References

Notes

This large list collects all references which the PISM authors have found convenient. There is no claim that all of these references get direct use, or even mention, in the PISM project files.

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• AbramowitzStegun:
  M. Abramowitz and I. A. Stegun, editors, 1965. Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables. Graduate Studies in Mathematics. Dover, New York.

• AIAAGuidelines:
  AIAA, 1998. Guide for the Verification and Validation of Computational Fluid Dynamics Simulations. Technical Report AIAA G-077-1998, American Institute of Aeronautics and Astronautics (AIAA).

• Albrechtetal2011:
  T. Albrecht, M. Martin, M. Haseloff, R. Winkelmann, and A. Levermann, 2011. Parameterization for subgrid-scale motion of ice-shelf calving fronts. The Cryosphere 5, 35–44.

• AlonsoSantillanaDawson:
  R. Alonso, M. Santillana, and C. Dawson, 2008. On the diffusive wave approximation of the shallow water equations. Eur. J. Appl. Math. 19 (5), 575–606.

• AscherPetzold:
  U. Ascher and L. Petzold, 1998. Computer methods for ordinary differential equations and differential-algebraic equations. SIAM Press, Philadelphia, PA.

• AschwandenBlatter:
  A. Aschwanden and H. Blatter, 2009. Mathematical modeling and numerical simulation of polythermal glaciers. J. Geophys. Res. 114. F01027, doi:10.1029/2008JF001028.

• AschwandenBuelerKhroulevBlatter:
  A. Aschwanden, E. Bueler, C. Khroulev, and H. Blatter, 2011. An enthalpy formulation for glaciers and ice sheets. Submitted to J. Glaciol.

• petsc-efficient:
  S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith, 1997. Efficient Management of Parallelism in Object Oriented Numerical Software Libraries. In E. Arge, A. M. Bruaset, and H. P. Langtangen, editors, Modern Software Tools in Scientific Computing, 163–202. Birkhäuser Press.

• petsc-user-ref:
  S. Balay et al., 2010. PETSc Users Manual. Technical Report ANL-95/11 - Revision 3.1, Argonne National Laboratory. http://www.mcs.anl.gov/petsc/petsc-as/snapshots/petsc-current/docs/manual.pdf.

• Balesetal2001:
  R. Bales, J. McConnell, E. Mosley-Thompson, and G. Lamorey, 2001. Accumulation map for the Greenland Ice Sheet: 1971-1990. Geophys. Res. Lett 28 (15), 2967–2970. URL: http://zero.eng.ucmerced.edu/rcbales/PARCA/.

• BamberLayberryGogenini:
  J. Bamber, R. Layberry, and S. Gogenini, 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), 33,773–33,780.

• BamberVaughanJoughin:
  J. L. Bamber, D. G. Vaughan, and I. Joughin, 2000. Widespread complex flow in the interior of the Antarctic ice sheet. Science 287, 1248–1250.

• Baraletal2001:
  D. R. Baral, K. Hutter, and R. Greve, 2001. Asymptotic theories of large-scale motion, temperature, and moisture distribution in land-based polythermal ice sheets: A critical review and new developments. Appl. Mech. Rev. 54 (3), 215–256. doi: 10.1115/1.3097296.

• Barenblatt:
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• Batchelor:
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• RIGGS1:
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• Blatter:
  H. Blatter, 1995. Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients. J. Glaciol. 41 (138), 333–344.

• Bodvardsson:
  G. Bodvardsson, 1955. On the flow of ice-sheets and glaciers. Jökull 5, 1–8.

• BoxSteffan2001:
  J. E. Box and K. Steffen, 2001. Sublimation on the Greenland ice sheet from automated weather station observations. J. Geophys. Res. 106 (D24), 33965–33981.

• Bracewell:
  R. N. Bracewell, 1978. The Fourier Transform and Its Applications. McGraw-Hill Book Company, New York, 2nd edition.

• Braess:
  D. Braess, 2007. Finite Elements. Cambridge University Press, Cambridge, third edition. Theory, fast solvers, and applications in elasticity theory, Translated from the German by Larry L. Schumaker.

