Skip to main content Accessibility help

An optimized method to calculate the geodetic mass balance of mountain glaciers



Understanding the effects of climate on glaciers requires precise estimates of ice volume change over several decades. This is achieved by the geodetic mass balance computed by two means: (1) the digital elevation model (DEM) comparison (SeqDEM) allows measurements over the entire glacier, however the low contrast over glacierized areas is an issue for the DEM generation through the photogrammetric techniques and (2) the profiling method (SePM) is a faster alternative but fails to capture the spatial variability of elevation changes. We present a new framework (SSD) that relies upon the spatial variability of the elevation change to densify a sampling network to optimize the surface-elevation change quantification. Our method was tested in two small glaciers over different periods. We conclude that the SePM overestimates the elevation change by ~20% with a mean difference of ~1.00 m (root mean square error (RMSE) = ~3.00 m) compared with results from the SeqDEM method. A variogram analysis of the elevation changes showed a mean difference of <0.10 m (RMSE = ~2.40 m) with SSD approach. A final assessment on the largest glacier in the French Alps confirms the high potential of our method to compute the geodetic mass balance, without going through the generation of a full-density DEM, but with a similar accuracy than the SeqDEM approach.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      An optimized method to calculate the geodetic mass balance of mountain glaciers
      Available formats

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      An optimized method to calculate the geodetic mass balance of mountain glaciers
      Available formats

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      An optimized method to calculate the geodetic mass balance of mountain glaciers
      Available formats


This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Correspondence: Rubén Basantes-Serrano <>


