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On the errors involved in ice-thickness estimates II: errors in digital elevation models of ice thickness

  • J. J. LAPAZARAN (a1), J. OTERO (a1), A. MARTÍN-ESPAÑOL (a1) (a2) and F. J. NAVARRO (a1)
Abstract

This paper is the second (Paper II) in a set of studies concerning the errors involved in the estimate of ice thickness and ice volume. Here we present a detailed analysis of the errors involved in the generation of ice-thickness DEMs constructed, most often, from GPR data, complemented by boundary data and sometimes, additional synthetic data arising from estimates based on theoretical considerations supported by independent data. We describe a complete methodology of error analysis that, starting from the errors in the data, propagates them to the grid nodes. In turn, the interpolation error at the grid nodes is calculated using a novel procedure that also provides an estimate of the bias introduced by the interpolation process. Finally, both errors are combined at the grid nodes to produce a gridpoint-dependent error estimate, which is complemented by an overall error estimate providing an assessment of the quality of the DEM. This methodology is illustrated with the case study of Werenskioldbreen, a land-terminating polythermal glacier in Svalbard.

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Copyright
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Corresponding author
Correspondence: J. J. Lapazaran <javier.lapazaran@upm.es>
References
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Ai, S and 6 others (2014) Topography, ice thickness and ice volume of the glacier Pedersenbreen in Svalbard, using GPR and GPS. Pol. Res., 33, 18533 (doi: 10.3402/polar.v33.18533)
Bamber, JL, Layberry, RL and Gogineni, SP (2001) A new ice thickness and bed data set for the Greenland ice sheet: 1. Measurement, data reduction, and errors. J. Geophys. Res., 106(D24), 3377333780 (doi: 10.1029/2001JD900054)
Bamber, JL and 10 others (2013) A new bed elevation dataset for Greenland. Cryosphere, 7, 499510 (doi: 10.5194/tc-7-499-2013)
Bernard, É and 5 others (2014) Where does a glacier end? GPR measurements to identify the limitsbetween valley slopes and actual glacier body. Application to the Austre Lovénbreen, Spitsbergen. Int. J. Appl. Earth Obs. Geoinf, 27, 100108 (doi: 10.1016/j.jag.2013.07.006)
Binder, D and 5 others (2009) Determination of total ice volume and ice-thickness distribution of two glaciers in the Hohe Tauern region, Eastern Alps, from GPR data. Ann. Glaciol., 50(51), 7179 (doi: 10.3189/172756409789097522)
Bolch, T, Menounos, B and Wheate, R (2010) Landsat-based inventory of glaciers in western Canada, 1985–2005. Remote Sens. Environ., 114, 127137 (doi: 10.1016/j.rse.2009.08.015)
Chainey, S and Stuart, N (1998) Stochastic simulation: an alternative interpolation technique for digital geographic information. In Carver, S ed. Innovations in GIS 5: selected papers from the Fifth National Conference on GIS Research UK (GISRUK). Taylor & Francis, London, 324 (doi: 10.1201/b16831-3)
Cressie, N (1993) Statistics for Spatial Data, Revised edition. Wiley, New York, 900 p.
den Hertog, D, Kleijnen, JPC and Siem, AYD (2006) The correct Kriging variance estimated by bootstrapping. J. Oper. Res. Soc., 57, 400409 (doi: 10.1057/palgrave.jors.2601997)
Deutsch, CV (1996) Correcting for negative weights in ordinary kriging. Comput. Geosci., 22(7), 765773 (doi: 10.1016/0098-3004(96)00005-2)
Farinotti, D, Huss, M, Bauder, A, Funk, M and Truffer, M (2009a) A method to estimate ice volume and ice-thickness distribution of alpine glaciers. J. Glaciol., 55(191), 422430 (doi: 10.3189/002214309788816759)
Farinotti, D, Huss, M, Bauder, A and Funk, M (2009b) An estimate of the glacier ice volume in the Swiss Alps. Global Planet. Change, 68(3), 225231 (doi: 10.1016/j.gloplacha.2009.05.004)
Farinotti, D, King, E, Albrecht, A, Huss, M and Gudmundsson, GH (2014) The bedrock topography of Starbuck Glacier, Antarctic Peninsula, as determined by radio-echo soundings and flow modeling. Ann. Glaciol., 55(67), 2228 (doi: 10.3189/2014AoG67A025)
Fischer, A (2009) Calculation of glacier volume from sparse ice-thickness data, applied to Schaufelferner, Austria. J. Glaciol., 55(191), 453460 (doi: 10.3189/002214309788816740)
Fischer, A and Kuhn, M (2013) Ground-penetrating radar measurements of 64 Austrian glaciers between 1995 and 2010. Ann. Glaciol., 54(64), 179188 (doi: 10.3189/2013AoG64A108)
Fretwell, P and 59 others (2013) Bedmap2: improved ice bed, surface and thickness datasets for Antarctica. Cryosphere, 7(1), 375393 (doi: 10.5194/tc-7-375-2013)
Gjermundsen, E and 5 others (2011) Assessment of multispectral glacier mapping methods and derivation of glacier area changes, 19782002, in the central Southern Alps, New Zealand, from ASTER satellite data, field survey and existing inventory data. J. Glaciol., 57, 667683 (doi: 10.3189/002214311797409749)
