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Geometry


Geometry (Ancient Greek: ?e?µet??a; geo- 'earth', -metri 'measurement') 'Earth-measuring' is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.

 
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Age and Paleomagnetism of the Okhotsk-chukotka Volcanic Belt (Ocvb...

By: M. I. Raikevich; D. B. Stone; P. W. Layer

Description: Geophysical Institute, University of Alaska, Fairbanks, Alaska, 99775, USA. Paleomagnetic results from the upper two thirds of the whole section of the Okhotsk-Chukotka Volcanic Belt (OCVB) volcanics exposed in the area around Lake El'gygytgyn, Chukotka yield stable, consistent magnetic vectors and well-preserved reversed directions. The magnetostratigraphy and 40Ar/39Ar geochronologic data reported here indicate that the sampled O...

Akinin, V. V. and Khanchuk, A. I.: The Okhotsk-Chukotka Volcanogenic Belt: Age revision based on new $^40$Ar/$^39$Ar and U-Pb isotope data, Dokl. Earth Sci., 405, 1131–1135, 2005.; Belyi, V. F.: Geology of Okhotsk-Chukchi volcanogenic belt, North East Interdisciplinary Research Institute Magadan, Russian Academy of Sciences Far East Branch, 76~pp., 1994 \mbox(in Russian).; Belyi, V. F.: Topical questions of phytostratigraphy of Middle�� Cretaceous of North-East USSR, Nor...

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Paleomagnetic Determination of Paleolatitude and Rotation of Berin...

By: D. B. Stone; P. S. Minyuk

Description: Northeast Interdisciplinary Scientific Research Institute, FEB, RAS, 16 Portavaya St., Magadan, 685010, Russia. A paleomagnetic study was carried out on Paleogene sedimentary rocks from Bering Island, Komandorsky islands, located at the far western end of the Aleutian Island Arc. The age of these sediments has been debated at length, but the combination of magnetostratigraphy with the fossil record indicates that the base of the section is of early Eocen...

Avé Lallemant, H. G.: Displacement partitioning and arc-parallel extension in the Aleutian volcanic island arc, Tectonophysics, 256, 279–293, 1996.; Avé Lallemant, H. G. and Oldow, J. S.: Active displacement partitioning and arc-parallel extension of the Aleutian volcanic arc based on Global Positioning System geodesy and kinematic analysis, Geology, 28, 739–742, 2000.; Bath, G. D., Carr, W. J., Gard Jr., M., and Quinliven, W. D.: Interpretation of an Aeromagnetic survey...

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Determination of Hydrological Roughness by Means of Close Range Re...

By: F. Neugirg; M. Schindewolf; F. Haas; J. Schmidt; A. Kaiser; M. Becht

Description: Technical University Bergakademie Freiberg, Germany. The objective of the presented work was to develop a method to acquire Manning's n by creating very high-resolution surface models with structure-from-motion methods. As hydraulic roughness is an essential parameter for physically based erosion models, a practical measuring technique is valuable during field work. Data acquisition took place during several field experiments in the Lainbach valle...

Abbott, E. J. and Firestone, F. A.: Specifying surface quality: a method based on accurate measurement and comparison, ASME Journal of Mechanical Engineering, 55, 569–572, 1933.; Agisoft: Lens: http://downloads.agisoft.ru/lens/doc/en/lens.pdf, last access: 10 May 2014.; Agisoft: PhotoScan: http://downloads.agisoft.ru/pdf/photoscan-pro_1_0_0_en.p...

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Determination of Hydrological Roughness by Means of Close Range Re...

By: M. Schindewolf; J. Schmidt; F. Haas; F. Neugirg; M. Becht; A. Kaiser

Description: Technical University Bergakademie Freiberg, Freiberg, Germany. The objective of the presented work was to develop a method to acquire Manning's n by creating very high resolution surface models with Structure from Motion-methods. As hydraulic roughness is an essential parameter for physically based erosion models, a practical measuring technique is valuable during field work. Data acquisition took place during several field experiments in the Lai...

Abbott, E. J. and Firestone, F. A.: Specifying surface quality: a method based on accurate measurement and comparison, Mech. Eng., 55, 569–572, 1933.; Agisoft: Lens, available at: http://downloads.agisoft.ru/lens/doc/en/lens.pdf (last access: 28 March 2015), 2014a.; Agisoft: PhotoScan, available at: http://downloads.agisoft.ru/pdf/photoscan-pro_...

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The Equilibrium Flow and Mass Balance of the Taku Glacier, Alaska ...

By: M. Lang; S. R. McGee; M. S. Pelto; M. J. Beedle; K. F. Sprenke; G. W. Adema; M. M. Miller

Description: Nichols College Dudley, MA 01571, USA. The Taku Glacier, Alaska has advanced 7.5 km since the late nineteenth century, while all other primary outlet glaciers of the Juneau Icefield are in retreat. The Juneau Icefield Research Program has completed field work on the Taku Glacier annually since 1946. The collected observations of surface mass balance, glacier velocity and glacier thickness at Profile IV 29 km above the terminus and 4 km above the equilib...

Arendt, A. A.: Volume changes of Alaska glaciers: contributions to rising sea level and links to climate change, Ph.D dissertation, University of Alaska, Fairbanks, 2006.; Arendt, A. A., Echelmeyer, K. A., Harrison, W. D., Lingle, C. S., and Valentine, V. B.: Rapid wastage of Alaskan glaciers and their contribution to rising sea level, Science, 297(5880), 382–385, 2002.; Daellenbach, K. and Welsch, W.: Determination of surface velocities, strain rates, and mass flow rate...

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Stand-alone Single-frequency Gps Ice Velocity Observations on Nord...

By: W. Boot; V. Pohjola; R. S. W. Van De Wal; M. A. G. Den Ouden; C. H. Reijmer; J. Oerlemans

Description: Institute for Marine and Atmospheric research Utrecht, Utrecht University, Utrecht, The Netherlands. Precise measurements of ice-flow velocities are necessary for a proper understanding of the dynamics of glaciers and their response to climate change. We use stand-alone single-frequency GPS receivers for this purpose. They are designed to operate unattended for 1–3 years, allowing uninterrupted measurements for long periods with hourly temporal resolutio...

Bingham, R. G., Hubbard, A. L., Nienow, P. W., and Sharp, M. J.: An investigation into the mechanisms controlling seasonal speedup events at a High Arctic glacier, J. Geophys. Res., 113, F02006, doi:10.1029/2007JF000832, 2008.; Hagen, J. O., Melvold, K., Pinglot, F., and Dowdeswell, J. A.: On the net mass balance of the glaciers and ice caps in Svalbard, Norwegian Arctic, Arct. Antarct. Alp. Res., 35(2), 264–270, 2003.; Hagen, J. O., Eiken, T., Kohler, J., and Melvold, K...

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Investigating Changes in Basal Conditions of Variegated Glacier Pr...

By: F. Gillet-chaulet; O. Gagliardini; M. Jay-allemand; M. Nodet

Description: Laboratoire de Glaciologie et de Géophysique de l'Environnement (LGGE), UMR5183, CNRS/UJF, Grenoble, BP 96, 38402 Saint Martin d'Hères Cedex, France. Variegated Glacier (Alaska) is known to surge periodically after a sufficient amount of cumulative mass balance is reached, but this observation is difficult to link with changes in the basal conditions. Here, using a 10-yr dataset, consisting of surface topography and surface velocity observations along a ...

Arthern, R. and Gudmundsson, G.: Initialization of ice-sheet forecasts viewed as an inverse Robin problem, J. Glaciol., 56, 527–533, 2010.; Bindschadler, R.: A Numerical Model of Temperate Glacier Flow Applied to the Quiescent Phase of a Surge-Type Glacier, J. Glaciol., 28, 239–265, 1982.; Bindschadler, R., Harrison, W. D., Raymond, C. F., and Crosson, R.: Geometry and dynamics of a surge-type glacier, J. Glaciol., 18, 181–194, 1977.; Cuffey, K. and Paterson, W. S. B.: T...

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An Improved Bathymetry Compilation for the Bellingshausen Sea, Ant...

By: F. O. Nitsche; R. D. Larter; A. G. C. Graham

Description: Ice Sheets programme, British Antarctic Survey, High Cross, Madingley Road, Cambridge, CB3 0ET, UK. The southern Bellingshausen Sea (SBS) is a rapidly-changing part of West Antarctica, where oceanic and atmospheric warming has led to the recent basal melting and break-up of the Wilkins ice shelf, the dynamic thinning of fringing glaciers, and sea-ice reduction. Accurate sea-floor morphology is vital for understanding the continued effects of each process...

Holland, P. R., Jenkins, A., and Holland, D. M.: Ice and ocean processes in the Bellingshausen Sea, Antarctica, J. Geophys. Res., 115, C05020, doi:10.1029/2008JC005219, 2010.; Jakobsson, M., Macnab, R., Mayer, L., Anderson, R., Edwards, M., Hatzky, J., Schenke, H. W., and Johnson, P.: An improved bathymetric portrayal of the Arctic Ocean: Implications for ocean modelling and geological, geophysical and oceanographic anal...

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Basal Crevasses in Larsen C Ice Shelf and Implications for Their G...

By: E. C. King; A. Luckman; P. Sammonds; D. I. Benn; B. Kulessa; D. Jansen

Description: College of Science, Swansea University, UK. Basal crevasses extend upwards from the base of ice bodies and can penetrate more than halfway through the ice column under conditions found commonly on ice shelves. As a result, they may locally modify the exchange of mass and energy between ice shelf and ocean, and by altering the shelf's mechanical properties could play a fundamental role in ice shelf stability. Although early studies revealed that such fea...

Barrett, B., Murray, T., and Clark, R.: Errors in radar CMP velocity estimates due to survey geometry, and their implication for ice water content estimation, J. Environ. Eng. Geophys., 12, 101–111, doi:10.2113/JEEG12.1.101, 2007.; Bassis, J. N., Coleman, R., Fricker, H. A., and Minster, J. B.: Episodic propagation of a rift on the Amery Ice Shelf, East Antarctica, Geophys. Res. Lett., 32, L06502,

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Stable Water Isotopes of Precipitation and Firn Cores from the Nor...

By: F. Fernandoy; H. Meyer; M. Tonelli

Description: Foundation Alfred Wegener Institute for Polar and Marine Research in the Helmholtz Association, Research Unit Potsdam, Potsdam, Germany. In order to investigate the climate variability in the northern Antarctic Peninsula region, this paper focuses on the relationship between stable isotope content of precipitation and firn, and main meteorological variables (air temperature, relative humidity, sea surface temperature, and sea ice extent). Between 2008 and...

Abram, N. J., Thomas, E. R., McConnell, J. R., Mulvaney, R., Bracegirdle, T. J., Sime, L. C., and Aristarain, A. J.: Ice core evidence for a 20th century decline of sea ice in the Bellingshausen Sea, Antarctica, J. Geophys. Res., 115, D23101, doi:10.1029/2010jd014644, 2010.; Blindow, N., Suckro, S., Rückamp, M., Braun, M., Schindler, M., Breuer, B., Saurer, H., Simoes, J., and Lange, M.: Geometry and thermal regime of th...

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Repeat Optical Satellite Images Reveal Widespread and Long Term De...

By: T. Heid; A. Kääb

Description: Department of Geosciences, University of Oslo, Box 1047 Blindern, 0316 Oslo, Norway. By matching of repeat optical satellite images it is now possible to investigate glacier dynamics within large regions of the world and also between regions to improve knowledge about glacier dynamics in space and time. In this study we investigate whether the negative glacier mass balance seen over large parts of the world has caused the glaciers to chan...

Bahr, D., Dyurgerov, M., and Meier, M.: Sea-level rise from glaciers and ice caps: a lower bound, Geophys. Res. Lett., 36, L03501, doi:10.1029/2008GL036309, 2009.; Bernstein, R.: Image geometry and rectification, in: Manual of Remote Sensing, American Society of Photogrammetry, Falls Church, VA, 881–884, 1983.; Berthier, E., Vadon, H., Baratoux, D., Arnaud, Y., Vincent, C., Feigl, K., Remy, F., and Legresy, B.: Surface m...

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Reanalysing Glacier Mass Balance Measurement Series : Volume 7, Is...

By: C. Nuth; D. Stumm; A. Fischer; H. Elvehøy; P. C. Joerg; L. M. Andreassen; H. Escher-vetter; M. Huss; E. Thibert; P. Jansson; M. Zemp; C. Mayer; B. Hynek; A. Mercer; S. U. Nussbaumer; C. Rolstad Denby; G. Moholdt

Description: Department of Geography, University of Zurich (UZH), Zurich, Switzerland. Glacier-wide mass balance has been measured for more than sixty years and is widely used as an indicator of climate change and to assess the glacier contribution to runoff and sea level rise. Until recently, comprehensive uncertainty assessments have rarely been carried out and mass balance data have often been applied using rough error estimation or without consideration of error...

Cogley, J. G., Hock, R., Rasmussen, L. A., Arendt, A. A., Bauder, A., Braithwaite, R. J., Jansson, P., Kaser, G., Möller, M., Nicholson, L., and Zemp, M.: Glossary of Glacier Mass Balance and Related Terms, IHP-VII Technical Documents in Hydrology No. 86, IACS Contribution No. 2, Paris, UNESCO-IHP, 114 pp., 2011.; Cox, L. H. and March, R. S.: Comparison of geodetic and glaciological mass-balance techniques, Gulkana Glacier, Alaska, USA, J. Glaciol., 50, 363–370, 2004.; C...

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A General Treatment of Snow Microstructure Exemplified by an Impro...

By: M. Schneebeli; F. Riche; H. Löwe

Description: WSL Institute for Snow and Avalanche Research SLF, Davos, Switzerland. Finding relevant microstructural parameters beyond density is a longstanding problem which hinders the formulation of accurate parameterizations of physical properties of snow. Towards a remedy, we address the effective thermal conductivity tensor of snow via anisotropic, second-order bounds. The bound provides an explicit expression for the thermal conductivity and predicts the...

Arons, E. and Colbeck, S.: Geometry of heat and mass-transfer in dry snow – A review of theory and experiment, Rev. Geophys., 33, 463–493, doi:10.1029/95RG02073, 1995.; Barber, D. G. and Nghiem, S.: The role of snow on the thermal dependence of microwave backscatter over sea ice, J. Geophys. Res., 104, 789–803, 1999.; Calonne, N., Flin, F., Morin, S., Lesaffre, B., du Roscoat, S. R., and Geindreau, C.: Numerical and experim...

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Thermal Conductivity of Snow Measured by Three Independent Methods...

By: M. Schneebeli; F. Riche

Description: WSL Institute for Snow and Avalanche Research SLF, Davos Dorf, Switzerland. The thermal conductivity of snow determines the temperature gradient, and by this, it has a direct effect on the rate of snow metamorphism. It is therefore a key property of snow. However, thermal conductivities measured with the transient needle probe and the steady-state, heat flux plate differ. In addition, the anisotropy of thermal conductivity plays an important role in the...

Abels, G.: Beobachtungen der täglichen Periode der Temperatur im Schnee und Bestimmung des Wärmeleitungsvermögens des Schnees als Function seiner Dichtigkeit, Kaiserl. Akad. Wissensch., Rep. Meteorologie, 16, 1–53, 1892 (in German).; Abu-Hamdeh, N. and Reeder, R.: Soil thermal conductivity: Effects of density, moisture, salt concentration, and organic matter, Soil Sci. Soc. Am. J., 64, 1285–1290, 2000.; Ams, C. H., Knackstedt, M. A., Pinczewski, W. V., and Lindquist, W. ...

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Fluctuations of a Greenlandic Tidewater Glacier Driven by Changes ...

By: B. R. Rea; F. M. Nick; M. Morlighem; P. W. Nienow; D. Van as; J. M. Lea; D. W. F. Mair; A. Weidick

Description: Department of Geography and the Environment, University of Aberdeen, Elphinstone Road, Aberdeen AB24 3UF, UK. Many tidewater glaciers in Greenland are known to have undergone significant retreat during the last century following their Little Ice Age maxima. Where it is possible to reconstruct glacier change over this period, they provide excellent records for comparison to climate records, as well as calibration/validation for numerical models. These gla...

Ahlstrøm, A. P., Andersen, S. B., Andersen, M. L., Machguth, H., Nick, F. M., Joughin, I., Reijmer, C. H., van de Wal, R. S. W., Merryman Boncori, J. P., Box, J. E., Citterio, M., van As, D., Fausto, R. S., and Hubbard, A.: Seasonal velocities of eight major marine-terminating outlet glaciers of the Greenland ice sheet from continuous in situ GPS instruments, Earth Syst. Sci. Data, 5, 277–287, doi:10.5194/essd-5-277-2013<...

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Combining Damage and Fracture Mechanics to Model Calving : Volume ...

By: J. Weiss; O. Gagliardini; G. Durand; J. Krug

Description: CNRS, LGGE, 38041 Grenoble, France. Calving of icebergs is a major negative component of polar ice-sheet mass balance. Here we present a new calving model relying on both continuum damage mechanics and linear elastic fracture mechanics. This combination accounts for both the slow sub-critical surface crevassing and the rapid propagation of crevasses when calving occurs. First, damage to the ice occurs over long timescales and enhances the viscous flow o...

Albrecht, T. and Levermann, A.: Fracture field for large-scale ice dynamics, J. Glaciol., 58, 165–-177, 2012.; Albrecht, T. and Levermann, A.: Fracture-induced softening for large-scale ice dynamics, The Cryosphere, 8, 587–605, doi:10.5194/tc-8-587-2014, 2014.; Andresen, C. S., Straneo, F., Ribergaard, M. H., Bjørk, A. A., Andersen, T. J., Kuijpers, A., Nørgaard-Pedersen, N., Kjær, K. H., Schjøth, F., Weckström, K., and...

