TC The Cryosphere TC 1994-0424 Copernicus GmbH Göttingen, Germany 10.5194/tc-7-141-2013 An estimate of global glacier volume Grinsted A. 1 2 College of Global Change and Earth System Science, Beijing Normal University, Beijing, China Centre for Ice and Climate, Niels Bohr Institute, University of Copenhagen, Denmark 30 01 2013 7 1 141 151 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.the-cryosphere.net/7/141/2013/tc-7-141-2013.html The full text article is available as a PDF file from http://www.the-cryosphere.net/7/141/2013/tc-7-141-2013.pdf

I assess the feasibility of using multivariate scaling relationships to estimate glacier volume from glacier inventory data. Scaling laws are calibrated against volume observations optimized for the specific purpose of estimating total global glacier ice volume. I find that adjustments for continentality and elevation range improve skill of area–volume scaling. These scaling relationships are applied to each record in the Randolph Glacier Inventory, which is the first globally complete inventory of glaciers and ice caps. I estimate that the total volume of all glaciers in the world is 0.35 ± 0.07 m sea level equivalent, including ice sheet peripheral glaciers. This is substantially less than a recent state-of-the-art estimate. Area–volume scaling bias issues for large ice masses, and incomplete inventory data are offered as explanations for the difference.

 References Adhikari, S. and Marshall, S. J.: Glacier volume-area relation for high-order mechanics and transient glacier states, Geophys. Res. Lett., 39, L16505, http://dx.doi.org/10.1029/2012GL052712doi:10.1029/2012GL052712, 2012. Arendt, A., Bolch, T., Cogley, J. G., Gardner, A., Hagen, J.-O., Hock ,R., Kaser, G., Pfeffer, W. T., Moholdt, G., Paul, F., Radi\'c, V., Andreassen, L., Bajracharya, S., Beedle, M., Berthier, E., Bhambri, R., Bliss, A., Brown, I., Burgess, E., Burgess, D., Cawkwell, F., Chinn, T., Copland, L., Davies, B., de Angelis, H. , Dolgova, E., Filbert, K., Forester, R., Fountain, A., Frey, H., Giffen, B., Glasser, N., Gurney, S., Hagg, W., Hall, D., Haritashya, U. K., Hartmann, G., Helm, C., Herreid, S., Howat, I., Kapustin, G., Khromova, T., Kienholz, C., Koenig, M., Kohler, J., Kriegel, D., Kutuzov, S., Lavrentiev, I., LeBris, R., Lund, J., Manley, W., Mayer, C., Miles, E., Li, X., Menounos, B., Mercer, A., Moelg, N., Mool, P., Nosenko, G., Negrete, A., Nuth, C., Pettersson, R., Racoviteanu, A., Ranzi, R., Rastner, P., Rau, F., Rich, J., Rott, H., Schneider, C., Seliverstov, Y., Sharp, M., Sigur\usson, O., Stokes, C., Wheate, R., Winsvold, S., Wolken, G., Wyatt, F., and Zheltyhina, N.: Randolph Glacier Inventory [v2.0]: A Dataset of Global Glacier Outlines. Global Land Ice Measurements from Space, Boulder Colorado, USA, Digital Media (with area corrections downloaded 2012), 2012. Arlot, S. and Celisse, A.: A survey of cross-validation procedures for model selection, Statistics Surveys, 4, 40–79, 2010. Armstrong, R., Raup, B., Khalsa, S. J. S., Barry, R., Kargel, J., Helm, C., and Kieffer, H.: GLIMS glacier database. Boulder, Colorado USA: National Snow and Ice Data Center, Digital media, (downloaded February), 2012. Bahr, D. B.: Global distributions of glacier properties: a stochastic scaling paradigm, Water Res., 33, 1669–1679, 1997. Bahr, D. B. and Radic', V.: Significant contribution to total mass from very small glaciers, The Cryosphere, 6, 763–770, http://dx.doi.org/10.5194/tc-6-763-2012doi:10.5194/tc-6-763-2012, 2012. Bahr, D. B., Meier, M. F., and Peckham, S.: The physical basis of glacier volume-area scaling, J. Geophys. Res., 102, 20355–20362, 1997. Björnsson, H. and Pálsson, F.: Icelandic glaciers, Jökull, 58, 365–386, 2008. Braithwaite, R. J: Calculation of degree-days for glacier-climate research, Zeitschrift für Gletscherkunde und Glazialgeologie, 20, 1–8, 