Monitoring of glacier albedo from optical remote-sensing data : 1 application to seasonal and annual surface mass balances 2 quantification in the French Alps for the 2000-2015 period 3 4 5

Less than 0.25 % of the 250,000 glaciers inventoried in the Randolph Glacier Inventory (RGI V.5) are currently monitored with in situ measurements of surface mass balance. Increasing this archive is very challenging, especially using time-consuming methods based on in situ measurements, and complementary methods are required to quantify the surface mass balance of unmonitored glaciers. The current study relies on the so-called albedo method, based on the analysis of albedo maps retrieved from optical satellite imagery acquired since 2000 by the MODIS sensor, onboard of TERRA satellite. Recent studies revealed substantial relationships between summer minimum glacier-wide surface albedo and annual surface mass balance, because this minimum surface albedo is directly related to the accumulation-area ratio and the equilibrium-line altitude. On the basis of 30 glaciers located in the French Alps where annual surface mass balance are available, our study conducted on the period 2000–2015 confirms the robustness and reliability of the relationship between the summer minimum surface albedo and the annual surface mass balance. At the seasonal scale, the integrated summer surface albedo is significantly correlated with the summer surface mass balance of the six glaciers seasonally monitored. For the winter season, four of the six glaciers showed a significant correlation when linking the winter surface mass balance and the integrated winter surface albedo, using glacier-dependent thresholds to filter the albedo signal (threshold from 0.53 to 0.76). These results are promising to monitor both annual and seasonal glacier-wide surface mass balances of individual glaciers at a regional scale using optical satellite images. A sensitivity study on the computed cloud masks revealed a high confidence in the retrieved albedo maps, restricting the number of omission errors. Albedo retrieval artifacts have been detected for topographically incised glaciers, highlighting limitations in the shadows correction algorithm, although inter-annual comparisons are not affected by systematic errors.

images processing, threshold on the winter albedo signal).Section 2 presents the available 98 SMB datasets used for the comparison and describes briefly the in situ automatic weather 99 stations (AWS) used to assess the quality of MODIS retrieved albedo.The method to retrieve 100 albedo maps is described in Sect.3. Results are presented and discussed in Sect. 4 and 5.The 101 conclusion gathers the main results of the study and provides perspectives for future works.102 2 Study area and data 103

Site description 104
The study focuses on 30 glaciers located in the French Alps (Fig. 1).Each glacier can be 105 classified as mountain glacier, extending over an altitudinal range from around 1600 m a.s.l.106 (Argentière and Mer de Glace glaciers) to 4028 m a.s.l.(Blanc Glacier), and located between 107 the coordinates: 44°51" N to 46° N and 6°09" E to 7°08" E. The cumulative glacial coverage 108 considered in the present study is 136 km 2 , i.e. half of the glacier surface area covered by 593 109 inventoried glaciers over the French Alps for the period 2006-2009 (Gardent et al., 2014).110 Studied glaciers have been selected following four criteria related to the availability of field 111 data and remote sensing constraints, namely: (i) the annual glacier-wide SMB for the study 112 period had to be available; (ii) the glacier surface area had to be wide enough to allow robust 113 multi-pixel analysis; (iii) the glacier had to be predominantly free of debris to allow remotely-114 sensed observations of the albedo of snow and ice surfaces; and (iv) seasonal SMB records 115 had to be available to consider seasonal variability.Finally, 11 glaciers have been selected in 116 the Ecrins range, 14 in Vanoise and 5 in Mont-Blanc (Fig. 1, and listed Table 1).117 118 The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.

Figure 1 Map of the region of interest with the studied glaciers shown in red (numbers refer to 120
Table 1).The four AWS used in the present study were set up on Saint-Sorlin Glacier (n°20).121 Adapted from Rabatel et al. (2016).122 123

MODIS satellite images 124
The MODIS sensor, onboard the TERRA -EOS/AM-1 satellite is acquiring near-daily images 125 of the Earth since February 25 th , 2000.With 36 spectral bands ranging from 0.459 to 14.385 126 µm, and spatial resolution ranging from 0.25 to 1 km depending on the spectral band, MODIS 127 The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License. is nowadays one of the most used optical sensors for land surface observations.Because of its 128 short temporal revisit time, its long acquisition period and its moderate resolution, images 129 from MODIS are the most suitable for the present work.We therefore rely on about 15,000 130 MODIS calibrated Level 1B (L1B) swath images.131 132 Table 1: List of studied glaciers, characteristics and albedo/mass balance correlations over 133 2000-2015, except for seasonal coefficients (over 2000-2010).For localization, refer to Fig. 1. 134 Highlighted rows exhibit glaciers where annual and seasonal in situ glacier-wide SMB data are 135 available.The mask size is expressed in number of pixels.To obtain the glacier mask area in 136 km 2 , one should multiply the mask size by 0.0625 km 2 .Determination coefficients are 137 expressed for each glacier (full plotted results are shown in supplementary material).Note the 138 units of r 2 (%), RMSE, P 1 and P 2 (m w. e.).139 140