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Deglaciation of the Caucasus Mountains, Russia/Georgia, in the 21S...

By: S. Kutuzov; G. Nosenko; O. Rototaeva; T. Khromova; M. Shahgedanova

Description: Department of Geography and Environmental Science and Walker Institute for Climate System Research, University of Reading, Whiteknights, Reading RG6 6AB, UK. Changes in the map area of 498 glaciers located on the Main Caucasus ridge (MCR) and on Mt. Elbrus in the Greater Caucasus Mountains (Russia and Georgia) were assessed using multispectral ASTER and panchromatic Landsat imagery with 15 m spatial resolution in 1999/2001 and 2010/2012. Changes in reces...

DeBeer, C. M. and Sharp, M. J.: Recent changes in glacier area and volume within the Southern Canadian Cordillera, Ann. Glaciol., 46, 215–221, 2007.; Andreassen, L. M., Paul, F., Kääb, A., and Hausberg, J. E.: Landsat-derived glacier inventory for Jotunheimen, Norway, and deduced glacier changes since the 1930s, The Cryosphere, 2, 131–145, doi:10.5194/tc-2-131-2008, 2008.; Bhambri, R., Bolch, T., Chaujar, R. K., and Kul...

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Fracture-induced Softening for Large-scale Ice Dynamics : Volume 8...

By: T. Albrecht; A. Levermann

Description: Earth System Analysis, Potsdam Institute for Climate Impact Research, Potsdam, Germany. Floating ice shelves can exert a retentive and hence stabilizing force onto the inland ice sheet of Antarctica. However, this effect has been observed to diminish by the dynamic effects of fracture processes within the protective ice shelves, leading to accelerated ice flow and hence to a sea-level contribution. In order to account for the macroscopic effect of fractu...

Albrecht, T. and Levermann, A.: Fracture field for large-scale ice dynamics, J. Glaciol., 58, 165–176, doi:10.3189/2012JoG11J191, 2012.; Bamber, J. L. and Aspinall, W. P.: An expert judgement assessment of future sea level rise from the ice sheets, Nat. Clim. Change, 3, 424–427, doi:10.1038/nclimate1778, 2013.; Bassis, J. N.: The statistical physics of iceberg calving a...

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Modelling Environmental Influences on Calving at Helheim Glacier i...

By: T. Murray; T. Zwinger; A. Luckman; N. Selmes; S. Cook; A. Goldsack; I. C. Rutt; T. D. James

Description: Glaciology Group, Geography Department, Swansea University, Swansea, SA2 8PP, UK. Calving is an important mass-loss process for many glaciers worldwide, and has been assumed to respond to a variety of environmental influences. We present a grounded, flowline tidewater glacier model using a physically-based calving mechanism, applied to Helheim Glacier, eastern Greenland. By qualitatively examining both modelled size and frequency of calving events, and...

Abdalati, W., Krabill, W., Frederick, E., Manizade, S., Martin, C., Sonntag, J., Swift, R., Thomas, R., Wright, W., and Yungel, J.: Outlet glacier and margin elevation changes: Near-coastal thinning of the Greenland Ice Sheet, J. Geophys. Res., 106, 33729–33742, 2001.; Amundson, J. M. and Truffer, M.: A unifying framework for iceberg-calving models, J. Glaciol., 56, 822–30, 2010.; Amundson, J. M., Fahnestock, M., Truffer, M., Brown, J., Lüthi, M. P., and Motyka, R.: Ice ...

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Brief Communication: Sudden Drainage of a Subglacial Lake Beneath ...

By: C. Porter; M. J. Noh; B. E. Smith; I. M. Howat; S. Jeong

Description: School of Earth Sciences and Byrd Polar Research Center, Ohio State University, Columbus, Ohio, USA. We report on the appearance of a 2 km wide, 70 m deep circular depression located 50 km inland of the southwestern margin of the Greenland Ice Sheet that provides the first direct evidence for concentrated, long-term storage, and sudden release, of meltwater at the bed. Drainage of the lake may have been triggered by the recent increase in meltwater runof...

Joughin, I., Smith, B. E., Howat, I. M., Scambos, T., and Moon, T.: Greenland flow variability from ice-sheet-wide velocity mapping, J. Glaciol., 56, 415–430, 2010.; Bartholomew, I., Nienow, P., Sole, A., Mair, D., Cowton, T., Palmer, S., and Wadham, J.: Supraglacial forcing of subglacial drainage in the ablation zone of the Greenland ice sheet, Geophys. Res. Lett., 38, L08502, doi:10.1029/2011GL047063, 2011.; Borsa, A. ...

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