1985. Cade, B. S. and Richards, J. D.: Permutation tests for least absolute deviation regression, Biometrics, 52, 886–902, 1996. Chen, J. and Ohmura, A.: Estimation of Alpine glacier water resources and their change since the 1870's, IAHS Publ., 193, 127–135, 1990. Chizhov, O. P. and Kotlyakov, V. M.: Studies of the Antarctic and present-day concepts of global glaciation, Ann. Glaciol., 3, 50–53, 1983. Church, J. A., Gregory, J. M., Huybrechts, P., Kuhn,M., Lambeck, K., Nhuan, M. T., Qin, D., and Woodworth, P. L.: Changes in sea level, in: Climate Change: The Scientific Basis, Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change, edited by:Houghton, J. T. , Ding, Y., Griggs, D. J., Noguer, M., van der Linden, P., Dai, X., Maskell, K., and Johnson, C. I., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 639–693, 2001. Cogley, J. G.: The future of the world's glaciers, in: The Future of the World's Climate, edited by: Henderson-Sellers, A. and McGuffie, K., Elsevier, chap. 8, 205–218, http://dx.doi.org/10.1016/B978-0-12-386917-3.00008-7doi:10.1016/B978-0-12-386917-3.00008-7, 2012. Cuffey K. M. and Paterson, W. S. B.: The Physics of Glaciers, Fourth Edition Academic Press ISBN: 9780123694614, 2010. Dowdeswell, J. A., Drewry, D. J., Cooper, A. P. R., Gorman, M. R., Liestøl, O., and Orheim, O.: Digital mapping of the Nordaustlandet ice caps from airborne geophysical investigations, Ann. Glaciol., 8, 51–58, 1986. Dowdeswell, J. A., Benham, T. J., Gorman, M. R., Burgess, D., and Sharp, M. J.: Form and flow of the Devon Island Ice Cap, Canadian Arctic, J. Geophys. Res., 109, F02002, http://dx.doi.org/10.1029/2003JF000095doi:10.1029/2003JF000095, 2004. Driedger, C. L. and Kennard, P. M.: Ice Volumes on Cascade Volcanoes: Mount Rainer, Mount Hood, Three Sisters, Mount Shasta, Available from Supt Doc, USGPO, Wash DC 20402, USGS Professional Paper 1365, 28 p., 1986. Erasov, N. V.: Method to determine the volume of mountain glaciers (in Russian), Mater, Glyatsiol, Issled, Khronika, Obsuzhdniya, 14, 307–308, 1968. Farinotti, D., Huss, M., Bauder, A., Funk, M., and Truffer, M.: A method to estimate ice volume and ice-thickness distribution of alpine glaciers, J. Glaciol., 55, 422–430, 2009. Haeberli, W. and Hoelzle, M.: Application of inventory data for estimating characteristics of and regional climate-change effects on mountain glaciers: a pilot study with the European Alps, Ann. Glaciol., 21, 206–212, 1995. Huss, M. and Farinotti, D.: Distributed ice thickness and volume of all glaciers around the globe, J. Geophys. Res., 117, F04010, http://dx.doi.org/10.1029/2012JF002523doi:10.1029/2012JF002523, 2012. Jarvis A., Reuter, H. I., Nelson, A., and Guevara, E.: Hole-filled seamless SRTM data V4, International Centre for Tropical Agriculture (CIAT), available at: http://srtm.csi.cgiar.org, 2008. Leclercq, P. W., Oerlemans, J., and Cogley, J. G.: Estimating the glacier contribution to sea-level rise over the period 1800–2005, Surv. Geophy., 32, 519–535, http://dx.doi.org/10.1007/s10712-011-9121-7doi:10.1007/s10712-011-9121-7, 2011. Lemke, P., Ren, J., Alley, R. B., Allison, I., Carrasco, J., Flato, G., Fujii, Y., Kaser, G., Mote, P., Thomas, R. H., and Zhang, T.: Observations: Changes in Snow, Ice and Frozen Ground, in: Climate Change 2007: The Physical Science Basis, Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K. B., Tignor, M., and Miller, H. L., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 2007. Macheret, Y. Y. and Zhuravlev, A. B.: Radio echo-sounding of Svalbard glaciers, J. Glaciol., 28, 295–314, 1982. Macheret, Y. Y., Zhuravlev, A. B., and Bobrova, L .I.: Tolshchina, podlednyy rel'yef i ob'yem lednikov Shpitsbergena po dannym radiozondirovaniya [Thickness, subglacial relief and volume of Svalbard glaciers based on radio echo-sounding data], Materialy Glyatsiologicheskikh