Surface mass balance data 141
In the French Alps, six glaciers allow both the seasonal and annual analyses to be conducted, 142 due to the availability of summer and winter SMB data ( 1).Among them, glacier-wide annual SMB b a of four glaciers (Argentière, Mer de 145 Glace, Gébroulaz and Saint-Sorlin glaciers) have also been calculated using the Lliboutry 146 approach (Lliboutry, 1974;Vincent, 2002;Vincent et al., 2000).The latter combines the 147 punctual in situ data and the glacier-wide surface elevation changes quantified from the 148 difference between DEM retrieved using aerial photogrammetry.In addition, glacier wide 149 annual SMB of the 30 studied glaciers were computed by Rabatel et al., 2016 using the end-150 of-summer snow line measured on optical remote-sensing images and the glacier-wide mass 151 change quantified from DEMs differencing.152 For the six glaciers where glacier-wide annual SMB are available from the two methods, i.e., 153 in situ and satellite measurements, the average of the two estimates was used to calibrate and 154 evaluate the albedo method.155

In situ albedo measurements 156
Albedo measurements acquired punctually using an AWS on Saint-Sorlin Glacier have been 157 used to evaluate the MODIS retrieved albedo.In situ albedo measurements were available for 158 reflection model for snow and ice has been preferred to the isotropic case, due to its closer 176 agreement with in situ measurements (Dumont et al., 2012).The MODImLab toolbox also 177 output sensor geometrical characteristics at the acquisition time such as the solar zenith angle 178 (SZA) and the observation zenith angle (OZA) used for post-processing the images (Sect.3.4).179 The MODImLab cloud detection algorithm is more conservative than the original MODIS 180 product (MOD35), and has been preferred as recommended in (Brun et al., 2015).181 The resulting number of pixels per glacier is listed in Table 1.205

Basis of the method 207
For glacier in the Alps (Dumont et al., 2012), the Himalayas (Brun et al., 2015) and in the 208 Southern Alps of New Zealand (Sirguey et al., 2016), the summer minimum glacier-wide 209 averaged albedo ( ) has been significantly correlated to the glacier-wide annual SMB.This 210 relation allowed the glacier-wide annual SMB reconstruction from satellite images on the 211 Brewster Glacier, New Zealand, over the period 2000-2014 (Sirguey et al., 2016).The 212 relationship between and glacier-wide SMB results from the fact that solar radiation is the 213 main source of energy for melting snow and ice, both at the surface and within the first 214 centimeters below the surface (Van As, 2011).But this is not sufficient to explain why 215 averaged surface albedo is suitable for monitoring glacier SMB.216 If we consider a temperate glacier in the mid-latitudes, its surface is fully covered by snow in 217 winter, leading to high and uniform surface albedo ( in Cuffey and Paterson, 2010).218 During the ablation season, the accumulation area is still covered with snow conversely to the 219 ablation area where the ice is exposed and sometimes covered by debris.The overall albedo of 220 the glacier surface is therefore decreasing over the course of the ablation season, providing 221 information on the ratio of these two areas.The ratio between the size of the accumulation or quantitatively (Dyurgerov et al., 2009).Therefore, assessing provides insights of the 225 relative share between the exposed ice and the snow-covered areas at the end of the ablation 226 season, also quantified by the AAR.227

From annual to seasonal surface mass balances 228
In this study, has been computed for the 30 glaciers in order to validate the method at a 229 has been computed without threshold over winter months (equivalent to ).Finally, 247 hundred thresholds ranging from 0 to 1 every 0.01 have been tested to assess the sensitivity of 248 the method to (discussed Sect.5).To compare each year together and remove the impact 249 of the variable integration time period for each glacier, both

Data filtering 260
MODIS offers the opportunity to get daily images, but retrieving daily maps of Earth surface 261 albedo remains challenging.Indeed, various sources of error require filtering the available 262 images in order to only capture physical changes of the observed surface and not artifacts.263 Clouds are known to be a major problem in optical remote sensing of the Earth surface 264 especially in the case of ice and snow covered surfaces.Even if some algorithms exist to 265 differentiate clouds and snow-covered areas (e.g., Ackerman et al., 1998;Sirguey et al., 2009), 266 omission errors are difficult to avoid, leading to erroneous albedo of the surface.267 In this study, all images with a presence of cloud greater than 30% of the total glacier surface 268 area have been discarded.This threshold is higher than that chosen in Brun et al. (2015) on the 269 Chhota Shigri Glacier (20%), and we thus discuss Sect.5.1 the impact of the computed cloud 270 threshold on the derived albedo results.When determining , 0% of cloud cover has been 271 imposed as a condition and visual check for each year and each glacier has been performed.272 Snapshots from the fusion of MODIS bands 1 to 3 and from bands 4 to 6 (Sirguey et al., 2009) 273 have been used to visually check the images, together with images from other satellites 274 (mostly from the Landsat archive) and pictures and comments from mountaineering forums.275 This last step, although laborious when studying 30 glaciers allowed the identification of the 276 summer minimum to be improved.Visual check of the images also confirms that projected 277 shadows of clouds are not affecting the albedo map.Another source of error is the impact of 278 the OZA.As mentioned in Sirguey et al. (2016), accuracy of the MODIS retrieved albedo 279 strongly decreases for viewing angles above 45° as pixel size increases from 2 to 5-folds from 280 OZA = 45° to 66° (Wolfe et al., 1998).This phenomenon is accentuated when observing 281 steep-sided snow/ice surfaces, surrounded by contrasted surfaces (rocks, forests, lakes...).This 282 distortion could lead to capture the mean albedo of a glacier plus its surroundings.Following 283 this, we decided to filter the images according to their OZA angle, as further described Sect.worth reminding some differences between the in situ measured albedo data and the one 291 retrieved using MODIS.The downward facing pyranometer stands at around 1 m above the 292 surface, corresponding to a monitored footprint of ca.300 m 2 (theoretical value for a flat 293 terrain) while the pixel area of MODImLab products matches 62,500 m 2 .Quantified albedos 294 from each method are therefore not representative of the same area.On the other hand, 295 incoming radiation data are extremely sensitive to a tilt of the sensor located on the AWS and 296 maintaining a constant angle throughout the monitoring period remains challenging, especially 297 during the ablation season.For instance, a tilt of 5° of the pyranometer at the summer solstice 298 can increase by 5% the error on the irradiance measurement (Bogren et al., 2016).No sensor 299 tilt was deployed on the AWS, thus preventing the application of tilt-correction methods (e.g., 300 Wang et al., 2016).Nonetheless, regular visit allowed to maintain the sensor horizontal and to 301 limit errors in the irradiance measurements.In Fig. 3, the spread between MODIS and AWS albedos is higher for low albedos (i.e.ablation 322 area).This is related to the footprint difference as described earlier, accentuating the albedo 323 differences when monitoring heterogeneous surface (snow patches, melt pounds…), even 324 more pronounced in summer.One can also note that MODIS albedo often over-estimate the 325 AWS albedo value.This over-estimation could be explained by: (1) the MODImLab albedo 326 retrieval algorithm.Indeed, under-estimation of the incoming radiation computed in the 327 MODImLab algorithm would lead to over-estimated retrieved albedo values, in addition the 328 atmospheric corrections used to compute the incident radiation could be hypothesized as 329 source of error (e.g.modeled transmittance through a simplified computed atmosphere, refer 330 to (Sirguey et al., 2009) for further description); (2) the AWS albedo measurements.Indeed, 331 view angles of AWS pyranometers (170°) could influence the retrieved albedo by monitoring 332 out-of-glacier features (e.g.moraines, rock walls, ...), resulting in under-estimated albedo 333 values.However, it is worth noting that most of the points are within the combined uncertainty 334 of both sensors and these differences in albedo retrieved from MODIS and the AWS are thus 335 hard to interpret.336 Finally, Fig. 3 shows substantial differences between OZA<10° and other OZA classes.For 337 OZA<10, MODIS albedos better agree with AWS albedos than for the three other classes.338 Integrating MODIS images with OZA>10° substantially deteriorate the agreement with AWS 339 albedos (in term of r 2 , RMSE and the slope P 1 MODIS ), especially on "narrow" targets as alpine 340 mountain glaciers.We therefore chose to prioritize images acquired with low OZA to avoid 341 detection of non-glacierized surfaces.Therefore, four classes of images have been selected 342 following the criteria presented in Table 2. 343 where stands for the standard deviation of the pixels albedo with N the number of pixels.352

Temporal variability of the albedo signal
observed that the albedo decreases from the beginning of summer (dashed red line), reaching 357 in August/September and rising again at the end of September.This cyclicality is a proxy 358 of surface processes.The snow cover decreases at the beginning of summer until reaching its 359 lowest extent, and finally increases again with the first snowfall in late summer to reach its 360 maximum extent in winter/spring.361  The periodicity the albedo signal is however not so well defined for some of the studied 369 glaciers.For instance, Argentière Glacier exhibits a severe drop of in winter, reaching 370 values as low as summer minimums ( 0.4).The observed drop of albedo in winter occurs 371 during more than one month centered on the winter solstice (December 21 st ) and is observed within the three studied mountain ranges but have the common characteristic to be very 375 incised with steep and high surrounding faces.We studied the albedo series as a function of 376 the SZA to reveal possible shadowing on the observed surfaces.Figure 5 displays the same 377 cycle as Fig. 4 for Argentière Glacier but providing information about SZA.As a reminder, 378 the MODImLab white-sky albedo is independent of the illumination geometry but the 379 computed albedo for each pixel can be subject to shadowing from the surrounding topography.380 Two mains observations stands out from the winter part of the cycle in Fig. 5: (i

