thinsp;0.521 upon removing those years is physically explicable: anticyclonic blocking simultaneously drives both PDD and bare-ice extent sharply upward, so discarding these co-elevated pairs reduces the apparent correlation without eliminating it. In non-blocking years, PDD still accounts for around 27% of bare-ice variance, reflecting a steady background thermal control that operates independently of large-scale circulation anomalies. The remaining variance is almost certainly driven by incoming shortwave radiation variability, surface albedo feedbacks, aerosol loading, and additional energy-balance processes that fall outside the degree-day framework (Box et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Tedesco et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec27\" class=\"Section2\"\u003e \u003ch2\u003e6.3. Comparison with Published Bare-Ice and Melt Studies\u003c/h2\u003e \u003cp\u003eThe bare-ice extents in this study (1,375\u0026ndash;11,033 km\u0026sup2;; mean 4,820 km\u0026sup2;) are in close agreement with Ryan et al. (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), who found similar bare-ice magnitudes and spatial patterns in the western GrIS from combined MODIS and Landsat data and noted a northward shift of bare-ice zones over time. The high bare-ice years of 2012 and 2010 match directly with the findings of Nghiem et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) and Tedesco et al. (2011), independently validating the MODIS time series at the event level. The non-significant PDD trend is consistent with Mu\u0026ntilde;oz-Sabater et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), who found strong interannual temperature variability in ERA5-Land over Arctic regions. Potential melt estimates (mean 0.383 m w.e.; range 0.308\u0026ndash;0.527 m w.e.) are broadly in line with ablation stake records at similar elevations in the western ablation zone (van den Broeke et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2011\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec28\" class=\"Section2\"\u003e \u003ch2\u003e6.4. Uncertainties and Limitations\u003c/h2\u003e \u003cp\u003eSeveral limitations apply. First, the 500 m MODIS pixel size prevents detection of sub-pixel bare-ice patches, and seasonal median compositing may miss short-duration melt events in cloud-heavy years. Second, our elevation-plus-NDSI proxy mask, while covering\u0026thinsp;~\u0026thinsp;89% of the GrIS per BedMachine V3, is not a rigorously defined ice boundary; in practice it likely incorporates a small proportion of high-elevation tundra and nunatak surfaces while leaving out parts of the coastal ice margin. Third, applying a spatially uniform DDF of 8 mm \u0026deg;C⁻\u0026sup1; day⁻\u0026sup1; smooths over real melt efficiency variation; published DDF values across the western ablation zone range from 6 to 10 mm \u0026deg;C⁻\u0026sup1; day⁻\u0026sup1; (van den Broeke et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Fourth, ERA5-Land at ~\u0026thinsp;9 km resolution cannot capture sharp temperature gradients near outlet glacier termini. Fifth, continental-scale Landsat lake vectorisation was not feasible within standard GEE compute limits; NDWI rasters for 2015 and 2024 are qualitative spatial indicators only. Sixth, the 25-year record restricts trend detection to signals above ~\u0026thinsp;216 km\u0026sup2;/yr, capping conclusions about gradual but real changes in bare-ice zone extent.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec29\" class=\"Section2\"\u003e \u003ch2\u003e6.5. Future Research Directions\u003c/h2\u003e \u003cp\u003eSeveral avenues warrant further investigation. Incorporating the NSIDC passive-microwave total melt area dataset alongside the MODIS bare-ice time series would enable a direct side-by-side evaluation of these methodologically distinct melt metrics, situating our results more clearly within the broader GrIS melt literature. Adding the MODIS MCD43A3 broadband shortwave albedo product to the GEE pipeline would allow the albedo\u0026ndash;melt feedback loop \u0026mdash; widely recognised as central to GrIS energy balance (Box et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Tedesco et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) \u0026mdash; to be monitored explicitly rather than inferred indirectly from NDSI data. Substituting our elevation-based proxy mask with the formal BedMachine V3 ice-sheet boundary (Morlighem et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) would improve the spatial integrity of the analysis and make comparisons with GRACE/GRACE-FO gravity-derived mass-balance estimates more straightforward (Mouginot et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Finally, pushing the time series back to 1979 using either passive-microwave melt reconstructions or downscaled climate model fields would embed the 2000\u0026ndash;2024 results within the longer centennial warming trajectory described in IPCC (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), offering a more complete perspective on how the observed interannual variability relates to the broader multi-decadal warming signal.\u003c/p\u003e \u003c/div\u003e"},{"header":"7. Conclusions","content":"\u003cp\u003eThis study measured bare-ice zone extent, melt duration, and positive degree days across the western GrIS ablation zone from 2000 to 2024 using four open-access satellite datasets processed entirely in Google Earth Engine. Six main conclusions emerge. First, bare-ice extent (NDSI\u0026thinsp;\u0026lt;\u0026thinsp;0.4, ice-sheet pixels only) ranged from 1,375 km\u0026sup2; (2018) to 11,033 km\u0026sup2; (2012), mean 4,820 km\u0026sup2;; these figures reflect bare-ice exposure only and are not comparable to passive-microwave total melt area, which includes wet-snow zones and is typically one to two orders of magnitude larger. Second, no significant linear trend in bare-ice extent was found over 2000\u0026ndash;2024 (+\u0026thinsp;12.5 km\u0026sup2;/yr, p\u0026thinsp;=\u0026thinsp;0.878, R\u0026sup2; = 0.001; Mann-Kendall: τ\u0026thinsp;=\u0026thinsp;0.020, p\u0026thinsp;=\u0026thinsp;0.907); power analysis shows trends below ~\u0026thinsp;216 km\u0026sup2;/yr are unresolvable at the observed interannual variance with n\u0026thinsp;=\u0026thinsp;25, so this is a detection limit, not evidence of physical stasis. Third, basin-mean summer PDD showed no significant trend (+\u0026thinsp;0.07\u0026deg;C-days/yr, p\u0026thinsp;=\u0026thinsp;0.728), consistent with interannual atmospheric circulation variability dominating any forced temperature signal over 2000\u0026ndash;2024. Fourth \u0026mdash; the principal result \u0026mdash; summer PDD and annual bare-ice extent were strongly correlated over the full record (r\u0026thinsp;=\u0026thinsp;0.814, p\u0026thinsp;=\u0026thinsp;7.23 \u0026times; 10⁻⁷); this relationship held after removing four extreme blocking years (r\u0026thinsp;=\u0026thinsp;0.521, p\u0026thinsp;=\u0026thinsp;0.016, n\u0026thinsp;=\u0026thinsp;21), confirming a real PDD\u0026ndash;melt coupling across the full melt intensity range, not an outlier artefact. Thermal forcing accounts for ~\u0026thinsp;66% of interannual bare-ice variance, supporting ERA5-Land PDD as a robust near-real-time monitoring proxy. Fifth, pixel-level melt duration mapping exposed spatial structure that is masked by the basin-mean statistics: south-western coastal areas at lower elevations are experiencing measurably longer bare-ice seasons, while higher-elevation interior grid cells show trends near zero or weakly negative, a pattern in keeping with the ELA-driven upslope migration of the ablation zone described by Ryan et al. (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Sixth, the study produced a fully reproducible, open-access GEE analytical pipeline that integrates MODIS MOD10A1, ERA5-Land, ArcticDEM V4, and Landsat 8 under a common processing framework, providing a practical template that can be updated annually or adapted for other cryosphere monitoring applications.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eDeclaration of Competing Interest\u003c/h2\u003e \u003cp\u003eThe authors declare no competing financial or personal interests that could have influenced the work reported in this paper.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding Statement\u003c/h2\u003e \u003cp\u003eThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\u003ch2\u003eAuthor Contributions\u003c/h2\u003e \u003cp\u003eJanwale Asaram: Conceptualization, GEE coding, data processing. Savita Mohurle: Statistical analysis, writing \u0026mdash; original draft, Richa Purohit: revision, Supervision, methodology review, writing \u0026mdash; review and editing. Minal Deshmukh: Data Curation, Validation. Mayur Deshmukh : Visualization, Project Admiration.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThe authors thank NASA Earthdata for MODIS MOD10A1, ECMWF/Copernicus for ERA5-Land, USGS for Landsat 8, and the Polar Geospatial Center (PGC) for ArcticDEM V4. All satellite processing used the Google Earth Engine cloud computing platform (Gorelick et al., 2017). The GEE analysis code is available from the corresponding author on reasonable request.\u003c/p\u003e\u003ch2\u003eData Availability Statement\u003c/h2\u003e \u003cp\u003eAll datasets used in this study are publicly available: MODIS MOD10A1 (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://earthdata.nasa.gov\u003c/span\u003e\u003cspan address=\"https://earthdata.nasa.gov\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e); ERA5-Land (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://cds.climate.copernicus.eu\u003c/span\u003e\u003cspan address=\"https://cds.climate.copernicus.eu\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e); Landsat 8 (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://earthexplorer.usgs.gov\u003c/span\u003e\u003cspan address=\"https://earthexplorer.usgs.gov\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e); ArcticDEM V4 (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.pgc.umn.edu/data/arcticdem\u003c/span\u003e\u003cspan address=\"https://www.pgc.umn.edu/data/arcticdem\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). The GEE analysis code is available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBamber, J.L., Oppenheimer, M., Kopp, R.E., Aspinall, W.P., Cooke, R.M., 2019. Ice sheet contributions to future sea-level rise from structured expert judgment. Proc. Natl. Acad. Sci. USA 116(23), 11195\u0026ndash;11200. https://doi.org/10.1073/pnas.1817205116\u003c/li\u003e\n\u003cli\u003eBox, J.E., Fettweis, X., Stroeve, J.C., Tedesco, M., Hall, D.K., Steffen, K., 2012. Greenland ice sheet albedo feedback: thermodynamics and atmospheric drivers. Cryosphere 6(4), 821\u0026ndash;839. https://doi.org/10.5194/tc-6-821-2012\u003c/li\u003e\n\u003cli\u003eGorelick, N., Hancher, M., Dixon, M., Ilyushchenko, S., Thau, D., Moore, R., 2017. Google Earth Engine: planetary-scale geospatial analysis for everyone. Remote Sens. Environ. 202, 18\u0026ndash;27. https://doi.org/10.1016/j.rse.2017.06.031\u003c/li\u003e\n\u003cli\u003eHall, D.K., Riggs, G.A., 2016. MODIS/Terra Snow Cover Daily L3 Global 500m SIN Grid, Version 6. NASA National Snow and Ice Data Center DAAC. https://doi.org/10.5067/MODIS/MOD10A1.006\u003c/li\u003e\n\u003cli\u003eHock, R., 2003. Temperature index melt modelling in mountain areas. J. Hydrol. 282(1\u0026ndash;4), 104\u0026ndash;115. https://doi.org/10.1016/S0022-1694(03)00257-9\u003c/li\u003e\n\u003cli\u003eHorn, B.K.P., 1981. Hill shading and the reflectance map. Proc. IEEE 69(1), 14\u0026ndash;47. https://doi.org/10.1109/PROC.1981.11918\u003c/li\u003e\n\u003cli\u003eHussain, M., Mahmud, I., 2019. pyMannKendall: a python package for non-parametric Mann Kendall family of trend tests. J. Open Source Softw. 4(39), 1556. https://doi.org/10.21105/joss.01556\u003c/li\u003e\n\u003cli\u003eIPCC, 2021. Climate Change 2021: The Physical Science Basis. Cambridge University Press, Cambridge. https://doi.org/10.1017/9781009157896\u003c/li\u003e\n\u003cli\u003eKendall, M.G., 1975. Rank Correlation Methods, 4th ed. Charles Griffin, London.\u003c/li\u003e\n\u003cli\u003eMann, H.B., 1945. Nonparametric tests against trend. Econometrica 13(3), 245\u0026ndash;259. https://doi.org/10.2307/1907187\u003c/li\u003e\n\u003cli\u003eMorlighem, M., et al., 2017. BedMachine v3: complete bed topography and ocean bathymetry mapping of Greenland from multibeam echo sounding combined with mass conservation. Geophys. Res. Lett. 44(21), 11051\u0026ndash;11061. https://doi.org/10.1002/2017GL074954\u003c/li\u003e\n\u003cli\u003eMouginot, J., et al., 2019. Forty-six years of Greenland Ice Sheet mass balance from 1972 to 2018. Proc. Natl. Acad. Sci. USA 116(19), 9239\u0026ndash;9244. https://doi.org/10.1073/pnas.1904242116\u003c/li\u003e\n\u003cli\u003eMu\u0026ntilde;oz-Sabater, J., et al., 2021. ERA5-Land: a state-of-the-art global reanalysis dataset for land applications. Earth Syst. Sci. Data 13(9), 4349\u0026ndash;4383. https://doi.org/10.5194/essd-13-4349-2021\u003c/li\u003e\n\u003cli\u003eNghiem, S.V., et al., 2012. The extreme melt across the Greenland ice sheet in 2012. Geophys. Res. Lett. 39(20), L20502. https://doi.org/10.1029/2012GL053611\u003c/li\u003e\n\u003cli\u003eNoh, M.J., Howat, I.M., 2015. Automated stereo-photogrammetric DEM generation at high latitudes: SETSM validation and demonstration over glaciated regions. GIScience Remote Sens. 52(2), 198\u0026ndash;217. https://doi.org/10.1080/15481603.2015.1008621\u003c/li\u003e\n\u003cli\u003eRyan, J.C., Smith, L.C., van As, D., Cooley, S.W., Cooper, M.G., Pitcher, L.H., Hubbard, A., 2019. Greenland Ice Sheet surface melt amplified by snowline migration and bare ice exposure. Sci. Adv. 5(3), eaav3738. https://doi.org/10.1126/sciadv.aav3738\u003c/li\u003e\n\u003cli\u003eTedesco, M., Fettweis, X., van den Broeke, M.R., van de Wal, R.S.W., Smeets, C.J.P.P., van de Berg, W.J., Serreze, M.C., Box, J.E., 2016. The role of albedo and accumulation in the 2010 melting record in Greenland. Environ. Res. Lett. 6(1), 014005. https://doi.org/10.1088/1748-9326/6/1/014005\u003c/li\u003e\n\u003cli\u003evan den Broeke, M.R., et al., 2011. Partitioning recent Greenland mass loss. Science 326(5955), 984\\–986. https://doi.org/10.1126/science.1178176\u003c/li\u003e\n\u003cli\u003evan den Broeke, M.R., et al., 2016. On the recent contribution of the Greenland ice sheet to sea level change. Cryosphere 10(5), 1933\\–1946. https://doi.org/10.5194/tc-10-1933-2016\u003c/li\u003e\n\u003cli\u003eWilliamson, A.G., Arnold, N.S., Banwell, A.F., Willis, I.C., 2017. A fully automated supraglacial lake area and volume tracking algorithm (FAST): development and application using MODIS imagery of West Greenland. Remote Sens. Environ. 