• BriggsHenson:
  W. L. Briggs and V. E. Henson, 1995. The DFT: An Owner's Manual for the Discrete Fourier Transform. SIAM Press, Philadelphia.

• Broughan:
  K. Broughan, 1997. Periodicity in an energy balance climate model. Nonlinear Analysis 30 (8), 4995–5002.

• BrownPresentation:
  J. Brown, 2006. Verifying PISM. UAF Master's project presentation http://www.dms.uaf.edu/~bueler/slidesJBrown.pdf.

• Brown2010:
  J. Brown, 2010. Efficient nonlinear solvers for nodal high-order finite elements in 3D. J. Sci. Comput. 45, 48–63. doi: 10.1007/s10915-010-9396-8.

• BrownSmithAhmadia:
  J. Brown, B. Smith, and A. Ahmadia, 2011. Achieving textbook multigrid efficiency for hydrostatic ice sheet flow. Submitted to JGR Earth Surface.

• BrownChurchill:
  J. W. Brown and R. V. Churchill, 2000. Fourier Series and Boundary Value Problems. McGraw-Hill, 6th edition.

• Bueler:
  E. Bueler, 2002. Numerical approximation of a two–dimensional thermomechanical model for ice flow. Dept. of Mathematical Sciences Tech. Rep. 02-02, University of Alaska, Fairbanks.

• BuelerEquilSheets:
  E. Bueler, 2006. Equilibrium ice sheets solve variational inequalities. Unpublished notes.

• BuelerTestK:
  E. Bueler, 2007. An exact solution to the temperature equation in a column of ice and bedrock. Preprint arXiv:0710.1314 .

• BuelerSpray:
  E. Bueler, 2008. Lessons from the short history of ice sheet model intercomparison. The Cryosphere Discussions 2, 399–412. http://www.the-cryosphere-discuss.net/2/399/2008/.

• BB:
  E. Bueler and J. Brown, 2006. On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets. Preprint arXiv:physics/0610106 .

• BBssasliding:
  E. Bueler and J. Brown, 2009. Shallow shelf approximation as a "sliding law" in a thermodynamically coupled ice sheet model. J. Geophys. Res. 114. F03008, doi:10.1029/2008JF001179.

• BBL:
  E. Bueler, J. Brown, and C. Lingle, 2007. Exact solutions to the thermomechanically coupled shallow ice approximation: effective tools for verification. J. Glaciol. 53 (182), 499–516.

• BKAJS:
  E. Bueler, C. Khroulev, A. Aschwanden, I. Joughin, and B. E. Smith, 2009. Modeled and observed fast flow in the Greenland ice sheet. Submitted.

• BLK2006earth:
  E. Bueler, C. S. Lingle, and J. A. Kallen-Brown, 2006. Computation of a combined spherical-elastic and viscous-half-space Earth model for ice sheet simulation. Preprint arXiv:physics/0606074 .

• BLKfastearth:
  E. Bueler, C. S. Lingle, and J. A. Kallen-Brown, 2007. Fast computation of a viscoelastic deformable Earth model for ice sheet simulation. Ann. Glaciol. 46, 97–105.

• BLKCB:
  E. Bueler, C. S. Lingle, J. A. Kallen-Brown, D. N. Covey, and L. N. Bowman, 2005. Exact solutions and numerical verification for isothermal ice sheets. J. Glaciol. 51 (173), 291–306.

• BurdenFaires:
  R. L. Burden and J. D. Faires, 2001. Numerical Analysis. Brooks/Cole, Pacific Grove, CA, seventh edition.

• Burgessetal2010:
  E. Burgess, R. Forster, J. Box, E. Mosley-Thompson, D. Bromwich, R. Bales, and L. Smith, 2010. A spatially calibrated model of annual accumulation rate on the Greenland Ice Sheet (1958–2007). J. Geophys. Res. 115 (F02004). doi: 10.1029/2009JF001293.

• CalovGreve05:
  R. Calov and R. Greve, 2005. Correspondence: A semi-analytical solution for the positive degree-day model with stochastic temperature variations. J. Glaciol 51 (172), 173–175.