and annual surface mass balance 397
The summer minimum average albedo for each year and each glacier has been linearly 398 correlated to the glacier-wide annual SMB. Figure 6 illustrates the relationship between Twenty-seven glaciers show significant correlations (refer to Table 1 for full results) if 412 considering a risk of error of 5% (according to a Student's t test).However, the linear 413 correlation has no statistical significance for three glaciers with r 2 < 0.25.A possible 414 explanation is the high number of removed images in summer due to manually checked thin 415  the best correlation between the two variables, together with correlation coefficients.442 443 Saint-Sorlin Glacier, together with the five other seasonally surveyed glaciers showed a 444 significant correlation between the two observed variables (from r 2 = 0.46 to r 2 = 0.94 with an 445 error risk < 5%, all statistics referred in Table 1).Conversely to , is slightly more 446 robust to the presence of undetected clouds as its value does not rely on a single image.The 447 lowest correlation has been found for Talèfre Glacier.The latter accounts for a relatively large 448 debris-covered tongue that has been excluded when delineating the glacier mask (see 449 supplementary material).Consequently, the low correlation could be partly explained by this For Argentière, Mer de Glace and Gébroulaz glaciers, a significant correlation is found 469 whatever the value of the albedo threshold is (Table 3).Furthermore, is far from being 470 uniform on the six glaciers (0.53 0.76).We therefore reconsider the idea of using a 471 threshold as a representative value of fresh snowfall, as there is no physical reason that this 472 threshold varies, at least within the same region.In this section, we first discuss the impact of the threshold applied to the cloud cover fraction 479 on the obtained results.Then, the observed discrepancies and artifacts of the winter albedo 480 signal on some of the studied glaciers have been analyzed through a sensitivity study focused 481 on the algorithm correcting the shadows.Afterward, we discuss the sensitivity of the 482 correlation, between and b w , toward the selected albedo threshold .We finally express 483 the main limitations and assessments of the albedo method.484

Cloud coverage threshold 485
As stated in Sect.3.4, a value of 30% of cloud coverage over the glacier mask has been 486 defined as the acceptable maximum value for considering the albedo map of the day.We 487 computed a sensitivity study on the impact of this threshold on the value of the obtained 488 correlations between the integrated summer albedo and the in situ summer SMB.The summer 489 period has been chosen as it represents the period when the albedo of the glacier is the most 490 contrasted, between bare ice and snow/firn.The glacier-wide average albedo in this period is 491 therefore more sensitive to possible shading of a part of the glacier.Figure 9 illustrates the 492 results for the six seasonally surveyed glaciers.The used value of the allowed cloud coverage 493 appears not to have a substantial impact on the correlation.This observation first implies that 494 the MODImLab cloud product is reliable enough to only compute surface albedo and to avoid 495 too frequent misclassification between the clouds and the surface.It also suggests that 496 removing too many images because of partial cloud cover removes information about the 497 glacier-wide average albedo variability.However, allowing all images, even when the glacier-498 wide average albedo is computed on only 10% of the glacier (90% of detected cloud 499 coverage), does not reduce significantly the correlation for most of the six glaciers.500 501 Nevertheless, hypothesizing that the glacier-wide average albedo of a small fraction of the 508 glacier (e.g., 10%) is suitable to represent the entire glacierized surface is questionable.It 509 therefore depends on the size of the observed glacier, where 10% of a glacier of 3 and 30 km 2 510 have not the same meaning, but also on the delineated mask (ablation area not entirely 511 considered because of debris coverage...).The summer-integrated albedo is also highly 512 dependent on the time gap between useful images.In other words, if an image has an 513 "anomalous" glacier-wide average albedo because of high cloud coverage, the impact on the 514 integrated value will be smaller if "normal condition" albedos are monitored at nearby dates.515 The average number of available images per year does not largely differ between the various 516 computed cloud coverage thresholds.It varies in average from 95 to 123 images per summer 517 period for respectively 0% and 100% cloud coverage threshold.Intermediate values are 106, 518 111 and 116 images per summer for 30, 50 and 75% cloud coverage threshold, respectively.519 The difference in significance of r 2 (according to a Student's t test) between opting for 0% and 520 100% is almost negligible, and choosing the best cloud threshold value is rather a compromise 521 between the number of used images and the resulting correlation with glacier-wide SMB.We 522 finally concluded that selecting cloud coverage threshold to 30% presents the best 523 determination coefficients between the integrated summer albedo and the summer balance for 524 most of the six glaciers without losing too much temporal resolution.525