196, 113\\–133. https://doi.org/10.1016/j.rse.2017.04.032\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"acta-geophysica","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"agph","sideBox":"Learn more about [Acta Geophysica](http://link.springer.com/journal/11600)","snPcode":"11600","submissionUrl":"https://www.editorialmanager.com/agph/default2.aspx","title":"Acta Geophysica","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Greenland Ice Sheet, bare-ice zone, MODIS NDSI, ERA5-Land, positive degree days","lastPublishedDoi":"10.21203/rs.3.rs-9498957/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9498957/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBare-ice zone dynamics along the western Greenland Ice Sheet (GrIS) ablation zone (60\u0026deg;N\u0026ndash;80\u0026deg;N; 25\u0026deg;W\u0026ndash;55\u0026deg;W) were examined over a 25-year period from 2000 to 2024. Surface ablation accounts for over half of total annual GrIS mass loss, yet the interannual drivers of bare-ice extent remain incompletely characterised. Bare-ice pixels were identified where the Normalised Difference Snow Index (NDSI) dropped below 0.4, marking full seasonal snow ablation and direct glacier ice exposure. Four open-access datasets were processed in Google Earth Engine (GEE): MODIS MOD10A1 Collection 6.1, ERA5-Land hourly 2-m air temperature, ArcticDEM V4 two-metre mosaic, and Landsat 8 OLI for supraglacial lake mapping. All calculations were confined to an ice-sheet proxy mask covering 1,524,897 km\u0026sup2; (~\u0026thinsp;89% of GrIS). Annual bare-ice extent ranged from 1,375 km\u0026sup2; (2018) to 11,033 km\u0026sup2; (2012), with a 25-year mean of 4,820 km\u0026sup2;. OLS regression and the Mann-Kendall test (α\u0026thinsp;=\u0026thinsp;0.05) found no significant trend in bare-ice extent (+\u0026thinsp;12.5 km\u0026sup2;/yr, p\u0026thinsp;=\u0026thinsp;0.878) or summer positive degree days (PDD; +0.07\u0026deg;C-days/yr, p\u0026thinsp;=\u0026thinsp;0.728). A power analysis shows the minimum detectable trend at 80% power is roughly 216 km\u0026sup2;/yr, meaning slower forced changes are statistically unresolvable at this record length. Despite the null trend, summer PDD and annual bare-ice extent were strongly correlated across the full record (r\u0026thinsp;=\u0026thinsp;0.814, p\u0026thinsp;=\u0026thinsp;7.23 \u0026times; 10⁻⁷); this relationship stayed significant after removing four documented blocking years (r\u0026thinsp;=\u0026thinsp;0.521, p\u0026thinsp;=\u0026thinsp;0.016, n\u0026thinsp;=\u0026thinsp;21), pointing to thermal forcing as the dominant control on interannual bare-ice variability.\u003c/p\u003e","manuscriptTitle":"Spatio-Temporal Analysis of Bare-Ice Melt Dynamics in the Western Greenland Ice Sheet (2000–2024)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-12 16:43:31","doi":"10.21203/rs.3.rs-9498957/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2026-05-05T06:16:48+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-05T00:02:23+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Acta Geophysica","date":"2026-04-30T12:30:03+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-29T12:09:30+00:00","index":"","fulltext":""},{"type":"submitted","content":"Acta Geophysica","date":"2026-04-27T01:58:31+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"acta-geophysica","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"agph","sideBox":"Learn more about [Acta Geophysica](http://link.springer.com/journal/11600)","snPcode":"11600","submissionUrl":"https://www.editorialmanager.com/agph/default2.aspx","title":"Acta Geophysica","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d0744f6d-ca55-46fd-9c8d-24c45e4e120e","owner":[],"postedDate":"May 12th, 2026","published":true,"recentEditorialEvents":[{"type":"reviewerAgreed","content":"","date":"2026-05-05T06:16:48+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-05T00:02:23+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Acta Geophysica","date":"2026-04-30T12:30:03+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-29T12:09:30+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-12T16:43:31+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-12 16:43:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9498957","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9498957","identity":"rs-9498957","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}