• HEINOwebpage:
  R. Calov and R. Greve, 2008. ISMIP-HEINO Ice Sheet Model Intercomparison Project: Heinrich Event INtercOmparison. http://www.pik-potsdam.de/~calov/heino.html.

• Calovetal2009HEINOfinal:
  R. Calov, R. Greve, A. Abe-Ouchi, E. Bueler, P. Huybrechts, J. V. Johnson, F. Pattyn, D. Pollard, C. Ritz, F. Saito, and L. Tarasov, submitted. Results from the ice sheet model intercomparison project—Heinrich event intercomparison (ISMIP HEINO). Submitted to J. Glaciol.

• CDV99:
  N. Calvo, J. Dìaz, and C. Vàzquez, 1999. Numerical approach of temperature distribution in a free boundary model for polythermal ice sheets. Numer. Math. 83, 557–580.

• CDV00:
  N. Calvo, J. Durany, and C. Vàzquez, 2000. Numerical computation of ice sheet profiles with free boundary models. Appl. Num. Math. 35, 111–128.

• CDV02:
  N. Calvo, J. Durany, and C. Vàzquez, 2002. Numerical approach of thermomechanical coupled problems with moving boundaries in theoretical glaciology. Math. Models and Methods in Appl. Sci. 12 (2), 229–248.

• CDDSV:
  N. Calvo et al., 2002a. On a doubly nonlinear parabolic obstacle problem modelling ice sheet dynamics. SIAM J. Appl. Math. 63 (2), 683–707.

• CareyetalError04:
  G. F. Carey et al., 2004. Modelling error and constitutive relations in simulation of flow and transport. Int. J. Numer. Meth. Fluids 46, 1211–1236.

• Cathles:
  L. M. Cathles, 1975. The Viscosity of the Earth's Mantle. Princeton University Press, Princeton, NJ.

• DeLaChapelleEtAl98:
  S. D. L. Chapelle, O. Castelnau, V. Lipenkov, and P. Duval, 1998. Dynamic recrystallization and texture development in ice as revealed by the study of deep cores in Antarctica and Greenland. J. Geophys. Res. 103 (B3), 5091–5105.

• ClarkAlleyPollard1999:
  P. U. Clark, R. B. Alley, and D. Pollard, 1999. Northern Hemisphere ice-sheet influences on global climate change. Science 286 (5442), 1104–1111. doi: 10.1126/science.286.5442.1104.

• Clarke05:
  G. K. C. Clarke, 2005. Subglacial processes. Annu. Rev. Earth Planet. Sci. 33, 247–276. doi: 10.1146/annurev.earth.33.092203.122621.

• CliffeMorland:
  K. Cliffe and L. Morland, 2001. A thermo-mechanically coupled test case for axi-symmetric ice sheet flow. Continuum Mechanics and Thermodynamics 13, 135–148.

• massbalanceglossary:
  G. Cogley et al., 2009. Glossary of Mass-Balance and Related Terms. http://www.cryosphericsciences.org/mass_balance_glossary/massbalanceglossary.draft3.pdf, iACS Working Group on Mass-balance Terminology and Methods, Draft 3, 10 July.

• ColingeRappaz:
  J. Colinge and J. Rappaz, 1999. A strongly nonlinear problem arising in glaciology. M2AN Math. Model. Numer. Anal. 33 (2), 395–406.

• Comiso:
  J. Comiso, 2000. Variability and trends in Antarctic surface temperatures from in situ and satellite infrared measurements. J. Climate 13, 1674–1696.

• Dansgaardetal1993:
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• Dasetal08:
  S. B. Das, I. Joughin, M. D. Behn, I. M. Howat, M. A. King, D. Lizarralde, and M. P. Bhatia, 2008. Fracture Propagation to the Base of the Greenland Ice Sheet During Supraglacial Lake Drainage. Science 320 (5877), 778–781. doi: 10.1126/science.1153360.

• VandenBergetal2006:
  J. V. den Berg, R. S. W. V. de Wal, and J. Oerlemans, 2006. Effects of spatial discretization in ice-sheet modelling using the shallow-ice approximation. J. Glaciol. 52 (176), 89–98.

• DiBenedetto:
  E. DiBenedetto, 1993. Degenerate Parabolic Equations. Springer-Verlag, Berlin.

• DuvautLions:
  G. Duvaut and J. L. Lions, 1976. Inequalities in Mechanics and Physics. Springer.

• Eisen2008:
  O. Eisen, 2008. Inference of velocity pattern from isochronous layers in firn, using an inverse method. J. Glaciol. 54 (187), 613–630.

• VostokCore:
  EPICA community members, 2004. Eight glacial cycles from an Antarctic ice core. Nature 429, 623–628. doi: 10.1038/nature02599.

• ERCOFTACGuidelines:
  ERCOFTAC, 2000. Best Practices Guidelines for Industrial Computational Fluid Dynamics. Technical report, European Research Community On Flow, Turbulence And Combustion (ERCOFTAC). Version 1.0.

• Ettemaetal2009:
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• Evans:
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• Fahnestocketal2001:
  M. Fahnestock, W. Abdalati, I. Joughin, J. Brozena, and P. Gogineni, 2001. High geothermal heat flow, basal melt, and the origin of rapid ice flow in central Greenland. Science 294, 2338–2342.

• Farrell:
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• Fastook:
  J. L. Fastook, 1999. A computationally efficient bedrock isostacy model. Unpublished.

• Faustoetal2009:
  R. S. Fausto, A. P. Ahlstrom, D. V. As, C. E. Boggild, and S. J. Johnsen, 2009. A new present-day temperature parameterization for Greenland. J. Glaciol. 55 (189), 95–105.

• FlowersClarke2002_theory:
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• FlowersClarke2002_trapridge:
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• Fowler97A:
  A. C. Fowler, 1997. Glaciers and ice sheets. In J. I. Dìaz, editor, The Mathematics of Models for Climatology and Environment, volume 48, 301–336. Springer.

• Fowler:
  A. C. Fowler, 1997. Mathematical Models in the Applied Sciences. Cambridge Univ. Press.

• Fowler01:
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• FowlerLarson1978:
  A. C. Fowler and D. A. Larson, 1978. On the flow of polythermal glaciers. I. Model and preliminary analysis. Proc. R. Soc. Lond. A 363, 217–242.

• Friedman:
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• HOMelmer:
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• GSL:
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• GilletChauletetal2005:
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• Glen:
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• GlowinskiRappaz:
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• Goldberg2011:
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• Goldbergetal2009:
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• GoldsbyKohlstedt97:
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• GoldsbyKohlstedt:
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• Greve97Greenland:
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• Greve:
  R. Greve, 1997. A continuum–mechanical formulation for shallow polythermal ice sheets. Phil. Trans. Royal Soc. London A 355, 921–974.

• Greve00:
  R. Greve, 2000. On the response of the Greenland ice sheet to greenhouse climate change. Climatic Change 46, 289–303.

• Greve2001:
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• GreveNotes:
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• Greve2005geothermal:
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• GreveBlatter2009:
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• GreveTakahamaCalov:
  R. Greve, R. Takahama, and R. Calov, 2006. Simulation of large-scale ice-sheet surges: The ISMIP-HEINO experiments. Polar Meteorol. Glaciol. 20, 1–15.

• Gudmundsson03:
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• Gudmundsson09:
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• HagdornThesis:
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• Halfar81:
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• Halfar83:
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• Hindmarsh:
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• Hindmarsh01:
  R. C. A. Hindmarsh, 2001. Notes on basic glaciological computational methods and algorithms. In B. Straughan et al., editors, Continuum Mechanics and Applications in Geophysics and the Environment, 222–249. Springer.

• Hindmarsh04compare:
  R. C. A. Hindmarsh, 2004. A numerical comparison of approximations to the Stokes equations used in ice sheet and glacier modeling. J. Geophys. Res. 109. doi: 10.1029/2003JF000065.

• Hindmarsh04:
  R. C. A. Hindmarsh, 2004. Thermoviscous stability of ice-sheet flows. J. Fluid Mech. 502, 17–40.

• HindmarshMembrane:
  R. C. A. Hindmarsh, 2006. The role of membrane-like stresses in determining the stability and sensitivity of the Antarctic ice sheets: back pressure and grounding line motion. Phil. Trans. R. Soc. A 364, 1733–1767. doi: 10.1089/rsta.2006.1797.

• Hindmarsh06:
  R. C. A. Hindmarsh, 2006. Stress gradient damping of thermoviscous ice flow instabilities. J. Geophys. Res. 111 (B12409). doi: 10.1029/2005JB004019.

• HindmarshPayne:
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• Hock05:
  R. Hock, 2005. Glacier melt: a review of processes and their modelling. Prog. Phys. Geog. 29 (3), 362–391.

• Hock2005b:
  R. Hock and B. Holmgren, 2005. A distributed surface energy-balance model for complex topography and its application to Storglaciären, Sweden. J. Glaciol. 51 (172), 25–36.

• Hollandetal2008:
  D. M. Holland, R. H. Thomas, B. de Young, M. H. Ribergaard, and B. Lyberth, 2008. Acceleration of Jakobshavn Isbræ triggered by warm subsurface ocean waters. Nature Geoscience 1, 659–664. doi: doi:10.1038/ngeo316.

• HolmlundJanssonPettersson2005:
  P. Holmlund, P. Jansson, and R. Pettersson, 2005. A re-analysis of the 58 year mass-balance record of Störglaciaren, Sweden. Ann. Glaciol. 42, 389–394.

• Hooke:
  R. Hooke, 1981. Flow law for polycrystalline ice in glaciers: comparison of theoretical predictions, laboratory data, and field measurements. Rev. Geophys. Space. Phys. 19 (4), 664–672.

• HowatJoughinScambos:
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• HulbeMacAyeal:
  C. L. Hulbe and D. R. MacAyeal, 1999. A new numerical model of coupled inland ice sheet, ice stream, and ice shelf flow and its application to the West Antarctic Ice Sheet. J. Geophys. Res. 104 (B11), 25349–25366.

• HumbertGreveHutter:
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• HunkeDukowicz97:
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• Hutter:
  K. Hutter, 1983. Theoretical Glaciology. D. Reidel.

• Hutter93:
  K. Hutter, 1993. Thermomechanically coupled ice–sheet response: cold, polythermal, temperate. J. Glaciology 39 (131), 65–86.

• HutterFreeBoundary:
  K. Hutter, 1999. Mathematical foundation of ice sheet and ice shelf dynamics: A physicist's view. In I. Athanasopoulos et al., editors, Free Boundary Problems: Theory and Applications, 192–203. Chapman & Hall.

• Huybrechts90:
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• HuybrechtsEISMINT:
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• Huybrechts02:
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• POLICEwebpage:
  P. Huybrechts, 2008. ISMIP-POLICE: A new intercomparison exercise to assess model uncertainties in polar ice sheet simulations under future climatic warming conditions. http://homepages.vub.ac.be/~phuybrec/police.html.

• HuybrechtsdeWolde:
  P. Huybrechts and J. de Wolde, 1999. The dynamic response of the Greenland and Antarctic ice sheets to multiple-century climatic warming. J. Climate 12, 2169–2188.

• Huybrechtsetal2004:
  P. Huybrechts, J. Gregory, I. Janssens, and M. Wild, 2004. Modelling Antarctic and Greenland volume changes during the 20th and 21st centuries forced by GCM time slice integrations. Global and Planetary Change 42, 83–105.

• EISMINT96:
  P. Huybrechts et al., 1996. The EISMINT benchmarks for testing ice-sheet models. Ann. Glaciol. 23, 1–12.

• Imbrieetal1984:
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• IvinsJames2005:
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• Jakobssonetal2008:
  M. Jakobsson, R. Macnab, L. Mayer, R. Anderson, M. Edwards, J. Hatzky, H. Schenke, and P. Johnson, 2008. An improved bathymetric portrayal of the Arctic Ocean: Implications for ocean modeling and geological, geophysical and oceanographic analyses. Geophys. Res. Lett. 35 (7). http://www.ngdc.noaa.gov/mgg/bathymetry/arctic/.

• JamesIvins1998:
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