Issledovaniy, Khronika, Obsuzhdeniya, 51, 49–63, 1984. Macheret, Y. Y., Cherkasov, P. A., and Bobrova, L. I.: Tolschina i ob'em lednikov djungarskogo alatau po danniy aeroradiozondirovaniya, Materialy Glyatsiologicheskikh Issledovanii: Khronika, Obsuzhdeniya, 62, 59–71, 1988. Meier, M. F. and Bahr, D. B.: Counting glaciers: Use of scaling methods to estimate the number and size distribution of the glaciers in the world, edited by: Hanover, N. H., CRREL Spec. Rep., US Army, 89–95, 1996. Meier, M. F., Bahr, D. B., Dyurgerov, M. B., and Pfeffer, W. T.: Comment by M.F. Meier et al. on "The potential for sea level rise: New estimates from glacier and ice cap area and volume distributions", edited by: Raper, S. C. B. and Braithwaite, R. J., Geophys. Res. Lett., 32, L17501, http://dx.doi.org/10.1029/2005GL023319doi:10.1029/2005GL023319, 2005. Mitrovica, J. X. and Milne, G. A.: On post-glacial sea level: I. General theory, Geophys. J. Int. 154, 253–267, 2003. Oerlemans, J.: Extracting a climate signal from 169 glacier records. Science, 308, 675–677, 2005. Radi\'c, V. and Hock, R. : Regional and global volumes of glaciers derived from statistical upscaling of glacier inventory data, J. Geophys. Res., 115, F01010, http://dx.doi.org/10.1029/2009JF001373doi:10.1029/2009JF001373, 2010. Radi\'c, V., Hock, R., and Oerlemans, J.: Volume area scaling vs flowline modelling in glacier volume projections, Ann. Glaciol., 46, 234–240, 2007. Raper, S. C. B. and Braithwaite, R. J.: The potential for sea level rise: New estimates from glacier and ice cap area and volume distribution, Geophys. Res. Lett., 32, L05502, http://dx.doi.org/10.1029/2004GL021981doi:10.1029/2004GL021981, 2005a. Raper, S. C. B. and Braithwaite, R. J.: Reply to comment by Meier, M. F. et al. on "The potential for sea level rise: New estimates from glacier and ice cap area and volume distributions", Geophys. Res. Lett., 32, L17502, http://dx.doi.org/10.1029/2005GL023460doi:10.1029/2005GL023460, 2005b. Shiyin, L., Wenxin, S., Yongping, S., and Gang, L.: Glacier changes since the Little Ice Age maximum in the western Qilian Shan, northwest China, and consequences of glacier runoff for water supply, J. Glaciol., 49, 117–124, 2003. Slangen, A. B. A., Katsman, C. A., van de Wal, R. S. W., Vermeersen, L. L. A., and Riva, R. E. M.: Towards regional projections of twenty-first century sea-level change based on IPCC SRES scenarios, Clim. Dynam., 38, 1191–1209, http://dx.doi.org/10.1007/s00382-011-1057-6doi:10.1007/s00382-011-1057-6, 2011. Van de Wal, R. S. W. and Wild, M.: Modelling the response of glaciers to climate change by applying volume-area scaling in combination with a high resolution GCM, Clim. Dynam., 18, 359–366, 2001. Verdin, K. L. and Greenlee, S. K: Development of continental scale digital elevation models and extraction of hydrographic features. In: Proceedings, Third International Conference/Workshop on Integrating GIS and Environmental Modeling, Santa Fe, New Mexico, 21–26~January, National Center for Geographic Information and Analysis, Santa Barbara, California, 1996. WGMS and NSIDC: World Glacier Inventory, Compiled and made available by the World Glacier Monitoring Service, Zurich, Switzerland, and the National Snow and Ice Data Center, Boulder CO, USA Digital Media, updated: 2012. Yafeng, S., Zongtai, W., and Chaohai, L.: Note on the glacier inventory in Qilian Shan Mountains, in: Glacier Inventory of China, 1, Qilian Mountains, Lanzhou, Institution of Glaciology and Geocryology, 1–9, 1981. Zhuravlev, A. B.: Korrelyatsionniy metod otsenki zapasov l'da v lednikakh, Materialy Glyatsiologicheskikh Issledovaniy, 52, 241–249, 1985. Zhuravlev, A. V.: The relation between glacier area and volume, in: Data of Glaciological Studies, vol. 40, edited by: Avsyuk, G. A. and Balkema, A. A., Rotterdam, The Netherlands, Russ. Transl. Ser., 67, 441–446, 1988.