Evaluation of winter albedo values 526
In light of the documented dispersion on during some of the winter months on several 527 studied glaciers (Sect.4.2), sensitivity of the MODIS retrieved albedo against correction of 528 shadows had been assessed.This work has only been conducted on the 250 m resolution raster 529 products and specifically on the cast shadow product because self-shadow corrections can be 530 considered as reliable enough because only related to the DEM accuracy.We thus defined a 531 pixel as "corrected" when at least one of its sub-pixels was classified as shadowed.From then 532 on, two glacier-wide albedos have been defined: (i) non-cor computed on non-corrected 533 equal to the glacier-wide average albedo.Figure 10 illustrates the difference between non-cor 535 and as a function of the percentage of corrected pixels over the entire glacier.The study 536 was performed on Argentière Glacier (111 pixels) that exhibited large artifacts in winter 537 (Fig. 5).The inner diagram allows emphasizing the annual "cycle" of modeled shadows, 538 contrasted between nearly no cast shadows in summer and an almost fully shadowed surface 539 in winter.We represent the 1 standard deviation of , averaged by classes of 5% corrected 540 pixels.In other words, it illustrates the mean variability of the glacier-wide surface albedo.541 Therefore, for images with non-cor -within the interval defined by 1 st.dev. of , errors 542 resulting from the correction algorithm are smaller than the spatial variability of the glacier-543 wide albedo glacier.We also selected only significant values, following a normal distribution 544 of the averaged .Consequently, only values at ±1σ (68.2%) in term of percentage of 545 corrected pixel have been retained (i.e. when the relative share of corrected pixels ranged from 546 15.9 to 84.1%).Between 0 and 15.9%, non-cor and are not sufficiently independent 547 because of low number of corrected pixels, and beyond 84.1%, non-cor is computed over a too 548 small number of pixels.As a consequence, even if the albedo correction in the shadowed parts 549 of the glacier could be improved, most of the errors related to this correction do not depreciate 550 the results.Above 80% of corrected pixels (December to early February), differences between 551 non-cor and exceed the monitored spatial variability of .These anomalies are at the root 552 of the observed artifacts Fig. 5 by the severe drops of albedos and described Sect.This could be explained by different localizations of shadowed area for a given ratio of 565 corrected pixel.As an example, a glacier could have in October a snow-and shadow-free 566 snout and a covered by fresh snow and shadowed upper section.This configuration would 567 induce a negative difference as we observe from June to November.Conversely, this glacier 568 could present in March (same ratio of corrected pixels than October) a complete snow 569 On the other hand, correcting shadows accurately and consistently is extremely challenging.573 As illustrated by Fig. 10, a way to confidently consider the albedo signal is to exclude values 574 with too large share of corrected pixels.However, because of the inter-annual approach carried 575 out in this study, such systematic artifact is not depreciating the results but would be a major 576 issue on studies focused on albedo values themselves (e.g.maps of snow extents…).577

Evaluation of the winter albedo threshold 578
The albedo threshold, , for which the winter albedo signal is integrated is considered in 579 Sirguey et al. (2016) as representative of the presence of fresh snow at the glacier surface.In 580 order to study the impact of on the correlation between the winter integrated albedo and 581 the in situ winter SMB, we computed the r 2 considering 100 values of (from 0 to 1).582 provides the same threshold maximizing r 2 .For Argentière and Mer de Glace, using a 584 threshold does not drastically maximize the relation and the integral can be processed without 585 using a threshold.These two glaciers also provide the best correlation coefficients compared 586 to the other four glaciers and are by far the largest glaciers of our monitoring set (14.59 and 587 23.45 km 2 for Argentière and Mer de Glace glaciers respectively).Indeed, a possible 588 explanation of this good correlation, even without threshold, relies on the morpho-topographic 589 features on these two large glaciers.With a glacier snout reaching 1600 m a.s.l., the tongue of 590 these glaciers can experience melting events (resulting in contrasted pixels in terms of albedo 591 value), even during the winter season.The glacier-wide albedo therefore provides a good 592 proxy of the winter SMB on the glacier because of the large altitudinal range of the glacier.593 For Saint-Sorlin Glacier, a threshold of 0.76 improves significantly the correlation, similarly to 594 the threshold found for Brewster Glacier by Sirguey et al. (2016).We can mention the analogy 595 These results finally question the use of as a threshold detecting only fresh snowfall events 617 and seems to maximize artificially the correlation between b w and .Large glaciers (>10 618 km 2 ) appear to be more robust for threshold-free detection but further studies on a more 619 exhaustive set of large glaciers would be required.620 variable correlations in between morpho-topographic features could be for instance envisaged.632

Limits of the albedo method 621
Using the albedo method at a seasonal scale has shown promising results, especially for the 633 summer period where significant correlations have been found for the six seasonally 634 monitored glaciers.There is still in this approach a step to retrieve the seasonal SMB of an 635 unmonitored glacier with high confidence.The winter season has shown results that are for 636 now not entirely satisfactory.Glaciers that experience complete snow coverage during most of 637 the winter season showed the lowest correlation (r 2 ≤ 0.33) while the two glaciers showing the 638 best correlations are subject to some events of surface melting in their lower reaches, 639 particularly at the end of the winter season.Therefore, studying the albedo signal in winter 640 could record snowfall events but seems to be little sensitive to snowfall intensity.641 An additional approach has been carried out, aiming at retrieving b w by deduction from the 642 reconstructed b a and b s from the albedo signal.This approach, not using the winter albedo 643 signal, is poorly correlated (r 2 <0.16) to in situ b w for the six seasonally monitored glaciers.644 Indeed, the result extremely depends on the quality of the correlations between b a , b s and the 645 albedo signals.Saint-Sorlin Glacier is a good example, being one of the glaciers with the 646 highest correlations for the annual (r 2 = 0.86) and summer (r 2 = 0.94) SMB.Subtracting b s 647 from b a to computed b w leads to an average difference between computed and measured b w of 648 ±0.41 m w.e for the 10 simulated years.As a consequence, in case of low correlations between 649 SMB and albedo, errors in the computed winter SMB become exacerbated.650

Conclusion 651
In this study, we used the so-called albedo method to correlate annual and seasonal SMB to 652 glacier-wide average albedos obtained from MODIS images.This method has been carried on The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.performed using the MODImLab algorithm, and filters on the images have been applied, 655 removing images with more than 30% cloud coverage, and excluding images with satellite 656 observation angles greater than 30°.Quality assessment has been performed and close 657 agreement has been found between albedos from AWS installed on Glacier de Saint-Sorlin 658 and MODIS retrieved albedo values.Annual SMB have been significantly correlated to the 659 summer minimum albedo for 27 of the 30 selected glaciers, confirming this variable as a good 660 proxy of the glacier-wide annual SMB.For the six seasonally monitored glaciers, summer 661 SMB obtained from the glaciological method have been significantly linked to the integral of 662 the summer albedo.For the winter season, implementing an albedo threshold for computing 663 the winter integral of the albedo has substantially improved the determination coefficients but 664 no uniform threshold has been found for the six selected glaciers.Two small glaciers, Saint-665 Sorlin and Talèfre presented high correlation using albedo threshold, providing the 666 opportunity to reconstruct missing years or extending time series of these glaciers.Good 667 results have been obtained without using albedo thresholds in winter for Argentière and Mer 668 de Glace glaciers (>10 km 2 ) and further study would be required on a more exhaustive set of 669 large glaciers.We hence reconsider the idea proposed by Sirguey et al. (2016) of using albedo 670 thresholds to detect snow falls covering the glacier surface but albedo thresholds seem to 671 maximize artificially the correlation between winter SMB and winter integrated surface 672

albedo. 673
Sensitivity study on the impact of the considered cloud coverage has revealed a high 674 confidence in the MODImLab cloud algorithm, limiting pixel misclassifications, and a rather 675 high tolerance of the integrated signal to the number of partly cloud-covered images.This 676 confidence on cloud filters is very promising to document unmonitored glaciers.Correction of 677 shadows by the MODImLab algorithm has however revealed some limitations when a large 678 share of the glacier is shadowed by the surrounding topography (around winter solstice).
three periods in the ablation zone (July-August 2006; June-August 2008; June-September 159 2009) and for one period in the accumulation zone (June-September 2008).Albedo data from 160 these AWS have been calculated as the ratio of the reflected to incident shortwave radiation 161 (0.3 to 2.8 µm) using two Kipp and Zonen pyranometers.With a potential tilt of the instrument 162 with respect to surface melting and the intrinsic sensor accuracy (±3%, Six et al., 2009), the 163 calculated albedo at the AWS shows a ±10% accuracy (Kipp and Zonen, 2009; Dumont et al., 164 products 167 MODIS L1B images were processed using the MODImLab toolbox (Sirguey, 2009).Image 168 fusion between MOD02QKM bands 1 and 2 at 250 m resolution and MOD02HKM bands 3 to 169 The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.al., 2008).Then, atmospheric and topographic corrections are applied that include multiple 171 reflections due to steep surrounding topography (Sirguey, 2009).Various products are derived 172 from the corrected ground reflectance including snow and ice surface albedo (Dumont et al., 173 2012).As recommended by Dumont et al. (2012) the WhiteSky (WS) albedo (estimated value 174 of the surface albedo under only diffuse illumination) is considered.The use of an anisotropic 175 According to Dumont et al. (2012) and further assessed by (Sirguey et al., 2016) the overall 182 accuracy of MODImLab albedo product under clear-sky conditions is estimated at ±10%.183 To mitigate the impact of shadows over the glaciers, MODImLab uses a DEM from the 184 Shuttle Radar Topography Mission (SRTM -90 m resolution -acquired in 2000) to estimate 185 the sky obstruction by the surrounding topography and to correct the impact of shadows (see The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.and 11h10 AM UTC (+1h in winter and +2h in summer for local time conversion) were 198 selected to get minimum SZA and limit projected shadows of surrounding reliefs.199 3.2 Glacier masks 200 Following Dumont et al. (2012) and Brun et al. (2015), we manually created raster masks of 201 the 30 glaciers, based on the glaciers' outlines from 1985-87 (Rabatel et al., 2013) and high 202 spatial resolution (6 m) SPOT-6 images from 2014.All debris-covered areas, together with 203 mixed pixel (rock-snow/ice) have been removed to capture only the snow/ice albedo signal.204 The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.predictor of SMB both qualitatively (LaChapelle, 1962; Meier and Post, 1962; Mercer, 1961) 224

Figure 2 :
Figure 2: Schematic of a typical albedo cycle over one year, displaying parameters which 254 have been linked to annual, summer (between 1 st May and 30 th September in the northern 255 hemisphere) and winter (between 1 st October and 30 rd April in the northern hemisphere) SMB.256 284 4.1.285 αa min The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.albedo assessment 287 A quantitative evaluation of the retrieved albedo has been performed with AWS deployed on 288 Saint-Sorlin Glacier.Measurements have been synchronized between punctual albedo for 289 MODIS and a 2-hour averaged albedo around MODIS acquisition time for the AWS.It is 290 302 303 The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.

Figure 3 :
Figure 3: MODIS albedo and AWS albedo data for different OZA classes on Saint-Sorlin 305 Glacier.Years indicated in the caption correspond to the year of acquisition while subscripts 306 express the AWS location in the accumulation or ablation areas.The mean discrepancy 307 between MODIS and AWS albedo per OZA is quantified by the RSS (residual sum of square).308 Correlation coefficient per OZA classes are also provided, with r 2 , RMSE together with the 309 number of compared measurements (Nb), and coefficients of the equation: 310

Figure 3
Figure 3 illustrates the comparison between the retrieved and measured albedos at the AWS 317 locations for various OZA classes.One can note minor differences between the data plotted in 318 Fig. 3 and those presented in Dumont et al. (2012, Fig. 2).These differences are related to 319 changes in the MODImLab algorithm and different computation of the in situ albedo, 320 integrated over a two-hour period in the current study.321 The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.344 Table 2: Filtering the images from OZA values.345 346 For the rest of the computation, the absolute ±10% accuracy per pixel estimated in Dumont et 347 al. (2012) has been considered.We determined the uncertainty on by accounting for the 348 spatial variability of the albedo signal within the glacier and considering that our sets of pixels 349 are independent from each other (Eq.(3)): 350 Eq. (3) 351 ., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.

Figure 4 :
Figure 4: ~16-yr albedo course for Saint-Sorlin Glacier.Glacier-wide averaged albedo is 363 represented with the continuous black line.The green dots spot for each summer the minimum 364 average albedo, and have been manually checked for all years and glaciers.Dashed red and 365 blue lines stand for the beginning of the defined ablation and accumulation seasons (May and 366 October 1 st respectively).367 368

389 Figure 5 :
Figure 5: Albedo cycle for Argentière Glacier as a function of the SZA.Each point 390 corresponds to glacier-wide averaged albedo for each available image.The 16 years are 391 displayed.Color scale gives indication on the date of the used image.The thick grey line 392describes the weekly albedo averaged over the entire study period.For readability purpose, the 393 averaged albedo has been smoothed, using a 7 points running average.394

Figure 6 :
Figure 6: Annual SMB as a function of the MODIS retrieved summer minimum glacier-wide 406 average albedo for Blanc Glacier.Error bars result on the dispersion of the available annual 407 SMB data and on the quadratic sum of the systematic errors made on each albedo 408 measurement.The thin dashed grey line illustrates the line of best fit, along with regression 409 coefficients and significance.410 overlying clouds not detected by the MODImLab cloud algorithm.RM SE = 0.29 m w.e.σslope = 2.8 m w.e.σintercept = 1.1 m w.e.The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.Looking at the 27 glaciers for which significant relationships have been found, 2001 is 417 regularly identified as an outlier.According to existing SMB datasets, 2001 is the only year of 418 the period 2000-2015 for which the annual SMB has been positive for all the studied glaciers 419 (0.80 m w.e.yr -1 in average).Hence, according to computed determination coefficients in 420 Table 1, correctly predicting the surface mass balance values for the year 2001 using the 421 albedo method would imply to monitor a high value of minimum glacier-wide average albedo, 422 often greater than 0.7 (i.e.0.83 and 0.95 for Rochemelon and Vallonnet glaciers, respectively).423 Taking into consideration snow metamorphisms during the summer period, melting at the 424 surface and possible deposition of debris or dusts, monitoring such high albedo values 425 averaged at the glacier scale is unrealistic.Furthermore, removing 2001 from the time series 426 does not increase the number of glaciers for which the correlation is significant.427 Finally, this study confirms the robust correlation between and b a for 27 of the 30 studied 428 glaciers.It also reveals some limitations by under-estimating the annual SMB value for years 429 with very positive annual SMB.430 4.3.2 and summer surface mass balance 431 Studying the integral of the albedo signal during the ablation season can provide insights on 432 the intensity of the ablation season and thus on the summer SMB b s .As described in Sect.433 3.3.2,has been computed and connected to the in situ b s .Figure 7 illustrates the results 434 for Saint-Sorlin Glacier.435 αa min αs int αs int The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.

Figure 7 :
Figure 7: Summer SMB b s expressed as a function of the integrated albedo over the entire 437 ablation season for Saint-Sorlin Glacier.Error bars result from the uncertainties related to the 438 glaciological method (measurements and interpolation at the glacier scale of the punctual 439 measurements, ±20 cm w.e. in total), and on the quadratic sum of the systematic errors made 440 on each albedo measurement.Thin dashed grey line represents the linear regression showing 441

Figure 8 :
Figure 8: Winter SMB, b w , expressed as a function of the integrated albedo over the entire 462 accumulation season for Argentière Glacier.Winter SMB of 2001 corresponds to the winter 463 2000/2001.Error bars result from the uncertainties related to the glaciological method and on 464 the quadratic sum of the systematic errors made on each albedo measurement.Thin dashed 465 grey line represents the linear regression showing the best correlation between the two 466 variables, together with correlation coefficients.467

473 474 Table 3 :
Coefficients of determination for the relationship between the winter SMB b w and the 475 integrated winter albedo, computed with and without the albedo threshold .

Figure 9 :
Figure 9: r 2 for the six seasonally surveyed glaciers for the albedo summer integral versus 502 summer SMB relationship against the cloud threshold above which images have been 503 discarded during the summer season.For the computation, hundred thresholds have been 504 tested between 0 and 100%.The inner histogram illustrates the number of considered images 505 per summer and averaged on the six glaciers.506 The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.pixels only, classified as non-shadowed; (ii) of both corrected and non-corrected pixels, 534

Figure 10 :
Figure 10: Impact of the ratio of corrected pixels toward the difference between non-corrected 555 and glacier-wide albedo.Each point corresponds to one acquisition and the 16 years are 556 therefore displayed on this graph.Color scale gives indication on the date of the acquired 557 The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.coverage, leading to a smaller difference between non-cor and (<0.1) that could even result 570 on positive difference as we observe from February to April.571Finally, observed albedo artifacts in winter are most likely due to the correction of shadows.572

Figure 11
Figure 11 displays the computed results for the six seasonally surveyed glaciers.No glacier 583

Figure 11 :Figure 12 :
Figure 11: r 2 of the albedo winter integral versus winter SMB relationship as a function of 600 chosen for the winter integration for the six seasonally monitored glaciers.Hundred thresholds 601 have been tested between 0 and 1. 602 In agreement withDumont et al. (2012) andBrun et al. (2015), retrieving the glacier annual 622 SMB from albedo summer minimums proves to be an efficient method.Low correlations often 623 result from high and persistent cloud coverage during summer, reducing the chance of spotting 624 the albedo summer minimum.For SMB reconstruction purpose, a future line of research could 625 rest upon linking morpho-topographic features of the glacier such has glacier surface area, 626 mean altitude or slope to the regression coefficients of both annual and seasonal SMB vs. w.e.] r 2 = 0.44 bw = 6.7 ᾱint w -3.0 RM SE = 0.29 m w.e.σslope = 6.1 m w.e.σintercept = 4.1 m w.e.., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.albedo relationships, giving the opportunity to establish analogy between monitored and 628 unmonitored glaciers.Tests have been carried out but no significant and satisfying results have 629 been obtained, due to a presumably too heterogeneous data set, where large glaciers (>10 km 2 ) 630 and/or south-facing glaciers are largely under-represented.Larger scale studies and multi-631

The
Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.anissue for inter-annual studies, but would be a serious issue on studies focused on albedo 682 values themselves.683Using optical satellite images to estimate glacier surface processes and quantify annual and 684 seasonal SMB from the albedo cycle is therefore very promising and should be expanded to 685 further regions.Using images from different satellites, combining high spatial and temporal 686 resolution instruments, could substantially reduces uncertainties, especially for spotting the 687 albedo summer minimum with more confidence, but also to improve the temporal resolution.688This method could then in the short term, become reliable for retrieving SMB of monitored 689 and unmonitored glaciers.690 691 Acknowledgment 692 This study was conducted within the Service National d'Observation GLACIOCLIM.Equipex 693 GEOSUD (Investissements d'avenir -ANR-10-EQPX-20) is acknowledged for providing the 694 2014 SPOT-6 images.The MODIS Level-1B data were processed by the MODIS Adaptive 695 Processing System (MODAPS) and the Goddard Distributed Active Archive Center (DAAC) 696 and are archived and distributed by the Goddard DAAC.In situ mass balance data for the 697 Glacier Blanc were kindly provided by the Parc National des Ecrins.The authors 698 acknowledge the contribution the Labex OSUG@2020 (Investissements d'avenir -ANR10 699 LABX56).Pascal Sirguey thanks the University of Grenoble Alpes and Grenoble-INP for the 700 6-month "invited professor grant" obtained in 2015-16.701 702 The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License.
b s and b w , respectively) obtained from 143 1 The Cryosphere Discuss., doi:10.5194/tc-2017-49,2017 Manuscript under review for journal The Cryosphere Discussion started: 18 April 2017 c Author(s) 2017.CC-BY 3.0 License. in situ measurements with the glaciological method (unpublished data, LGGE internal report, 144 listed Table