Herzfeld, UC (2004) Atlas of Antarctica: topographic maps from Geostatistical analysis of satellite radar altimeter data. Springer-Verlag, Berlin, 364 p.
Herzfeld, UC, Wallin, BF, Leuschen, CJ and Plummer, J (2011) An algorithm for generalizing topography to grids while preserving subscale morphologic characteristics−creating a glacier bed DEM for Jakobshavn trough as low-resolution input for dynamic ice-sheet models. Comput. Geosci., 37(11), 17931801 (doi: 10.1016/j.cageo.2011.02.021)
Journel, AG (1986) Geostatistics: models and tools for the earth sciences. Math. Geol., 18(1), 119140 (doi: 10.1007/BF00897658)
Koppes, M, Hallet, B and Anderson, J (2009) Synchronous acceleration of ice loss and glacial erosion, Glaciar Marinelli, Chilean Tierra del Fuego. J. Glaciol., 55(190), 207220 (doi: 10.3189/002214309788608796)
Lapazaran, J and 6 others (2013) Ice volume changes (1936–1990–2007) and ground-penetrating radar studies of Ariebreen, Hornsund, Spitsbergen. Pol. Res., 32, 11068 (doi: 10.3402/polar.v32i0.11068)
Lapazaran, JJ, Otero, J, Martín-Español, A and Navarro, FJ (2016) On the errors involved in ice-thickness estimates I: ground-penetrating radar measurement errors. J. Glaciol. (doi: 10.1017/jog.2016.93)
Lindbäck, K and 8 others (2014) High-resolution ice thickness and bed topography of a land-terminating section of the Greenland Ice Sheet. Earth Syst. Sci. Data, 6, 331338 (doi: 10.5194/essd-6-331-2014)
Martín-Español, A and 7 others (2013) Radio-echo sounding and ice volume estimates of western Nordenskiöld Land glaciers, Svalbard. Ann. Glaciol., 54(64), 211217 (doi: 10.3189/2013AoG64A109)
Martín-Español, A, Lapazaran, JJ, Otero, J, Navarro, FJ (2016) On the errors involved in ice-thickness estimates III: error in volume. J. Glaciol. (doi: 10.1017/jog.2016.95)
Morlighem, M and 5 others (2011) A mass conservation approach for mapping glacier ice thickness. Geophys. Res. Lett., 38(19), L19503 (doi: 10.1029/2011GL048659)
Morlighem, M and 6 others (2013) High-resolution bed topography mapping of Russell Glacier, Greenland, inferred from Operation IceBridge data. J. Glaciol., 59(218), 10151023 (doi: 10.3189/2013JoG12J235)
Navarro, FJ and 6 others (2014) Ice volume estimates from ground-penetrating radar surveys, Wedel Jarlsberg Land glaciers, Svalbard. Arct. Antarct. Alp. Res., 46(2), 394406 (doi: 10.1657/1938-4246-46.2.394)
Nuth, C and 7 others (2013) Decadal changes from a multi-temporal glacier inventory of Svalbard. Cryosphere, 7(5), 16031621 (doi: 10.5194/tc-7-1603-2013)
Otero, J, Navarro, FJ, Martín, C, Cuadrado, ML and Corcuera, MI (2010) A three-dimensional calving model: numerical experiments on Johnsons Glacier, Livingston Island, Antarctica. J. Glaciol., 56(196), 200214 (doi: 10.3189/002214310791968539)
Paul, F and 19 others (2013) On the accuracy of glacier outlines derived from remote sensing data. Ann. Glaciol., 54, 171182 (doi: 10.3189/2013AoG63A296)
Pettersson, R, Jansson, P and Holmlund, P (2003) Cold surface layer thinning on Storglaciären, Sweden, observed by repeated ground penetrating radar surveys. J. Geophys. Res., 108(F1), 6004 (doi: 10.1029/2003JF000024)
Pettersson, R and 5 others (2011) Ice thickness and basal conditions of Vestfonna ice cap, eastern Svalbard. Geogr. Ann.: Ser. A Phys. Geog., 93(4), 311322 (doi: 10.1111/j.1468-0459.2011.00438.x)
Pfeffer, WT and 19 others (2014) The Randolph Glacier Inventory: a globally complete inventory of glaciers. J. Glaciol., 60(221), 537552 (doi: 10.3189/2014JoG13J176)
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 (doi: 10.3189/002214307783258459)
Sugiyama, S, Sakakibara, D, Tsutaki, S, Maruyama, M and Sawagaki, T (2015) Glacier dynamics near the calving front of Bowdoin Glacier, northwestern Greenland. J. Glaciol., 61(226), 223232 (doi: 10.3189/2015JoG14J127)
Szidarovszky, F, Baafi, EY and Kim, YC (1987) Kriging without negative weights. Math. Geol., 19(6), 549559 (doi: 10.1007/BF00896920)
Wackernagel, H (2003) Multivariate geostatistics. An introduction with applications. 3rd completely revised edition, Springer-Verlag, Berlin, 388 p (doi: 10.1007/978-3-662-05294-5)
Welch, BC, Pfeffer, WT, Harper, JT and Humphrey, NF (1998) Mapping subglacial surfaces below temperate valley glaciers using 3-dimensional radio-echo sounding techniques. J. Glaciol., 44(146), 164170
Wilkens, N and 5 others (2015) Thermal structure and basal sliding parametrisation at Pine Island Glacier – a 3-D full-Stokes model study. Cryosphere, 9(2), 675690 (doi: 10.5194/tc-9-675-2015)
Yamamoto, JK (2000) An alternative measure of the reliability of ordinary kriging estimates. Math. Geol., 32(4), 489509 (doi: 10.1023/A:1007577916868)
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