Hide All
Adalgeirsdóttir, G, Echelmeyer, KA and Harrison, WD (1998) Elevation and volume changes on the Harding Icefield, Alaska. J. Glaciol. 44(148), 570582
Arendt, AA, Echelmeyer, KA, Harrison, WD, Lingle, CS and Valentine, VB (2002) Rapid wastage of Alaska glaciers and their contribution to rising sea level. Science 297(5580), 382386
Bader, H (1960) Theory of densification of dry snowon high polar glaciers. U.S. Snow, Ice Permafr. Res. Establ. Res. Rep. 769, 18
Baillard, C, Dissard, O, Jamet, O and Maître, H (1998) Extraction and textural characterization of above-ground areas from aerial stereo pairs: a quality assessment. ISPRS. J. Photogramm. Remote. Sens. 53(2), 130141.
Bamber, JL and Rivera, A (2007) A review of remote sensing methods for glacier mass balance determination. Glob. Planet. Change 59(1–4), 138148
Basantes-Serrano, R (2015) Contribution à l’étude de l’évolution des glaciers et du changement climatique dans les Andes équatoriennes depuis les années 1950. University of Grenoble Alps, Grenoble
Basantes-Serrano, R and 7 others (2016) Slight mass loss revealed by reanalyzing glacier mass-balance observations on Glaciar Antisana 15α (inner tropics) during the 1995–2012 period. J. Glaciol. 62(231), 124136
Berthier, E, Schiefer, E, Clarke, G, Menounos, B and Rémy, F (2010) Contribution of Alaskan glaciers to sea-level rise derived from satellite imagery. Nat. Geosci. 3(2), 9295
Berthier, E and 10 others (2014) Glacier topography and elevation changes derived from Pléiades sub-meter stereo images. Cryosphere 8(6), 22752291
Bivand, RS, Pebesma, EJ and Gomez-Rubio, V (2008) Applied spatial data analysis with R. Springer Science, New York (doi: 10.1007/978-0-387-78171-6)
Cogley, JG and 10 others (2011) Glossary of glacier mass balance and related terms., IHP-VII Te.
Cox, LH and March, RS (2004) Comparison of geodetic and glaciological mass balance, Gulkana Glacier, Alaska, USA. J. Glaciol. 50(170), 363370
Cressie, N (1988) Spatial prediction and ordinary kriging. Math. Geol. 20(4), 405421
Cullen, NJ and 9 others (2017) An 11-year record of mass balance of Brewster Glacier, New Zealand, determined using a geostatistical approach. J. Glaciol. 63(238), 199217
Echelmeyer, KA and 8 others (1996) Airborne surface profiling of glaciers: a case-study in Alaska. J. Glaciol. 42(142), 538547
Fischer, M, Huss, M and Hoelzle, M (2015) Surface elevation and mass changes of all Swiss glaciers 1980–2010. Cryosphere 9(2), 525540
Gruen, A and Akca, D (2005) Least squares 3D surface and curve matching. ISPRS J. Photogramm. Remote Sens. 59(3), 151174
Hirschmuller, H (2005) Accurate and efficient stereo processing by semi-global matching and mutual information. Comput. Vis. Pattern Recognition, 2005. CVPR 2005. IEEE Comput. Soc. Conf. 2, 807814
Hock, R and Jensen, H (1999) Application of kriging interpolation for glacier mass balance computations. Geogr. Ann. Ser. A, Phys. … 81(4), 611619
Huss, M (2013) Density assumptions for converting geodetic glacier volume change to mass change. Cryosphere 7(4), 877887
IPCC (2013) Climate change 2013: the physical science basis. Contribution of working group I to the fifth assessment report of the intergovernmental panel on climate change. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA
Jayaraman, K (1999) A statistical manual for forestry research. FAO (May), 231
Kish, L (1965) Survey sampling. Syst. Biol. 46(4), 643 (doi: 10.1093/sysbio/syr041)
Kodde, MPM, Pfeifer, N, Gorte, BGHB, Geist, T and Höfle, B (2007) Automatic glacier surface analysis from airborne laser scanning. Int. Arch. Photogramm. Remote Sens. XXXVI(October 2001), 221226
Magnússon, E, Muñoz-Cobo Belart, J, Pálsson, F, Ágústsson, H and Crochet, P (2016) Geodetic mass balance record with rigorous uncertainty estimates deduced from aerial photographs and lidar data – case study from Drangajökull ice cap, NW Iceland. Cryosphere 10(1), 159177
Matheron, G (1962) Traité de géostatistique appliquée. Technip, Paris
Maurer, JM, Rupper, SB and Schaefer, JM (2016) Quantifying ice loss in the eastern Himalayas since 1974 using declassified spy satellite imagery. Cryosphere 10(5), 22032215
Melles, SJ and 6 others (2011) Optimizing the spatial pattern of networks for monitoring radioactive releases. Comput. Geosci. 37(3), 280288
Noh, M-J and Howat, IM (2015) Automated stereo-photogrammetric DEM generation at high latitudes: surface extraction with TIN-based search-space minimization (SETSM) validation and demonstration over glaciated regions. GIScience Remote Sens. 52(2), 198217
Nuth, C and Kääb, A (2011) Co-registration and bias corrections of satellite elevation data sets for quantifying glacier thickness change. Cryosphere 5(1), 271290
Papasodoro, C, Berthier, E, Royer, A, Zdanowicz, C and Langlois, A (2015) Area, elevation and mass changes of the two southernmost ice caps of the Canadian Arctic archipelago between 1952 and 2014. Cryosphere 9(4), 15351550
Paterson, KM and Cuffey, WS. (2010) The physics of glaciers. Elsevier, Boston, MA (doi: 10.1016/0016-7185(71)90086-8)
Pebesma, EJ and Wesseling, CG (1998) Gstat: a program for geostatistical modelling, prediction and simulation. Comput. Geosci. 24(1), 1731
Pellikka, PKE and Rees, G (2010) Remote sensing of glaciers: techniques for topographic, spatial, and thematic mapping of glaciers. CRC Press, London
Rabatel, A, Machaca, A, Francou, B and Jomelli, V (2006) Glacier recession on Cerro Charquini (16°S), Bolivia, since the maximum of the Little Ice Age (17th century). J. Glaciol. 52(176), 110118 (doi: 10.3189/172756506781828917)
Rabatel, A and 27 others (2013) Current state of glaciers in the tropical Andes: a multi-century perspective on glacier evolution and climate change. Cryosphere 7(1), 81102
Rabatel, A, Dedieu, JP and Vincent, C (2016) Spatio-temporal changes in glacier-wide mass balance quantified by optical remote sensing on 30 glaciers in the French Alps for the period 1983-2014. J. Glaciol. 62(236), 11531166
Rolstad, C, Haug, T and Denby, B (2009) Spatially integrated geodetic glacier mass balance and its uncertainty based on geostatistical analysis: application to the western Svartisen ice cap, Norway. J. Glaciol. 55(192), 666680
Rotschky, G and 6 others (2007) A new surface accumulation map for western Dronning Maud Land, Antarctica, from interpolation of point measurements. J. Glaciol. 53(182), 385398
Sapiano, JJ, Harrison, WD and Echelmeyer, KA (1998) Elevation, volume and terminus changes of nine glaciers in North America. J. Glaciol. 44(146)
Shean, DE and 6 others (2016) An automated, open-source pipeline for mass production of digital elevation models (DEMs) from very-high-resolution commercial stereo satellite imagery. ISPRS J. Photogramm. Remote Sens. 116, 101117
Six, D, Wagnon, P, Sicart, JE and Vincent, C (2009) Meteorological controls on snow and ice ablation for two contrasting months on Glacier de Saint-Sorlin, France. Ann. Glaciol. 50(50), 6672
Soruco, A and 9 others (2009) Mass balance of Glaciar Zongo, Bolivia, between 1956 and 2006, using glaciological, hydrological and geodetic methods. Ann. Glaciol. 50(50), 18
Stosius, R and Herzfeld, UC (2004) Geostatistical estimation from radar altimeter data with respect to morphological units outlined by SAR data: application to Lambert Glacier/Amery Ice shelf, East Antarctica. Ann. Glaciol. 39(October 1997), 251255
Thibert, E, Blanc, R, Vincent, C and Eckert, N (2008) Glaciological and volumetric mass balance measurements: error analysis over 51 years for the Sarennes glacier, French Alps. J. Glaciol. 54(54186), 522532
Vincent, C, Vallon, M, Reynaud, L and Le Meur, E (2000) Dynamic behaviour analysis of glacier de Saint Sorlin, France, from 40 years of observations, 1957–97. J. Glaciol. 46(154), 499506
Vincent, C and 10 others (2013) Balanced conditions or slight mass gain of glaciers in the Lahaul and Spiti region (northern India, Himalaya) during the nineties preceded recent mass loss. Cryosphere 7(2), 569582
Vincent, C, Harter, M, Gilbert, A, Berthier, E and Six, D (2014) Future fluctuations of Mer de Glace, French Alps, assessed using a parameterized model calibrated with past thickness changes. Ann. Glaciol. 55(66), 1524
Wang, J-F and 7 others (2013) Design-based spatial sampling: theory and implementation. Environ. Model. Softw. 40, 280288
WGMS (2017) Fluctuations of glaciers database (doi: 10.5904/wgms-fog-2017-10)
Zemp, M and 38 others (2015) Historically unprecedented global glacier decline in the early 21st century. J. Glaciol. 61(228), 745762



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed